ScienceFrom Wikipedia, the free encyclopedia

A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect.

Representation of DNA, which determines the genetic makeup of all life. Discovered in the 1950s, each strand of DNA is a chain of nucleotides, matching each other in the center to form what look like rungs on a twisted ladder. Today, the human genome project has succeed in mapping virtually all of the important genes, which are specific parts of DNAFor the periodical, see Science (journal).

Science (from the Latin scientia, 'knowledge'), in the broadest sense, refers to any systematic knowledge or practice.[1] In a more restricted sense, science refers to a system of acquiring knowledge based on the scientific method, as well as to the organized body of knowledge gained through such research.[2][3] This article focuses on the more restricted use of the word.Fields of science are commonly classified along two major lines:

Natural sciences , which study natural phenomena (including biological life), and Social sciences , which study human behavior and societies.

These groupings are empirical sciences, which means the knowledge must be based on observable phenomena and capable of being experimented for its validity by other researchers working under the same conditions.[4]

Mathematics, which is sometimes classified within a third group of science called formal science, has both similarities and differences with the natural and social sciences.[3] It is similar to empirical sciences in that it involves an objective, careful and systematic study of an area of knowledge; it is different because of its method of verifying its knowledge, using a priori rather than empirical methods.[5] Formal science, which also includes statistics and logic, is vital to the empirical sciences. Major advances in formal science have often led to major advances in the physical and biological sciences. The formal sciences are essential in the formation of hypotheses, theories, and laws,[6] both in discovering and describing how things work (natural sciences) and how people think and act (social sciences).Science as discussed in this article is sometimes termed experimental science to differentiate it from applied science, which is the application of scientific research to specific human needs, though the two are often interconnected./tt/file_convert/5a9fc4dd7f8b9a8e178d261f/document.doc 1/122

Contents1 Etymology 2 Scientific method 3 Philosophy of science 4 Mathematics and the scientific method 5 Goal(s) of science

5.1 What the goal is not 6 Scientific literature 7 Fields of science 8 Scientific institutions 9 See also 10 Notes 11 References 12 Further reading 13 External links

EtymologyThe word science comes through the Old French, and is derived from the Latin word scientia for knowledge, which in turn comes from scio. 'I know'. The Indo-European root means to discern or to separate, akin to Sanskrit chyati, he cuts off, Greek schizein, to split, Latin scindere, to split.[7] From the Middle Ages to the Enlightenment, science or scientia meant any systematic recorded knowledge.[8] Science therefore had the same sort of very broad meaning that philosophy had at that time. In other languages, including French, Spanish, Portuguese, and Italian, the word corresponding to science also carries this meaning.From classical times until the advent of the modern era, "philosophy" was roughly divided into natural philosophy and moral philosophy. In the 1800s, the term natural philosophy gradually gave way to the term natural science. Natural science was gradually specialized to its current domain, which typically includes the physical sciences and biological sciences. The social sciences, inheriting portions of the realm of moral philosophy, are currently also included under the auspices of science to the extent that these disciplines use empirical methods. As currently understood, moral philosophy still retains the study of ethics, regarded as a branch of philosophy.Today, the primary meaning of "science" is generally limited to empirical study involving use of the scientific method.[9]

Scientific methodMain article: Scientific method

The Bohr model of the atom, like many ideas in the history of science, was at first prompted by and later partially disproved by experiment.The scientific method seeks to explain the events of nature in a reproducible way, and to use these reproductions to make useful predictions. It is done through observation of natural phenomena, and/or through experimentation that tries to simulate natural events under controlled conditions. It provides an objective process to find solutions to problems in a number of scientific and technological fields. Often scientists have a preference for one outcome over another, and scientists are conscientious that it is important that this preference does not bias their interpretation. A strict following of the scientific method attempts to minimize the influence of a scientist's bias on

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Scientists use models to refer to a description or depiction of something, specifically one which can be used to make predictions that can be tested by experiment or observation. A hypothesis is a contention that has been neither well supported nor yet ruled out by experiment. A theory, in the context of science, is a logically self-consistent model or framework for describing the behavior of certain natural phenomena. A theory typically describes the behavior of much broader sets of phenomena than a hypothesis—commonly, a large number of hypotheses may be logically bound together by a single theory. A physical law or law of nature is a scientific generalization based on a sufficiently large number of empirical observations that it is taken as fully verified.Scientists never claim absolute knowledge of nature or the behavior of the subject of the field of study. Unlike a mathematical proof, a scientific theory is empirical, and is always open to falsification, if new evidence is presented. Even the most basic and fundamental theories may turn out to be imperfect if new observations are inconsistent with them. Critical to this process is making every relevant aspect of research publicly available, which permits peer review of published results, and also allows ongoing review and repeating of experiments and observations by multiple researchers operating independently of one another. Only by fulfilling these expectations can it be determined how reliable the experimental results are for potential use by others.Isaac Newton's Newtonian law of gravitation is a famous example of an established law that was later found not to be universal—it does not hold in experiments involving motion at speeds close to the speed of light or in close proximity of strong gravitational fields. Outside these conditions, Newton's Laws remain an excellent model of motion and gravity. Since general relativity accounts for all the same phenomena that Newton's Laws do and more, general relativity is now regarded as a more comprehensive theory.

Philosophy of scienceMain article: Philosophy of science

The philosophy of science seeks to understand the nature and justification of scientific knowledge and its ethical implications. It has proven difficult to provide a definitive account of the scientific method that can decisively serve to distinguish science from non-science. Thus there are legitimate arguments about exactly where the borders are. There is nonetheless a set of core precepts that have broad consensus among published philosophers of science and within the scientific community at large. (see: Problem of demarcation)Science is reasoned-based analysis of sensation upon our awareness. As such, the scientific method cannot deduce anything about the realm of reality that is beyond what is observable by existing or theoretical means. When a manifestation of our reality previously considered supernatural is understood in the terms of causes and consequences, it acquires a scientific explanation.Resting on reason and logic, along with other guidelines such as parsimony, scientific theories are formulated and repeatedly tested by analyzing how the collected evidence compares to the theory. Some of the findings of science can be very counter-intuitive. Atomic theory, for example, implies that a granite boulder which appears a heavy, hard, solid, grey object is actually a combination of subatomic particles with none of these properties, moving very rapidly in space where the mass is concentrated in a very small fraction of the total volume. Many of humanity's preconceived notions about the workings of the universe have been challenged by new scientific discoveries. Quantum mechanics, particularly, examines phenomena that seem to defy our most basic postulates about causality and fundamental understanding of the world around us. Science is the branch of knowledge dealing with people and the understanding we have of our environment and how it works.There are different schools of thought in the philosophy of scientific method. Methodological naturalism maintains that scientific investigation must adhere to empirical study and independent verification as a process for properly developing and evaluating natural explanations for observable phenomena. Methodological naturalism, therefore, rejects supernatural explanations, arguments from authority and biased observational studies. Critical rationalism instead holds that unbiased observation is not possible and a demarcation between natural and supernatural explanations is arbitrary; it instead proposes falsifiability as the landmark of empirical theories and falsification as the universal empirical method.

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Critical rationalism argues for the primacy of science, but at the same time against its authority, by emphasizing its inherent fallibility. It proposes that science should be content with the rational elimination of errors in its theories, not in seeking for their verification (such as claiming certain or probable proof or disproof; both the proposal and falsification of a theory are only of methodological, conjectural, and tentative character in critical rationalism). Instrumentalism rejects the concept of truth and emphasizes merely the utility of theories as instruments for explaining and predicting phenomena.

Mathematics and the scientific method Velocity-distribution data of a gas of rubidium atoms,

confirming the discovery of a new phase of matter, the Bose–Einstein condensate.Mathematics is essential to many sciences. One important function of mathematics in science is the role it plays in the expression of scientific models. Observing and collecting measurements, as well as hypothesizing and predicting, often require mathematical models and extensive use of mathematics. Mathematical branches most often used in science include calculus and statistics, although virtually every branch of mathematics has

applications, even "pure" areas such as number theory and topology. Mathematics is fundamental to the understanding of the natural sciences and the social sciences, all of which rely heavily on statistics. Statistical methods, comprised of accepted mathematical formulas for summarizing data, allow scientists to assess the level of reliability and the range of variation in experimental results.Whether mathematics itself is properly classified as science has been a matter of some debate. Some thinkers see mathematicians as scientists, regarding physical experiments as inessential or mathematical proofs as equivalent to experiments. Others do not see mathematics as a science, since it does not require experimental test of its theories and hypotheses. In practice, mathematical theorems and formulas are obtained by logical derivations which presume axiomatic systems, rather than a combination of empirical observation and method of reasoning that has come to be known as scientific method. In general, mathematics is classified as formal science, while natural and social sciences are classified as empirical sciences.

Goal(s) of scienceThe underlying goal or purpose of science to society and individuals is to produce useful models of reality. To achieve this, one can form hypotheses based on observations that they make in the world. By analyzing a number of related hypotheses, scientists can form general theories. These theories benefit society or human individuals who make use of them.In short, science produces models with useful predictions. Science attempts to describe what is, but avoids trying to determine what is (which is for practical reasons impossible). Science is a useful tool. . . it is a growing body of understanding by which one can contend more effectively with surroundings and to better adapt and evolve as a social whole as well as independently.For a large part of recorded history, science had little bearing on people's everyday lives. Scientific knowledge was gathered for its own sake, and it had few practical applications. However, with the dawn of the Industrial Revolution in the 18th century, this rapidly changed. Today, science has a profound effect on the way humans interact with and act upon nature, largely through its applications in new technology.Some forms of technology have become so well established that it is easy to forget the great scientific achievements that they represent. The refrigerator, for example, owes its existence to a discovery that liquids take in energy when they evaporate, a phenomenon known as latent heat. The principle of latent heat was first exploited in a practical way in 1876, and the refrigerator has played a major role in maintaining public health ever since (see Refrigeration). The first automobile, dating from the 1880s, made use of many advances in physics and engineering, including reliable ways of generating high-

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voltage sparks, while the first computers emerged in the 1940s from simultaneous advances in electronics and mathematics.

Part of a scientific laboratory at the University of Cologne.Other fields of science also play an important role in the things the developed world use or consume every day. Research in food technology has created new ways of preserving and flavoring of edible products (see Food processing). Research in industrial chemistry has created a vast range of plastics and other synthetic materials, which have thousands of uses in the home and in industry. Synthetic materials are easily formed into complex shapes and can be used to make machine, electrical, and automotive parts, scientific and industrial

instruments, decorative objects, containers, and many other items.Alongside these achievements, science has also brought about technology that helps save human and non-human life. The kidney dialysis machine enables many people to survive kidney diseases that would once have proved fatal, and artificial valves allow sufferers of coronary heart disease to return to active living. Biochemical research is responsible for the antibiotics and vaccinations that protect living things from infectious diseases, and for a wide range of other drugs used to combat specific health problems. As a result, the majority of people in the developed world live longer and healthier lives than ever before.However, scientific discoveries can also have a negative impact in human affairs. Over the last hundred years, some of the technological advances that make life easier or more enjoyable have proved to have unwanted and often unexpected long-term effects. Industrial and agricultural chemicals pollute the global environment, even in places as remote as Antarctica, and the air in many cities is contaminated by toxic gases from vehicle exhausts (see Pollution). The increasing pace of innovation means that products become rapidly obsolete, adding to a rising tide of waste (see Solid Waste Disposal). Most significantly of all, the burning of fossil fuels such as coal, oil, and natural gas releases into the atmosphere carbon dioxide and other substances known as greenhouse gases. These gases have altered the composition of the entire atmosphere, producing global warming and the prospect of major climate change in years to come.Science has also been used to develop technology that raises complex ethical questions. This is particularly true in the fields of biology and medicine (see Medical Ethics). Research involving genetic engineering, cloning, and in vitro fertilization gives scientists the unprecedented power to bring about new life, or to devise new forms of living things. At the other extreme, science can also generate technology that is designed to deliberately hurt or to kill. The fruits of this research include chemical and biological warfare, and also nuclear weapons, by far the most destructive weapons that the world has ever known.What the goal is notDespite popular impressions of science, it is not the goal of science to answer all questions. The goal of the sciences is to answer only those that pertain to perceived reality. Also, science cannot possibly address nonsensical, or untestable questions, so the choice of which questions to answer becomes important. Science does not and can not produce absolute and unquestionable truth. Rather, science tests some aspect of nature and attempts to provide a precise, unequivocal framework to explain it. This is a goal of science, but it is not an absolutely necessary one. Usually the framework for a scientific theory is a mechanical or physical model, but it may only merely be a mathematical model. In the latter case, the role of science is lessened from that of explaining phenomena to that of merely predicting future phenomena or observations, given certain input conditions or observations.The separate roles of explanation and prediction must be differentiated, because science must always provide a clear prediction of future phenomena (by definition) but is not always able to provide or differentiate between possible explanations for the causes of phenomena. As an often cited example, there exist a number of models of quantum mechanics which differ in explanation of quantum phenomena and in physical models for them, but are all mathematically equivalent in prediction. For this reason, the /tt/file_convert/5a9fc4dd7f8b9a8e178d261f/document.doc 5/122

possible explanations and physical models cannot be differentiated. In such cases, natural science does not and cannot provide a preferred explanation or mechanical model for reality, but because it continues to provide a clear predictive mathematical model for reality, it retains its classification as science.Science is not a source of equivocal value judgments, though it can certainly speak to matters of ethics and public policy by pointing to the likely consequences of actions. What one projects from the currently most unequivocal scientific hypothesis onto other realms of interest is not a scientific issue, and the scientific method offers no assistance for those who wish to do so. Scientific justification (or refutation) for many things is, nevertheless, often claimed. Certain value judgments are intrinsic to science itself. For example, scientists value relative truth and knowledge, and the actual progress of science requires cooperation between scientists, and is highly intolerant of dishonesty. Cooperation and honesty are thus values which are intrinsic to the actual social practice of the scientific method itself.

Scientific literatureMain article: Scientific literature

An enormous range of scientific literature is published in today's world. Scientific journals communicate and document the results of research carried out in universities and various other research institutions. Most scientific journals cover a scientific field and publish the research within that field; the research is normally expressed in the form of a scientific paper. Science has become so pervasive in modern societies that it is generally considered necessary to communicate the achievements, news, and dreams of scientists to a wider populace. Science magazines (e.g. New Scientist, Scientific American) cater to the needs of a wider readership and provide a non-technical summary of popular areas of research, including notable discoveries and advances in certain fields of research. Additionally, science books and magazines on science fiction ignite the interest of many more people. A significant fraction of literature in science is also available on the World Wide Web; most reputable journals and news magazines maintain their own websites. A growing number of people are being attracted towards the vocation of science popularization and science journalism.[citation needed]

Fields of scienceMain article: Fields of science

Science is broadly subdivided into the categories of natural sciences and the social sciences. There are also related disciplines that are grouped into interdisciplinary and applied sciences, such as engineering and health science. Within these categories are specialized scientific fields that can include elements of other scientific disciplines but often possess their own terminology and body of expertise.[10]

The status of social sciences as an empirical science has been a matter of debate in the 20th century, see Positivism dispute.[11] Discussion and debate abound in this topic with some fields like the social and behavioural sciences accused by critics of being unscientific. In fact, many groups of people from academicians like Nobel Prize physicist Percy W. Bridgman,[12] or Dick Richardson, Ph.D.—Professor of Integrative Biology at the University of Texas at Austin,[13] to politicians like U.S. Senator Kay Bailey Hutchison and other co-sponsors,[14] oppose giving their support or agreeing with the use of the label "science" in some fields of study and knowledge they consider non-scientific or scientifically irrelevant compared with other fields.

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Scientific institutions Louis XIV visiting the Académie des sciences in 1671.

Learned societies for the communication and promotion of scientific thought and experimentation have existed since the Renaissance period.[15] The oldest surviving institution is the Accademia dei Lincei in Italy.[16] National Academy of Sciences are distinguished institutions that exist in a number of countries, beginning with the British Royal Society in 1660[17] and the French Académie des Sciences in 1666.[18]

International scientific organizations, such as the International Council for Science, have since been formed to promote cooperation between the scientific communities of different nations. More recently, influential government agencies have been created to support scientific research, including the National Science Foundation in the U.S.Other prominent organizations include:

In Australia, CSIRO In France, Centre national de la recherche scientifique In Germany, Max Planck Society and Deutsche Forschungsgemeinschaft In Spain, CSIC

See alsoScience Portal

Main lists: List of basic science topics and List of science topics

Controversy

Controversial science Fringe science Junk science Pathological science Pseudoscience Relationship between religion and science Creation-evolution controversy Scientific misconduct Scientific skepticism (cf.

Pseudoskepticism)

History

History of science and technology Historiography of science Protoscience Scientific constants named after people Scientific laws named after people Scientific phenomena named after people Scientific revolution Scientific units named after people

Philosophy Philosophy of science Rhetoric of science Scientific method

History of science (how the various fields of science came to be) Scientist (lists of people active in each of these fields) Engineering (science applied) Fields of science Knowledge (goal of science) List of inventors List of publications in science Mathematics (complements science, and is its main tool)

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Military funding of science Perfection Philosophy (foundation of inquiry)

o Philosophy of science (foundation of science) Karl Popper

Scientific computing Scientific data archiving Scientific enterprise Scientific materialism Technology (result of science) Science and technology

Notes1. ̂ http://www.m-w.com/dictionary/science Merriam Webster definition of science, Retrieved

September 12, 2007 "2 a : a department of systematized knowledge as an object of study <the science of theology> b : something (as a sport or technique) that may be studied or learned like systematized knowledge <have it down to a science>"

2. ̂ "science" defined by various dictionaries at "reference.com" 3. ^ a b (Popper 1959, p. 3) 4. ̂ (Popper 1959, p. 20) 5. ̂ (Popper 1959, pp. 10–11) 6. ̂ (Popper 1959, pp. 79–82) 7. ̂ Etymology of "science" at Etymology Online 8. ̂ MacMorris, Neville (1989). The Natures of Science. New York: Fairleigh Dickinson University

Press, pp. 31–33. ISBN 0838633218.  9. ̂ See, e.g. [1]. The first usage, which is fairly representative of standard dictionaries today,

describes science as: "a. The observation, identification, description, experimental investigation, and theoretical explanation of phenomena. b. Such activities restricted to a class of natural phenomena. c. Such activities applied to an object of inquiry or study." From the American Heritage® Dictionary of the English Language, Fourth Edition copyright ©2000 by Houghton Mifflin Company. Updated in 2003

10. ̂ See: Editorial Staff (March 7, 2007). Scientific Method: Relationships among Scientific Paradigms. Seed magazine. Retrieved on 2007-09-12.

11. ̂ Critical examination of various positions on this issue can be found in Karl R. Popper's The Poverty of Historicism.

12. ̂ Siepmann, J. P. (1999). "What is Science? (Editorial)". Journal of Theoretics 3. Retrieved on 2007-07-23. 

13. ̂ Richardson, R. H. (Dick) (January 28, 2001). Economics is NOT Natural Science! (It is technology of Social Science.). The University of Texas at Austin. Retrieved on 2007-07-23.

14. ̂ Staff (May 19, 2006). Behavioral and Social Science Are Under Attack in the Senate. American Sociological Association. Retrieved on 2007-07-23.

15. ̂ Parrott, Jim (August 9, 2007). Chronicle for Societies Founded from 1323 to 1599. Scholarly Societies Project. Retrieved on 2007-09-11.

16. ̂ Benvenuto nel sito dell'Accademia Nazionale dei Lincei (Italian). Accademia Nazionale dei Lincei (2006). Retrieved on 2007-09-11.

17. ̂ Brief history of the Society. The Royal Society. Retrieved on 2007-09-11. 18. ̂ Meynell, G.G.. The French Academy of Sciences, 1666-91: A reassessment of the French

Académie royale des sciences under Colbert (1666-83) and Louvois (1683-91). Topics in Scientific & Medical History. Retrieved on 2007-09-11.

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References Feyerabend, Paul K. 2005. Science, history of the philosophy of. Oxford Companion to

Philosophy. Oxford. Papineau, David. 2005. Science, problems of the philosophy of. Oxford Companion to Philosophy.

Oxford. Popper, Karl [1959] (2002). The Logic of Scientific Discovery, 2nd English edition, New York,

NY: Routledge Classics, 3. ISBN 0-415-27844-9. OCLC 59377149.  Richard P. Feynman. "The Pleasure of Finding Things Out"

Further reading A Book List of Popularized Natural and Behavioral Sciences Baxter, Charles "Myth versus science in educational systems" PDF  (66.4 KiB) "Classification of the Sciences". Dictionary of the History of Ideas. Cole, K. C., "Things your teacher never told you about science (Nine shocking revelations!);

Maybe you think that science is devoted to gathering and cataloguing facts, and that scientists are a dull, dreary lot who don't know how to have fun. Maybe you should think again.". Newsday, Long Island, New York, March 23, 1986, pg 21+

Krige, John, and Dominique Pestre, eds., Science in the Twentieth Century, Routledge 2003, ISBN 0-415-28606-9

MacComas, William F. "The principal elements of the nature of science: Dispelling the myths" PDF  (189 KiB) Rossier School of Education, University of Southern California. Direct Instruction News. Spring 2002 24–30.

"Nature of Science" University of California Museum of Paleontology Obler, Paul C.; Estrin, Herman A. (1962). The New Scientist: Essays on the Methods and Values

of Modern Science. Anchor Books, Doubleday. 

External linksFind more information on Science by searching

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Learning resources from Wikiversity Math and e-Science PDF  (120 KiB) http://www.newscientist.com/ http://www.sciam.com/ http://www.scienceresourceonline.com

Textbooks: "GSCE Science textbook". Wikibooks.org National Center for Biotechnology Information Bookshelf

News:

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Brightsurf Science News and Current Science Events Current Events . New Scientist Magazine, Reed Business Information, Ltd. ScienceDaily Discover Magazine

Resources: The Vega Science Trust Hours of science video including scientific lectures (Feynman, Kroto,

Davis, etc.), discussions (nanotechnology, GM, stem cells, etc.), career programmes, interviews with Nobel Laureates, and school resources.

United States Science Initiative . Selected science information provided by U.S. Government agencies, including research and development results.

Fun science: Fun science experiments by Steve Spangler Science Fun for Kids ScienceMadeSimple Resources Live Science Experiments and Easy Science Experiments for Kids Null Hypothesis, the Journal of Unlikely Science Fun, interesting, wacky science Scientific AmeriKen : Delving into all the sciences for the purpose of gathering statistics and

knowledge for the benefit of mankind. http://www.tryengineering.org Features "Ask an Engineer," engineering games, college searches,

and other resources for students, parents, and teachers This Week in Science Radio show that gives a hip and irreverent take on current science news. Science Projects for Kids Easy and fun science projects that you can try at home with your kids.

Great ideas for science fair projects! Science Made Fun: Making science fun for people of all ages!

Retrieved from "http://en.wikipedia.org/wiki/Science"

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Scientific methodFrom Wikipedia, the free encyclopedia

Scientific method Portal

Scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. It is based on gathering observable, empirical and measurable evidence subject to specific principles of reasoning,[1] the collection of data through observation and experimentation, and the formulation and testing of hypotheses.[2]

Although procedures vary from one field of inquiry to another, identifiable features distinguish scientific inquiry from other methodologies of knowledge. Scientific researchers propose hypotheses as explanations of phenomena, and design experimental studies to test these hypotheses. These steps must be repeatable in order to predict dependably any future results. Theories that encompass wider domains of inquiry may bind many hypotheses together in a coherent structure. This in turn may help form new hypotheses or place groups of hypotheses into context.Among other facets shared by the various fields of inquiry is the conviction that the process must be objective to reduce a biased interpretation of the results. Another basic expectation is to document, archive and share all data and methodology so it is available for careful scrutiny by other scientists, thereby allowing other researchers the opportunity to verify results by attempting to reproduce them. This practice, called full disclosure, also allows statistical measures of the reliability of these data to be established.

Contents 1 Introduction to scientific method 2 Truth and belief 3 Elements of scientific method

o 3.1 DNA example o 3.2 Characterizations

3.2.1 Uncertainty 3.2.2 Definition 3.2.3 DNA-

characterizations 3.2.4 Precession of

Mercury o 3.3 Hypothesis development

3.3.1 DNA-hypotheses o 3.4 Predictions from the

hypothesis 3.4.1 DNA-predictions 3.4.2 General relativity

o 3.5 Experiments 3.5.1 DNA-experiments

4 Evaluation and iteration o 4.1 Testing and improvement

4.1.1 DNA-iterations o 4.2 Confirmation

5 Models of scientific inquiry

o 5.1 Classical model o 5.2 Pragmatic model o 5.3 Computational approaches

6 Philosophy and sociology of science 7 Communication, community, culture

o 7.1 Peer review evaluation o 7.2 Documentation and

replication 7.2.1 Archiving 7.2.2 Dearchiving 7.2.3 Limitations

o 7.3 Dimensions of practice 8 History 9 Relationship with mathematics 10 Notes and references 11 Further reading 12 See also

o 12.1 Synopsis of related topics o 12.2 Logic, mathematics,

methodology o 12.3 Problems and issues o 12.4 History, philosophy,

sociology 13 External links

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Introduction to scientific method Ibn Al-Haytham 965 – 1039, Basra

Main article: Introduction to scientific methodFrom Alhacen (Ibn Al-Haytham 965 – 1039, a pioneer of scientific method) to the present day, the emphasis has been on seeking truth: "Truth is sought for its own sake. And those who are engaged upon the quest for anything for its own sake are not interested in other things. Finding the truth is difficult, and the road to it is rough. ..." [3]

"How does light travel through transparent bodies? Light travels through transparent bodies in straight lines only. ... We have explained this exhaustively in our Book of Optics. But let us now mention something to prove this convincingly: the fact that light travels in straight lines is clearly observed in the lights which enter into dark rooms through holes. ... the entering light will be clearly observable in the dust which fills the air." -- Alhacen[4]

Alhacen (1000): light travels in straight linesThe conjecture that "Light travels through transparent bodies in straight lines only", was corroborated by Alhacen only after years of effort. His demonstration of the conjecture was to place a straight stick or a taut thread next to the light beam[5], to prove that light travels in a straight line.Thus scientific method has been practiced by some for at least one thousand

years. There are difficulties in a formulaic statement of method, however. As William Whewell (1794-1866) noted in his History of Inductive Science (1837) and in Philosophy of Inductive Science (1840), "invention, sagacity, genius" are required at every step in scientific method. It is not enough to base scientific method on experience alone[6]; multiple steps are needed in scientific method, ranging from our experience to our imagination, back and forth.In the twentieth century, a hypothetico-deductive model for scientific method was formulated (For a more formal discussion, see below.):

1. Use your experience - consider the problem and try to make sense of it. Look for previous explanations; if this is a new problem to you, then do 2. Conjecture an explanation - when nothing else is yet known, try to state your explanation, to someone else, or to your notebook. 3. Deduce a prediction from that explanation- if 2 were true, then state a consequence of that explanation. 4. Test - look for the opposite of that consequence in order to disprove 2. It is a logical error to seek 3 directly as proof of 2. This error is called affirming the consequent.

This model underlies the scientific revolution. One thousand years ago, Alhacen demonstrated the importance of steps 1 and 4. Galileo (1638) also showed the importance of step 4 (also called Experiment) in Two New Sciences. One possible sequence in this model would be 1, 2, 3, 4. If the outcome of 4 holds, and 3 is not yet disproven, you may continue with 3, 4, 1, and so forth; but if the outcome of 4 shows 3 to be false, you will have go back to 2 and try to invent a new 2, deduce a new 3, look for 4, and so forth. Note that 2 can never be shown to be absolutely true by scientific method[7]; only that 2 can be shown to be absolutely false by scientific method. (This is what Einstein meant when he said "No amount of experimentation can ever prove me right; a single experiment can prove me wrong.")In the twentieth century, Ludwik Fleck (1896-1961) and others found that we need to consider our experiences more carefully, because our experience may be biased, and that we need to be more exact when describing our experiences. These considerations are discussed below.

Flying horse depiction: disproven; see below

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Truth and beliefMain article: Truth

A belief need not be true (although a belief can be true, even if its origins were myth).[8]

Needham's Science and Civilisation in China uses the 'flying horse' image as an example of observation: in it, a horse's legs are depicted as splayed, when the stop-action picture by Eadweard Muybridge shows otherwise. Note that the moment that no hoof is touching the ground, the horse's legs are gathered together and are not splayed.

Eadweard Muybridge's studies of a horse gallopingEarlier paintings depict the incorrect flying horse observation. This demonstrates Ludwik Fleck's caution that we see what we expect to observe, until shown otherwise; our beliefs will affect our observations (and therefore our subsequent actions). But repeated application of scientific method can help us solve our problems by exposing those parts of our beliefs which are false. A scientific community will have the same interests,

which allows it to help solve problems together.

Elements of scientific methodThere are many ways of outlining the basic method shared by all fields of scientific inquiry. The following examples are typical classifications of the most important components of the method on which there is wide agreement in the scientific community and among philosophers of science. There are, however, disagreements about some aspects.The following set of methodological elements and organization of procedures tends to be more characteristic of natural sciences and experimental psychology than of social sciences. In the social sciences mathematical and statistical methods of verification and hypotheses testing may be less stringent. Nonetheless the cycle of hypothesis, verification and formulation of new hypotheses will resemble the cycle described below.The essential elements[9][10][11] of a scientific method[12] are iterations [13] , recursions [14] , interleavings, and orderings of the following:

Characterizations (Quantifications, observations[15] , and measurements) Hypotheses [16] [17] (theoretical, hypothetical explanations of observations and measurements)[18] Predictions (reasoning including logical deduction [19] from hypothesis and theory) Experiments [20] (tests of all of the above)

Imre Lakatos and Thomas Kuhn had done extensive work on the "theory laden" character of observation. Kuhn (1961) said the scientist generally has a theory in mind before designing and undertaking experiments so as to make empirical observations, and that the "route from theory to measurement can almost never be traveled backward". This implies that the way in which theory is tested is dictated by the nature of the theory itself, which led Kuhn (1961, p. 166) to argue that "once it has been adopted by a profession ... no theory is recognized to be testable by any quantitative tests that it has not already passed".Each element of a scientific method is subject to peer review for possible mistakes. These activities do not describe all that scientists do (see below) but apply mostly to experimental sciences (e.g., physics, chemistry). The elements above are often taught in the educational system.[21]

Scientific method is not a recipe: it requires intelligence, imagination, and creativity[22]. It is also an ongoing cycle, constantly developing more useful, accurate and comprehensive models and methods. For example, when Einstein developed the Special and General Theories of Relativity, he did not in any way refute or discount Newton's Principia. On the contrary, if the astronomically large, the vanishingly small, and the extremely fast are reduced out from Einstein's theories — all phenomena that Newton could not have observed — Newton's equations remain. Einstein's theories are expansions and refinements of Newton's theories, and observations that increase our confidence in them also increase our confidence in Newton's approximations to them.

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A linearized, pragmatic scheme of the four points above is sometimes offered as a guideline for proceeding:[citation needed]

1. Define the question 2. Gather information and resources (observe) 3. Form hypothesis 4. Perform experiment and collect data 5. Analyze data 6. Interpret data and draw conclusions that serve as a starting point for new hypothesis 7. Publish results 8. Retest (frequently done by other scientists)

The iterative cycle inherent in this step-by-step methodology goes from point 3 to 6 back to 3 again.While this schema outlines a typical hypothesis/testing method,[23] it should also be noted that a number of philosophers, historians and sociologists of science (perhaps most notably Paul Feyerabend) claim that such descriptions of scientific method have little relation to the ways science is actually practiced.The "operational" model combines the concepts of factory-style processing, operational definition, and utility:The essential elements of a scientific method are operations, observations, models, and a utility function for evaluating models.[citation needed]

Operation - Some action done to the system being investigated Observation - What happens when the operation is done to the system Model - A fact, hypothesis, theory, or the phenomenon itself at a certain moment Utility Function - A measure of the usefulness of the model to explain, predict, and control, and of

the cost of use of it. One of the elements of any scientific utility function is the refutability of the model. Another is its simplicity, on the Principle of Parsimony also known as Occam's Razor.

The Keystones of Science project, sponsored by the journal Science, has selected a number of scientific articles from that journal and annotated them, illustrating how different parts of each article embody scientific method. Here is an annotated example of this scientific method example titled Microbial Genes in the Human Genome: Lateral Transfer or Gene Loss?.DNA example

Each element of scientific method is illustrated below by an example from the discovery of the structure of DNA:

DNA-characterizations : in this case, although the significance of the gene had been established, the mechanism was unclear, as of 1950, to anyone.

DNA-hypotheses : Crick and Watson hypothesized that the gene had a physical basis - it was helical.

DNA-predictions : from earlier work on tobacco mosaic virus, Watson was aware of the significance of Crick's formulation of the transform of a helix.[24] Thus he was primed for the significance of the X-shape in photo 51.

DNA-experiments : Watson sees photo 51. The examples are continued in "Evaluations and iterations" with DNA-iterations.

CharacterizationsScientific method depends upon increasingly more sophisticated characterizations of subjects of the investigation. (The subjects can also be called unsolved problems or the unknowns). For example, Benjamin Franklin correctly characterized St. Elmo's fire as electrical in nature, but it has taken a long series of experiments and theory to establish this. While seeking the pertinent properties of the subjects, this careful thought may also entail some definitions and observations; the observations often demand careful measurements and/or counting.The systematic, careful collection of measurements or counts of relevant quantities is often the critical difference between pseudo-sciences, such as alchemy, and a science, such as chemistry or biology. Scientific measurements taken are usually tabulated, graphed, or mapped, and statistical manipulations,

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such as correlation and regression, performed on them. The measurements might be made in a controlled setting, such as a laboratory, or made on more or less inaccessible or unmanipulatable objects such as stars or human populations. The measurements often require specialized scientific instruments such as thermometers, spectroscopes, or voltmeters, and the progress of a scientific field is usually intimately tied to their invention and development.UncertaintyMeasurements in scientific work are also usually accompanied by estimates of their uncertainty. The uncertainty is often estimated by making repeated measurements of the desired quantity. Uncertainties may also be calculated by consideration of the uncertainties of the individual underlying quantities that are used. Counts of things, such as the number of people in a nation at a particular time, may also have an uncertainty due to limitations of the method used. Counts may only represent a sample of desired quantities, with an uncertainty that depends upon the sampling method used and the number of samples taken.DefinitionMeasurements demand the use of operational definitions of relevant quantities. That is, a scientific quantity is described or defined by how it is measured, as opposed to some more vague, inexact or "idealized" definition. For example, electrical current, measured in amperes, may be operationally defined in terms of the mass of silver deposited in a certain time on an electrode in an electrochemical device that is described in some detail. The operational definition of a thing often relies on comparisons with standards: the operational definition of "mass" ultimately relies on the use of an artifact, such as a certain kilogram of platinum-iridium kept in a laboratory in France.The scientific definition of a term sometimes differs substantially from its natural language usage. For example, mass and weight overlap in meaning in common discourse, but have distinct meanings in mechanics. Scientific quantities are often characterized by their units of measure which can later be described in terms of conventional physical units when communicating the work.New theories sometimes arise upon realizing that certain terms had not previously been sufficiently clearly defined. For example, Albert Einstein's first paper on relativity begins by defining simultaneity and the means for determining length. These ideas were skipped over by Isaac Newton with, "I do not define time, space, place and motion, as being well known to all." Einstein's paper then demonstrates that they (viz., absolute time and length independent of motion) were approximations. Francis Crick cautions us that when characterizing a subject, however, it can be premature to define something when it remains ill-understood.[25] In Crick's study of consciousness, he actually found it easier to study awareness in the visual system, rather than to study Free Will, for example. His cautionary example was the gene; the gene was much more poorly understood before Watson and Crick's pioneering discovery of the structure of DNA; it would have been counterproductive to spend much time on the definition of the gene, before them.

DNA-characterizationsThe history of the discovery of the structure of DNA is a classic example of the elements of scientific method: in 1950 it was known that genetic inheritance had a mathematical description, starting with the studies of Gregor Mendel. But the mechanism of the gene was unclear. Researchers in Bragg's laboratory at Cambridge University made X-ray diffraction pictures of various molecules, starting with crystals of salt, and proceeding to more complicated substances. Using clues which were painstakingly assembled over the course of decades, beginning with its chemical composition, it was determined that it should be possible to characterize the physical structure of DNA, and the X-ray images would be the vehicle. .. 2. DNA-hypotheses

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Precession of Mercury Precession of the perihelion (exaggerated)

The characterization element can require extended and extensive study, even centuries. It took thousands of years of measurements, from the Chaldean, Indian, Persian, Greek, Arabic and European astronomers, to record the motion of planet Earth. Newton was able to condense these measurements into consequences of his laws of motion. But the perihelion of the planet Mercury's orbit exhibits a

precession which is not fully explained by Newton's laws of motion. The observed difference for Mercury's precession, between Newtonian theory and relativistic theory (approximately 43 arc-seconds per century), was one of the things that occurred to Einstein as a possible early test of his theory of General Relativity.

Hypothesis developmentA hypothesis is a suggested explanation of a phenomenon, or alternately a reasoned proposal suggesting a possible correlation between or among a set of phenomena.Normally hypotheses have the form of a mathematical model. Sometimes, but not always, they can also be formulated as existential statements, stating that some particular instance of the phenomenon being studied has some characteristic and causal explanations, which have the general form of universal statements, stating that every instance of the phenomenon has a particular characteristic.Scientists are free to use whatever resources they have — their own creativity, ideas from other fields, induction, Bayesian inference, and so on — to imagine possible explanations for a phenomenon under study. Charles Sanders Peirce, borrowing a page from Aristotle (Prior Analytics, 2.25) described the incipient stages of inquiry, instigated by the "irritation of doubt" to venture a plausible guess, as abductive reasoning. The history of science is filled with stories of scientists claiming a "flash of inspiration", or a hunch, which then motivated them to look for evidence to support or refute their idea. Michael Polanyi made such creativity the centrepiece of his discussion of methodology.Karl Popper, following others, developing and inverting the views of the Austrian logical positivists, has argued that a hypothesis must be falsifiable, and that a proposition or theory cannot be called scientific if it does not admit the possibility of being shown false. It must at least in principle be possible to make an observation that would show the proposition to be false, even if that observation had not yet been made.William Glen observes that

the success of a hypothesis, or its service to science, lies not simply in its perceived "truth", or power to displace, subsume or reduce a predecessor idea, but perhaps more in its ability to stimulate the research that will illuminate … bald suppositions and areas of vagueness.[26]

In general scientists tend to look for theories that are "elegant" or "beautiful". In contrast to the usual English use of these terms, they here refer to a theory in accordance with the known facts, which is nevertheless relatively simple and easy to handle. Occam's Razor serves as a rule of thumb for making these determinations.

DNA-hypothesesLinus Pauling proposed that DNA was a triple helix. Francis Crick and James Watson learned of Pauling's hypothesis, understood from existing data that Pauling was wrong and realized that Pauling would soon realize his mistake. So the race was on to figure out the correct structure. Except that Pauling did not realize at the time that he was in a race! ..3. DNA-predictions

Predictions from the hypothesisAny useful hypothesis will enable predictions, by reasoning including deductive reasoning. It might predict the outcome of an experiment in a laboratory setting or the observation of a phenomenon in nature. The prediction can also be statistical and only talk about probabilities.

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It is essential that the outcome be currently unknown. Only in this case does the eventuation increase the probability that the hypothesis be true. If the outcome is already known, it's called a consequence and should have already been considered while formulating the hypothesis.If the predictions are not accessible by observation or experience, the hypothesis is not yet useful for the method, and must wait for others who might come afterward, and perhaps rekindle its line of reasoning. For example, a new technology or theory might make the necessary experiments feasible.

DNA-predictionsWhen Watson and Crick hypothesized that DNA was a double helix, Francis Crick predicted that an X-ray diffraction image of DNA would show an X-shape. Also in their first paper they predicted that the double helix structure that they discovered would prove important in biology, writing "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material". ..4. DNA-experiments

General relativity Einstein's prediction (1907): Light bends in a gravitational field

Einstein's theory of General Relativity makes several specific predictions about the observable structure of space-time, such as a prediction that light bends in a gravitational field and that the amount of bending depends in a precise way on the strength of that gravitational field. Arthur Eddington's observations made during a 1919 solar eclipse supported General Relativity rather than Newtonian gravitation.

ExperimentsMain article: Experiments

The control is very important.Once predictions are made, they can be tested by experiments. If test results contradict predictions, then the hypotheses are called into question and explanations may be sought. Sometimes experiments are conducted incorrectly and are at fault. If the results confirm the predictions, then the hypotheses are considered likely to be correct but might still be wrong and are subject to further testing.Depending on the predictions, the experiments can have different shapes. It could be a classical experiment in a laboratory setting, a double-blind study or an archaeological excavation. Even taking a plane from New York to Paris is an experiment which tests the aerodynamical hypotheses used for constructing the plane.Scientists assume an attitude of openness and accountability on the part of those conducting an experiment. Detailed record keeping is essential, to aid in recording and reporting on the experimental results, and providing evidence of the effectiveness and integrity of the procedure. They will also assist in reproducing the experimental results. This tradition can be seen in the work of Hipparchus (190 BCE - 120 BCE), when determining a value for the precession of the Earth over 2100 years ago, and 1000 years before Al-Batani (853 CE – 929 CE).

DNA-experimentsBefore proposing their model Watson and Crick had previously seen x-ray diffraction images by Rosalind Franklin, Maurice Wilkins, and Raymond Gosling. However, they later reported that Franklin initially rebuffed their suggestion that DNA might be a double helix. Franklin had immediately spotted flaws in the initial hypotheses about the structure of DNA by Watson and Crick. The X-shape in X-ray images helped confirm the helical structure of DNA[27]. ..1. DNA-characterizations

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Evaluation and iterationTesting and improvementThe scientific process is iterative. At any stage it is possible that some consideration will lead the scientist to repeat an earlier part of the process. Failure to develop an interesting hypothesis may lead a scientist to re-define the subject they are considering. Failure of a hypothesis to produce interesting and testable predictions may lead to reconsideration of the hypothesis or of the definition of the subject. Failure of the experiment to produce interesting results may lead the scientist to reconsidering the experimental method, the hypothesis or the definition of the subject.Other scientists may start their own research and enter the process at any stage. They might adopt the characterization and formulate their own hypothesis, or they might adopt the hypothesis and deduce their own predictions. Often the experiment is not done by the person who made the prediction and the characterization is based on experiments done by someone else. Published results of experiments can also serve as a hypothesis predicting their own reproducibility.

DNA-iterationsAfter considerable fruitless experimentation, being discouraged by their superior from continuing, and numerous false starts, Watson and Crick were able to infer the essential structure of DNA by concrete modeling of the physical shapes of the nucleotides which comprise it. They were guided by the bond lengths which had been deduced by Linus Pauling and Rosalind Franklin's X-ray diffraction images. .. DNA Example

ConfirmationScience is a social enterprise, and scientific work tends to be accepted by the community when it has been confirmed. Crucially, experimental and theoretical results must be reproduced by others within the science community. Researchers have given their lives for this vision; Georg Wilhelm Richmann was killed by lightning (1753) when attempting to replicate the 1752 kite-flying experiment of Benjamin Franklin.[28]

To protect against bad science and fraudulent data, government research granting agencies like NSF and science journals like Nature and Science have a policy that researchers must archive their data and methods so other researchers can access it, test the data and methods and build on the research that has gone before. Scientific data archiving can be done at a number of national archives in the U.S. or in the World Data Center.

Models of scientific inquiryMain article: Models of scientific inquiry

Classical modelThe classical model of scientific inquiry derives from Aristotle[29], who distinguished the forms of approximate and exact reasoning, set out the threefold scheme of abductive, deductive, and inductive inference, and also treated the compound forms such as reasoning by analogy.Pragmatic model

Main article: Pragmatic theory of truthCharles Peirce considered scientific inquiry to be a species of the genus inquiry, which he defined as any means of fixing belief, that is, any means of arriving at a settled opinion on a matter in question. He observed that inquiry in general begins with a state of uncertainty and moves toward a state of certainty, sufficient at least to terminate the inquiry for the time being. He graded the prevalent forms of inquiry according to their evident success in achieving their common objective, scoring scientific inquiry at the high end of this scale. At the low end he placed what he called the method of tenacity, a die-hard attempt to deny uncertainty and fixate on a favored belief. Next in line he placed the method of authority, a determined attempt to conform to a chosen source of ready-made beliefs. After that he placed what might be called the method of congruity, also called the a priori, the dilettante, or the what is agreeable to reason method. Peirce observed the fact of human nature that almost everybody uses almost all of these /tt/file_convert/5a9fc4dd7f8b9a8e178d261f/document.doc 18/122

methods at one time or another, and that even scientists, being human, use the method of authority far more than they like to admit. But what recommends the specifically scientific method of inquiry above all others is the fact that it is deliberately designed to arrive at the ultimately most secure beliefs, upon which the most successful actions can be based.[30]

Computational approachesMany subspecialties of applied logic and computer science, to name a few, artificial intelligence, machine learning, computational learning theory, inferential statistics, and knowledge representation, are concerned with setting out computational, logical, and statistical frameworks for the various types of inference involved in scientific inquiry, in particular, hypothesis formation, logical deduction, and empirical testing. Some of these applications draw on measures of complexity from algorithmic information theory to guide the making of predictions from prior distributions of experience, for example, see the complexity measure called the speed prior from which a computable strategy for optimal inductive reasoning can be derived.

Philosophy and sociology of scienceMain article: Philosophy of scienceFurther information: Sociology of science

While the philosophy of science has limited direct impact on day-to-day scientific practice, it plays a vital role in justifying and defending the scientific approach. Philosophy of science looks at the underpinning logic of the scientific method, at what separates science from non-science, and the ethic that is implicit in science.We find ourselves in a world that is not directly understandable. We find that we sometimes disagree with others as to the facts of the things we see in the world around us, and we find that there are things in the world that are at odds with our present understanding. The scientific method attempts to provide a way in which we can reach agreement and understanding. A "perfect" scientific method might work in such a way that rational application of the method would always result in agreement and understanding; a perfect method would arguably be algorithmic, and so not leave any room for rational agents to disagree. As with all philosophical topics, the search has been neither straightforward nor simple. Logical Positivist, empiricist, falsificationist, and other theories have claimed to give a definitive account of the logic of science, but each has in turn been criticized.Thomas Samuel Kuhn examined the history of science in his The Structure of Scientific Revolutions, and found that the actual method used by scientists differed dramatically from the then-espoused method.Paul Feyerabend similarly examined the history of science, and was led to deny that science is genuinely a methodological process. In his book Against Method he argues that scientific progress is not the result of applying any particular method. In essence, he says that "anything goes", by which he meant that for any specific methodology or norm of science, successful science has been done in violation of it. Criticisms such as his led to the strong programme, a radical approach to the sociology of science.In his 1958 book, Personal Knowledge, chemist and philosopher Michael Polanyi (1891-1976) criticized the common view that the scientific method is purely objective and generates objective knowledge. Polanyi cast this view as a misunderstanding of the scientific method and of the nature of scientific inquiry, generally. He argued that scientists do and must follow personal passions in appraising facts and in determining which scientific questions to investigate. He concluded that a structure of liberty is essential for the advancement of science - that the freedom to pursue science for its own sake is a prerequisite for the production of knowledge through peer review and the scientific method.The postmodernist critiques of science have themselves been the subject of intense controversy and heated dialogue. This ongoing debate, known as the science wars, is the result of the conflicting values and assumptions held by the postmodernist and realist camps. Whereas postmodernists assert that scientific knowledge is simply another discourse and not representative of any form of fundamental truth, realists in the scientific community maintain that scientific knowledge does reveal real and fundamental truths about reality. Many books have been written by scientists which take on this problem and challenge

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the assertions of the postmodernists while defending science as a legitimate method of deriving truth.[31][32]

[33][34][35]

Communication, community, cultureFrequently the scientific method is not employed by a single person, but by several people cooperating directly or indirectly. Such cooperation can be regarded as one of the defining elements of a scientific community. Various techniques have been developed to ensure the integrity of the scientific method within such an environment.Peer review evaluationScientific journals use a process of peer review, in which scientists' manuscripts are submitted by editors of scientific journals to (usually one to three) fellow (usually anonymous) scientists familiar with the field for evaluation. The referees may or may not recommend publication, publication with suggested modifications, or, sometimes, publication in another journal. This serves to keep the scientific literature free of unscientific or crackpot work, helps to cut down on obvious errors, and generally otherwise improve the quality of the scientific literature. Work announced in the popular press before going through this process is generally frowned upon. Sometimes peer review inhibits the circulation of unorthodox work, especially if it undermines the establishment in the particular field, and at other times may be too permissive. Other drawbacks includes cronyism and favoritism. The peer review process is not always successful, but has been very widely adopted by the scientific community.Documentation and replicationSometimes experimenters may make systematic errors during their experiments, unconsciously veer from the scientific method (Pathological science) for various reasons, or, in rare cases, deliberately falsify their results. Consequently, it is a common practice for other scientists to attempt to repeat the experiments in order to duplicate the results, thus further validating the hypothesis.

ArchivingAs a result, researchers are expected to practice scientific data archiving in compliance with the policies of government funding agencies and scientific journals. Detailed records of their experimental procedures, raw data, statistical analyses and source code are preserved in order to provide evidence of the effectiveness and integrity of the procedure and assist in reproduction. These procedural records may also assist in the conception of new experiments to test the hypothesis, and may prove useful to engineers who might examine the potential practical applications of a discovery.

DearchivingWhen additional information is needed before a study can be reproduced, the author of the study is expected to provide it promptly - although a small charge may apply. If the author refuses to share data, appeals can be made to the journal editors who published the study or to the institution who funded the research.

LimitationsNote that it is not possible for a scientist to record everything that took place in an experiment. He must select the facts he believes to be relevant to the experiment and report them. This may lead, unavoidably, to problems later if some supposedly irrelevant feature is questioned. For example, Heinrich Hertz did not report the size of the room used to test Maxwell's equations, which later turned out to account for a small deviation in the results. The problem is that parts of the theory itself need to be assumed in order to select and report the experimental conditions. The observations are hence sometimes described as being 'theory-laden'.Dimensions of practiceThe primary constraints on contemporary western science are:

Publication, i.e. Peer review Resources (mostly funding)

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It has not always been like this: in the old days of the "gentleman scientist" funding (and to a lesser extent publication) were far weaker constraints.Both of these constraints indirectly bring in a scientific method — work that too obviously violates the constraints will be difficult to publish and difficult to get funded. Journals do not require submitted papers to conform to anything more specific than "good scientific practice" and this is mostly enforced by peer review. Originality, importance and interest are more important - see for example the author guidelines for Nature.Criticisms (see Critical theory) of these restraints are that they are so nebulous in definition (e.g. "good scientific practice") and open to ideological, or even political, manipulation apart from a rigorous practice of a scientific method, that they often serve to censor rather than promote scientific discovery.[citation needed] Apparent censorship through refusal to publish ideas unpopular with mainstream scientists (unpopular because of ideological reasons and/or because they seem to contradict long held scientific theories) has soured the popular perception of scientists as being neutral or seekers of truth and often denigrated popular perception of science as a whole.

Further information: Rhetoric of science

HistoryMain article: History of scientific methodSee also: Timeline of the history of scientific method

The development of the scientific method is inseparable from the history of science itself. Ancient Egyptian documents, such as early papyri, describe methods of medical diagnosis. In ancient Greek culture, the method of empiricism was described. The first experimental scientific method was developed by Muslim scientists, who introduced the use of experimentation and quantification to distinguish between competing scientific theories set within a generally empirical orientation, which emerged with Alhacen's optical experiments in his Book of Optics (1021).[36][37] The modern scientific method crystallized no later than in the 17th and 18th centuries. In his work Novum Organum (1620) — a reference to Aristotle's Organon — Francis Bacon outlined a new system of logic to improve upon the old philosophical process of syllogism. Then, in 1637, René Descartes established the framework for a scientific method's guiding principles in his treatise, Discourse on Method. The writings of Alhacen, Bacon and Descartes are considered critical in the historical development of the modern scientific method.In the late 19th century, Charles Sanders Peirce proposed a schema that would turn out to have considerable influence in the development of current scientific method generally. Peirce accelerated the progress on several fronts. Firstly, speaking in broader context in "How to Make Our Ideas Clear" (1878) [3], Peirce outlined an objectively verifiable method to test the truth of putative knowledge on a way that goes beyond mere foundational alternatives, focusing upon both deduction and induction. He thus placed induction and deduction in a complementary rather than competitive context (the latter of which had been the primary trend at least since David Hume, who wrote in the mid-to-late 18th century). Secondly, and of more direct importance to modern method, Peirce put forth the basic schema for hypothesis/testing that continues to prevail today. Extracting the theory of inquiry from its raw materials in classical logic, he refined it in parallel with the early development of symbolic logic to address the then-current problems in scientific reasoning. Peirce examined and articulated the three fundamental modes of reasoning that, as discussed above in this article, play a role in inquiry today, the processes that are currently known as abductive, deductive, and inductive inference. Thirdly, he played a major role in the progress of symbolic logic itself — indeed this was his primary specialty.Karl Popper (1902–1994), beginning in the 1930s and with increased vigor after World War II, argued that a hypothesis must be falsifiable and, following Peirce and others, that science would best progress using deductive reasoning as its primary emphasis, known as critical rationalism. His astute formulations of logical procedure helped to rein in excessive use of inductive speculation upon inductive speculation, and also strengthened the conceptual foundation for today's peer review procedures.

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Relationship with mathematicsScience is the process of gathering, comparing, and evaluating proposed models against observables. A model can be a simulation, mathematical or chemical formula, or set of proposed steps. Science is like mathematics in that researchers in both disciplines can clearly distinguish what is known from what is unknown at each stage of discovery. Models, in both science and mathematics, need to be internally consistent and also ought to be falsifiable (capable of disproof). In mathematics, a statement need not yet be proven; at such a stage, that statement would be called a conjecture. But when a statement has attained mathematical proof, that statement gains a kind of immortality which is highly prized by mathematicians, and for which some mathematicians devote their lives[38].Mathematical work and scientific work can inspire each other[39]. For example, the concept of time arose in science, and timelessness was a hallmark of a mathematical topic. But today, the Poincaré conjecture is in the process of being proven, using time as a mathematical concept, in which objects can flow (see Ricci flow).George Pólya's work on problem solving [40] , the construction of mathematical proofs, and heuristic [41] [42] show that mathematical method and scientific method differ in detail, while resembling each other in the use of iterative or recursive steps.

Mathematical method Scientific method

1 Understanding Characterization from experience and observation

2 Analysis Hypothesis: a proposed explanation

3 Synthesis Deduction: prediction from the hypothesis

4 Review/Extend Test and experiment

In Pólya's view, understanding involves restating unfamiliar definitions in your own words, resorting to geometrical figures, and questioning what we know and do not know already; analysis, which Pólya takes from Pappus [43] , involves free and heuristic construction of plausible arguments, working backward from the goal, and devising a plan for constructing the proof; synthesis is the strict Euclidean exposition of step-by-step details[44] of the proof; review involves reconsidering and re-examining the result and the path taken to it.

Notes and references1. ̂ Isaac Newton (1687, 1713, 1726). "[4] Rules for the study of natural philosophy", Philosophiae

Naturalis Principia Mathematica, Third edition. The General Scholium containing the 4 rules follows Book 3, The System of the World. Reprinted on pages 794-796 of I. Bernard Cohen and Anne Whitman's 1999 translation, University of California Press ISBN 0-520-08817-4, 974 pages.

2. ̂ scientific method, Merriam-Webster Dictionary. 3. ̂ Alhazen (Ibn Al-Haytham) Critique of Ptolemy, translated by S. Pines, Actes X Congrès internationale

d'histoire des sciences, Vol I Ithaca 1962, as referenced on p.139 of Shmuel Sambursky (ed. 1974) Physical Thought from the Presocratics to the Quantum Physicists ISBN 0-87663-712-8

4. ̂ Alhazen, translated into English from German by M. Schwarz, from "Abhandlung über das Licht", J. Baarmann (ed. 1882) Zeitschrift der Deutschen Morgenländischen Gesellschaft Vol 36 as referenced on p.136 by Shmuel Sambursky (1974) Physical thought from the Presocratics to the Quantum Physicists ISBN 0-87663-712-8

5. ̂ p.136, as quoted by Shmuel Sambursky (1974) Physical thought from the Presocratics to the Quantum Physicists ISBN 0-87663-712-8

6. ̂ "... the statement of a law - A depends on B - always transcends experience." p.6 —Max Born (1949), Natural Philosophy of Cause and Chance

7. ̂ "I believe that we do not know anything for certain, but everything probably." —Christiaan Huygens, Letter to Pierre Perrault, 'Sur la préface de M. Perrault de son traité del'Origine des fontaines' [1763], Oeuvres Complétes de Christiaan Huygens (1897), Vol. 7, 298. Quoted in Jacques Roger, The Life Sciences in Eighteenth-Century French Thought, ed. Keith R. Benson and trans. Robert Ellrich (1997), 163. Quotation selected by W.F. Bynum and Roy Porter (eds., 2005), Oxford Dictionary of Scientific Quotations ISBN 0-19-858409-1 p. 317 quotation 4.

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8. ̂ "Observation and experiment are subject to a very popular myth. ... The knower is seen as a ... Julius Caesar winning his battles according to ... formula. Even research workers will admit that the first observation may have been a little imprecise, whereas the second and third were 'adjusted to the facts' ... until tradition, education, and familiarity have produced a readiness for stylized (that is directed and restricted) perception and action; until an answer becomes largely pre-formed in the question, and a decision confined merely to 'yes' or 'no' or perhaps to a numerical determination; until methods and apparatus automatically carry out the greatest part of the mental work for us." Fleck labels this thought style (Denkstil). Ludwik Fleck, p.84 of Genesis and Development of a Scientific Fact (written in German, 1935, Entstehung und Entwickelung einer wissenschaftlichen Tatsache: Einführung in die Lehre vom Denkstil und Denkkollectiv) ISBN 0-226-25325-2

9. ̂ See the hypothethico-deductive method, for example: p.236 —Peter Godfrey-Smith (2003), Theory and Reality: An introduction to the philosophy of science ISBN 0-226-30063-3

10. ̂ pp.265-6 (in the Dover edition) —William Stanley Jevons (1873), The principles of science: a treatise on logic and scientific method. ISBN 1430487755

11. ̂ pp.65,73,92,398 —Andrew J. Galambos, Sic Itur ad Astra ISBN 0-88078-004-5(AJG learned scientific method from Felix Ehrenhaft)

12. ̂ Galileo Galilei Linceo (1638), Discorsi e Dimonstrazioni Matematiche, intorno a due nuoue scienze. In Leida, Apresso gli Elsevirri M.D.C.XXXVIII. Two New Sciences was selected from the collection of the Library of Congress by Leonard C. Bruno (1988), The Landmarks of Science ISBN 0-8160-2137-6

13. ̂ Iteration example: Chaldean astronomers such as Kidinnu compiled astronomical data. Hipparchus was to use this data to calculate the precession of the Earth's axis. Fifteen hundred years after Kiddinu, Al-Batani, born in what is now Turkey, would use the collected data and improve Hipparchus' value for the precession of the Earth's axis. Al-Batani's value, 54.5 arc-seconds per year, compares well to the current value of 49.8 arc-seconds per year (26,000 years for Earth's axis to round the circle of nutation).

14. ̂ Recursion example: the Earth is itself a magnet, with its own North and South Poles William Gilbert (in Latin 1600) De Magnete, or On Magnetism and Magnetic Bodies. Translated from Latin to English, selection by Forest Ray Moulton and Justus J. Schifferes (eds., Second Edition 1960) The Autobiography of Science pp.113-117

15. ̂ "The foundation of general physics ... is experience. These ... everyday experiences we do not discover without deliberately directing our attention to them. Collecting information about these is observation." —Hans Christian Ørsted("First Introduction to General Physics" ¶13, part of a series of public lectures at the University of Copenhagen. Copenhagen 1811, in Danish, printed by Johan Frederik Schulz. In Kirstine Meyer's 1920 edition of Ørsted's works, vol.III pp. 151-190. ) "First Introduction to Physics: the Spirit, Meaning, and Goal of Natural Science". Reprinted in German in 1822, Schweigger's Journal für Chemie und Physik 36, pp.458-488. Translated to English by Karen Jelved, Andrew D. Jackson, and Ole Knudsen, (translators 1997) Selected Scientific Works of Hans Christian Ørsted, ISBN 0-691-04334-5 p. 292

16. ̂ "When it is not clear under which law of nature an effect or class of effect belongs, we try to fill this gap by means of a guess. Such guesses have been given the name conjectures or hypotheses." —Hans Christian Ørsted(1811) "First Introduction to General Physics" ¶18. Selected Scientific Works of Hans Christian Ørsted, ISBN 0-691-04334-5 p.297

17. ̂ "In general we look for a new law by the following process. First we guess it. ...", p. 156 —Richard Feynman (1965), The Character of Physical Law ISBN 0-262-56003-8

18. ̂ "... the statement of a law - A depends on B - always transcends experience." p.6 —Max Born (1949), Natural Philosophy of Cause and Chance

19. ̂ "The student of nature ... regards as his property the experiences which the mathematican can only borrow. This is why he deduces theorems directly from the nature of an effect while the mathematician only arrives at them circuitously." —Hans Christian Ørsted(1811) "First Introduction to General Physics" ¶17. Selected Scientific Works of Hans Christian Ørsted, ISBN 0-691-04334-5 p.297

20. ̂ Salviati speaks: "I greatly doubt that Aristotle ever tested by experiment whether it be true that two stones, one weighing ten times as much as the other, if allowed to fall, at the same instant, from a height of, say, 100 cubits, would so differ in speed that when the heavier had reached the ground, the other would not have fallen more than 10 cubits." p.61[1] —Galileo (1638), Two New Sciences as translated from Italian to English by Henry Crew and Alfonso di Salvio (1914). A more extended quotation is referenced on pp.80-81 by Forest Ray Moulton and Justus J. Schifferes (eds., Second Edition 1960) The Autobiography of Science

21. ̂ In the inquiry-based education paradigm, the stage of "characterization, observation, definition, …" is more briefly summed up under the rubric of a Question.

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22. ̂ "To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science." p.92, Albert Einstein and Leopold Infeld (1938), The Evolution of Physics: from early concepts to relativity and quanta ISBN 0-671-20156-5

23. ̂ See, e.g., Gauch, Hugh G., Jr., Scientific Method in Practice (2003), esp. chapters 5-8 24. ̂ Cochran W, Crick FHC and Vand V. (1952) "The Structure of Synthetic Polypeptides. I. The Transform

of Atoms on a Helix", Acta Cryst., 5, 581-586. 25. ̂ Crick, Francis (1994), The Astonishing Hypothesis ISBN 0-684-19431-7 p.20 26. ̂ Glen,William (ed.), The Mass-Extinction Debates: How Science Works in a Crisis, Stanford University

Press, Stanford, CA, 1994. ISBN 0-8047-2285-4. pp. 37-38. 27. ̂ "The instant I saw the picture my mouth fell open and my pulse began to race." -- James D. Watson

(1968), The Double Helix, page 167. New York: Atheneum, Library of Congress card number 68-16217. Page 168 shows the X-shaped pattern of the B-form of DNA, clearly indicating crucial details of its helical structure to Watson and Crick.

28. ̂ See, e.g., Physics Today, Vol. 59, #1, p42. [2] 29. ̂ Aristotle, "Prior Analytics", Hugh Tredennick (trans.), pp. 181-531 in Aristotle, Volume 1, Loeb

Classical Library, William Heinemann, London, UK, 1938. 30. ̂ Peirce, C.S., "Lectures on Pragmatism", Cambridge, MA, March 26 – May 17, 1903. Reprinted in part,

Collected Papers, CP 5.14–212. Reprinted with Introduction and Commentary, Patricia Ann Turisi (ed.), Pragmatism as a Principle and a Method of Right Thinking: The 1903 Harvard "Lectures on Pragmatism", State University of New York Press, Albany, NY, 1997. Reprinted, pp. 133–241, Peirce Edition Project (eds.), The Essential Peirce, Selected Philosophical Writings, Volume 2 (1893–1913), Indiana University Press, Bloomington, IN, 1998.

31. ̂ Higher Superstition: The Academic Left and Its Quarrels with Science, The Johns Hopkins University Press, 1997

32. ̂ Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science, Picador; 1st Picador USA Pbk. Ed edition, 1999

33. ̂ The Sokal Hoax: The Sham That Shook the Academy, University of Nebraska Press, 2000 ISBN 0803279957

34. ̂ A House Built on Sand: Exposing Postmodernist Myths About Science, Oxford University Press, 2000 35. ̂ Intellectual Impostures, Economist Books, 2003 36. ̂ Rosanna Gorini (2003), "Al-Haytham the Man of Experience, First Steps in the Science of Vision",

International Society for the History of Islamic Medicine, Institute of Neurosciences, Laboratory of Psychobiology and Psychopharmacology, Rome, Italy: "According to the majority of the historians al-Haytham was the pioneer of the modern scientific method. With his book he changed the meaning of the term optics and established experiments as the norm of proof in the field. His investigations are based not on abstract theories, but on experimental evidences and his experiments were systematic and repeatable."

37. ̂ David Agar (2001). Arabic Studies in Physics and Astronomy During 800 - 1400 AD. University of Jyväskylä.

38. ̂ "When we are working intensively, we feel keenly the progress of our work; we are elated when our progress is rapid, we are depressed when it is slow." page 131, in the section on 'Modern heuristic'-- the mathematician George Pólya (1957), How to solve it, Second edition.

39. ̂ "Philosophy [i.e., physics] is written in this grand book--I mean the universe--which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth." —Galileo Galilei, Il Saggiatore (The Assayer, 1623) as referenced by G. Toraldo di Francia (1981), The Investigation of the Physical World ISBN 0-521-29925-X

40. ̂ George Pólya, How to Solve It 41. ̂ George Pólya, Mathematics and Plausible Reasoning Volume I: Induction and Analogy in Mathematics, 42. ̂ George Pólya, Mathematics and Plausible Reasoning Volume II: Patterns of Plausible Reasoning. 43. ̂ George Pólya (1957), How to Solve It Second edition p.142 44. ̂ George Pólya (1957), How to Solve It Second edition p.144

Further reading Bacon, Francis Novum Organum (The New Organon), 1620. Bacon's work described many of the accepted

principles, underscoring the importance of theory, empirical results, data gathering, experiment, and independent corroboration.

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Bauer, Henry H. , Scientific Literacy and the Myth of the Scientific Method, University of Illinois Press, Champaign, IL, 1992

Beveridge, William I. B. , The Art of Scientific Investigation, Vintage/Alfred A. Knopf, 1957. Bernstein, Richard J. , Beyond Objectivism and Relativism: Science, Hermeneutics, and Praxis, University

of Pennsylvania Press, Philadelphia, PA, 1983. Bozinovski, Stevo , Consequence Driven Systems: Teaching, Learning, and Self-Learning Agents,

GOCMAR Publishers, Bitola, Macedonia, 1991. Brody, Baruch A. , and Grandy, Richard E., Readings in the Philosophy of Science, 2nd edition, Prentice

Hall, Englewood Cliffs, NJ, 1989. Burks, Arthur W. , Chance, Cause, Reason — An Inquiry into the Nature of Scientific Evidence, University

of Chicago Press, Chicago, IL, 1977. Chomsky, Noam , Reflections on Language, Pantheon Books, New York, NY, 1975. Dewey, John , How We Think, D.C. Heath, Lexington, MA, 1910. Reprinted, Prometheus Books, Buffalo,

NY, 1991. Earman, John (ed.), Inference, Explanation, and Other Frustrations: Essays in the Philosophy of Science,

University of California Press, Berkeley & Los Angeles, CA, 1992. Fraassen, Bas C. van , The Scientific Image, Oxford University Press, Oxford, UK, 1980. Feyerabend, Paul K. , Against Method, Outline of an Anarchistic Theory of Knowledge, 1st published, 1975.

Reprinted, Verso, London, UK, 1978. Gadamer, Hans-Georg , Reason in the Age of Science, Frederick G. Lawrence (trans.), MIT Press,

Cambridge, MA, 1981. Giere, Ronald N. (ed.), Cognitive Models of Science, vol. 15 in 'Minnesota Studies in the Philosophy of

Science', University of Minnesota Press, Minneapolis, MN, 1992. Hacking, Ian , Representing and Intervening, Introductory Topics in the Philosophy of Natural Science,

Cambridge University Press, Cambridge, UK, 1983. Heisenberg, Werner , Physics and Beyond, Encounters and Conversations, A.J. Pomerans (trans.), Harper

and Row, New York, NY 1971, pp. 63–64. Holton, Gerald , Thematic Origins of Scientific Thought, Kepler to Einstein, 1st edition 1973, revised

edition, Harvard University Press, Cambridge, MA, 1988. Jevons, William Stanley , The Principles of Science: A Treatise on Logic and Scientific Method, 1874,

1877, 1879. Reprinted with a foreword by Ernst Nagel, Dover Publications, New York, NY, 1958. Kuhn, Thomas S. , "The Function of Measurement in Modern Physical Science", ISIS 52(2), 161–193,

1961. Kuhn, Thomas S., The Structure of Scientific Revolutions, University of Chicago Press, Chicago, IL, 1962.

2nd edition 1970. 3rd edition 1996. Kuhn, Thomas S., The Essential Tension, Selected Studies in Scientific Tradition and Change, University

of Chicago Press, Chicago, IL, 1977. Latour, Bruno , Science in Action, How to Follow Scientists and Engineers through Society, Harvard

University Press, Cambridge, MA, 1987. Losee, John , A Historical Introduction to the Philosophy of Science, Oxford University Press, Oxford, UK,

1972. 2nd edition, 1980. Maxwell, Nicholas , The Comprehensibility of the Universe: A New Conception of Science, Oxford

University Press, Oxford, 1998. Paperback 2003. McComas, William F. , ed. The Principle Elements of the Nature of Science: Dispelling the

Myths PDF  (189 KiB), from The Nature of Science in Science Education, pp53-70, Kluwer Academic Publishers, Netherlands 1998.

Misak, Cheryl J. , Truth and the End of Inquiry, A Peircean Account of Truth, Oxford University Press, Oxford, UK, 1991.

Newell, Allen , Unified Theories of Cognition, Harvard University Press, Cambridge, MA, 1990. Peirce, C.S. , Essays in the Philosophy of Science, Vincent Tomas (ed.), Bobbs–Merrill, New York, NY,

1957. Peirce, C.S. , "Lectures on Pragmatism", Cambridge, MA, March 26 – May 17, 1903. Reprinted in part,

Collected Papers, CP 5.14–212. Reprinted with Introduction and Commentary, Patricia Ann Turisi (ed.), Pragmatism as a Principle and a Method of Right Thinking: The 1903 Harvard "Lectures on Pragmatism", State University of New York Press, Albany, NY, 1997. Reprinted, pp. 133–241, Peirce Edition Project (eds.), The Essential Peirce, Selected Philosophical Writings, Volume 2 (1893–1913), Indiana University Press, Bloomington, IN, 1998.

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Peirce, C.S. , Collected Papers of Charles Sanders Peirce, vols. 1-6, Charles Hartshorne and Paul Weiss (eds.), vols. 7-8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931-1935, 1958. Cited as CP vol.para.

Piattelli-Palmarini, Massimo (ed.), Language and Learning, The Debate between Jean Piaget and Noam Chomsky, Harvard University Press, Cambridge, MA, 1980.

Poincaré, Henri , Science and Hypothesis, 1905, Eprint Popper, Karl R. , The Logic of Scientific Discovery, 1934, 1959.[4] Popper, Karl R. , Unended Quest, An Intellectual Autobiography, Open Court, La Salle, IL, 1982. Putnam, Hilary , Renewing Philosophy, Harvard University Press, Cambridge, MA, 1992. Rorty, Richard , Philosophy and the Mirror of Nature, Princeton University Press, Princeton, NJ, 1979. Salmon, Wesley C. , Four Decades of Scientific Explanation, University of Minnesota Press, Minneapolis,

MN, 1990. Shimony, Abner , Search for a Naturalistic World View: Vol. 1, Scientific Method and Epistemology, Vol.

2, Natural Science and Metaphysics, Cambridge University Press, Cambridge, UK, 1993. Thagard, Paul , Conceptual Revolutions, Princeton University Press, Princeton, NJ, 1992. Ziman, John (2000). Real Science: what it is, and what it means. Cambridge, Uk: Cambridge University

Press.

See alsoSynopsis of related topics

Confirmability Contingency Falsifiability Hypothesis Hypothesis testing

Inquiry Reproducibility Research Statistics Strong inference

Tautology Testability Theory Verification and Validation

Logic, mathematics, methodology Inference o Abductive reasoning o Deductive reasoning o Inductive reasoning

Information theory Logic Mathematics Methodology

Problems and issues Ockham's razor Poverty of the stimulus Reference class problem

Underdetermination Holistic science

History, philosophy, sociology Cudos Epistemology Epistemic truth History of science

History of scientific method Philosophy of science Science studies

Social research Sociology of scientific knowledge Timeline of scientific method

External linksWikibooks has a book on the topic of The Scientific Method

An Introduction to Science: Scientific Thinking and a scientific method by Steven D. Schafersman.

Introduction to a scientific method Theory-ladenness by Paul Newall at The Galilean Library Lecture on Scientific Method by Greg Anderson Using the scientific method for designing science fair projects

Retrieved from "http://en.wikipedia.org/wiki/Scientific_method"

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TechnologyFrom Wikipedia, the free encyclopedia

By the mid 20th century humans had achieved a mastery of technology sufficient to leave the surface of the Earth for the first time and explore space.

Technology Portal

Technology is a broad concept that deals with a species' usage and knowledge of tools and crafts, and how it affects a species' ability to control and adapt to its environment. In human society, it is a consequence of science and engineering, although several technological advances predate the two concepts. Technology is a term with origins in the Greek "technologia", "τεχνολογία" — "techne", "τέχνη" ("craft") and "logia", "λογία" ("saying").[1] However, a strict definition is elusive; "technology" can refer to material objects of use to humanity, such as machines, hardware or utensils, but can also encompass broader themes, including systems, methods of organization, and techniques. The term can either be applied generally or to specific areas: examples include "construction technology", "medical technology", or "state-of-the-art technology".The human race's use of technology began with the conversion of natural resources into simple tools. The prehistorical discovery of the ability to control fire increased the available sources of food and the invention of the wheel helped humans in travelling in and controlling their environment. Recent technological developments, including the printing press, the telephone, and the Internet, have lessened physical barriers to communication and allowed humans to interact on a global scale. However, not all technology has been used for peaceful purposes; the development of weapons of ever-increasing destructive power has progressed throughout history, from clubs to nuclear weapons.Technology has affected society and its surroundings in a number of ways. In many societies, technology has helped develop more advanced economies (including today's global economy) and has allowed the rise of a leisure class. Many technological processes produce unwanted by-products, known as pollution, and deplete natural resources, to the detriment of the Earth and its environment. Various implementations of technology influence the values of a society and new technology often raises new ethical questions. Examples include the rise of the notion of efficiency in terms of human productivity, a term originally applied only to machines, and the challenge of traditional norms.Philosophical debates have arisen over the present and future use of technology in society, with disagreements over whether technology improves the human condition or worsens it. Neo-Luddism, anarcho-primitivism, and other similar movements criticise the pervasiveness of technology in the modern world, claiming that it alienates people and destroys culture; proponents of ideologies such as transhumanism and techno-progressivism view continued technological progress as beneficial to society and the human condition. Indeed, until recently, it was believed that the development of technology was restricted only to human beings, but recent scientific studies indicate that other primates and certain dolphin communities have developed simple tools and learned to pass their knowledge to other generations.

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Contents1 Definition and usage 2 Science, engineering and technology 3 History

3.1 Prehistory (— 5000BCE) 3.2 Ancient history (5000BCE — 0CE) 3.3 Modern history (0CE —)

4 Technology and society 5 Technology and philosophy

5.1 Technicism 5.2 Optimism 5.3 Pessimism 5.4 Appropriate technology

6 Other species 7 See also

7.1 Theories and concepts in technology 7.2 Economics of technology

8 Notes 9 References

9.1 Printed sources 9.2 Online sources

10 Further reading

Definition and usage The invention of the printing press made it possible for scientists and

politicians to communicate their ideas with ease, leading to the Age of Enlightenment; an example of technology as a cultural force.In general, "technology" is the relationship that society has with its tools and crafts, and to what extent society can control its environment. The Merriam-Webster dictionary offers a definition of the term: "the practical application of knowledge especially in a particular area" and "a capability given by the practical application of knowledge".[1] Ursula Franklin, in her 1989 "Real World of Technology" lecture, gave another definition of the concept; it is "practice, the way we do things around here".[2] The term is often used to imply a specific field of technology, or to refer to high technology, rather than technology as a whole.[3] However, the term is mostly used in three different contexts: when referring to a tool (or machine); a technique; the cultural force; or a combination of the three.Technology can be most broadly defined as the entities, both material and

immaterial, created by the application of mental and physical effort in order to achieve some value. In this usage, technology refers to tools and machines that may be used to solve real-world problems. It is a far-reaching term that may include simple tools, such as a crowbar or wooden spoon, or more complex machines, such as a space station or particle accelerator. Tools and machines need not be material; virtual technology, such as computer software and business methods, fall under this definition of technology.[4]

The word "technology" can also be used to refer to a collection of techniques. In this context, it is the current state of humanity's knowledge of how to combine resources to produce desired products, to solve problems, fulfill needs, or satisfy wants; it includes technical methods, skills, processes, techniques, tools and raw materials. When combined with another term, such as "medical technology" or "space technology", it refers to the state of the respective field's knowledge and tools. "State-of-the-art technology" refers to the high technology available to humanity in any field.Technology can be viewed as an activity that forms or changes culture.[5] A modern example is the rise of communication technology, which has lessened barriers to human interaction and, as a result, has helped /tt/file_convert/5a9fc4dd7f8b9a8e178d261f/document.doc 28/122

spawn new subcultures; the rise of cyberculture has, at its basis, the development of the Internet and the computer.[6] Not all technology enhances culture in a creative way; technology can also help facilitate political oppression and war via tools such as guns. As a cultural activity, technology predates both science and engineering, each of which formalize some aspects of technological endeavor.

Science, engineering and technologyThe distinction between science, engineering and technology is not always clear. Science is the reasoned investigation or study of phenomena, aimed at discovering enduring principles among elements of the phenomenal world by employing formal techniques such as the scientific method.[7] Technologies are not usually exclusively products of science, because they have to satisfy requirements such as utility, usability and safety.Engineering is the goal-oriented process of designing and building tools and systems to exploit natural phenomena for practical human means, using results and techniques from science. The development of technology may draw upon many fields of knowledge, including scientific, engineering, mathematical, linguistic, and historical knowledge, to achieve some practical result.Technology is often a consequence of science and engineering — although technology as a human activity preceeds the two fields. For example, science might study the flow of electrons in electrical conductors, by using already-existing tools and knowledge. This new-found knowledge may then be used by engineers to create new tools and machines, such as semiconductors, computers, and other forms of advanced technology. In this sense, scientists and engineers may both be considered technologists; the three fields are often considered as one for the purposes of research and reference.[8]

HistoryMain articles: History of technology and Timeline of invention

Prehistory (— 5000BCE) A Paleolithic flint spear and sword, used by early humans for hunting

and fighting.The history of technology is at least as old as humankind, if not older. Primitive tools have been discovered with almost every find of ancient human remains.[9] Archaeologists have uncovered tools made by humanity's ancestors more than two million years ago,[10] and the earliest direct evidence of tool usage, found in the Great Rift Valley, dates back to 2.5 million years ago.[11] The hunter-gatherer lifestyle, characteristic of the Lower Paleolithic era, involved a limited use of technology, and the earliest tools, such as the handaxe and scraper, were developed to aid early humans in that role.[12][13]

The discovery and utilization of fire, a simple energy source with many profound uses, was a turning point in the technological evolution of humankind.[14] The exact date of its discovery is not known; evidence of burnt animal bones at the Cradle of Humankind suggests that the domestication of fire occurred before 1,000,000 BCE;[15] scholarly consensus indicates that Homo erectus had controlled fire by between

500,000 BCE and 400,000 BCE.[16][17] Fire, fueled with wood and charcoal, allowed early humans to cook their food to increase its digestibility, improving its nutrient value and broadening the number of foods that could be eaten.[18]

Other technological advances made during the Paleolithic era were clothing and shelter; the adoption of both technologies cannot be dated exactly, but they were key to humanity's progress. As the Paleolithic era progressed, dwellings became more sophisticated and more elaborate; as early as 380,000 BCE, humans were constructing temporary wood huts.[19][20] Clothing, adapted from the fur and hides of hunted animals, helped humanity expand into colder regions; humans began to migrate out of Africa by 200,000 BCE and into other continents, such as Eurasia.[21]

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A more sophisticated toolmaking technique was developed at around the same time. Known as the prepared-core technique, it enabled the creation of more controlled and consistent flakes, which could be hafted onto wooden shafts as arrows.[citation needed] This new technique helped to form more efficient composite tools and weapons, and combined with fire, this new technique enabled humans to hunt more effectively; wooden spears with fire-hardened points have been found as early as 250,000 BCE.[citation needed]

Technological developments in the Upper Paleolithic era, helped by the development of language, included advances in flint tool manufacturing, with industries based on fine blades rather than simple flakes.[citation needed] Humans began to work bones, antler, and hides, as evidenced by burins and racloirs produced during this period.[citation needed]

Ancient history (5000BCE — 0CE)Continuing improvements led to the furnace and bellows and provided the ability to smelt and forge native metals (naturally occurring in relatively pure form).[22] Gold, copper, silver, and lead, were such early metals. The advantages of copper tools over stone, bone, and wooden tools were quickly apparent to early humans, and native copper was probably used from near the beginning of Neolithic times (about 8000 BCE). Native copper does not naturally occur in large amounts, but copper ores are quite common and some of them produce metal easily when burned in wood or charcoal fires. Eventually, the working of metals led to the discovery of alloys such as bronze and brass (about 4000 BCE). The first uses of iron alloys such as steel dates to around 1400 BCE.Meanwhile, humans were learning to harness other forms of energy. The earliest known use of wind power is the sailboat. The earliest record of a ship under sail is shown on an Egyptian pot dating back to 3200 BCE. From prehistoric times, Egyptians probably used "the power of the Nile" annual floods to irrigate their lands, gradually learning to regulate much of it through purposely-built irrigation channels and 'catch' basins. Similarly, the early peoples of Mesopotamia, the Sumerians, learned to use the Tigris and Euphrates rivers for much the same purposes. But more extensive use of wind and water (and even human) power required another invention.

The wheel was invented in circa 4000 BCE.According to archaeologists, the wheel was invented around 4000 B.C. The wheel was likely independently invented in Mesopotamia (in present-day Iraq) as well. Estimates on when this may have occurred range from 5500 to 3000 B.C., with most experts putting it closer to 4000 B.C. The oldest artifacts with drawings that depict wheeled carts date from about 3000 B.C.; however, the wheel may have been in use for millenia before these drawings were made. There is also evidence from the same period of time that wheels were used for the production of pottery. (Note that the original potter's wheel was probably not a wheel, but rather an irregularly shaped slab of flat wood with a small hollowed or pierced area near the center and mounted on a peg driven into the earth. It would have been rotated by

repeated tugs by the potter or his assistant.) More recently, the oldest-known wooden wheel in the world was found in the Ljubljana marshes of Slovenia.[23]

The invention of the wheel revolutionized activities as disparate as transportation, war, and the production of pottery (for which it may have been first used). It didn't take long to discover that wheeled wagons could be used to carry heavy loads and fast (rotary) potters' wheels enabled early mass production of pottery. But it was the use of the wheel as a transformer of energy (through water wheels, windmills, and even treadmills) that revolutionized the application of nonhuman power sources.

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Modern history (0CE —)Tools include both simple machines (such as the lever, the screw, and the pulley), and more complex machines (such as the clock, the engine, the electric generator and the electric motor, the computer, radio, and the Space Station, among many others).

An integrated circuit — a key foundation for modern computers.As tools increase in complexity, so does the type of knowledge needed to support them. Complex modern machines require libraries of written technical manuals of collected information that has continually increased and improved — their designers, builders, maintainers, and users often require the mastery of decades of sophisticated general and specific training. Moreover, these tools have become so complex that a comprehensive infrastructure of technical knowledge-based lesser tools, processes and practices (complex tools in themselves) exist to support them, including engineering, medicine, and computer science. Complex

manufacturing and construction techniques and organizations are needed to construct and maintain them. Entire industries have arisen to support and develop succeeding generations of increasingly more complex tools.

Technology and societyMain article: Technology and society

Technology and philosophyTechnicismGenerally, technicism is an over reliance or overconfidence in technology as a benefactor of society.Taken to extreme, some argue that technicism is the belief that humanity will ultimately be able to control the entirety of existence using technology. In other words, human beings will eventually be able to master all problems, supply all wants and needs, possibly even control the future. Some, such as Monsma, connect these ideas to the abdication of religion as a higher moral authority.More commonly, technicism is a criticism of the commonly held belief that newer, more recently-developed technology is "better." For example, more recently-developed computers are faster than older computers, and more recently-developed cars have greater gas efficiency and more features than older cars. Because current technologies are generally accepted as good, future technological developments are not considered circumspectly, resulting in what seems to be a blind acceptance of technological developments.Optimism

See also: Extropianism Optimistic assumptions are made by proponents of ideologies such as transhumanism and singularitarianism, which view technological development as generally having beneficial effects for the society and the human condition. In these ideologies, technological development is morally good. Some critics see these ideologies as examples of scientism and techno-utopianism and fear the notion of human enhancement and technological singularity which they support. Some have described Karl Marx as a techno-optimist.[24]

PessimismSee also: Neo-luddism, Anarcho-Primitivism, and Bioconservatism

On the somewhat pessimistic side are certain philosophers like Herbert Marcuse and John Zerzan, who believe that technological societies are inherently flawed a priori. They suggest that the result of such a society is to become evermore technological at the cost of freedom and psychological health (and probably physical health in general, as pollution from technological products is dispersed).Even philosophers as prominent as Martin Heidegger had serious reservations about technology. Wrote Heidegger in The Question Concerning Technology[1]: "Thus we shall never experience our relationship /tt/file_convert/5a9fc4dd7f8b9a8e178d261f/document.doc 31/122

to the essence of technology so long as we merely conceive and push forward the technological, put up with it, or evade it. Everywhere we remain unfree and chained to technology, whether we passionately affirm or deny it."In fictional literature such as Faust by Goethe, Faust's selling his soul to the devil in return for power over the physical world, is also often interpreted as a metaphor for the adoption of industrial technology. Some of the most poignant criticisms of technology are found in what are now considered to be dystopian literary classics, for example Aldous Huxley's Brave New World and other writings, Anthony Burgess's A Clockwork Orange, and George Orwell's Nineteen Eighty-Four.Perhaps the most widely read overtly anti-technological treatise is Industrial Society and Its Future which was written by Theodore Kaczynski (aka The Unabomber) and was printed in several major newspapers (and later books) as part of an effort to end his bombing campaign of the techno-industrial infrastructure.Appropriate technology

See also: Technocriticism and Technorealism The notion of appropriate technology, however, was developed in the 20th century (e.g., see the work of Jacques Ellul) to describe situations where it was not desirable to use very new technologies or those that required access to some centralized infrastructure or parts or skills imported from elsewhere. The eco-village movement emerged in part due to this concern.

Other species Credit: Public Library of Science

This adult gorilla uses a branch as a walking stick to gauge the water's depth; an example of technology usage by primates.The use of basic technology is also a feature of other species apart from humans. These include primates such as chimpanzees and/or some dolphin communities.[25][26]

The ability to make and use tools was once considered a defining characteristic of the genus Homo.[27] However, the discovery of tool construction among chimpanzees and related primates has discarded the notion of the use

of technology as unique to humans. For example, researchers have observed wild chimpanzees utilising tools for foraging: some of the tools used include leaf sponges, termite fishing probes, pestles and levers.[28] West African chimpanzees also use stone hammers and anvils for cracking nuts.[29]

See alsoFind more information on Technology by searching Wikipedia's sister projects

Dictionary definitions from Wiktionary

Textbooks from Wikibooks

Quotations from Wikiquote

Source texts from Wikisource

Images and media from Commons

News stories from Wikinews

Learning resources from WikiversityMain list: List of basic technology topics.

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Bernard Stiegler Golden hammer Critique of technology High technology History of science and technology Innovation Internet Knowledge economy Lewis Mumford

Luddite Technique Technology assessment Timeline of invention Technological convergence Technology tree List of "ologies" Science and technology Technological superpowers

Theories and concepts in technologyMain list: Theories of technology

Appropriate technology Diffusion of innovations Paradigm Philosophy of technology Posthumanism Precautionary principle Strategy of technology Techno-progressivism

Technocriticism Technological evolution Technological determinism Technological nationalism Technological singularity Technological society Technorealism Technological revival Transhumanism

Economics of technology Technocapitalism Technological diffusion Technology acceptance model Technology lifecycle Technology transfer

Notes1. ^ a b Definition of technology. Merriam-Webster. Retrieved on 2007-02-16. 2. ̂ Franklin, Ursula. Real World of Technology. Anansi Press. Retrieved on 2007-02-13. 3. ̂ Technology news. BBC News. Retrieved on 2006-02-17. 4. ̂ Industry, Technology and the Global Marketplace: International Patenting Trends in Two New

Technology Areas. Science and Engineering Indicators 2002. National Science Foundation. Retrieved on 2007-05-07.

5. ̂ Borgmann, Albert (2006). "Technology as a Cultural Force: For Alena and Griffin" (fee required). The Canadian Journal of Sociology 31 (3): 351-360. Retrieved on 2007-02-16. 

6. ̂ Macek, Jakub. Defining Cyberculture. Retrieved on 2007-05-25. 7. ̂ Science. Dictionary.com. Retrieved on 2007-02-17. 8. ̂ Intute: Science, Engineering and Technology. Intute. Retrieved on 2007-02-17. 9. ̂ Bower, Bruce. Ancient Asian Tools Crossed the Line. Science News Online. Retrieved on 2007-02-17. 10. ̂ Ancient 'tool factory' uncovered. BBC News (1999-05-06). Retrieved on 2007-02-18. 11. ̂ Heinzelin, Jean de; et al (April 1989). "Environment and Behavior of 2.5-Million-Year-Old Bouri

Hominids" (fee required). Science 284 (5414): pp. 625-629.  12. ̂ Schick, Kathy D.; Toth, Nicholas (1994). Making Silent Stones Speak : Human Evolution and the Dawn

of Technology. Simon & Schuster. ISBN 978-0671875381.  13. ̂ Stanford, C.B (1996). "The hunting ecology of wild chimpanzees; implications for the behavioral

ecology of Pliocene hominids". American Anthropologist 98 (1): pp. 96-113.  14. ̂ Crump, Thomas (2001). A Brief History of Science. Constable, p. 9. ISBN 1-84119-235-X. “As Charles

Darwin noted, 'the discovery of fire, possibly the greatest ever made by man, excepting language, dates from before the dawn of history'.” 

15. ̂ Fossil Hominid Sites of Sterkfontein, Swartkrans, Kromdraai, and Environs. UNESCO. Retrieved on 2007-03-10.

16. ̂ History of Stone Age Man. History World. Retrieved on 2007-02-13.

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17. ̂ James, Steven R. (February 1989). "Hominid Use of Fire in the Lower and Middle Pleistocene" (fee required). Current Anthropology 30 (1): pp. 1-26.  "Most archaeologists accept the idea [...] that Homo erectus was using fire in the Middle Pleistocene about 0.5 million years ago".

18. ̂ Stahl, Ann B. (1984). "Hominid dietary selection before fire" (fee required). Current Anthropology 25: pp. 151—168. 

19. ̂ O'Neil, Dennis. Evolution of Modern Humans: Archaic Homo sapiens Culture. Palomar College. Retrieved on 2007-03-31.

20. ̂ Villa, Paola (1983). Terra Amata and the Middle Pleistocene archaeological record of southern France. Berkeley: University of California Press, 303 pages. ISBN 0-520-09662-2. 

21. ̂ Cordaux, Richard; Stoneking, Mark (2003). "South Asia, the Andamanese and the genetic evidence for an "early" human dispersal out of Africa". American Journal of Human genetics 72: p. 1586. 

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22. ̂ Cramb, Alan W. A Short History of Metals. Carnegie Mellon University. Retrieved on 2007-01-08. 23. ̂ Slovenian Marsh Yields World's Oldest Wheel. Ameriška Domovina (2003-03-27). Retrieved on 2007-

02-13. 24. ̂ Hughes, James (2002). "Democratic Transhumanism 2.0". Retrieved on 2007-01-26. 25. ̂ Sagan, Carl; Druyan, Ann; Leakey, Richard. Chimpanzee Tool Use. Retrieved on 2007-02-13. 26. ̂ Rincon, Paul (2005-06-07). Sponging dolphins learn from mum.. BBC News. Retrieved on 2007-02-13. 27. ̂ Oakley, K. P. (1976). Man the Tool-Maker. University of Chicago Press. ISBN 978-0226612706.  28. ̂ McGrew, W. C (1992). Chimpanzee Material Culture. ISBN 978-0521423717.  29. ̂ Boesch, Christophe; Boesch, Hedwige (1984). "Mental map in wild chimpanzees: An analysis of

hammer transports for nut cracking" (fee required). Primates (25): 160-170. 

Online sources Ambrose, Stanley H. (2001-03-02). "Paleolithic Technology and Human Evolution". Science. Retrieved on

2007-03-10.

Further reading Bernard Stiegler , Technics and Time, 1: The Fault of Epimetheus (Stanford: Stanford University

Press, 1998).

Major fields of technology

Applied science

Artificial intelligence • Ceramic engineering • Computing technology • Electronics • Energy • Energy storage • Engineering physics • Environmental technology • Materials science & engineering • Microtechnology • Nanotechnology • Nuclear technology • Optical engineering

Information and communication Communication • Graphics • Music technology • Speech recognition • Visual technology

Industry Construction • Financial engineering • Manufacturing • Machinery • Mining

Military Bombs • Guns and Ammunition • Military technology and equipment • Naval engineering

Domestic Domestic appliances • Domestic technology • Educational technology • Food technology

Engineering

Aerospace • Agricultural • Architectural • Bioengineering • Biochemical • Biomedical • Ceramic • Chemical • Civil • Computer • Construction • Cryogenic • Electrical • Electronic • Environmental • Food • Industrial • Materials • Mechanical • Mechatronics • Metallurgical • Mining • Naval • Nuclear • Petroleum • Software • Structural • Systems • Textile • Tissue

Health and safety

Biomedical   engineering • Bioinformatics • Biotechnology • Cheminformatics • Fire protection engineering • Health   technologies • Pharmaceuticals • Safety engineering • Sanitary engineering

Transport Aerospace • Aerospace engineering • Marine engineering • Motor vehicles • Space technology • Transport

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Technology lifecycleFrom Wikipedia, the free encyclopediaMost new technologies follow a similar technology lifecycle describing the technological maturity of a product. This is not similar to a product life cycle, but applies to an entire technology, or a generation of a technology.Technology adoption is the most common phenomenon driving the evolution of industries along the industry lifecycle. After expanding new uses of resources they end with exhausting the efficiency of those processes, producing gains that are first easier and larger over time then exhaustingly more difficult.

Technology perception dynamicsThere is usually technology hype at the introduction of any new technology, but only after some time has passed can it be judged as mere hype or justified true acclaim. Because of the logistic curve nature of technology adoption, it is difficult to see in the early stages whether the hype is excessive.The two errors commonly committed in the early stages of a technology's development are[citation needed]:

fitting an exponential curve to the first part of the growth curve, and assuming eternal exponential growth

fitting a linear curve to the first part of the growth curve, and assuming that takeup of the new technology is disappointing

Similarly, in the later stages, the opposite mistakes can be made relating to the possibilities of technology maturity and market saturation.Technology adoption typically occurs in an S curve, as modelled in diffusion of innovations theory. This is because customers respond to new products in different ways. Diffusion of innovations theory, pioneered by Everett Rogers, posits that people have different levels of readiness for adopting new innovations and that the characteristics of a product affect overall adoption.

StagesFrom a layman's perspective, the technology life cycle can be broken down into five distinct stages.

1. Bleeding edge - any technology that shows high potential but hasn't demonstrated its value or settled down into any kind of consensus. Early adopters may win big, or may be stuck with a white elephant.

2. Leading edge - a technology that has proven itself in the marketplace but is still new enough that it may be difficult to find knowledgeable personnel to implement or support it.

3. State of the art - when everyone agrees that a particular technology is the right solution. 4. Dated - still useful, still sometimes implemented, but a replacement leading edge technology is

readily available. 5. Obsolete - has been superseded by state-of-the-art technology, maintained but no longer

implemented.

See also Diffusion Disruptive technology Technology Adoption LifeCycle Network effects Tipping point Product life cycle management Industry lifecycle

New product development Product management Mature technology diffusion of innovations Everett Rogers Toolkits for User Innovation Configuration System

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Disruptive technologyFrom Wikipedia, the free encyclopediaA disruptive technology or disruptive innovation is a technological innovation, product, or service that eventually overturns the existing dominant technology or status quo product in the market. Disruptive innovations can be broadly classified into lower-end and new-market disruptive innovations. A new-market disruptive innovation is often aimed at non-consumption, whereas a lower-end disruptive innovation is aimed at mainstream customers who were ignored by established companies. Sometimes, a disruptive technology comes to dominate an existing market by either filling a role in a new market that the older technology could not fill (as more expensive, lower capacity but smaller-sized hard disks did for newly developed notebook computers in the 1980s) or by successively moving up-market through performance improvements until finally displacing the market incumbents (as digital photography has begun to replace film photography).The concept shares many similarities with biological evolution.By contrast, "sustaining technology or innovation" improves product performance of established products. Sustaining technologies are often incremental; however, they can also be radical or discontinuous.

Contents1 History and usage of the term 2 The theory 3 Examples of disruptive innovations 4 Business implications 5 See also 6 References 7 Additional Readings 8 External links

History and usage of the termThe term disruptive technology was coined by Clayton M. Christensen and introduced in his 1995 article Disruptive Technologies: Catching the Wave, which he coauthored with Joseph Bower. He describes the term further in his 1997 book The Innovator's Dilemma. In his sequel, The Innovator's Solution, Christensen replaced disruptive technology with the term disruptive innovation because he recognized that few technologies are intrinsically disruptive or sustaining in character. It is the strategy or business model that the technology enables that creates the disruptive impact. The concept of disruptive technology continues a long tradition of the identification of radical technical change in the study of innovation by economists, and the development of tools for its management at a firm or policy level.

The theoryChristensen distinguishes between "low-end disruption" which targets customers who do not need the full performance valued by customers at the high-end of the market and "new-market disruption" which targets customers who could previously not be served profitably by the incumbent."Low-end disruption" occurs when the rate at which products improve exceeds the rate at which customers can adopt the new performance. Therefore, at some point the performance of the product overshoots the needs of certain customer segments. At this point, a disruptive technology may enter the market and provide a product which has lower performance than the incumbent but which exceeds the requirements of certain segments, thereby gaining a foothold in the market.

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How low-end disruption occurs over time.In low-end disruption, the disruptor is focused initially on serving the least profitable customer, who is happy with a good enough product. This type of customer is not willing to pay premium for enhancements in product functionality. Once the disruptor has gained foot hold in this customer segment, it seeks to improve its profit margin. To get higher profit margins, the disruptor needs to enter the segment where the customer is willing to pay a little more for higher quality. To ensure this quality in its product, the disruptor needs to innovate. The incumbent will not do much to retain its share in a not so profitable segment, and will move up-market and focus on its more attractive customers. After a number of such encounters, the incumbent is squeezed into smaller markets than it was previously serving. And then finally the disruptive technology meets the demands of the most profitable segment and drives the established company out of the market."New market disruption" occurs when a product that is inferior by most measures of performance fits a new or emerging market segment. The Linux operating system (OS) when introduced was inferior in performance to other server operating systems like Unix and Windows NT. But the Linux OS distributed through Red Hat is supposed to be inexpensive compared to other server operating systems. After years of improvements in this easily available operating system, the functionality has improved so much that it threatens to displace the leading commercial UNIX distributions.Not all disruptive technologies are of lower performance. There are several examples where the disruptive technology outperforms the existing technology but is not adopted by existing majors in the market. This situation occurs in industries with a high investment into the older technology. To move to the new technology, an existing player not only must invest in it but also must replace (and perhaps dispose of at high cost) the older infrastructure. It may simply be the most cost effective for the existing player to "milk" the current investment during its decline - mostly by insufficient maintenance and lack of progressive improvement to maintain the long term utility of the existing facilities. A new player is not faced with such a balancing act.Some examples of high-performance disruption:

The rise of containerization and the success of the Port of Oakland, California, while the port of San Francisco neglected modernization - perhaps wisely due to its inconvenient location at the end of a peninsula not oriented with the prevailing freight traffic. Rather than attempt to compete in the oceanic freight terminal business, the city's resources were directed elsewhere, primarily toward becoming the leading financial center on the west coast through the encouragement of the construction of high rise buildings for office space.

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VoIP phone technology is a disruptive innovation. At its best, the quality of voice that is available over this phone system is at least as good as that has been offered by traditional players.

Examples of disruptive innovationsDisruptive Innovation

Displaced or Marginalized

technologyNotes

Agriculture and Pastoralism Hunting and gathering

The development of food production technology led to other disruptive technologies such as cities, writing, metal working, wheeled vehicles, and much of the remainder of world civilization.

steam engines and internal-combustion engines

horses and humans (for powering machines)

The new engines took centuries to establish themselves, but eventually rendered animal/people power obsolete on their ability to scale up to much higher power outputs and offer greater reliability.

Automobiles Horses (for transport)

Early roads were designed for horses, not cars. Nevertheless, the potential for greater convenience, reliability and speed offered by the motor car meant that the road system was eventually redesigned in its favor, after overcoming many obstacles, both technical and political (such as the Red Flag Act).

Hydraulic excavators

Cable-operated excavators

Hydraulic excavators were clearly innovative at the time of introduction but they gain widespread use only decades after. However, cable-operated excavators are still used in some cases, mainly for large excavations.

Mini steel mills vertically integrated Steel mills

By using mostly locally available scrap and power sources these mills can be cost effective even though not large

Container ships and containerization

"Break cargo" ships and stevedores

In addition to efficiency these also provide a great reduction in opportunities for pilferage and integrate well with both rail and truck transport.

Desktop publishing Traditional publishing

Early desktop-publishing systems could not match high-end professional systems in either features or quality. Nevertheless, they lowered the cost of entry to the publishing business, and economies of scale eventually enabled them to match, and then surpass, the functionality of the older dedicated publishing systems.

Digital photography

originally, instant photography, now increasingly all chemical photography

Early digital cameras suffered from low picture quality and resolution and long shutter lag. Quality and resolution are no longer major issues and shutter lag is much less than what it used to be. The convenience of small memory cards and portable hard drives that hold hundreds or thousands of pictures, as well as the lack of the need to develop these pictures, also helped. Digital cameras have a high power consumption (but several lightweight battery packs can provide enough power for thousands of pictures). Cameras for classic photography are stand-alone devices.

Semiconductors vacuum tubes

Electronic systems built up with semiconductors require less energy, are smaller and more reliable than such with tubes. However for high power device semiconductor solutions are not always available (or from more complicated design)

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"Bug logic'" Discrete components

Medium Scale Integration (MSI) - electronic circuits (such as a flip-flop) built upon a single substrate require less energy, are smaller and more reliable than such built upon circuit boards.

Large Scale Integration (LSI) "Bug logic"

Complete electronic systems upon a single substrate require less energy, are smaller and more reliable than such built by mounting simpler Integrated circuits ("bug logic") upon complex circuit boards, extending to the current implementations of entire central processing units, memory, and supporting logic on a single chip.

Minicomputers MainframesThough mainframes survive in a niche market which persists to this day, minicomputers have themselves been disrupted into extinction.

Personal computers Minicomputers, Workstations

Workstations still exist, but are increasingly assembled from high-end personal computer parts, to the point that the distinction is fading

High speed CMOS video sensors Photographic film

When first introduced, high speed CMOS sensors were less sensitive, had lower resolution, and cameras based on them had less duration (record time). The advantage of rapid setup time, editing in the camera, and nearly-instantaneous review quickly eliminated 16 mm high speed film systems. CMOS-based cameras also require less power (single phase 110 V AC and a few amperes of current vs. 208 V single, double and even triple phase cameras requiring 20-50 A for film cameras. Continuing advances have overtaken 35 mm film and are challenging 70 mm film applications.

Cassette Tape Eight Track Cassette tapes gave longer play times, a smaller size of player and media, and more functionality.

Compact Disc Phonograph record, and later Cassette Tape

Compact Discs give higher quality, smaller size, eventual portability, and cheaper production costs.

Digital audio player Compact DiscFrom 15-20 songs per CD to 100's and 1000's of songs in a smaller form factor, with content that can be transferred effortlessly through the internet.

MusketsCrossbows, longbows and the Knight military unit

The development of firearms allowed essentially anyone to become an effective soldier with very little training. Earlier military units like bowmen and knights needed years of practice to master the skills.

Steamships Sailing ships

The first steamships were deployed on inland waters where sailing ships were less effective, instead of on the higher profit margin seagoing routes. Hence steamships originally only competed in traditional shipping lines' "worst" markets.

Telephones Telegraphy

When Western Union infamously declined to purchase Alexander Graham Bell's telephone patents for $100,000, their highest-profit market was long-distance telegraphy. Telephones were only useful for very local calls. Short-distance telegraphy barely existed as a market segment, if at all. So Western Union's decision was quite understandable at the time.

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Not all technologies promoted as disruptive innovations have actually prospered as well as their proponents had hoped. However, some of these technologies have only been around for a few years, and their ultimate fate has not yet been determined.Unresolved examples of technologies promoted as 'disruptive innovations'

Music downloads and file sharing vs. compact discs ebooks vs. paper books VoIP (and VoIP over 802.11) vs. traditional telephone and mobile phone service. Reconfigurable Computing as part of a dual paradigm approach to High Performance Computing

vs. traditional computing exclusively based on the von Neumann machine paradigm.

Business implicationsDisruptive technologies are not always disruptive to customers, and often take a long time before they are significantly disruptive to established companies. They are often difficult to recognize. Indeed, as Christensen points out and studies have shown, it is often entirely rational for incumbent companies to ignore disruptive innovations, since they compare so badly with existing technologies or products, and the deceptively small market available for a disruptive innovation is often very small compared to the market for the established technology.Even if a disruptive innovation is recognized, existing businesses are often reluctant to take advantage of it, since it would involve competing with their existing (and more profitable) technological approach. Christensen recommends that existing firms watch for these innovations, invest in small firms that might adopt these innovations, and continue to push technological demands in their core market so that performance stays above what disruptive technologies can achieve.Disruptive technologies, too, can be subtly disruptive, rather than prominently so. Examples include digital photography (the sharp decline in consumer demand for common 35mm print film has had a deleterious effect on free-riders such as slide and infrared film stocks, which are now more expensive to produce) and IP/Internet telephony, where the replacement technology does not, and sometimes cannot practically replace all of the non-obvious attributes of the older system (sustained operation through municipal power outages, national security priority access, the higher degree of obviousness that the service may be life-safety critical or deserving of higher restoration priority in catastrophes, etc).

See alsoThis article has been illustrated as part of WikiProject WikiWorld.(Click image for full size version.)

Paradigm shift Technology strategy Disruptive Technology Office Category killer Obsolescence

References Bower, Joseph L. & Christensen, Clayton M. (1995). "Disruptive Technologies: Catching the

Wave" Harvard Business Review, January-February 1995. How to Identify and Build Disruptive New Businesses, MIT Sloan Management Review Spring

2002 Christensen, Clayton M. (1997). The Innovator's Dilemma. Harvard Business School Press. ISBN

0-87584-585-1.  Christensen, Clayton M.;Raynor, Michael E. (2003). The Innovator's Solution. Harvard Business

School Press. ISBN 1-57851-852-0.  Christensen, Clayton M., Anthony, Scott D., & Roth, Erik A. (2004). Seeing What's Next. Harvard

Business School Press. ISBN 1-59139-185-7. 

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Christensen, Clayton M. & Overdorf, Michael. (2000). "Meeting the Challenge of Disruptive Change" Harvard Business Review, March-April 2000.

Christensen, Clayton M., Bohmer, Richard, & Kenagy, John. (2000). "Will Disruptive Innovations Cure Health Care?" Harvard Business Review, September 2000.

Christensen, Clayton M., Baumann, Heiner, Ruggles, Rudy, & Sadtler, Thomas M. (2006). "Disruptive Innovation for Social Change" Harvard Business Review, December 2006.

Mountain, Darryl R., Could New Technologies Cause Great Law Firms to Fail? Mountain, Darryl R. (2006). Disrupting conventional law firm business models using document

assembly, International Journal of Law and Information Technology 2006; doi: 10.1093/ijlit/eal019

Tushman, M.L. & Anderson, P. (1986). Technological Discontinuities and Organizational Environments. Administrative Science Quarterly 31: 439-465.

Additional Readings Danneels, Erwin (2006), “From the Guest Editor: Dialogue on The Effects of Disruptive

Technology on Firms and Industries,” Journal of Product Innovation Management, 23 (1): 2-4 Danneels, Erwin (2004), “Disruptive Technology Reconsidered: A Critique and Research

Agenda,” Journal of Product Innovation Management, 21 (4): 246-258

External links "The Disruptive Potential of Game Technologies: Lessons Learned from its Impact on the

Military Simulation Industry", by Roger Smith in Research Technology Management (Sept/Oct 2006)

Disruptive Technology at c2.com Disruptive Innovation Theory Disruptive Technology at The Economist: The blood of incumbents RSS: Disruptive Technology Hiding in Plain Sight The Myth of Disruptive Technologies . Note that Dvorák's definition of disruptive technology does

not necessarily match the standard one described above. He complains about the overuse of the term and goes as far as claiming there are no disruptive technologies.

On Disruption Disruption: The best way for companies to create new growth. Blog of ideas on disruption and interviews with Thought Leaders on disrupting markets to create growth.

The Disruption Group Set of tools for managing disruption and *Financial Post Columns On Disruptionarticles on the benefits of disruption for organizations.

Bibliography of Christensen’s "Theory of Disruptive Innovation" as it relates to higher education Disruptive Technology Portfolio by InformationWeek and Credit Suisse

Retrieved from "http://en.wikipedia.org/wiki/Disruptive_technology"

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Disruptive Innovation http://innovationzen.com/blog/2006/10/04/disruptive-innovation/ The disruptive innovation is probably one of the most important innovation theories of the last decade. The core concepts behind it circulated so fast that already in 1998, one year after the publication of the theory, people were using the term without making reference to Harvard professor Clayton Christensen or to his book The Innovator’s Dilemma (Harvard Business School Press).This article is the seventh part of the Innovation Management Theory series, you can check the previous six clicking here.Disruptive InnovationThe term disruptive innovation as we know it today first appeared in the 1997 best-seller The Innovator’s Dilemma. In the book Harvard Business School professor Clayton Christensen investigated why some innovations that were radical in nature reinforced the incumbent’s position in a certain industry, contrary to what previous models (for instance the Henderson – Clark model) would predict. More specifically he analyzed extensively the disk drive industry because it represented the most dynamic, technologically discontinuous and complex industry one could find in our economy. Just consider that the memory capacity packed into a square inch of disk increased by 35% per year, from 50 kilobytes in 1967 to 1,7 megabytes in 1973, 12 megabytes in 1981 and 1100 megabytes in 1995.Christensen describes how one of his friends was responsible for that choice when he commented that “those who study genetics avoid studying humans because new generations come along only every thirty years or so, it takes a long time to understand the cause and effect of any changes. Instead, they study fruit flies, because they are conceived, born, mature and die all within a single day. If you want to understand why something happens in business, study the disk drive industry. Those companies are the closest things to fruit flies that the business world will ever see”.Sustaining vs. Disruptive InnovationThe central theory of Christensen’s work is the dichotomy of sustaining and disruptive innovation. A sustaining innovation hardly results in the downfall of established companies because it improves the performance of existing products along the dimensions that mainstream customers value.Disruptive innovation, on the other hand, will often have characteristics that traditional customer segments may not want, at least initially. Such innovations will appear as cheaper, simpler and even with inferior quality if compared to existing products, but some marginal or new segment will value it.The disk drive industryThe first disk drive was developed in IBM’s San Jose research laboratories, around 1954. It was as large as a refrigerator and it could store 5 megabytes of data. By 1976 $1 billion worth of disk drives was being produced annually, divided between integrated producers (IBM, Control Data, Univac, and others) and OEM producers (Nixdorf, Wang, Prime, and others).By 1996 the disk drive market was worth $18 billions, but out of the many companies that were operating in 1976 only IBM was still in the market. About 129 firms entered the market during that period, and 109 of them ceased to exist. Most of the technological discontinuities that emerged in the industry were sustaining innovations. For example in the 1970’s the oxide disks started to reach a physical limit (in terms of bytes of information contained), forcing the leading companies to develop an alternative. IBM, Control Data and other incumbents invested more than $50 million developing thin-film coatings, and virtually all of the established firms managed to keep their position in the face of such sustaining innovation.In contrast, there have been very few disruptive innovations over the same period, but those were responsible for the downfall of established firms. As Christensen highlights the most important disruptive technologies were the architectural innovations that shrunk the size of the drives, from 14-inch diameter disks to 8’, 5.25’ and 3.5’, and then from 2.5’ to 1.8’.

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The passage from 14-inch to 8-inch disksThe 14-inch disk drives were produced to supply mainframes, and the two parameters mainframe producers would consider as a performance measure were the capacity and the cost per megabyte. Around 1980 some new firms ( including Micropolis, Priam and Quantum) developed smaller 8-inch drives, but those packed 10 to 40 megabytes of capacity while mainframes were demanding 400 megabyte drives. The leading companies producing 14-inch drives could have developed 8-inch drives internally without much of a trouble, after all the technological innovation involved was simple and architectural in nature. Why they did not, you might ask? Because their main customers, the mainframe manufacturers, were not interested at all in the smaller hard drives.The new entrants would not be able to sell the 8’inch drive for mainframe producers; consequently they were forced to look for new applications that would eventually value the characteristics of their product, mainly the reduced size. They found such application in the minicomputer. Manufacturers likes DEC, Prime and HP were willing to pay a higher cost per megabyte in order to get smaller disk drives.Customer demand for capacity was growing at 25% every year, while producers of 8’inch disk drives found that with sustaining innovations they were able to increase their disk capacity by 40% every year, almost twice as fast. Notice that most disruptive innovations will improve faster than what is demanded by mainstream customers, meaning that after some time disruptors should be able to attack established firms as the figure below illustrates.

After some years the 8-inch drives were offering an inferior cost per megabyte than 14-inch ones and the capacity was already enough to supply lower-end mainframes. The incumbents of the 14-inch generation witnessed their markets being invaded; and obviously it was too late to react. Only one third of 14-inch producers managed to make the transition into the new technology, but eventually all of them went out of the market.The story repeats itselfThe same pattern was observed when Seagate introduced the 5.25-inch disk drive, its capacity of 10 megabytes was of no interest to microcomputer producers. Seagate and the other 5.25-inch drive producers (Computer Memories, International Memories, Miniscribe and others) needed again to find a new application for their product. As Christensen writes “they went by trial and error, selling drives to whomever would buy them”.The application was found in the desktop computers, and just like with under the 8-inch generation 5.25-inch disk drives improved their performance via sustaining innovations faster than what minicomputer customers were demanding. After a couple of years 5.25 drives invaded the 8-inch market, and virtually all the leaders under the 8-inch technology struggled out of the market.By now I think you are already guessing what happened when the 3.5-inch disk drives emerged right? Almost all of the established players under the 5.25 generation were again forced out of the market.What are the reasons?How could we possibly explain such pattern? Clearly it was not a matter of technological complexity, incumbents were perfectly able to cope with the architectural innovations that shrunk the disk drive sizes. Some of the leading 5.25-inch producers even developed the 3.5-inch drives internally before new entrants, but they shelved the innovation as soon as their mainstream customers demonstrated no interest in them (5.25 drives were used for desktop computers while the 3.5-inch ones would be employed in /tt/file_convert/5a9fc4dd7f8b9a8e178d261f/document.doc 44/122

notebooks). According to Christensen the crucial factor to understand is the concept of value network, described as “the context within which a firm identifies and responds to customers’ needs, solve problems, procure inputs, react to competitors and strive for profits”.First of all, operating under such value network might lead a company to “listen too much” to its main customers. As a result it will not recognize potentially disruptive innovations that serve only marginal customers. Secondly large companies will not be interested in small markets; they hardly offer significant growth opportunities. Again this will lead companies to completely ignore the disruptive innovation or to wait until the market is “large enough to be attractive”. That is exactly when new entrants attack incumbent’s turf, and by that time it is usually too late.What is a possible solution?In order to solve both of these problems organizations should create an independent business unit whose size matches the emerging market. Quantum Corporation, a leading producer of 8-inch drives, recognized that 3.5-inch drives could have some applications in the computer industry, but they were not sure what those applications were exactly. Instead of shelving the project they created a spin-off unit to develop such 3.5.inch drives. After ten years the 8-inch market had completely disappeared while their small venture had grown to become the world largest disk drive producer.Other examples of disruptive innovations:

telephone (disrupted the telegraph) semiconductors (disrupted vacuum tubes) steamships (disrupted sailing ships)

You can check the Innosight website (Christensen’s consulting firm) for more information on disruptive innovation.

October 04th, 2006 | Innovation TheoryRelated posts:

Disruptive Innovation and Newspapers How to be a Disruptor Innovation Management Theory - Round Up

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The blood of incumbentsOct 28th 2004 From The Economist print editionON THE record, any top executive in the IT, consumer-electronics and telecoms industries today will profess that his firm is leading the way towards simplicity. But are those claims justified? In theory, says Ray Lane, a venture capitalist, the company best placed to deliver simplicity should be Microsoft. It controls virtually all of the world's PCs and laptop computers (albeit smaller shares of mobile phones, hand-held and server computers), so if its software became simpler, everything else would too. The bitter irony, says Mr Lane, is that Microsoft is one of the least likely companies to make breakthroughs in simplification. It cannot cannibalise itself, says Mr Lane. It faces the dilemma. The dilemma? These days, whenever anybody in the IT industry mentions that word, it is instantly understood to refer to The Innovator's Dilemma, a book by Clayton Christensen, a professor at Harvard Business School, who has since followed it up with a sequel, The Innovator's Solution. In a nutshell, the dilemma is this: firms that succeed in one generation of innovation almost inevitably become hamstrung by their own success and thus doomed to lose out in the next wave of innovation.…

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The Myth of Disruptive Technology 08.17.04 By John C. Dvorak People love a good, unified explanation for the ways things are. One current favorite is the concept of disruptive technology, a coinage and concept put forth by Harvard Business

School professor Clayton Christensen and explained in his book The Innovator's Dilemma. This guy has so many honors that apparently whatever he says is gospel. The concept of disruptive technology goes to the top of my list as the biggest crock of the new millennium.A disruptive technology is defined as a low-performance, less expensive technology that enters a heated-up scene where the established technology is outpacing people's ability to adapt to it. The new technology gains a foothold, continues to improve, and then bumps the older, once-better technology into oblivion. Sounds good. The problem is that there is not one example of this ever happening. When boiled down, the notion is essentially a rewrite of the adage Adam Osborne devised to explain the mediocrity of the Osborne 1: "Adequacy is sufficient."The theory goes on and on, with a seemingly reasoned explanation of how this unfolds. Christensen says the idea stems from his fascination with the collapse of Digital Equipment Corp. Eureka! The microcomputer came along as the cheap, inferior, disruptive technology, eventually supplanting the mini. "Throw out the VAX, Gomez, we've got an Apple II!"No matter that the CEO of DEC was a screwball who thought advertising was only for proving to your mom that you worked for a real company. No matter that HP, IBM, and Sun continued to prosper selling "minicomputers"—though Sun has a zany CEO too!The microcomputer was never a "less expensive" and "inferior" replacement for minicomputers. It was a more expensive and superior replacement for calculators and slide rules. It was never used "instead of" a minicomputer (or mainframe for that matter) but "in addition to."Even the spreadsheet, which is what actually made the desktop computer popular, had no real antecedent except a pad and pen. It didn't replace anything better. It was new.In the Harvard Business School alumni bulletin highlighting this nonsense, there is a list of supposedly disruptive technologies. Not one is disruptive. At the top of the list are electric cars supplanting gasoline vehicles. On what planet? Internet sales supplanting bookstores. Hmm, Barnes & Noble is packed with people. Restaurants are being affected by the disruptive technology of grocers' takeout. Are you laughing yet? Motorcycles being affected by the disruptive technology of dirt bikes—does anyone see a pattern here? Is this an April Fools' gag?James Burke's marvelous PBS TV series Connections offers a better explanation for disruption. When there is true disruption, it comes from inventions, regulatory and social change, complementary technologies, coincidence, and demand.The closest Christensen comes to a real disruptive technology is digital photography. But it was invented in 1972 and has never been "cheaper" than film. The atom bomb is surely disruptive, but neither cheaper nor inferior. The car replaced the horse, but it costs more, and it became a success because of the invention of pavement and the pneumatic tire; asphalt was never cheaper than or inferior to dirt.There is no such thing as a disruptive technology. There are inventions and new ideas, many of which fail while others succeed. That's it. This concept only services venture capitalists who need a new term for the PowerPoint show to sucker investors.One could almost make an argument for Linux as a disruptive technology. It's free, so that helps. But what is it disrupting? Microsoft? In 1992, when Linux was invented, Microsoft had about $2.2 billion in the bank. Now Microsoft has over $70 billion in the bank and continues to grow. Some disruption.One problem in our society is the increasing popularity of false-premise concepts that are blindly used for decision making. The amount of money squandered during the dot-com era because of "paradigm shifts" and "new economies" is staggering. People actually believed that all retailing would be online and that all groceries would be delivered to the home as they were in the 1920s, despite changes that make delivery impractical. Who cares about reality? We have a disruptive technology at work!

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The concept of disruptive technology is not the only daft idea floating around to be lapped up obediently by the business community. There are others. But the way these dingbat bromides go unchallenged makes you wonder whether anyone can think independently anymore.

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Technology adoption lifecycleFrom Wikipedia, the free encyclopedia(Redirected from Technology Adoption LifeCycle) The technology adoption lifecycle is a sociological model, originally developed by Joe M. Bohlen and George M. Beal in 1957 at Iowa State College.[1] Its purpose was to track the purchase patterns of hybrid seed corn by farmers. Approximately six years later Everett Rogers broadened the use of this model in his book, Diffusion of Innovations.

Rogers' bell curve

The technology adoption lifecycle model describes the adoption or acceptance of a new product or innovation, according to the demographic and psychological characteristics of defined adopter groups. The process of adoption over time is typically illustrated as a classical normal distribution or "bell curve." The model indicates that the first group of people to use a new product is called "innovators," followed by "early adopters." Next come the early and late majority, and the last group to eventually adopt a product are called "laggards."The demographic and psychological (or "psychographic") profiles of each adoption group were originally specified by the North Central Rural Sociology Committee, Subcommittee for the Study of the Diffusion of Farm Practices (as cited by Beal and Bohlen in their study above).The report summarised the categories as:

innovators - had larger farms, were more educated, more prosperous and more risk-oriented early adopters - younger, more educated, tended to be community leaders early majority - more conservative but open to new ideas, active in community and influence to

neighbours late majority - older, less educated, fairly conservative and less socially active laggards - very conservative, smalls farms and capital, oldest and least educated

The full text of the original report is available online.[2]

Adaptations of the modelThe model has spawned a range of adaptations that extend the concept or apply it to specific domains of interest.In his book, Crossing the Chasm, Geoffrey Moore proposes a variation of the original lifecycle. He suggests that for discontinuous or disruptive innovations, there is a gap or chasm between the first two adopter groups (innovators/early adopters), and the early majority.In Educational technology, Lindy McKeown has provided a similar model (a pencil metaphor[3]) describing the ICT uptake in education.

See also Diffusion (business) Diffusion of Innovations Crossing the Chasm

Notes1. ̂ Bohlen, Joe M. & George M. Beal (May 1957), "The Diffusion Process", Special Report No. 18

(Agriculture Extension Service, Iowa State College) 1: 56-77 2. ̂ http://www.soc.iastate.edu/extension/publications/Diffusion%20Process.pdf 3. ̂ http://www.teachers.ash.org.au/lindy/pencil/pencil.htm

Retrieved from "http://en.wikipedia.org/wiki/Technology_adoption_lifecycle"

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Product life cycle managementFrom Wikipedia, the free encyclopediaThis article is about managing the life of a product in the market. For managing product design and production details, see Product lifecycle management.The conditions a product is sold under will change over time. The Product Life Cycle refers to the succession of stages a product goes through. Product Life Cycle Management is the succession of strategies used by management as a product goes through its life cycle.The product lifecycle goes through many phases and involves many professional disciplines and requires many skills, tools and processes. Product life cycle (PLC) is to do with the life of a product in the market with respect to business/commercial costs and sales measures; whereas Product Lifecycle Management (PLM) is more to do with managing descriptions and properties of a product through its development and useful life, mainly from a business/engineering point of view.

Contents1 The stages 2 Market evolution

2.1 Market Identification 3 Technology Life Cycle 4 Lessons of the Product Life Cycle (PLC) 5 See also 6 Finding related topics 7 References 8 External links

The stages

A Typical Product Life CycleProducts tend to go through five stages:

1. New product development stage o very expensive o no sales revenue o losses

2. Market introduction stage o cost high o sales volume low o no/little competition - competitive manufacturers watch for acceptance/segment growth o losses o demand has to be created o customers have to be prompted to try the product

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3. Growth stage o costs reduced due to economies of scale o sales volume increases significantly o profitability o public awareness o competition begins to increase with a few new players in establishing market o prices to maximize market share

4. Mature stage o costs are very low as you are well established in market & no need for publicity. o sales volume peaks o increase in competitive offerings o prices tend to drop due to the proliferation of competing products o brand differentiation, feature diversification, as each player seeks to differentiate from

competition with "how much product" is offered o very profitable

5. Decline or Stability stage o costs become counter-optimal o sales volume decline or stabilize o prices, profitability diminish o profit becomes more a challenge of production/distribution efficiency than increased sales o consumer demand for spare parts, maintenance and or product servicing

Market evolutionMarket Evolution is a process that parallels the product life cycle. As a product category matures, the industry goes through stages that mirror the five stages of a product life cycle:

1. Market Crystallization - latent demand for a product category is awakened with the introduction of the new product

2. Market Expansion - additional companies enter the market and more consumers become aware of the product category

3. Market Fragmentation - the industry is subdivided into numerous well populated competitive groupings as too many firms enter

4. Market Consolidation - firms start to leave the industry due to stiff competition, falling prices, and falling profits

5. Market Termination - consumers no longer demand the product and companies stop producing it Market IdentificationA "micro-market" can be used to describe a Walkman, more portable, as well as individually and privately recordable; and then Compact Discs ("CDs") brought increased capacity and CD-R offered individual private recording...and so the process goes. The below section on the "technology lifecycle" is a most appropriate concept in this context.In short, termination is not always the end of the cycle; it can be the end of a micro-entrant within the grander scope of a macro-environment. The auto industry, fast-food industry, petro-chemical industry, are just a few that demonstrate a macro-environment that overall has not terminated even while micro-entrants over time have come and gone.

Technology Life CycleThe Technology Life Cycle is closely associated with the economic potential of obtaining gain through the exploitation of a process or manufacturing system, taking into consideration such attributes of the product or process as its patents, knowhow, trademarks, and/or trade-secrets, the reputation of the proprietor of the technology and other associated intangibles. See The Technology Life Cycle. It is very important in the business

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Lessons of the Product Life Cycle (PLC)It is claimed that every product has a life cycle. It is launched, it grows, at some point, may die. A fair comment is that - at least in the short term - not all products/services die. Jeans may die, but clothes probably won't. Legal services, medical services, may die, but depending on a social political climate, probably won't.Even though its validity is questionable, it can offer a useful 'model' for managers to keep at the back of their mind. Indeed, if their products are in the introductory or growth phases, or in that of decline, it perhaps should be at the front of their mind; for the predominant features of these phases may be those revolving around such life and death. Between these two extremes, it is salutary for them to have that vision of mortality in front of them.The most important aspect of product life-cycles is, however, that - even under normal conditions - to all practical intents and purposes they often do not exist (hence, there needs to be more emphasis on model/reality mappings). In most markets the majority of the major (dominant) brands have held their position for at least two decades. The dominant product life-cycle, that of the brand leaders which almost monopolize many markets, is therefore one of continuity.In the most respected criticism of the product life cycle, Dhalla & Yuspeh [cite] state;"...clearly, the PLC is a dependent variable which is determined by market actions; it is not an independent variable to which companies should adapt their marketing programs. Marketing management itself can alter the shape and duration of a brand's life cycle."Thus, the life cycle may be useful as a description, but not as a predictor; and usually should be firmly under the control of the marketer! The important point is that in many, if not most, markets the product or brand life cycle is significantly longer than the planning cycle of the organisations involved. It, thus, offers little of practical value for most marketers. Even if the PLC (and the related PLM support) exists for them, their plans will be based just upon that piece of the curve where they currently reside (most probably in the 'mature' stage); and their view of that part of it will almost certainly be 'linear' (and limited), and will not encompass the whole range from growth to decline.

See also Product management New Product Development Software product management Technology lifecycle marketing products

Planned obsolescence Extending the Product Life Cycle Product lifecycle Material selection Toolkits for User Innovation

Finding related topics list of management topics list of economics topics list of finance topics list of human resource management topics list of accounting topics list of information technology management topics list of business law topics list of production topics list of business ethics, political economy, and philosophy of business topics list of business theorists list of economists list of corporate leaders

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References Box, J. (1983) Extending product lifetime: Prospects and opportunities, European Journal of

Marketing, vol 17, 1983, pp 34-49. Day, G. (1981) The product life cycle: Analysis and applications issues, Journal of Marketing, vol

45, Autumn 1981, pp 60-67. Levitt, T. (1965) Exploit the product life cycle, Harvard Business Review, vol 43, November-

December 1965, pp 81-94. N. K. Dhalla and S. Yuspeh, Forget the product life cycle concept, 'Harvard Business Review'

(January-February 1976)

External links PWGSC Environment Canada ISO

Retrieved from "http://en.wikipedia.org/wiki/Product_life_cycle_management"

Industry lifecycleFrom Wikipedia, the free encyclopediaIndustry lifecycle is a theory linking the intensity of competition in a particular market with the time since the breakthrough innovation that made that market possible.The lifecycle passes through 5 distinct stages:

I - dormant stage with low numbers of competitors enjoying high monopoly profits II - "takeoff" stage with soaring entry and virtually non-existent exit from the market III - high turnover stage with many firms entering the market and leaving it IV - "shakeout" stage with mass exit via mergers, bankruptcies, etc. V - stabilization stage during which a stable oligopoly emerges

Industry lifecycle is commonly correlated with the cycle of product and process innovation. Other factors that may launch industry lifecycle include:

government intervention (e.g., deregulation), liberalization of external trade, lower transportation costs.

References Michael Gort, Steven Klepper. Time paths in the diffusion of product innovations. Economic

Journal, vol.92, no.367. (September, 1982) Pp.630-653.

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New product developmentFrom Wikipedia, the free encyclopediaIn business and engineering, new product development (NPD) is the term used to describe the complete process of bringing a new product or service to market. There are two parallel paths involved in the NPD process : one involves the idea generation, product design, and detail engineering ; the other involves market research and marketing analysis. Companies typically see new product development as the first stage in generating and commercializing new products within the overall strategic process of product life cycle management used to maintain or grow their market share.

Contents1 Types of new products 2 The process 3 Protecting new products 4 Fuzzy Front End 5 See also 6 Notes 7 References 8 External links

Types of new productsThere are several general categories of new products. Some are new to the market (ex. DVD players into the home movie market), some are new to the company (ex. Game consoles for Sony), some are completely novel and create totally new markets (ex. the airline industry). When viewed against a different criteria, some new product concepts are merely minor modifications of existing products while some are completely innovative to the company. These different characterizations are displayed in the following diagram.

Types of new products

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The processThere are several stages in the new product development process...not always followed in order:

1. Idea Generation (The "fuzzy front end" of the NPD process, see below) o Ideas for new products can be obtained from customers (employing user innovation), the

company's R&D department, competitors, focus groups, employees, salespeople, corporate spies, trade shows, or through a policy of Open Innovation. Ethnographic discovery methods (searching for user patterns and habits) may also be used to get an insight into new product lines or product features.

o Formal idea generation techniques can be used, such as attribute listing, forced relationships, brainstorming, morphological analysis and problem analysis

2. Idea Screening o The object is to eliminate unsound concepts prior to devoting resources to them. o The screeners must ask at least three questions:

Will the customer in the target market benefit from the product? Is it technically feasible to manufacture the product? Will the product be profitable when manufactured and delivered to the customer at

the target price? 3. Concept Development and Testing

o Develop the marketing and engineering details Who is the target market and who is the decision maker in the purchasing process? What product features must the product incorporate? What benefits will the product provide? How will consumers react to the product? How will the product be produced most cost effectively? Prove feasibility through virtual computer aided rendering, and rapid prototyping What will it cost to produce it?

o test the concept by asking a sample of prospective customers what they think of the idea 4. Business Analysis

o Estimate likely selling price based upon competition and customer feedback o Estimate sales volume based upon size of market o Estimate profitability and breakeven point

5. Beta Testing and Market Testing o Produce a physical prototype or mock-up o Test the product (and its packaging) in typical usage situations o Conduct focus group customer interviews or introduce at trade show o Make adjustments where necessary o Produce an initial run of the product and sell it in a test market area to determine customer

acceptance 6. Technical Implementation

o New program initiation o Resource estimation o Requirement publication o Engineering operations planning o Department scheduling o Supplier collaboration o Logistics plan o Resource plan publication o Program review and monitoring o Contingencies - what-if planning

7. Commercialization (often considered post-NPD) o Launch the product o Produce and place advertisements and other promotions

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o Fill the distribution pipeline with product o Critical path analysis is most useful at this stage

These steps may be iterated as needed. Some steps may be eliminated. To reduce the time that the NPD process takes, many companies are completing several steps at the same time (referred to as concurrent engineering or time to market). Most industry leaders see new product development as a proactive process where resources are allocated to identify market changes and seize upon new product opportunities before they occur (in contrast to a reactive strategy in which nothing is done until problems occur or the competitor introduces an innovation). Many industry leaders see new product development as an ongoing process (referred to as continuous development) in which the entire organization is always looking for opportunities.For the more innovative products indicated on the diagram above, great amounts of uncertainty and change may exist, which makes it difficult or impossible to plan the complete project before starting it. In this case, a more flexible approach may be advisable.Because the NPD process typically requires both engineering and marketing expertise, cross-functional teams are a common way of organizing projects. The team is responsible for all aspects of the project, from initial idea generation to final commercialization, and they usually report to senior management (often to a vice president or Program Manager). In those industries where products are technically complex, development research is typically expensive, and product life cycles are relatively short, strategic alliances among several organizations helps to spread the costs, provide access to a wider skill set, and speeds the overall process.Also, notice that because engineering and marketing expertise are usually both critical to the process, choosing an appropriate blend of the two is important. Observe (for example, by looking at the See also or References sections below) that this article is slanted more toward the marketing side. For more of an engineering slant, see the Ulrich and Eppinger reference below.People respond to new products in different ways. The adoption of a new technology can be analyzed using a variety of diffusion theories such as the Diffusion of innovations theory.it include economical support of social serctor

Protecting new productsWhen developing a new product many legal questions arise, including: How do I protect the innovation from imitators?; Can the innovation be legally protected?; For how long?; How much will this cost?. The answers are complicated by the fact that several legal concepts may apply to any given innovation, product, process, or creative work. These include patents, trademarks, service marks, tradenames, copyrights, and trade secrets. It is necessary to know which are applicable and when each is appropriate. This varies somewhat from jurisdiction to jurisdiction. The advice of a lawyer that specializes in these matters and is knowledgeable with your corporate philosophy regarding IP protection is essential.Generally, copyrights are fairly easy to obtain but are applicable only in certain instances. Patents on the other hand, tend to involve complex claims and approval processes, tend to be expensive to obtain, and even more expensive to defend and preserve.

Fuzzy Front EndThe Fuzzy Front End is the messy "getting started" period of new product development processes. It is in the front end where the organization formulates a concept of the product to be developed and decides whether or not to invest resources in the further development of an idea. It is the phase between first consideration of an opportunity and when it is judged ready to enter the structured development process (Kim and Wilemon , 2002; Koen et al., 2001). It includes all activities from the search for new opportunities through the formation of a germ of an idea to the development of a precise concept. The Fuzzy Front End ends when an organization approves and begins formal development of the concept.Although the Fuzzy Front End may not be an expensive part of product development, it can consume 50% of development time (see Chapter 3 of the Smith and Reinertsen reference below), and it is where major commitments are typically made involving time, money, and the product’s nature, thus setting the course for the entire project and final end product. Consequently, this phase should be considered as an /tt/file_convert/5a9fc4dd7f8b9a8e178d261f/document.doc 56/122

essential part of development rather than something that happens “before development,” and its cycle time should be included in the total development cycle time.Koen et al. (2001, pp.47-51) distinguish five different front-end elements (not necessarily in a particular order):1. Opportunity Identification2. Opportunity Analysis3. Idea Genesis4. Idea Selection5. Concept and Technology DevelopmentThe first element is the opportunity identification. In this element, large or incremental business and technological chances are identified in a more or less structured way. Using the guidelines established here, resources will eventually be allocated to new projects.... which then lead to a structured NPPD (New Product & Process Development)strategy. The second element is the opportunity analysis. It is done to translate the identified opportunities into implications for the business and technology specific context of the company. Here extensive efforts may be made to align ideas to target customer groups and do market studies and/or technical trials and research. The third element is the idea genesis, which is described as evolutionary and iterative process progressing from birth to maturation of the opportunity into a tangible idea. The process of the idea genesis can be made internally or come from outside inputs, e.g. a supplier offering a new material/technology, or from a customer with an unusual request. The fourth element is the idea selection. Its purpose is to choose whether to pursue an idea by analyzing its potential business value. The fifth element is the concept and technology development. During this part of the front-end, the business case is developed based on estimates of the total available market, customer needs, investment requirements, competition analysis and project uncertainty. Some organizations consider this to be the first stage of the NPPD process (i.e., Stage 0).The Fuzzy Front End is also described in literature as "Front End of Innovation", "Phase 0", "Stage 0" or "Pre-Project-Activities".

See also Flexible product development Time to market Social design Product management Requirements management Product life cycle management brand management marketing

Engineering product Document management Industrial Design Association of International Product

Marketing & Management Conceptual economy

References Belliveau, P., Griffin, A. and Somermeyer, S. (2002) PDMA ToolBook 1 for New Product

Development, John Wiley, New York, 2002. Belliveau, P., Griffin, A. and Somermeyer, S. (2004) PDMA ToolBook 2 for New Product

Development, John Wiley, New York, 2004. Cooper, Robert G. (2001) Winning at New Products - Accelerating the Process from Idea to

Launch, Third Edition, Product Development Institute, 2001. Crawford, M. (1977) Marketing research and the new product failure rate, Journal of Marketing,

vol 41, April 1977, pp 51-61. Drucker, P.F. (1985) 'Innovation and Entrepreneurship' (Heinemann, 1985) Drucker, P.F. (1985) The discipline of innovation, Harvard Business Review, vol 63, May-June

1985, pp 67-72. Ironmonger, D. (1972) New commodities and consumer behaviour, University of Cambridge

Department of Applied Economics, Monograph 20, Cambridge University Press, Aberdeen, 1972. This source is an economics book rather than a management or marketing one. It introduces the concept of new product development to the economics of consumer behaviour.

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Kahn, Kenneth B. (2004) PDMA Handbook of New Product Development, Second Edition, John Wiley, New York, 2004.

Kerin, R.A., Harvey, M.G. and Rothe (1978), Cannibalism and new product development, 'Business Horizons' (October 1978).

Kim, J. and Wilemon, D. (2002), Sources and assessment of complexity in NPD projects. R&D Management, 33 (1), pp. 16-30.

Koen et al. (2001), Providing clarity and a common language to the ‘fuzzy front end’. Research Technology Management, 44 (2), pp.46-55.

Lehmann R. Donald and Russell S. Winer (2004), Product Management, 4 edition, McGraw-Hill/Irwin, New York

Levitt, T. (1983), 'The Marketing Imagination' (Free Press 1983) Lynn, G., Marone, J. and Paulson, A. (1996) Marketing and discontinuous innovation, California

Management Review, spring 1996, pp. 8-37. McGrath, Michael E., Next Generation Product Development: How to Increase Productivity, Cut

Costs, and Reduce Cycle Times, McGraw-Hill, New York, 2004. Peters, T.J. and Waterman, R.H. Jr (1982), 'In Search of Excellence' (Harper and Row, 1982) Smith, Preston G. and Reinertsen, Donald G. (1998) Developing Products in Half the Time, 2nd

Edition, John Wiley and Sons, New York, 1998. Ulrich, Karl T. and Eppinger, Steven D (2004) Product Design and Development, 3rd Edition,

McGraw-Hill, New York, 2004. Urban, G. and Hauser, J. (1993) Design and marketing of new products, 2nd Edition, Prentice

Hall, Englewood Cliffs, 1993. Urban, G., Hauser, J. and Dholakia, N. (1987) Essentials of new product management, Prentice

Hall, Englewood Cliffs, 1987. ISBN 0-13-286584-X The idea of categorizing new products according to their "newness to market" and their "newness

to the company" originated in: New Product Management for the 1980s, Booz, Allen, and Hamilton, New York, 1982.

External links Product Development and Management Association (PDMA) Stage-gate - Product Development and Innovation, Benchmarking Product Development Institute - Dr. Robert Cooper and Dr. Scott J. Edgett - World's Top

Innovation Scholars | Masters In Innovation - Platform on open innovation, technology and new product development

Retrieved from "http://en.wikipedia.org/wiki/New_product_development"

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Diffusion of innovationsFrom Wikipedia, the free encyclopediaThe study of the diffusion of innovation is the study of how, why, and at what rate new ideas and technology spread through cultures.

Contents1 The S-Curve and technology adoption

1.1 Caveats and criticisms 2 See also 3 References 4 External links

The S-Curve and technology adoption

The adoption curve becomes a s-curve when cumulative adoption is used.Rogers theorized that innovations would spread through society in an S curve, as the early adopters select the technology first, followed by the majority, until a technology or innovation is common.The speed of technology adoption is determined by two characteristics p, which is the speed at which adoption takes off, and q, the speed at which later growth occurs. A cheaper technology might have a higher p, for example, taking off more quickly, while a technology that has network effects (like a fax machine, where the value of the item increases as others get it) may have a higher q.Caveats and criticismsCritics of this model have suggested that it is an overly simplified representation of a complex reality. [citation needed]

A number of other phenomena can influence innovation adoption rates, such as -1. Customers often adapt technology to their own needs, so the innovation may actually change in

nature from the early adopters to the majority of users. 2. Disruptive technologies may radically change the diffusion patterns for established technology by

starting a different competing S-curve. 3. Lastly, path dependence may lock certain technologies in place, as in the QWERTY keyboard.

See also Bass diffusion model Creativity techniques Crossing the Chasm Cultural evolution Development communication Disruptive technology Dual inheritance theory Early adopter

Logistic function Meme Path dependence Percolation Technology acceptance model Technology lifecycle TRIZ Two-step flow of communication

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References Rogers, Everett M. (1962). Diffusion of Innovations.  Rogers, Everett M. (2003). Diffusion of Innovations, Fifth Edition. New York, NY: Free Press.

ISBN 0-7432-2209-1. 

External links Historical look at the Technology Adoption Lifecycle The Diffusion Simulation Game , about adopting an innovation in education The Pencil Metaphor on diffusion of innovation particularly ICT in education Modeling Market Adoption in Excel with a simplified s-curve

Retrieved from "http://en.wikipedia.org/wiki/Diffusion_of_innovations"

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Historical Perspective: The Technology Adoption Lifecycle http://www.hightechstrategies.com/profiles.html The technology adoption lifecycle was originally developed in 1957 at Iowa State College. Its purpose was to track the purchase patterns of hybrid seed corn by farmers. Approximately six years later Everett Rogers broadened the use of this model in his book, Diffusion of Innovations. The following psychographic profiles were abstracted from the North Central Rural Sociology Committee, Subcommittee for the Study of the Diffusion of Farm Practices. The Diffusion Process. Ames: Agriculture Extension Service, Iowa State College, Special Report No. 18, 1957 InnovatorsThey have larger than average farms, are well educated and usually come from well established families.They usually have a relatively high net worth and, probably more important, a large amount of risk capital. They can afford and do take calculated risks on new products. They are respected for being successful, but ordinarily do not enjoy the highest prestige in the community. Because innovators adopt new ideas so much sooner than the average farmer, they are sometimes ridiculed by their conservative neighbors. This neighborhood group pressure is largely ignored by the innovators, however. The innovations are watched by their neighbors, but they are not followed immediately in new practices. The activities of innovators often transcend local community boundaries. Rural innovators frequently belong to formal organizations at the county, regional, state, or national level. In addition, they are likely to have many informal contacts outside the community: they may visit with others many miles away who are also trying a new technique or product, or who are technical experts. Early AdoptersThey are younger than the average farmer, but not necessarily younger than the innovators. They also have a higher average education, and participate more in the formal activities of the community through such organizations as churches, the PTA, and farm organizations. They participate more than the average in agricultural cooperatives and in government agency programs in the community (such as Extension Service or Soil Conservation). In fact, there is some evidence that this group furnishes a disproportionate amount of the formal leadership (elected officers) in the community. The early adopters are also respected as good sources of new farm information by their neighbors. Early MajorityThe early majority are slightly above average in age, education, and farming experience. They have medium high social and economic status. They are less active in formal groups than innovators or early adopters, but more active than those who adopt later. In many cases, they are not formal leaders in the community organizations, but they are active members in these organizations. They also attend Extension meetings and farm demonstrations. The people in this category are most likely to be informal rather than elected leaders. They have a following insofar as people respect their opinions, their "high morality and sound judgment." They are "just like their following, only more so." They must be sure an idea will work before they adopt it. If the informal leader fails two or three times, his following looks elsewhere for information and guidance. Because the informal leader has more limited resources than the early adopters and innovators, he cannot afford to make poor decisions: the social and economic costs are too high. These people tend to associate mainly in their own community. When people in the community are asked to name neighbors and farmers with whom they talk over ideas, these early majority are named disproportionally frequently. On their parts, they value highly the opinions their neighbors and friends hold about them, for this is their main source of status and prestige. The early majority may look to the early adopters for their new farm information. Late majorityThose in this group have less education and are older than the average farmer. While they participate less actively in formal groups, they probably form the bulk of the membership in these formal organizations. Individually they belong to fewer organizations, are less active in organizational work, and take fewer

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leadership roles than earlier adopters. They do not participate in as many activities outside the community as do people who adopt earlier. LaggardsThey have the least education and are the oldest. They participate least in formal organizations, cooperatives, and government agency programs. They have the smallest farms and the least capital. Many are suspicious of county extension agents and agricultural salesmen.

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Modeling market adoption in Excel with a simplified s-curveApr 24th, 2007 by Juan C. Mendez Often business analysts need to model the adoption of a new product or service for financial planning. There are several approaches, but a common one is the s-curve (see Wikipedia article). Here is a simple implementation in Excel that can be easily added to your spreadsheets. It reduces all the math to just three parameters:

saturation - What is the maximum expected penetration after the product becomes mainstream? i.e. what is the value that the top of the s-curve will reach?

start of fast growth - By this year, the penetration will be 10% of the saturation value, and it will start to grow rapidly. 10% was an arbitrary choice to simplify the model, and by doing some math you could change the formula to any value. It is a reasonable choice in most cases. We’ll call this parameter hypergrowth

takeover time - How long it will take for the product to “catch on”? - The operational assumption in the formula is that this number of years after the start of fast growth, the product would have reached 90% of the saturation value and will start to slow down. Again, 90% is an arbitrary value I chose.

The s-curve model focuses in the early phases of the product lifecycle, until maturity is reached. Penetration decay is NOT covered by this model.The formula for each year’s penetration would simply be:=saturation/(1+81^((hypergrowth+takeover/2-year)/takeover))See it in action:

In the sample spreadsheet above, look at cell B8 where you can see the formula in use. It is the same for all row 8.

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saturation, hypergrowth and takeover are names defined for the parameters on rows 2 to 5 (you use names in your models instead of plain cell references, don’t you?)Very simple, easy to maintain, light on calculation times… happy market adoption modeling!PS: The chart shown is NeoOffice, an open source alternative to Excel for Macintosh users, based on OpenOffice

Math on the simplified market adoption s-curve for ExcelJul 6th, 2007 by Juan C. Mendez I’ve got a number of questions on the simplified Excel s-curve formula I published some time ago, so here are more details for those interested in the math behind it. The previous posting focused on how business analysts sometimes need to model market adoption, and provided a simple and easy to maintain formula to do so in Excel.The formula =saturation/(1 + 81^((hypergrowth + takeover/2 - year)/takeover)) suggested for Excel is a simplification of the formula for a sigmoid function (See the Wikipedia article)

The graphic below shows the shape of both functions is identical. The saturation parameter just scales the function to a desired value, instead of going from 0 to 1. The factor 81 on the Excel formula determines how “sharp” the curve is, in this particular case, reaching 0.1 at the period hypergrowth and 0.9 at hypergrowth + takeover. Note that 81^x can be re-written as e^(ln(81)*x), so whatever factor is used there is simply going to affect the shape by compressing or expanding it horizontally.

This is how the scaling factor can be computed. Let’s say we want the penetration to be 5% at the period specified by hypergrowth. We can work out the solution off the second function. We need to solve for 1/(1+e^(-x) == 0.05, which gives x=-2.94444. Since the function is symmetrical, we also know for x=2.94444 P(x) == 0.95.Since factor^((hypergrowth + takeover/2 - year)/takeover)) can be re-written as e^(ln(factor)*(hypergrowth + takeover/2 - year)/takeover)), we can solve ln(factor)*(hypergrowth + takeover/2 - (hypergrowth + takeover))/takeover == 2.94444. Reducing all the math, we arrive to1/(1 + e^(-0.5*ln(factor))) == 0.95, and factor would be 361. If the

desired penetration at hypergrowth is 20%, then we solve 1/(1 + e^(-0.5*ln(factor))) == 0.80,leading to factor == 16

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InnovationFrom Wikipedia, the free encyclopedia

For other uses, see Innovation (disambiguation).Look up Innovation in Wiktionary, the free dictionary.

The classic definitions of innovation include:1. the process of making improvements by introducing something new 2. the act of introducing something new: something newly introduced (The American Heritage

Dictionary). 3. the process of translating new ideas into tangible societal impact (Krisztina Holly, Vice Provost,

University of Southern California, and Executive Director of USC Stevens Institute for Innovation)

4. the introduction of something new. (Merriam-Webster Online) 5. a new idea, method or device. (Merriam-Webster Online) 6. the successful exploitation of new ideas (Department of Trade and Industry, UK). 7. change that creates a new dimension of performance Peter Drucker (Hesselbein, 2002) 8. A creative idea that is realized [(Frans Johansson)] (Harvard Business School Press, 2004) 9. "The capability of continuously realizing a desired future state" ([John Kao, The Innovation

Manifesto, 2005]) 10. "The staging of value and/or the conservation of value." (Daniel Montano 2006.)[1]

In economics, business and government policy,- something new - must be substantially different, not an insignificant change. In economics the change must increase value, customer value, or producer value. Innovations are intended to make someone better off, and the succession of many innovations grows the whole economy.The term innovation may refer to both radical and incremental changes to products, processes or services. The often unspoken goal of innovation is to solve a problem. Innovation is an important topic in the study of economics, business, technology, sociology, and engineering. Since innovation is also considered a major driver of the economy, the factors that lead to innovation are also considered to be critical to policy makers.In the organisational context, innovation may be linked to performance and growth through improvements in efficiency, productivity, quality, competitive positioning, market share, etc. All organisations can innovate, including for example hospitals, universities, and local governments.While innovation typically adds value, innovation may also have a negative or destructive effect as new developments clear away or change old organisational forms and practices. Organisations that do not innovate effectively may be destroyed by those that do. Hence innovation typically involves risk. A key challenge in innovation is maintaining a balance between process and product innovations where process innovations tend to involve a business model which may develop shareholder satisfaction through improved efficiencies while product innovations develop customer support however at the risk of costly R&D that can erode shareholder returns.Four commonly accepted types of innovation are Product, Process, Position and Paradigm (Tidd, Bessant and Pavitt, 2005)

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Contents1 Conceptualizing innovation

1.1 Distinguishing from Invention and other concepts 1.2 Innovation in organizations 1.3 Technological concepts of innovation 1.4 Economic conceptions of innovation 1.5 Transaction cost and network theory perspectives

2 Types of innovation 2.1 Incremental innovation v Radical Innovation

2.1.1 Disruptive vs. sustaining innovation 2.1.2 Further reading

2.2 Systemic innovation 3 Innovation and market outcome 4 Sources of innovation 5 Diffusion of innovations 6 Goals of innovation 7 Failure of innovation 8 Measures of innovation 9 Public awareness 10 See also 11 References 12 Innovation Links 13 External links

Conceptualizing innovationInnovation has been studied in a variety of contexts, including in relation to technology, commerce, social systems, economic development, and policy construction. There are, therefore, naturally a wide range of approaches to conceptualising innovation in the scholarly literature. See, e.g., Fagerberg et al. (2004).Fortunately, however, a consistent theme may be identified: innovation is typically understood as the introduction of something new and useful, for example introducing new methods, techniques, or practices or new or altered products and services.Distinguishing from Invention and other concepts"An important distinction is normally made between invention and innovation. Invention is the first occurrence of an idea for a new product or process, while innovation is the first attempt to carry it out into practice" (Fagerberg, 2004: 4)It is useful, when conceptualizing innovation, to consider whether other words suffice. Recent authors point out that invention - the creation of new tools or the novel compilation of existing tools - is often confused with innovation. Many product and service enhancements may fall more rigorously under the term improvement. Change and creativity are also words that may often be substituted for innovation. What, then, is innovation that makes it necessary to have a different word from these others, or is it a catch-all word, a loose synonym? Much of the current business literature blurs the concept of innovation with value creation, value extraction and operational execution. In this view, an innovation is not an innovation until someone successfully implements and makes money on an idea. Extracting the essential concept of innovation from these other closely linked notions is no easy thing.One emerging approach is to use these other notions as the constituent elements of innovation as an action: Innovation occurs when someone uses an invention - or uses existing tools in a new way - to change how the world works, how people organize themselves, and how they conduct their lives.Note in this view inventions may be concepts, physical devices or any other set of things that facilitate an action. An innovation in this light occurs whether or not the act of innovating succeeds in generating value for its champions. Innovation is distinct from improvement in that it causes society to reorganize. It

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is distinct from problem solving and is perhaps more rigorously seen as new problem creation. And in this view, innovation applies whether the act generates positive or negative results.Innovation in organizationsA convenient definition of innovation from an organizational perspective is given by Luecke and Katz (2003), who wrote:

"Innovation . . . is generally understood as the introduction of a new thing or method . . . Innovation is the embodiment, combination, or synthesis of knowledge in original, relevant, valued new products, processes, or services. (p. 2)"

Don Sheelen also placed inovation at the pinnacle of modern business stating that:"Innovation is the lifeblood of any organization." Sheelan emphasizes that "without it, not only is their no growth, but, inevitably, a slow death."

Innovation typically involves creativity, but is not identical to it: innovation involves acting on the creative ideas to make some specific and tangible difference in the domain in which the innovation occurs. For example, Amabile et al (1996) propose:

"All innovation begins with creative ideas . . . We define innovation as the successful implementation of creative ideas within an organization. In this view, creativity by individuals and teams is a starting point for innovation; the first is necessary but not sufficient condition for the second". (p. 1154-1155).

For innovation to occur, something more than the generation of a creative idea or insight is required: the insight must be put into action to make a genuine difference, resulting for example in new or altered business processes within the organisation, or changes in the products and services provided.A further characterization of innovation is as an organizational or management process. For example, Davila et al (2006), write:

"Innovation, like many business functions, is a management process that requires specific tools, rules, and discipline." (p. xvii)

From this point of view the emphasis is moved from the introduction of specific novel and useful ideas to the general organizational processes and procedures for generating, considering, and acting on such insights leading to significant organizational improvements in terms of improved or new business products, services, or internal processes.Through these varieties of viewpoints, creativity is typically seen as the basis for innovation, and innovation as the successful implementation of creative ideas within an organization (c.f. Amabile et al 1996 p.1155). From this point of view, creativity may be displayed by individuals, but innovation occurs in the organizational context only.It should be noted, however, that the term 'innovation' is used by many authors rather interchangeably with the term 'creativity' when discussing individual and organizational creative activity. As Davila et al (2006) comment,

"Often, in common parlance, the words creativity and innovation are used interchangeably. They shouldn't be, because while creativity implies coming up with ideas, it's the "bringing ideas to life" . . . that makes innovation the distinct undertaking it is."

The distinctions between creativity and innovation discussed above are by no means fixed or universal in the innovation literature. They are however observed by a considerable number of scholars in innovation studies.

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Technological concepts of innovationThe OECD defines Technological Innovation in the Oslo Manual (1995) as:

Technological product and process (TPP) innovations comprise implemented technologically new products and processes and significant technological improvements in products and processes. A TPP innovation has been implemented if it has been introduced on the market (product innovation) or used within a production process (process innovation). TPP innovations involve a series of scientific, technological, organisational, financial and commercial activities. The TPP innovating firm is one that has implemented technologically new or significantly technologically improved products or processes during the period under review.

A 2005/6 MIT survey of innovation in technology found a number of characteristics common to innovators working in that field.

1. they are not troubled by the idea of failure, 2. they realise that failure can be learned from and that the 'failed' technology can later be re-used for

other purposes, 3. they know innovation requires that one works in advanced areas where failure is a real possibility, 4. innovators are curious about what is happening in a myriad of disciplines, not only their own

specialism, 5. innovators are open to third-party experiments with their products, 6. they recognize that a useful innovation must be "robust", flexible and adaptable, 7. innovators delight in spotting a need that we don't even know we harbor, and then fulfilling that

need with a new innovation, and as such 8. innovators like to make products that are immediately useful to their first users.

Economic conceptions of innovationJoseph Schumpeter defined economic innovation in 1934:

1. The introduction of a new good —that is one with which consumers are not yet familiar—or of a new quality of a good.

2. The introduction of a new method of production, which need by no means be founded upon a discovery scientifically new, and can also exist in a new way of handling a commodity commercially.

3. The opening of a new market, that is a market into which the particular branch of manufacture of the country in question has not previously entered, whether or not this market has existed before.

4. The conquest of a new source of supply of raw materials or half-manufactured goods, again irrespective of whether this source already exists or whether it has first to be created.

5. The carrying out of the new organization of any industry, like the creation of a monopoly position (for example through trustification) or the breaking up of a monopoly position

Schumpeter's focus on innovation is reflected in Neo-Schumpeterian economics.Innovation is also studied by economists in a variety of contexts, for example in theories of entrepreneurship or in Paul Romer's New Growth Theory.Transaction cost and network theory perspectivesAccording to Regis Cabral (1998, 2003):

"Innovation is a new element introduced in the network which changes, even if momentarily, the costs of transactions between at least two actors, elements or nodes, in the network."

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Types of innovationScholars have identified at a variety of classifications for types innovations. Here is an unordered ad-hoc list of examples:Business model innovation

involves changing the way business is done in terms of capturing value e.g. Compaq vs. Dell, hub and spoke airlines vs. Southwest, and Hertz/Avis vs. Enterprise.

Marketing innovation is the development of new marketing methods with improvement in product design or packaging, product promotion or pricing.

Organizational innovation involves the creation or alteration of business structures, practices, and models, and may therefore include process, marketing and business model innovation.

Process innovation involves the implementation of a new or significantly improved production or delivery method.

Product innovation involves the introduction of a new good or service that is new or substantially improved. This might include improvements in functional characteristics, technical abilities, ease of use, or any other dimension.

Service innovation refers to service product innovation which might be, compared to goods product innovation or process innovation, relatively less involving technological advance but more interactive and information-intensive (Miles, 2004 in Fagerberg et al.), mainly due to the characteristics of services per se. This type of innovation can be found both in manufacturing and service firms since they can, particularly obviously at present, provide services to customers. See also, e.g., Barras (1986), Evangelista (2000), Miles (2000), Sapprasert (2007).

Supply chain innovation where innovations occur in the sourcing of input products from suppliers and the delivery of output products to customers

Substantial innovation Introducing a different product or service within the same line, such as the movement of a candle company into marketing the electric lightbulb.

Financial innovation through which new financial services and products are developed, by combining basic financial attributes (ownership, risk-sharing, liquidity, credit) in progressive innovative ways, as well as reactive exploration of borders and strength of tax law. Through a cycle of development, directive compliance is being sharpened on opportunities, so new financial services and products are continuously shaped and progressed to be adopted. The dynamic spectrum of financial innovation, where business processes, services and products are adapted and improved so new valuable chains emerge, therefore may be seen to involve most of the above mentioned types of innovation.

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Incremental innovation v Radical InnovationInnovation studies have traditionally conceived of 2 types of innovation to nurture revenues by effectively growing market share:Incremental innovations

is a step forward along a technology trajectory, or from the known to the unknown, with little uncertainty about outcomes and success and is generally minor improvements made by those working day to day with existing methods and technology (both process and product), responding to short term goals. Most innovations are incremental innovations. A value-added business process, this involves making minor changes over time to sustain the growth of a company without making sweeping changes to product lines, services, or markets in which competition currently exists.

Breakthrough, disruptive or radical innovation Launching an entirely novel product or service rather than providing improved products & services along the same lines as currently. The uncertainty of breakthrough innovations means that seldom do companies achieve their breakthrough goals this way, but those times that breakthrough innovation does work, the rewards can be tremendous. Involves larger leaps of understanding, perhaps demanding a new way of seeing the whole problem, probably taking a much larger risk than many people involved are happy about. There is often considerable uncertainty about future outcomes. There may be considerable opposition to the proposal and questions about the ethics, practicality or cost of the proposal may be raised. People may question if this is, or is not, an advancement of a technology or process. Radical innovation involves considerable change in basic technologies and methods, created by those working outside mainstream industry and outside existing paradigms.

Sometimes it is very hard to draw a line between both.

Disruptive vs. sustaining innovationMain article: disruptive technology

How low-end disruption occurs over time.More recently the concepts of disruptive v. sustaining innovation have been popularised, where innovation is often characterized by its impact on existing markets or businesses. Sustaining innovations allows organizations to continue to approach markets the same way, such as the development of a faster or more fuel efficient car. Disruptive innovations on the other hand, significantly change a market or product category, such as the invention of a cheap, safe personal flying machine that could replace cars.Prof. Clayton M. Christensen of the Harvard Business

School, maintained a database of innovative changes in the production and sale of hard-disks from 1975 to 1995. There were 116 new technologies introduced, 111 of them were sustaining in nature, and every established firm in the industry was able to copy or replicate those innovations with 100% success. (Sustaining innovations also tend to be evolutionary.) In contrast there were 5 disruptive innovations. None of the disruptive products involved any new technology, yet for the established firms in the industry the adoption rate in the disruptive technologies was zero. See "Leading for Innovation" Hesselbein, (2002), page 204.For the leading firms, the new technologies offered their existing customers little advantage. The success of the disruptive technology often promised lower profit margins to established firms. The decision makers values and the goals of the firm forbid giving serious consideration to technologies that will destroy an established market. These disruptive technologies were adopted by small firms that were not

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established in the market, and for whom adoption of the disruptive innovation represented new opportunity.

Further reading Carlota Perez Technological revolutions, paradigm shifts and socio-institutional change Breakthrough Innovation Case Study — (PDF document. Adobe Acrobat required) What Innovation Is - How Companies Develop Operating Systems For Innovation — (PDF

document. Adobe Acrobat required) Profile and Interview of Clayton Christensen: The Innovation Trainor - Business Innovation

Factory Research Advisor Systemic innovationAs innovation in specific technologies, services or methods that are of interest at firm level, scholars such as Christopher Freeman have proposed two levels of innovation that are important at an industry or economy level:New technological systems (systemic innovations)

that may give rise to new industrial sectors, and induce major change across several branches of the economy. These systemic innovations are based on a range of radical and incremental socio-technical innovation.

Technological revolutions or new techno-economic paradigms clusters of innovations that can change the whole economy, corresponding to Joseph Schumpeter's 'creative gales of destruction'. These revolutions can take decades to occur, as they involve massive innovation of economic, social and cultural practices.

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Innovation and market outcomeMarket outcome from innovation can be studied from different lenses. The industrial organizational approach of market characterization according to the degree of competitive pressure and the consequent modelling of firm behaviour often using sophisticated game theoretic tools, while permitting mathematical modelling, has shifted the ground away from an intuitive understanding of markets. The earlier visual framework in economics, of market demand and supply along price and quantity dimensions, has given way to powerful mathematical models which though intellectually satisfying has led policy makers and managers groping for more intuitive and less theoretical analyses to which they can relate to at a practical level. Non quantifiable variables find little place in these models, and when they do, mathematical gymnastics (such as the use of different demand elasticities for differentiated products) embrace many of these qualitative variables, but in an intuitively unsatisfactory way.In the management (strategy) literature on the other hand, there is a vast array of relatively simple and intuitive models for both managers and consultants to choose from. Most of these models provide insights to the manager which help in crafting a strategic plan consistent with the desired aims. Indeed most strategy models are generally simple, wherein lie their virtue. In the process however, these models often fail to offer insights into situations beyond that for which they are designed, often due to the adoption of frameworks seldom analytical, seldom rigorous. The situational analyses of these models often tend to be descriptive and seldom robust and rarely present behavioural relationship between variables under study.From an academic point of view, there is often a divorce between industrial organisation theory and strategic management models. While many economists view management models as being too simplistic, strategic management consultants perceive academic economists as being too theoretical, and the analytical tools that they devise as too complex for managers to understand.Innovation literature while rich in typologies and descriptions of innovation dynamics is mostly technology focused. Most research on innovation has been devoted to the process (technological) of innovation, or has otherwise taken a how to (innovate) approach. The integrated innovation model of Soumodip Sarkar goes some way to providing the academic, the manager and the consultant an intuitive understanding of the innovation – market linkages in a simple yet rigorous framework in his book , Innovation, Market Archetypes and Outcome- An Integrated Framework.[2]

The integrated model presents a new framework for understanding firm and market dynamics, as it relates to innovation. The model is enriched by the different strands of literature - industrial organization, management and innovation. The integrated approach that allows the academic, the management consultant and the manager alike to understand where a product (or a single product firm) is located in an integrated innovation space, why it is so located and which then provides valuable clues as to what to do while designing strategy. The integration of the important determinant variables in one visual framework with a robust and an internally consistent theoretical basis is an important step towards devising comprehensive firm strategy. The integrated framework provides vital clues towards framing a what to guide for managers and consultants. Furthermore, the model permits metrics and consequently diagnostics of both the firm and the sector and this set of assessment tools provide a valuable guide for devising strategy.

Sources of innovationThere are two main sources of innovation. In the linear model the traditionally recognized source is manufacturer innovation. This is where an agent (person or business) innovates in order to sell the innovation. The other source of innovation, only now becoming widely recognized, is end-user innovation. This is where an agent (person or company) develops an innovation for their own (personal or in-house) use because existing products do not meet their needs. Eric von Hippel has identified end-user innovation as, by far, the most important and critical in his classic book on the subject, Sources of Innovation.[3]

Innovation by businesses is achieved in many ways, with much attention now given to formal research and development for "breakthrough innovations." But innovations may be developed by less formal on-the-job modifications of practice, through exchange and combination of professional experience and by many other routes. The more radical and revolutionary innovations tend to emerge from R&D, while /tt/file_convert/5a9fc4dd7f8b9a8e178d261f/document.doc 72/122

more incremental innovations may emerge from practice - but there are many exceptions to each of these trends.Regarding user innovation, rarely user innovators may become entrepreneurs, selling their product, or more often they may choose to trade their innovation in exchange for other innovations. Nowadays, they may also choose to freely reveal their innovations, using methods like open source. In such networks of innovation the creativity of the users or communities of users can further develop technologies and their use.Whether innovation is mainly supply-pushed (based on new technological possibilities) or demand-led (based on social needs and market requirements) has been a hotly debated topic. Similarly, what exactly drives innovation in organizations and economies remains an open question.More recent theoretical work moves beyond this simple dualistic problem, and through empirical work shows that innovation does not just happen within the industrial supply-side, or as a result of the articulation of user demand, but though a complex processes that links many different players together - not only developers and users, but a wide variety of intermediary organistions such as consultancies, standards bodies etc. Work on social networks suggests that much of the most successful innovation occures at the boundaries of organisations and industries where the problems and needs of users, and the potential of technologies can be linked together in a creative process that challenges both.

Diffusion of innovationsMain article: diffusion of innovationsOnce innovation occurs, innovations may be spread from the innovator to other individuals and groups. This process has been studied extensively in the scholarly literature from a variety of viewpoints, most notably in Everett Rogers' classic book, The Diffusion of Innovations. However, this 'linear model' of innovation has been substantinally challenged by scholars in the last 20 years, and much research has shown that the simple invention-innovation-diffusion model does not do justice to the multilevel, non-linear processes that firms,

entrepreneurs and users participate in to create successful and sustainable innovations.Rogers proposed that the life cycle of innovations can be described using the ‘s-curve’ or diffusion curve. The s-curve maps growth of revenue or productivity against time. In the early stage of a particular innovation, growth is relatively slow as the new product establishes itself. At some point customers begin to demand and the product growth increases more rapidly. New incremental innovations or changes to the product allow growth to continue. Towards the end of its life cycle growth slows and may even begin to decline. In the later stages, no amount of new investment in that product will yield a normal rate of return.The s-curve is derived from half of a normal distribution curve. There is an assumption that new products are likely to have "product Life". i.e. a start-up phase, a rapid increase in revenue and eventual decline. In fact the great majority of innovations never get off the bottom of the curve, and never produce normal returns.Innovative companies will typically be working on new innovations that will eventually replace older ones. Successive s-curves will come along to replace older ones and continue to drive growth upwards. In the figure above the first curve shows a current technology. The second shows an emerging technology that current yields lower growth but will eventually overtake current technology and lead to even greater levels of growth. The length of life will depend on many factors.

Goals of innovationPrograms of organizational innovation are typically tightly linked to organizational goals and objectives, to the business plan, and to market competitive positioning.

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For example, one driver for innovation programs in corporations is to achieve growth objectives. As Davila et al (2006) note,

"Companies cannot grow through cost reduction and reengineering alone . . . Innovation is the key element in providing aggressive top-line growth, and for increasing bottom-line results" (p.6)

It is not surprising, therefore, that companies such as General Electric and Procter & Gamble have embraced the management of innovation enthusiastically, with the primary goal of driving growth and, consequently, improving shareholder value.In general, business organisations spend a significant amount of their turnover on innovation i.e. making changes to their established products, processes and services. The amount of investment can vary from as low as a half a percent of turnover for organisations with a low rate of change to anything over twenty percent of turnover for organisations with a high rate of change.The average investment across all types of organizations is four percent. For an organisation with a turnover of say one billion currency units, this represents an investment of forty million units. This budget will typically be spread across various functions including marketing, product design, information systems, manufacturing systems and quality assurance.The investment may vary by industry and by market positioning.One survey across a large number of manufacturing and services organisations found, ranked in decreasing order of popularity, that systematic programs of organizational innovation are most frequently driven by:

1. Improved quality 2. Creation of new markets 3. Extension of the product range 4. Reduced labour costs 5. Improved production processes 6. Reduced materials 7. Reduced environmental damage 8. Replacement of products/services 9. Reduced energy consumption 10. Conformance to regulations

These goals vary between improvements to products, processes and services and dispel a popular myth that innovation deals mainly with new product development. Most of the goals could apply to any organisation be it a manufacturing facility, marketing firm, hospital or local government.

Failure of innovationAttaining goals must be the ultimate objective of the innovation process. Unfortunately, most innovation fails to meet organisational goals.Figures vary considerably depending on the research. Some research quotes failure rates of fifty percent while other research quotes as high as ninety percent of innovation has no impact on organisational goals. One survey regarding product innovation quotes that out of three thousand ideas for new products, only one becomes a success in the marketplace (needs source). Failure is an inevitable part of the innovation process, and most successful organisations factor in an appropriate level of risk. Perhaps it is because all organisations experience failure that many choose not to monitor the level of failure very closely. The impact of failure goes beyond the simple loss of investment. Failure can also lead to loss of morale among employees, an increase in cynicism and even higher resistance to change in the future.Innovations that fail are often potentially ‘good’ ideas but have been rejected or ‘shelved’ due to budgetary constraints, lack of skills or poor fit with current goals. Failures should be identified and screened out as early in the process as possible. Early screening avoids unsuitable ideas devouring scarce resources that are needed to progress more beneficial ones. Organizations can learn how to avoid failure when it is openly discussed and debated. The lessons learned from failure often reside longer in the organisational consciousness than lessons learned from success. While learning is important, high failure rates throughout the innovation process are wasteful and a threat to the organisation's future.

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The causes of failure have been widely researched and can vary considerably. Some causes will be external to the organisation and outside its influence of control. Others will be internal and ultimately within the control of the organisation. Internal causes of failure can be divided into causes associated with the cultural infrastructure and causes associated with the innovation process itself. Failure in the cultural infrastructure varies between organisations but the following are common across all organisations at some stage in their life cycle (O'Sullivan, 2002):

1. Poor Leadership 2. Poor Organisation 3. Poor Communication 4. Poor Empowerment 5. Poor Knowledge Management

Common causes of failure within the innovation process in most organisations can be distilled into five types:

1. Poor goal definition 2. Poor alignment of actions to goals 3. Poor participation in teams 4. Poor monitoring of results 5. Poor communication and access to information

Poor goal definition requires that organisations state explicitly what their goals are in terms understandable to everyone involved in the innovation process. This often involves stating goals in a number of ways. Poor alignment of actions to goals means linking explicit actions such as ideas and projects to specific goals. It also implies effective management of action portfolios. Poor participation in teams refers to the behaviour of individuals and teams. It also refers to the explicit allocation of responsibility to individuals regarding their role in goals and actions and the payment and rewards systems that link individuals to goal attainment. Finally, poor monitoring of results refers to monitoring all goals, actions and teams involved in the innovation process.Innovation can fail if seen as an organisational process whose success stems from a mechanistic approach i.e. 'pull lever obtain result'. While 'driving' change has an emphasis on control, enforcement and structure it is only a partial truth in achieving innovation. Organisational gatekeepers frame the organisational environment that "Enables" innovation; however innovation is "Enacted" - recognised, developed, applied and adopted - through individuals.Individuals are the 'atom' of the organisation close to the minutiae of daily activities. Within individuals gritty appreciation of the small detail combines with a sense of desired organisational objectives to deliver (and innovate for) a product/service offer.From this perspective innovation succeeds from strategic structures that engage the individual to the organisation's benefit. Innovation pivots on intrinsically motivated individuals, within a supportive culture, informed by a broad sense of the future.Innovation, implies change, and can be counter to an organisation's orthodoxy. Space for fair hearing of innovative ideas is required to balance the potential autoimmune exclusion that quells an infant innovative culture.

Measures of innovationIndividual and team-level assessment can be conducted by surveys and workshops. Business measures related to finances, processes, employees and customers in balanced scorecards can be viewed from the innovation perspective (e.g. new product revenue, time to market, customer and employee perception & satisfaction). Organizational capabilities can be evaluated through various evaluation frameworks e.g. efqm (European foundation for quality management) -model.The OECD Oslo Manual from 1995 suggests standard guidelines on measuring technological product and process innovation. Some people consider the Oslo Manual complementary to the Frascati Manual from 1963. The new Oslo manual from 2005 takes a wider perspective to innovation, and includes marketing and organizational innovation. Other ways of measuring innovation have traditionally been expenditure,

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for example, investment in R&D (Research and Development) as percentage of GNP (Gross National Product). Whether this is a good measurement of Innovation has been widely discussed and the Oslo Manual has incorporated some of the critique against earlier methods of measuring. This being said, the traditional methods of measuring still inform many policy decisions. The EU Lisbon Strategy has set as a goal that their average expenditure on R&D should be 3 % of GNP.The Oslo Manual is focused on North America, Europe, and other rich economies. In 2001 for Latin America and the Caribbean countries it was created the Bogota ManualMany scholars claim that there is a great bias towards the "science and technology mode" (S&T-mode or STI-mode), while the "learning by doing, using and interacting mode" (DUI-mode) is widely ignored. For an example, that means you can have the better high tech or software, but there are also crucial learning tasks important for innovation. But these measurements and research are rarely done.

Public awarenessPublic awareness of innovation is an important part of the innovation process. This is further discussed in the emerging fields of innovation journalism and innovation communication.

See also Creative destruction Creative problem solving Diffusion (anthropology) Edward de Bono Hype cycle Idea Management Individual capital Induced innovation Ingenuity Invention Open Innovation Patent

Public domain Research The International Society for Professional

Innovation Management Timeline of invention Toolkits for User Innovation TRIZ User innovation Value network Six Thinking Hats Lateral Thinking

References1. ̂ Montano, Daniel (2006). Innovation Strategies of the World's Most Innovative Companies. 2. ̂ Sarkar, Soumodip (2007). Innovation, Market Archetypes and Outcome- An Integrated Framework.

Springer Verlag. ISBN 10:379081945X.  3. ̂ von Hippel, Eric (1988). The Sources of Innovation. Oxford University Press. ISBN 0-19-509422-0.  Amabile, Teresa (1996). Creativity in Context. New York: Westview Press.  Amabile, Teresa; Regina Conti, Heather Coon, et al. (October 1996). "Assessing the work environment for

creativity". Academy of Management Journal 39 (5): 1154-1184.  Barras, R. (1984). "Towards a theory of innovation in services". Research Policy 15: 161-73.  Cabral, Regis (2003). "Development, Science and", in Heilbron, J.: The Oxford Companion to The History

of Modern Science. New York: Oxford University Press, 205-207.  Cabral, Regis (1998). "Refining the Cabral-Dahab Science Park Management Paradigm". Int. J.

Technology Management 16 (8): 813-818. DOI:10.1504/IJTM.1998.002694. . Chakravorti, Bhaskar (2003). The Slow Pace of Fast Change: Bringing Innovations to Market in a

Connected World. Boston, MA: Harvard Business School Press.  Chesbrough, Henry William (2003). Open Innovation: The New Imperative for Creating and Profiting

from Technology. Boston, MA: Harvard Business School Press.. ISBN 1-57851-837-7.  Christensen, Clayton M. (1997). The Innovator's Dilemma. Boston, MA: Harvard Business School Press.

ISBN 0-06-052199-6.  Davila, Tony; Marc J. Epstein and Robert Shelton (2006). Making Innovation Work: How to Manage It,

Measure It, and Profit from It. Upper Saddle River: Wharton School Publishing. ISBN 0-13-149786-3.  Dosi, Giovanni (1982). "Technological paradigms and technological trajectories". Research Policy 11 (3). . Ettlie, John (2006). Managing Innovation, Second Edition. Butterworth-Heineman, an imprint of Elsevier.

ISBN 0-7506-7895-X. 

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Evangelista, Rinaldo (2000). "Sectoral patterns of technological change in services, economics of innovation". Economics of Innovation and New Technology 9: 183-221. 

Fagerberg, Jan (2004). "Innovation: A Guide to the Literature", in Fagerberg, Jan, David C. Mowery and Richard R. Nelson: The Oxford Handbook of Innovations. Oxford University Press, 1-26. ISBN 0-19-926455-4. 

Freeman, Chris (1984). "Prometheus Unbound". Futures 16 (5): 494-507..  (2002) in Hesselbein, Frances, Marshall Goldsmith, and Iain Sommerville: Leading for Innovation: And

organizing for results. Jossey-Bass. ISBN 0-7879-5359-8.  Luecke, Richard; Ralph Katz (2003). Managing Creativity and Innovation. Boston, MA: Harvard Business

School Press. ISBN 1-59139-112-1.  Mansfield, Edwin (1985). "How Rapidly Does New Industrial Technology Leak Out?". Journal of

Industrial Economics 34 (2): 217–223..  Miles, Ian (2000). "Services Innovation: Coming of Age in the Knowledge Based Economy". International

Journal of Innovation Management 14 (4): 371-389..  Miles, Ian (2004). "Innovation in Services", in Fagerberg, Jan, David C. Mowery and Richard R. Nelson:

The Oxford Handbook of Innovations. Oxford University Press, 433-458. ISBN 0-19-926455-4.  Nelson, Richard; Winter, S (1977). "In search of a useful theory of Innovation". Research Policy 6 (1): 36-

76.  Nordfors, David (November 2004). "The Role of Journalism in Innovation Systems" (pdf). Innovation

Journalism 1 (7). ISSN 1549-9049.  OECD The Measurement of Scientific and Technological Activities. Proposed Guidelines for Collecting

and Interpreting Technological Innovation Data. Oslo Manual. 2nd edition, DSTI, OECD / European Commission Eurostat, Paris 31 Dec 1995.

O'Sullivan, David (2002). "Framework for Managing Development in the Networked Organisations". Journal of Computers in Industry 47 (1): 77-88. ISSN 0166-3615. 

Rogers, Everett M. (1962). Diffusion of Innovation. New York, NY: Free Press.  Rosenburgh, Nathan (1975). Perspectives on Technology. Cambridge, London and N.Y.: Cambridge

University Press.  Schumpeter, Joseph (1934). The Theory of Economic Development. Cambridge, MA: Harvard University

Press.  Sapprasert, Koson (2007). "The impact of ICT on the growth of the service industries". TIK working

papers on Innovation Studies 20070531.  Scotchmer, Suzanne (2004). Innovation and Incentives. Cambridge, MA: MIT Press.  Silverstein, David; Neil DeCarlo and Michael Slocum (2005). INsourcing Innovation: How to Transform

Business as Usual into Business as Exceptional. Longmont, CO: Breakthrough Performance Press. ISBN 0-9769010-0-5. 

Sloane, Paul (2003). The Leader's Guide to Lateral Thinking Skills. Kogan Page.  Stein, Morris (1974). Stimulating creativity. New York: Academic Press.  Utterback, James M.; Fernando F. Suarez. (1993). "Innovation, Competition, and Industry Structure".

Research Policy 22 (1): 1–21.  von Hippel, Eric (2005). Democratizing Innovation. MIT Press. ISBN 0-262-22074-1.  Woodman, Richard .W.; John E. Sawyer, Ricky W. Griffin (1993). "Toward a theory of organizational

creativity". Academy of Management Review'' 18 (2): 293-321.  Wolpert, John (2002). "Breaking Out of the Innovation Box". Harvard Business Review August. 

Innovation Links SPRU Science and Technology Policy Research - Origin of the concept of 'Systems of Innovation'

and centre of research and learning on innovation policy and innovation management. Innovation Studies at Centre for Technology, Innovation and Culture (TIK), University of Oslo -

One of the world's leading research centres on Innovation Studies. TIK working papers on Innovation studies at RePec . Research effort in Understanding Innovation (Centre for Advanced Study). PREST : now part of Manchester Institute of Innovation Research, centre for research, consultancy

and teaching on innovation (especially in services), innovation policy, and related topics such as research evaluation and Technlogy Foresight.

Welcome to the DTI's Innovation Home Page - Department of Trade and Industry, UK.

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Innovation and Technology Policy - Organisation for Economic Co-operation and Development (OECD).

Welcome to The Innovation Unit's homepage - The Innovation Unit - one of the UK's leading organisations for promoting innovation to improve education.

Academic article on Being a Systems Innovator on SSRN European Union:

o "Communication on Innovation policy: updating the Union’s approach in the context of the Lisbon strategy" - The European Commission.

o Innovation articles .

External links An interview with Larry Keeley, an innovation guru , 4 March 2007 http://upload.wikimedia.org/wikipedia/en/7/75/The_Industry_Standard_Open_Platform.pdf Business Innovation Factory - Community of innovators collaborating to explore and test better

ways to deliver value Technorati blogs, posts and content for Innovation Innovation promoting and information

Retrieved from "http://en.wikipedia.org/wiki/Innovation"

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Path dependenceFrom Wikipedia, the free encyclopediaPath-dependence is a phrase used to mean one of two things (Pierson 2004). Some authors use path-dependence to mean simply "history matters" - a broad conception - while others use it to mean that institutions are self reinforcing - a narrow conception. It is this narrow conception which has the most explanatory force and of which the discussions below are examples. The "history matters" claim is trivially true and reduces simply to "everything has causes".Consider as an example the technological development of videocassette recorders (VCRs) for home use. It is argued that management errors and minor design choices by Sony led to its Betamax format being defeated in market competition by VHS in the 1980s. Two mechanisms can explain why the small but early lead gained by VHS became larger over time. The first is the bandwagon effect of VCR manufacturers in favor of the VHS format in the U.S. and Europe, who switched because they expected VHS to win the standards battle. The second was a network effect: videocassette rental stores observed that more people had VHS players and stocked up on VHS tapes; this in turn led other people to buy VHS players, and so on until there was complete vendor lock-in to VHS. An alternative explanation, of course, is that VHS was better adapted to market demands (in particular to the demand for longer cassettes for recording sports games) and that path dependence had little or nothing to do with its success. There is also some support for this latter claim.Positive feedback mechanisms like bandwagon and network effects are at the origin of path-dependence. They lead to a reinforcing pattern, in which industries 'tip' towards one or another product design. Uncoordinated standardisation can be observed in many other situations.Examples from economics, history, software, and biology are presented below.

Contents1 Economics 2 History and the social sciences 3 Typography 4 Technology 5 Biological evolution 6 Physics 7 Notes 8 References 9 External links

EconomicsPath dependency theory was originally developed by economists to explain technology adoption processes and industry evolution. The theoretical ideas have had a strong influence on evolutionary economics (e.g., Nelson & Winter 1982).There are many models and empirical cases where economic processes do not progress steadily toward some pre-determined and unique equilibrium, so that the nature of any equilibrium achieved depends partly on the process of getting there. The outcome of a path dependent process will often not converge towards a unique equilibrium but instead reach one of several equilibria (sometimes known as absorbing states).This dynamic vision of economic evolution is very different from the neo-classical economics tradition, which in its simplest form assumed that only a single outcome could possibly be reached, regardless of initial conditions or transitory events. With path dependence, both the starting point and 'accidental' events (noise) can have significant effects on the ultimate outcome. In each of the following examples it is possible to identify some random events that disrupted the ongoing course, with irreversible consequences:

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In the 1980s, the U.S. dollar exchange rate appreciated, lowering the world price of tradable goods below the cost of production in many (previously successful) U.S. manufactures. Some of the factories which closed as a result could now be run at a (cash-flow) profit, because the dollar has declined. However, re-opening them is too expensive. This is an example of hysteresis and irreversiblity.

In economic development, it is said (initially by Paul David in 1985) that a standard which is first-to-market can become entrenched (like the QWERTY layout in typewriters still used in computer keyboards). He called this "path dependence", and argued that inferior standards can persist simply because of the legacy they have built up. The case against QWERTY has been criticized (e.g. by The Fable of the Keys), but standards are clearly very important in modern economies, and the significance of path dependence in determining how they form is the subject of economic debate.

Economists since Adam Smith have noted that businesses of a certain type tend to congregate geographically, attracting workers with skills in that business, which draw in more businesses looking for employees with experience. There may not have been any particular reason to prefer one place to another before the industry developed, but as it has become concentrated in one place any new entrants elsewhere are at a disadvantage, and will tend to move into the hub if possible, further increasing its relative efficiency. The mechanism at work is a network effect. New Trade Theory and Krugman's "New Economic Geography" are based partly on this story.

If the economy follows adaptive expectations, future inflation is partly determined by past experience with inflation, since experience determines expected inflation and this is a major determinant of realized inflation.

A transitory high rate of unemployment during a recession can lead to a permanently higher unemployment rate because of the skills loss (or skill obsolescence) by the unemployed along with a deterioration of work attitudes. In other words, cyclical unemployment may generate structural unemployment. The negative effects get reinforced by potential employers' negative view of the capacities of job-seekers who have been out of a job for a long time. This structural hysteresis model of the labour market differs from the prediction of a "natural" unemployment rate or NAIRU, around which 'cyclical' unemployment is said to move randomly. Since structural unemployment is endogenous, the NAIRU is also endogenous (see the article by Hargreaves Heap cited below).

Liebowitz and Margolis distinguish between different types of path dependence. Some types of path dependence do not imply inefficiencies and, while they may be interesting to study for other reasons, do not challenge the policy implications of neoclassical economics. Only what they call "third degree" path dependence - for example, a situation where society would be better off if everybody switched standards simultaneously, but they do not do so because there is no central authority to force them to, and they cannot all coordinate - involves such a challenge. They argue that such situations can be expected to be rare for theoretical reasons and that this prediction is borne out by what they consider the unconvincing examples typically discussed in this context (mainly VHS vs. Beta and QWERTY vs. Dvorak).In technical terms, a path-dependence (stochastic system) can be defined as "one possessing an asymptotic distribution that evolves as a consequence (function of) the process's own history". This is also known as a "non-ergodic stochastic process". Confusingly, the use of "path dependent" to describe labour market hysteresis has the opposite sense to the term's meaning in the adaptive expectations model of inflation. In labour market economics, some "path dependent" models have unemployment following a driftless random walk, based solely on its previous level (a Markov process).

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History and the social sciencesSee also: historical institutionalism

The history of humanity is almost by definition path-dependent. Accidental events such as the death at an early age of major historical figures like Napoleon or Hitler would likely have altered the political geography of Europe and even the languages spoken in different countries today.Recent methodological work in comparative politics and sociology has adapted the concept of path dependence into analyses of political and social phenomenon. Path dependence has primarily been used in comparative-historical analyses to analyze the development and persistence of institutions, whether they be social, political, or cultural. There are arguably two discernable types of path-dependent processes:

One is the "critical juncture" framework, most notably utilized by Ruth and David Collier in political science. In the critical juncture framework, antecedent conditions define and delimit agency during a critical juncture in which actors make contingent choices that set a specific trajectory of institutional development and consolidation that is difficult to reverse. This is akin to the concepts of vendor lock-in or positive feedback derived from path dependence in economics.

The critical juncture framework has been used to explain the development and persistence of welfare states, labor incorporation in Latin America, and the variations in economic development between countries, among other things.An influential attempt to give some formal rigor to thinking about path dependence in political science is notably that of Paul Pierson. Pierson draws in part on ideas from economics (see above). His efforts in this regard have been questioned by Herman Schwartz, who argues that forces analogous to those identified in the economic literature are not pervasive in the political realm, where larger forces and the strategic exercise of power give rise to, maintain, and transform institutions.In a related vein, scholars such as Kathleen Thelen caution that the historical determinism in path-dependent frameworks ignore the constant renegotiation of institutional configurations. She suggests that institutions undergo moments of institutional evolution wherein key actors renegotiate the configuration and purpose of institutions.

The other path-dependent process deals with "reactive sequences" where a primary event sets off a temporally-linked and causally-tight chain of events that is nearly uninterruptible. These reactive sequences have been used to link the death of Martin Luther King, Jr. with welfare expansion and the industrial revolution in England with the development of the steam engine.

TypographyPath dependence also influences the progression of language, grammar and typographical conventions. For example, in the contrast between American and British English, there are different grammatical rules for the placement of punctuation relative to quotation marks in a sentence.For example, compare the following: There are 720 permutations of the sequence "1, 2, 3, 4, 5, 6". (U.K. but not U.S.) There are 720 permutations of the sequence "1, 2, 3, 4, 5, 6." (U.S. but not U.K.)

This difference has been attributed to path dependence. Historically, when print was handset, American printers found it expedient to always place the period inside quotation marks, even when not logically consistent with the text, because this made it easier to prevent accidental displacement of the period. Even though the technical justifications for this convention no longer apply, the grammatical rule has persisted.[1]

TechnologyIn the computer and software markets, legacy systems indicate path dependence: customers' needs in the present market often include the ability to read data or run programs from past generations of products. Thus, for instance, a customer may need not merely the best available word processor but rather the best available word processor that can read Microsoft Word files. Such limitations in compatibility contribute to lock-in, and more subtly, to design compromises for independently developed products if they attempt

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to be compatible. It is not clear, however, that there is any inefficiency involved in the costs of remaining compatible with past decisions.

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Biological evolutionEvolution is considered by some to be path-dependent: random mutations occurring in the past have had long-term effects on current life forms, some of which may no longer be adaptive to current conditions. For instance, there is a controversy about whether the panda's thumb is a leftover trait or not.

PhysicsThe process of Spontaneous symmetry breaking in physics is very similar to path dependence. For example, in materials that exhibit Ferromagnetism, magnetic domains form in otherwise completely homogeneous materials.

Notes1. ̂ (see e.g., http://grammar.ccc.commnet.edu/grammar/marks/quotation.htm#footnote,

http://www.grammartips.homestead.com/inside.html, Quotation_mark#Typographical_considerations

References Arrow, Kenneth J. (1963), 2nd ed. Social Choice and Individual Values. Yale University Press,

New Haven, pp. 119-120 (constitutional transitivity as alternative to path dependence on the status quo).

Arthur, W. Brian (1994), Increasing Returns and Path Dependence in the Economy, Ann Arbor, Michigan: University of Michigan Press.

David, Paul A. (2000), "Path dependence, its critics and the quest for ‘historical economics’", in P. Garrouste and S. Ioannides (eds), Evolution and Path Dependence in Economic Ideas: Past and Present, Edward Elgar Publishing, Cheltenham, England.

Liebowitz, S.J. and Stephen E. Margolis (1990), "The Fable of the Keys", Journal of Law & Economics vol. XXXIII (April 1990)

Mahoney, James (2000), “Path Dependence in Historical Sociology,” Theory and Society 29:4, pp. 507-548.

Stephen E. Margolis and S.J. Liebowitz (2000), "Path Dependence, Lock-In, and History" Nelson, R. & S. Winter (1982), An evolutionary theory of economic change. Harvard University

Press. Pierson, Paul (2000). "Increasing Returns, Path Dependence, and the Study of Politics." American

Political Science Review, June. _____ (2004), "Politics in Time" Puffert, Douglas J. (1999), ["Path Dependence in Economic History"] (based on the entry

“Pfadabhängigkeit in der Wirtschaftsgeschichte,” in the Handbuch zur evolutorischen Ökonomik) _____ (2001), "Path Dependence in Spatial Networks: The Standardization of Railway Track

Gauge" Schwartz, Herman. "Down the Wrong Path: Path Dependence, Increasing Returns, and Historical

Institutionalism." http://www.people.virginia.edu/~hms2f/Path.pdf

External links Article on Path Dependence from EH.NET's Encyclopedia "QWERTY, Lock-in, and Path Dependence" Web page that argues that lock-in leads to market

failure and provides a list of references although it short shrifts articles from those on the other side.

Shawn Hargreaves Heap (1980), "Choosing the Wrong 'Natural' Rate: Accelerating Inflation or Decelerating Employment and Growth?" Economic Journal 90(359) (Sept): 611-20 (ISSN 0013-0133) develops the idea that persistently high unemployment can cause the "natural" rate of unemployment to rise.

"Doctoral Program Research on Organizational Paths" Web page form the Freie Universitaet Berlin Faculty of Business Administration and Economic.

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ParadoxA paradox is an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition. Typically, either the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the premises themselves are not all really true or cannot all be true together. The word paradox is often used interchangeably and wrongly with contradiction; but whereas a contradiction asserts its own opposite, many paradoxes do allow for resolution of some kind.The recognition of ambiguities, equivocations, and unstated assumptions underlying known paradoxes has led to significant advances in science, philosophy and mathematics. But many paradoxes, such as Curry's paradox, do not yet have universally accepted resolutions.Sometimes the term paradox is used for situations that are merely surprising. The birthday paradox, for instance, is unexpected but perfectly logical. This is also the usage in economics, where a paradox is a counterintuitive outcome of economic theory. In literature it can be any contradictory or obviously untrue statement, which resolves itself upon later inspection.

Contents1 Logical paradox 2 Moral paradox 3 See also 4 References 5 External links

Logical paradoxSee also: List of paradoxes

Common themes in paradoxes include direct and indirect self-reference, infinity, circular definitions, and confusion of levels of reasoning. Other paradoxes involve false statements or half-truths and the resulting biased assumptions. For example, consider a situation in which a father and son are driving down the road. The car collides with a tree and the father is killed. The boy is rushed to the nearest hospital where he is prepped for emergency surgery. On entering the surgery suite, the surgeon says, "I can't operate on this boy. He's my son." The apparent paradox is caused by the bandwagon fallacy. The reader, upon seeing the word surgeon, applies a poll of their knowledge of surgeons (regardless of its depth) and reasons that since the majority of surgeons are male, the surgeon is a man, hence the contradiction: the father of the child, a man, was killed in the crash. The paradox is resolved if it is revealed that the surgeon is a woman, the boy's mother. Other assumptions whose resolution would also resolve the paradox are based on cognitive bias; the reader, reading terms like "father" and "son" and thinking of a familial relationship, may assume a traditional family (biological father, biological mother, and son) because other combinations are unknown or disregarded out of prejudicial views. The paradox would resolve itself if it were revealed that the child was adopted and therefore had a biological and adopted father, or if a divorce resulted in the boy having a father and step-father, or if a homosexual male couple had adopted a son or entered a committed relationship after one had already fathered a son.Paradoxes which are not based on a hidden error generally happen at the fringes of context or language, and require extending the context or language to lose their paradoxical quality. Paradoxes that arise from apparently intelligible uses of language are often of interest to logicians and philosophers. This sentence is false is an example of the famous liar paradox: it is a sentence which cannot be consistently interpreted as true or false, because if it is false it must be true, and if it is true it must be false. Therefore, it can be concluded the sentence is neither true nor false. Russell's paradox, which shows that the notion of the set of all those sets that do not contain themselves leads to a contradiction, was instrumental in the development of modern logic and set theory.Thought experiments can also yield interesting paradoxes. The grandfather paradox, for example, would arise if a time traveler were to kill his own grandfather, thereby preventing his own birth.W. V. Quine (1962) distinguished between three classes of paradoxes./tt/file_convert/5a9fc4dd7f8b9a8e178d261f/document.doc 84/122

A veridical paradox produces a result that appears absurd but is demonstrated to be true nevertheless. Thus, the paradox of Frederic's birthday in The Pirates of Penzance establishes the surprising fact that a person's fifth birthday is the day he turns twenty, if born on a leap day. Likewise, Arrow's impossibility theorem involves behaviour of voting systems that is surprising but true.

A falsidical paradox establishes a result that not only appears false but actually is false; there is a fallacy in the supposed demonstration. The various invalid proofs (e.g. that 1 = 2) are classic examples, generally relying on a hidden division by zero. Another example would be the inductive form of the Horse paradox.

A paradox which is in neither class may be an antinomy, which reaches a self-contradictory result by properly applying accepted ways of reasoning. For example, the Grelling-Nelson paradox points out genuine problems in our understanding of the ideas of truth and description.

A fourth kind has sometimes been asserted since Quine's work. A paradox which is both true and false at the same time in the same sense is called a dialetheia. In

Western logics it is often assumed, following Aristotle, that no dialetheia exist, but they are sometimes accepted in Eastern traditions and in paraconsistent logics. An example might be to affirm or deny the statement "John is in the room" when John is standing precisely halfway through the doorway. It is reasonable (by human thinking) to both affirm and deny it ("well, he is, but he isn't"), and it is also reasonable to say that he is neither ("he's halfway in the room, which is neither in nor out"), despite the fact that the statement is to be exclusively proven or disproven.

Moral paradoxIn moral philosophy, paradox plays a central role in ethics debates. For instance, it may be considered that an ethical admonition to "love thy neighbour" is not just in contrast with, but in contradiction to armed neighbours actively trying to kill you: if they succeed, you will not be able to love them. But to preemptively attack them or restrain them is not usually understood as loving. This might be termed an ethical dilemma. Another example is the conflict between an injunction not to steal and one to care for a family that you cannot afford to feed without stolen money. Such a paradox between two maxims is normally resolved through weakening one or the other of the maxims (the need for survival is greater than the need to avoid harm to your neighbor). However, as maxims are added for consideration, the questions of which to weaken in the general case and by how much pose issues related to Arrow's theorem (see above); it may be impossible to formulate a single system of ethics rules with a definite order of preference in the general case, a so-called "ethical calculus".

See also List of paradoxes Paradox (database) Temporal paradox Impossible object Formal fallacy

Dilemma Puzzle Zeno's paradoxes Self refuting ideas Paradoxes of set theory

References R. M. Sainsbury (1988). Paradoxes. Cambridge. W. V. Quine (1962). "Paradox". Scientific American, April 1962, pp. 84–96. Michael Clarke (2002). Paradoxes from A to Z. London: Routledge.

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External linksListen to this article (info/dl)

This audio file was created from an article revision dated 2005-07-07, and may not reflect subsequent edits to the article. (Audio help)More spoken articles

Some paradoxes - an anthology Paradoxes at the Open Directory Project Insolubles (at the Stanford Encyclopedia of Philosophy) "Zeno and the Paradox of Motion"

Logic Portal

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List of paradoxesLogic Portal

This is a list of paradoxes, grouped thematically. Note that many of the listed paradoxes have a clear resolution. — see Quine's Classification of Paradoxes.

Contents1 Logical (except mathematical)

1.1 Self-referential 1.2 Vagueness

2 Mathematical and statistical 2.1 Probability 2.2 Infinity 2.3 Geometry and topology

3 Decision theoretic 4 Chemical 5 Physical 6 Philosophical 7 Economic 8 See also

Logical (except mathematical)Main article: Logic

Paradox of entailment : Inconsistent premises always make an argument valid. Raven paradox (or Hempel's Ravens): Observing a red apple increases the likelihood of all ravens

being black. Horse paradox : All horses are the same color. Unexpected hanging paradox : The day of the hanging will be a surprise, so it cannot happen at all,

so it will be a surprise. The Bottle Imp paradox uses similar logic. Drinker paradox : In any pub there is a customer such that, if he or she drinks, everybody in the

pub drinks. Carroll's paradox : "Whatever Logic is good enough to tell me is worth writing down..." Lottery paradox : it is philosophically justifiable to believe that every individual lottery ticket

won't win, but not justifiable to believe that no lottery ticket will win. Self-referentialThese paradoxes have in common a contradiction arising from self-reference.

Berry paradox : The phrase "the first number not nameable in under ten words" appears to name it in nine words.

Curry's paradox : "If this sentence is true, the world will end in a week." Epimenides paradox : A Cretan says "All Cretans are liars". Exception paradox : "If there is an exception to every rule, then every rule must have at least one

exception, excepting this one" ...is there an exception to the rule that states that there is an exception to every rule?

Grelling-Nelson paradox : Is the word "heterological", meaning "not applicable to itself," a heterological word? (Another close relative of Russell's paradox.)

Hegel 's paradox: "Man learns from history that man learns nothing from history." Intentionally blank page : Many documents contain pages on which the text "This page is

intentionally blank" is printed, thereby making the page not blank. Liar paradox : "This sentence is false." This is the canonical self-referential paradox. Also "Is the

answer to this question no?"

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The Y combinator in the lambda calculus and combinatory logic has been called the paradoxical combinator since it is related to the self-referential antinomies.

Petronius ' paradox: "Moderation in all things, including moderation." Quine's paradox : "yields a falsehood when appended to its own quotation" yields a falsehood

when appended to its own quotation. Paradox of the Court : A law student agrees to pay his teacher after winning his first case. The

teacher then sues the student (who has not yet won a case) for payment. Russell's paradox : Does the set of all those sets that do not contain themselves contain itself?

Russell popularized it with the Barber paradox: The adult male barber who shaves all men who do not shave themselves, and no-one else.

Richard's paradox : We appear to be able to use simple English to define a decimal expansion in a way which is self-contradictory.

Vagueness Ship of Theseus (a.k.a. George Washington's or Grandfather's old axe): It seems like you can

replace any component of a ship, and it will still be the same ship. So you can replace them all, or one at a time, and it will still be the same ship. But then you can take all the original pieces, and assemble them into a ship. That, too, is the same ship you started with.

Sorites paradox : One grain of sand is not a heap. If you don't have a heap, then adding only one grain of sand won't give you a heap. Then no number of grains of sand will make a heap. Similarly, one hair can't make the difference between being bald and not being bald. But then if you remove one hair at a time, you will never become bald.

Mathematical and statistical The Monty Hall paradox: which door do you choose?

See also: Category:Mathematics paradoxes

Apportionment paradox : Some systems of apportioning representation can have unintuitive results due to rounding

o Alabama paradox : Increasing the total number of seats might shrink one block's seats. o New states paradox : Adding a new state or voting block might increase the number of

votes of another. o Population paradox : A fast growing state can lose votes to a slow growing state.

Arithmetic paradoxes : Proofs of obvious contradictions; for example, proving that 2=1 by writing a huge expression and dividing by another expression that is zero.

Arrow's paradox /Voting paradox You can't have all the attributes of an ideal voting system at once.

Benford's law : In lists of numbers from many real-life sources of data, the leading digit 1 occurs much more often than the others.

Condorcet's paradox : A group of separately rational individuals may have preferences which are irrational in the aggregate.

Elevator paradox : Elevators can seem to be mostly going in one direction, as if they were being manufactured in the middle of the building and being disassembled on the roof and basement.

Inspection paradox : Why you will wait longer for that bus than you should. Interesting number paradox : The first number that can be considered "dull" rather than

"interesting" becomes interesting because of that fact. Intransitive dice : You can have three dice, called A, B, and C, such that A is likely to win in a roll

against B, B is likely to win in a roll against C, and C is likely to win in a roll against A. Lindley's paradox : tiny errors in the null hypothesis are magnified when large data sets are

analyzed, leading to false but highly statistically significant results

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Low birth weight paradox : Low birth weight and mothers who smoke contribute to a higher mortality rate. Babies of smokers have lower average birth weight, but low birth weight babies born to smokers have a lower mortality rate than other low birth weight babies. (A special case of Simpson's paradox.)

Missing dollar paradox : Faulty logic makes it appear as if a dollar from a restaurant bill has gone missing. Not in the same class as the others.

Statistical paradox: It is quite possible to draw wrong conclusions from correlation. For example, towns with a larger number of churches generally have a higher crime rate — because both result from higher population. A professional organization once found that economists with a Ph.D. actually had a lower average salary than those with a BS — but this was found to be due to the fact that those with a Ph.D. worked in academia, where salaries are generally lower. This is also called a spurious relationship.

Will Rogers phenomenon : the mathematical concept of an average, whether defined as the mean or median, leads to apparently paradoxical results — for example, it is possible that moving an entry from an encyclopedia to a dictionary would increase the average entry length on both books.

Smallest number paradox describes how a rolling object should be able to attain a velocity of the smallest positive number.

ProbabilitySee also: Category:Probability theory paradoxes

Berkson's paradox : a complicating factor arising in statistical tests of proportions Bertrand's paradox (probability) : Different common-sense definitions of randomness give quite

different results. Birthday paradox : What is the chance that two people in a room have the same birthday? Borel's paradox : Conditional probability density functions are not invariant under coordinate

transformations. Boy or Girl : A two-child family has at least one boy. What is the probability that it has a girl? Monty Hall problem : An unintuitive consequence of conditional probability. Essentially the same

as the Three Prisoners Problem. Necktie Paradox  : A wager between two people seems to favour them both. Very similar in

essence to the Two-envelope paradox. Simpson's paradox : An association in sub-populations may be reversed in the population. It

appears that two sets of data separately support a certain hypothesis, but, when considered together, they support the opposite hypothesis.

Sleeping Beauty problem : A probability problem that can be correctly answered as one half or one third depending on how the question is approached.

Three cards problem : When pulling a random card, how do you determine the color of the underside?

Two-envelope paradox : You are given two indistinguishable envelopes and you are told one contains twice as much money as the other. You may open one envelope, examine its contents, and then, without opening the other, choose which envelope to take.

Infinity Burali-Forti paradox : If the ordinal numbers formed a set, it would be an ordinal number which is

smaller than itself. Galileo's paradox : Though most numbers are not squares, there are no more numbers than squares.

(See also Cantor, Diagonal Argument) Hilbert's paradox of the Grand Hotel : If a hotel with infinitely many rooms is full, it can still take

in more guests. Skolem's paradox : Countably infinite models of set theory contain uncountably infinite sets. Supertasks can result in paradoxes such as the Ross-Littlewood paradox and Benardete's paradox.

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Geometry and topology

The Banach–Tarski paradox: A ball can be decomposed and reassembled into two balls the same size as the original.

Banach–Tarski paradox : Cut a ball into 5 pieces, re-assemble the pieces to get two balls, both of equal size to the first.

Gabriel's Horn or Torricelli's trumpet: A simple object with finite volume but infinite surface area. Also, the Mandelbrot set and various other fractals are covered by a finite shape, but have an infinite perimeter (in fact, there are no two distinct points on the boundary of the Mandelbrot set that can be reached from one another by moving a finite distance along that boundary, which also implies that in a sense you go no further if you walk "the wrong way" around the set to reach a nearby point).

Hausdorff paradox : There exists a countable subset C of the sphere S such that S\C is equidecomposable with two copies of itself.

Coastline paradox : the perimeter of a landmass is in general ill-defined

Smale's paradox states that it is possible to turn a sphere inside out in 3-space with possible self-intersections but without creating any crease. One such construction, a Morin surface, seen from "above".

Smale's paradox : A sphere can, topologically, be turned inside out.

Missing square puzzle : Two similar figures appear to have different areas while built from the same pieces.

No Shortcuts paradox : The length of the hypotenuse in a right triangle is not shorter then the sum of the two axis-parallel legs, i.e., the direct connection between two points (which should amount to the euclidean distance) is not shorter than a path with segments that are orthogonal to each other (which amounts to the Manhattan distance). (See this reference)

Decision theoreticMain article: Decision theory

Abilene paradox : People can make decisions based not on what they actually want to do, but on what they think that other people want to do, with the result that everybody decides to do something that nobody really wants to do, but only what they thought that everybody else wanted to do.

Buridan's ass : How can a rational choice be made between two outcomes of equal value? Control paradox : Man can never be free of control, for to be free of control is to be controlled by

oneself. Morton's fork : Choosing between unpalatable alternatives. Paradox of hedonism : When one pursues happiness itself, one is miserable; but, when one pursues

something else, one achieves happiness. Newcomb's paradox : How do you play a game against an omniscient opponent? Kavka's toxin puzzle : Can one intend to drink the deadly toxin, if the intention is the only thing

needed to get the reward?

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Chemical SAR paradox : Exceptions to the principle that a small change in a molecule causes a small change

in its chemical behavior are frequently profound. The Levinthal paradox : The length of time in which a protein chain finds its folded state is many

orders of magnitude shorter than it would be if it freely searched all possible configurations.

PhysicalMain article: physical paradox

Robert Boyle's self-flowing flask fills itself in this diagram, but perpetual motion machines cannot exist (according to our current understanding of physics).

Archimedes Paradox : A massive battleship can float in a few litres of water. Bell's spaceship paradox : concerning relativity. Bell's Theorem : Measurement of quantum particles do not satisfy mathematical probability theory. Black hole information paradox : Black holes violate a commonly assumed tenet of science — that

information cannot be destroyed. Braess' paradox : Sometimes adding extra capacity to a network can reduce overall performance. Carroll's paradox : The angular momentum of a stick should be zero, but is not. D'Alembert's paradox : An inviscid liquid produces no drag. Denny's paradox : Surface-dwelling arthropods (such as the water strider) should not be able to

propel themselves horizontally. Ehrenfest paradox : On the kinematics of a rigid, rotating disk. Einstein-Podolsky-Rosen paradox : Can far away events influence each other in quantum

mechanics? Fermi paradox : If there are, as probability would suggest, many other sentient species in the

Universe, then where are they? Shouldn't their presence be obvious? Gibbs paradox : In an ideal gas, is entropy an extensive variable? The GZK paradox: High-energy cosmic rays have been observed which seem to violate the

Greisen-Zatsepin-Kuzmin limit which is a consequence of special relativity. The Irresistible force paradox: what would happen if an unstoppable force hits an immovable

object? Ladder paradox : A classic relativity problem. Loschmidt's paradox : Why is there an inevitable increase in entropy when the laws of physics are

invariant under time reversal? The time reversal symmetry of physical laws appears to allow the second law of thermodynamics to be broken.

Mpemba paradox : Hot water can under certain conditions freeze faster than cold water, even though it must pass the lower temperature on the way to freezing.

Olbers' paradox : Why is the night sky black if there is an infinity of stars? Ontological paradox : Can a time traveler send himself information with no outside source? Schrödinger's cat paradox : A quantum paradox — Is the cat alive or dead before we look? Supplee's paradox : the buoyancy of a relativistic object (such as a bullet) appears to change when

the reference frame is changed from one in which the bullet is at rest to one in which the fluid is at rest.

Twin paradox : When the traveling twin returns, he is younger and older than his sibling who stayed put.

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Philosophical Epicurean paradox : The existence of evil seems to be incompatible with the existence of an

omnipotent and caring God. Newcomb's paradox : A paradoxical game between two players, one of whom can predict the

actions of the other. Grandfather paradox : You travel back in time and kill your grandfather before he meets your

grandmother which precludes your own conception and, therefore, you couldn't go back in time and kill your grandfather.

Hutton's Paradox : If asking oneself "Am I dreaming?" in a dream proves that one is, what does it prove in waking life?

Liberal paradox : It is impossible to have both a commitment to "Minimal Liberty", and Pareto optimality.

Mere addition paradox : Does a large population barely tolerably living live better than a small happy population?

Moore's paradox : "It's raining, but I don't believe that it is." Nihilist paradox : If truth does not exist, the statement "truth does not exist" is a truth, thereby

proving itself incorrect. Omnipotence paradox : Can an omnipotent being create a rock too heavy to lift? Irresistible force paradox : Can an irresistible force move an immovable object? Paradox of hedonism : In seeking happiness, one does not find happiness. Predestination paradox : A man travels back in time to discover the cause of a famous fire. While

in the building where the fire started, he accidentally knocks over a kerosene lantern and causes a fire, the same fire that would inspire him, years later, to travel back in time. The ontological paradox is closely tied to this, in which as a result of time travel, information or objects appear to have no beginning. A classic example occurs in the film Somewhere in Time, in which a pocket watch is given to a young man by an older woman, only for the younger man to travel back in time, then give it to that same woman's younger self, who then goes on to give it to him. At no point is it ever revealed where the watch came from.

Zeno's paradoxes : "You will never reach point B from point A as you must always get half-way there, and half of the half, and half of that half, and so on..."

Future Paradox : If the future hasn't happened, it does not exist. The future cannot come, because the day in the future becomes the present.

EconomicSee also: Category:Economics paradoxes

Abilene paradox : A group of people often has to decide against each member's own personal interests or views.

Allais paradox : A change in a possible outcome which is shared by different alternatives affects people's choices among those alternatives, in contradiction with expected utility theory.

Bertrand paradox : Two players reaching a state of Nash equilibrium both find themselves with no profits.

Diamond-water paradox (or paradox of value) Neither water nor diamonds are rare, but water is cheaper than diamonds, though humans need water to survive, not diamonds.

Edgeworth paradox : With capacity constraints, there may not be an equilibrium. Ellsberg paradox : People exhibit ambiguity aversion (as distinct from risk aversion), in

contradiction with expected utility theory. Gibson's paradox : Why were interest rates and prices correlated? Giffen paradox : Increasing the price of bread makes poor people eat more of it. Jevons paradox : Increases in efficiency lead to even larger increases in demand. Leontief paradox : Some countries export labor-intensive commodities and import capital-intensive

commodities, in contradiction with Heckscher-Ohlin theory. Paradox of thrift : If everyone saves more money during times of recession, then aggregate demand

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Parrondo's paradox : It is possible to play two losing games alternately to eventually win. Productivity paradox , Solow computer paradox Worker productivity may go down, despite

technological improvements... St. Petersburg paradox : People will only offer a modest fee for a reward of infinite value.

See also Bracketing paradox Buttered cat paradox , a humorous example of a paradox from contradicting folk tales Ethics Impossible object Proof that 0.999... equals 1 Logical fallacy Puzzle

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Some paradoxes - an anthology http://www.paradoxes.co.uk/

Maintained by Geoff Wilkins - email paradoxes@geoffwilkins.net2,164,197 hits between October 2006 and August 2007

God is not all-powerful as he cannot build a wall he cannot jump

Contents  Catch-22 A paradoxical notice

Some proofs: Happiness or a ham sandwich? Proof that either Tweedledum or

Tweedledee exists Proof that Tweedledoo exists Proofs that Santa Claus exists Proof that there exists a unicorn Proof that you are either conceited or

inconsistent Proof that I am Dracula

Liars and truthtellers: Epimenides the Cretan The liar paradox Hanging or beheading Knights and knaves The visiting logician Cellini and Bellini Quine's paradox -' yields falsehood when

preceded by its quotation' Infinity:

Hilbert's hotel paradox Infinite income-tax Schrödinger's cat Time travel paradoxes (video) 1 ; 2 Olbers' paradox - why is the night sky

dark? The unexpected hanging

Prediction paradox - Newcomb's problem Hempel's ravens (the confirmation

paradox) The barber paradox "Interesting" and "uninteresting" numbers Russell's paradox of classes Berry's paradox - the least integer not

nameable in fewer than nineteen syllables Two of Zeno's paradoxes

Achilles and the tortoise Paradox of the arrow The ship of Theseus Protagoras's pupil Sorites paradox (paradox of the heap)

Escher: Drawing hands Belvedere Waterfall Mobius band Penrose triangle Freemish crate Ames room Geometrical paradox

Arithmetic and algebraic paradoxes: Proving that 2 = 1 Proving that 3 + 2 = 0 Proving that n = n + 1 Bibliography

Catch-22 There was only one catch and that was Catch-22, which specified that concern for one's own safety in the face of dangers that were real and immediate was the process of a rational mind. Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. Orr would be crazy to fly more missions and sane if he didn't, but if he was sane he had to fly them. If he flew them he was crazy and didn't have to; but if he didn't want to he was sane and had to. Joseph Heller, Catch-22

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A paradoxical notice Hughes & Brecht, p. 2

Some proofs Happiness or a ham sandwich? Which is better, eternal happiness or a ham sandwich? It would appear that eternal happiness is better, but this is really not so! After all, nothing is better than eternal happiness, and a ham sandwich is certainly better than nothing. Therefore a ham sandwich is better than eternal happiness. Smullyan (1), p. 219 Proof that either Tweedledum or Tweedledee exists

(1) TWEEDLEDUM DOES NOT EXIST (2) TWEEDLEDEE DOES NOT EXIST (3) AT LEAST ONE SENTENCE IN THIS BOX IS FALSE

Proof that Tweedledoo exists

(1) TWEEDLEDOO EXISTS (2) BOTH SENTENCES IN THIS BOX ARE FALSE

Proofs that Santa Claus exists

IF THIS SENTENCE IS TRUE THEN SANTA CLAUS EXISTS

THIS SENTENCE IS FALSE AND SANTA CLAUS DOES NOT EXIST

Proof that there exists a unicorn I wish to prove to you that there exists a unicorn. To do this it obviously suffices to prove the (possibly) stronger statement that there exists an existing unicorn. (By an existing unicorn I of course mean one that exists.) Surely if there exists an existing unicorn, then there must exist a unicorn. So all I have to do is prove that an existing unicorn exists. Well, there are exactly two possibilities: (1) An existing unicorn exists. (2) An existing unicorn does not exist. Possibility (2) is clearly contradictory: How could an existing unicorn not exist? Just as it is true that a blue unicorn is necessarily blue, an existing unicorn must necessarily be existing. Proof that you are either conceited or inconsistent A human brain is but a finite machine, therefore there are only finitely many propositions which you believe. Let us label these propositions p 1, p 2, ..., pn , where n is the number of propositions you believe. So you believe each of the propositions p 1, p 2, ..., pn . Yet, unless you are conceited, you know that you sometimes make mistakes, hence not everything you believe is true. Therefore, if you are not conceited, you know that at least one of the propositions, p 1, p 2, ..., pn is false. Yet you believe each of the propositions p 1, p 2, ..., pn .

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PLEASE IGNORE THIS NOTICE

Proof that I am Dracula (1) Everyone is afraid of Dracula. (2) Dracula is afraid of only me. Therefore I am Dracula. Doesn't that argument sound like just a silly joke? Well it isn't; it is valid. Since everyone is afraid of Dracula, then Dracula is afraid of Dracula. So Dracula is afraid of Dracula, but also is afraid of no one but me. Therefore I must be Dracula!

Smullyan (1), pp. 213-18, 224 Liars and truth-tellers The following is often given as the "liar paradox": Epimenides the Cretan Eubulides, the Megarian sixth century B.C. Greek philosopher, and successor to Euclid, invented the paradox of the liar. In this paradox, Epimenides, the Cretan, says, "All Cretans are liars." If he is telling the truth he is lying; and if he is lying, he is telling the truth.

Hughes & Brecht, p.7 This is not in fact a paradox at all. Epimenides cannot be telling the truth, but he may be lying: the truth may be that some Cretans, including Epimenides, are liars, but not all. The liar paradox The following version is the version which we will refer to as the liar paradox. Consider the statement in the following box:

THIS SENTENCE IS FALSE

Is that sentence true or false? If it is false then it is true, and if it is true then it is false... The following version of the liar paradox was first proposed by the English mathematician P E B Jourdain in 1913. It is sometimes referred to as "Jourdain's Card Paradox".

We have a card on one side of which is written:

Then you turn the card over, and on the other side is written:

(2) THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS FALSE

... Another popular version of the liar paradox is given by the following three sentences written on a card.

(1) THIS SENTENCE CONTAINS FIVE WORDS (2) THIS SENTENCE CONTAINS EIGHT WORDS (3) EXACTLY ONE SENTENCE ON THIS CARD IS TRUE

Smullyan (1), p. 227

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(1) THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS TRUE

Hanging or beheading Poaching on the hunting preserves of a powerful prince was punishable by death, but the prince further decreed that anyone caught poaching was to be given the privilege of deciding whether he should be hanged or beheaded. The culprit was permitted to make a statement - if it were false, he was to be hanged; if it were true, he was to be beheaded. One logical rogue availed himself of this dubious prerogative - to be hanged if he didn't and to be beheaded if he did - by stating: "I shall be hanged." Here was a dilemma not anticipated. For, as the poacher put it, "If you now hang me, you break the laws made by the prince, for my statement is true, and I ought to be beheaded, but if you behead me, you are also breaking the laws, for then what I said was false and I should therefore be hanged."

Kasner & Newman, pp. 187-8

1. This Book has 597 Pages. 2. The Author of this Book is Confucius. 3. The Statements Numbered 1, 2, and 3 are all False.

Kasner & Newman, p.189 Knights and knaves There is a wide variety of puzzles about an island in which certain inhabitants called "knights" always tell the truth, and others called "knaves" always lie. It is assumed that every inhabitant of the island is either a knight or a knave... Suppose A says, "Either I am a knave or else two plus two equals five." What would you conclude.? If A is a knight, then two plus two equals five, which is not true. If A is a knave, then he is speaking the truth, which is not possible. Smullyan comments: The only valid conclusion is that the author of this problem is not a knight. The fact is that neither a knight nor a knave could make such a statement. The visiting logician We are back on the Island of Knights and Knaves, where the following three propositions hold: (1) knights make only true statements; (2) knaves make only false ones; (3) every inhabitant is either a knght or a knave. These three propositions will be collectively referred to as the "rules of the island." We recall that no inhabitant can claim that he is not a knight, since no knight would make the false statement that he isn't a knight and no knave would make the true statement that he isn't a knight. Now suppose a logician visits the island and meets a native who makes the following statement to him: " You will never know that I am a knight. " Do we get a paradox? Let us see. The logician starts reasoning as follows: "Suppose he is a knave. Then his statement is false, which means that at some time I will know that he is a knight, but I can't know that he is a knight unless he really is one. So, if he is a knave, it follows that he must be a knight, which is a contradiction. Therefore he can't be a knave; he must be a knight." So far so good - there is as yet no contradiction. But then he continues reasoning: "Now I know that he is a knight, although he said that I never would. Hence his statement was false, which means that he must be a knave. Paradox!" Question. Is this a genuine paradox?

Smullyan (2), pp.67-8

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Cellini and Bellini ... whenever Cellini made a sign, he inscribed a false statement on it, and whenever Bellini made a sign, he inscribed a true statement on it. Also, we shall assume that Cellini and Bellini were the only sign-makers of their time... You come across the following sign:

THIS SIGN WAS MADE BY CELLINI

Who made the sign? If Cellini made it, then he wrote a true sentence on it - which is impossible. If Bellini made it, then the sentence on it is false - which is again impossible. So who made it? Now, you can't get out of this one by saying that the sentence on the sign is not well-grounded! It certainly is well-grounded; it states the historical fact that the sign was made by Cellini; if it was made by Cellini then the sign is true, and if it wasn't, the sign is false. So what is the solution? The solution, of course, is that I gave you contradictory information. If you actually came across the above sign, then it would mean either that Cellini sometimes wrote true inscriptions on signs (contrary to what I told you) or that at least one other sign-maker sometimes wrote false statements on signs (again, contrary to what I told you). So this is not really a paradox, but a swindle.

Smullyan (1), pp. 230-31Quine's paradox "yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation.Can you see why this is a paradox?Infinity Hilbert's hotel paradox Imagine a hotel with a finite number of rooms, and assume that all the rooms are occupied. A new guest arrives and asks for a room. "Sorry" - says the proprietor - "but all the rooms are occupied." Now let us imagine a hotel with an infinite number of rooms, and all the rooms are occupied. To this hotel, too, comes a new guest and asks for a room. "But of course!" - exclaims the proprietor, and he moves the person previously occupying room N1 into room N2, the person from room N2 into room N3, the person from room N3 into room N4, and so on... And the new customer receives room N1, which becomes free as a result of these transpositions. Let us imagine now a hotel with an infinite number of rooms, all taken up, and an infinite number of new guests who come in, and ask for rooms. "Certainly, gentlemen," says the proprietor, "just wait a minute." He moves the occupant of N1 into N2, the occupant of N2 into N4, the occupant of N3 into N6, and so on, and so on... Now all odd numbered rooms become free and the infinity of new guests can easily be accommodated in them.

Gamow, p. 17 The proprietor's "just wait a minute" seems optimistic; it would surely take him an infinite time to shift the guests around. Infinite income-tax Now if a man had an unlimited income, it is an immediate inference that, however low income-tax may be, he would have to pay annually to the Exchequer of his nation a sum equal in value to his whole income. Further, if his income was derived from a capital invested at a finite rate of interest (as is usual), the annual payments of income-tax would each be equal in value to the man's whole capital. If, then, the man with an unlimited income chose to be discontented, he would be sure of a sympathetic audience among philosophers and business acquaintances; but discontent could not last long, for the thought of the difficulties he would put in the way of the Chancellor of the Exchequer, who would find the drawing up of his budget most puzzling, would be amusing. Again, the discovery that, after paying an infinite

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income-tax, the income would be quite undiminished, would obviously afford satisfaction, though perhaps the satisfaction might be mixed with a slight uneasiness as to any action the Commissioners of Income Tax might take in view of this fact.

Jourdain, pp. 66-7 Schrödinger's cat In the world of quantum mechanics, the laws of physics that are familiar from the everyday world no longer work. Instead, events are governed by probabilities. A radioactive atom, for example, might decay, emitting an electron, or it might not. It is possible to set up an experiment in such a way that there is a precise fifty-fifty chance that one of the atoms in a lump of radioactive material will decay in a certain time and that a detector will register the decay if it does happen. Schrödinger, as upset as Einstein about the implications of quantum theory, tried to show the absurdity of these implications by imagining such an experiment set up in a closed room, or box, which also contains a live cat and a phial of poison, so arranged that if the radioactive decay does occur then the poison container is broken and the cat dies. In the everyday world, there is a fifty-fifty chance that the cat will be killed, and without looking inside the box we can say, quite happily, that the cat inside is either dead or alive. But now we encounter the strangeness of the quantum world. According to the theory, neither of the two possibilities open to the radioactive material, and therefore to the cat, has any reality unless it is observed. The atomic decay has neither happened nor not happened, the cat has neither been killed nor not killed, until we look inside the box. Theorists who accept the pure version of quantum mechanics say that the cat exists in some indeterminate state, neither dead nor alive, until an observer looks into the box to see how things are getting on. Nothing is real unless it is observed.

Gribbin, pp. 2-3 Olbers' paradox - why is the night sky dark?... the apparent paradox, stated in 1826 and now explained by postulating a finite expanding universe, that the sky is dark at night although, as there are an infinite number of stars, it should be uniformly bright.

The Chambers Dictonary 10th edition, 2006 The unexpected hanging [A man condemned to be hanged] was sentenced on Saturday. "The hanging will take place at noon," said the judge to the prisoner, "on one of the seven days of next week. But you will not know which day it is until you are so informed on the morning of the day of the hanging." The judge was known to be a man who always kept his word. The prisoner, accompanied by his lawyer, went back to his cell. As soon as the two men were alone, the lawyer broke into a grin. "Don't you see?" he exclaimed. "The judge's sentence cannot possibly be carried out." "I don't see," said the prisoner. "Let me explain They obviously can't hang you next Saturday. Saturday is the last day of the week. On Friday afternoon you would still be alive and you would know with absolute certainty that the hanging would be on Saturday. You would know this before you were told so on Saturday morning. That would violate the judge's decree." "True," said the prisoner. "Saturday, then is positively ruled out," continued the lawyer. "This leaves Friday as the last day they can hang you. But they can't hang you on Friday because by Thursday only two days would remain: Friday and Saturday. Since Saturday is not a possible day, the hanging would have to be on Friday. Your knowledge of that fact would violate the judge's decree again. So Friday is out. This leaves Thursday as the last possible day. But Thursday is out because if you're alive Wednesday afternoon, you'll know that Thursday is to be the day." "I get it," said the prisoner, who was beginning to feel much better. "In exactly the same way I can rule out Wednesday, Tuesday and Monday. That leaves only tomorrow. But they can't hang me tomorrow because I know it today!"

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... He is convinced, by what appears to be unimpeachable logic, that he cannot be hanged without contradicting the conditions specified in his sentence. Then on Thursday morning, to his great surprise, the hangman arrives. Clearly he did not expect him. What is more surprising, the judge's decree is now seen to be perfectly correctly. The sentence can be carried out exactly as stated.

Gardner (3), pp. 11-13 Here is a version from Raymond Smullyan, with his solution: On a Monday morning, a professor says to his class, "I will give you a surprise examination someday this week. It may be today, tomorrow, Wednesday, Thursday, or Friday at the latest. On the morning of the examination, when you come to class, you will not know that this is the day of the examination." Well, a logic student reasoned as follows: "Obviously I can't get the exam on the last day, Friday, because if I haven't gotten the exam by the end of Thursday's class, then on Friday morning I'll know that this is the day, and the exam won't be a surprise. This rules out Friday, so I now know that Thursday is the last possible day. And, if I don't get the exam by the end of Wednesday, then I'll know on Thursday morning that this must be the day (because I have already ruled out Friday), hence it won't be a surprise. So Thursday is also ruled out." The student then ruled out Wednesday by the same argument, then Tuesday, and finally Monday, the day on which the professor was speaking. He concluded: "Therefore I cannot get the exam at all; the professor cannot possibly fulfil his statement." Just then, the professor said: "Now I will give you your exam." The student was most surprised! ... Let me put myself in the student's place. I claim that I could get a surprise examination on any day, even on Friday! Here is my reasoning: Suppose Friday morning comes and I haven't got the exam yet. What would I then believe? Assuming I believed the professor in the first place (and this assumption is necessary for the problem), could I consistently continue to believe the professor on Friday morning if I hadn't gotten the exam yet? I don't see how I could. I could certainly believe that I would get the exam today (Frida?), but I couldn't believe that I'd get a surprise exam today. Therefore, how could I trust the professor's accuracy? Having doubts about the professor, I wouldn't know what to believe. Anything could happen as far as I'm concerned, and so it might well be that I could be surprised by getting the exam on Friday. Actually, the professor said two things: (1) You will get an exam someday this week; (2) You won't know on the morning of the exam that this is the day. I believe it is important that these two statements should be separated. It could be that the professor was right in the first statement and wrong in the second. On Friday morning, I couldn't consistently believe that the professor was right about both statements, but I could consistently believe his first statement. However, if I do, then his second statement is wrong (since I will then believe that I will get the exam today.) On the other hand, if I doubt the professor's first statement, then I won't know whether or not I'll get the exam today, which means that the professor's second statement is fulfilled (assuming he keeps his word and gives me the exam). So the surprising thing is that the professor's second statement is true or false depending respectively on whether I do not or do believe his first statement. Thus the one and only way the professor can be right is if I have doubts about him; if I doubt him, that makes him right, whereas if I fully trust him, that makes him wrong!

Smullyan (2), pp. 8-9 Prediction paradox (Newcomb's problem)Two closed boxes, Bl and B2, are on a table. Bl contains $1,000. B2 contains either nothing or $1 million. You do not know which. You have an irrevocable choice between two actions:1. Take what is in both boxes. 2. Take only what is in B2. At some time before the test a superior Being has made a prediction about what you will decide. It is not necessary to assume determinism. You only need be persuaded that the Being's predictions are "almost certainly" correct. If you like, you can think of the Being as God, but the paradox is just as strong if you regard the Being as a superior intelligence from another planet or a supercomputer capable of probing your brain and making highly accurate predictions about your decisions. If the Being expects you to

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choose both boxes, he has left B2 empty. If he expects you to take only B2, he has put $1 million in it. (If he expects you to randomize your choice by, say, flipping a coin, he has left B2 empty.) In all cases Bl contains $1,000. You understand the situation fully, the Being knows you understand, you know that he knows, and so on. What should you do? Clearly it is not to your advantage to flip a coin, so that you must decide on your own. The paradox lies in the disturbing fact that a strong argument can be made for either decision. Both arguments cannot be right. The problem is to explain why one is wrong.Let us look first at the argument for taking only B2. You believe the Being is an excellent predictor. If you take both boxes, the Being almost certainly will have anticipated your action and have left B2 empty. You will get only the $1,000 in Bl. On the other hand, if you take only B2, the Being, expecting that, almost certainly will have placed $1 million in it. Clearly it is to your advantage to take only B2. Convincing? Yes, but the Being made his prediction, say a week ago and then left. Either he put the $1 million in B2, or he did not. "If the money is already there, it will stay there whatever you choose. It is not going to disappear. If it is not already there, it is not going to suddenly appear if you choose only what is in the second box." It is assumed that no "backward causality" is operating; that is, your present actions cannot influence what the Being did last week. So why not take both boxes and get everything that is there? If B2 is filled, you get $1,001,000. If it is empty, you get at least $1,000. If you are so foolish as to take only B2, you know you cannot get more than $1 million, and there is even a slight possibility of getting nothing. Clearly it is to your advantage to take both boxes!"I have put this problem to a large number of people, both friends and students in class," writes Nozick. "To almost everyone it is perfectly clear and obvious what should be done. The difficulty is that people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly."

Gardner (3), pp. 582-3Hempel's ravens (the confirmation paradox)While taking a group of benefactors on a tour through the new aviary they had just helped to build, a noted ornithologist commented, "And here we have two of the finest examples of ravens that I have ever seen. Notice the lustrous black plumage for which all ravens are famous." The ornithologist continued his lecture, commenting on the corvine feeding and nesting habits as well as on the birds' legendary role as harbingers of ill fortune.When the ornithologist had finished, a young man said, "Sir, excuse me, but did you say that 'All ravens are black'?" "I don't know if I said exactly that, but it's true. All ravens are black." "But, how do you know that - for certain, I mean?" asked the young man."Well, I've seen a few hundred ravens in my day and every one of them has been black.""Yes, but a few hundred are not all. How many ravens are there, anyway?" "I would guess several million. As for your question, many other scientists, and non-scientists for that matter, have observed ravens over thousands of years and so far the birds have all been black. At least, I don't know of a single instance in which someone has produced a non-black raven." "That's true, but it's still not all - just most." "True, but there is other evidence. For example, take all these lovely multicolored birds we have seen today - the parrots, toucans, the peacocks -" "They're lovely, but what do they have to do with your claim that all ravens are black?" "Don't you see?" asked the ornithologist. "No, I don't see. Please explain." "Well, you accept the idea that every new instance of another black raven that is observed adds to the support of the generalization that all ravens are black?" "Yes, of course."

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"Well then, the statement 'All ravens are black' is logically equivalent to the statement 'All non-black things are non-ravens.' This being so and because whatever confirms a statement also confirms any logically equivalent statement, it's clear that any non-black non-raven supports the generalization 'All ravens are black.' Hence, all these colorful, non-black non-ravens also support the generalization." "That's ridiculous," chided the young man. "In that case you might as well say that your blue jacket and gray pants also confirm the statement 'All ravens are black.' After all, they're also non-black non-ravens." "That's correct," said the ornithologist. "Now you're beginning to think like a true scientist." Who is reasoning correctly, the ornithologist or the young man?

Falleta, pp. 126-73. Sets and subsets The barber paradox In a certain village there is a man, so the paradox runs, who is a barber; this barber shaves all and only those men in the village who do not shave themselves. Query: Does the barber shave himself? Any man in this village is shaved by the barber if and only if he is not shaved by himself. Therefore in particular the barber shaves himself if and only if he does not. We are in trouble if we say the barber shaves himself and we are in trouble if we say he does not.

Quine, p.4 Quine disarms the paradox thus: What are we to say to the argument that goes to prove this unacceptable conclusion? Happily it rests on assumptions. We are asked to swallow a story about a village and a man in it who shaves all and only those men in the village who do not shave themselves. This is the source of our trouble; grant this and we end up saying, absurdly, that the barber shaves himself only if he does not. The proper conclusion to draw is just that there is no such barber. We are confronted with nothing more than what logicians have been referring to for a couple of thousand years as a reductio ad absurdum . We disprove the barber by assuming him and deducing the absurdity that he shaves himself if and only if he does not. The paradox is simply a proof that no village can contain a man who shaves all and only those men in it who do not shave themselves. Another "swindle", like Cellini and Bellini above? "Interesting" and "uninteresting" numbers The question arises: Are there any uninteresting numbers? We can prove that there are none by the following simple steps. If there are dull numbers, then we can divide all numbers into two sets - interesting and dull. In the set of dull numbers there will be only one number that is the smallest. Since it is the smallest uninteresting number it becomes, ipso facto , an interesting number. We must therefore remove it from the dull set and place it in the other. But now there will be another smallest uninteresting number. Repeating this process will make any dull number interesting.

Gardner (1), p. 131 Russell's paradox of classes Most sets, it would seem, are not members of themselves - for example, the set of walruses is not a walrus, the set containing only Joan of Arc is not Joan of Arc (a set is not a person) - and so on. In this respect, most sets are rather "run-of-the-mill". However, some "self-swallowing" sets do contain themselves as members, such as the set of all sets, or the set of all things except Joan of Arc, and so on. Clearly, every set is either run-of-the-mill or self-swallowing, and no set can be both. Now nothing prevents us from inventing R: the set of all run-of-the-mill sets . At first, R might seem rather a run-of-the-mill invention - but that opinion must be revised when you ask yourself, "Is R itself a run-of-the-mill set or a self-swallowing set?" You will find that the answer is: "R is neither run-of-the-mill nor self-swallowing, for either choice leads to paradox."

Hofstadter, p. 20

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Berry's paradox - the least integer not nameable in fewer than nineteen syllables (Devised by G G Berry of the Bodleian Library) The number of syllables in the English names of finite integers tend to increase as the integers grow larger, and must gradually increase indefinitely, since only a finite number of names can be made with a given finite number of syllables. Hence the names of some integers must consist of at least nineteen syllables, and among them there must be a least. Hence "the least integer not nameable in fewer than nineteen syllables" must denote a definite integer; in fact, it denotes 111,777. But "the least integer not nameable in fewer than nineteen syllables" is itself a name consisting of eighteen syllables; hence the least integer not nameable in fewer than nineteen syllables can be named in eighteen syllables.

Russell & Whitehead, p. 61 Two of Zeno's paradoxesAchilles and the tortoiseZeno's second paradox of motion, of Achilles and the tortoise, is probably the best known of his four paradoxes of motion. In this problem, the fleet Greek warrior runs a race against a slow-moving tortoise. Assume Achilles runs at ten times the speed of the tortoise (1 meter per second to 0.1 meter per second). The tortoise is given a 100-meter handicap in a race that is 1,000 meters. By the time Achilles reaches the tortoise's starting point T0, the tortoise will have moved on to point T1. Soon, Achilles will reach point T1, but by then the tortoise would have moved on to T2, and so on, ad infinitum. Every time Achilles reaches a point where the tortoise has just been, the tortoise has moved on a bit. Although the distances between the two runners will diminish rapidly, Achilles can never catch up with the tortoise, or so it would seem.

Falletta, pp.190-91Bertrand Russell commented: This argument... shows that, if Achilles ever overtakes the tortoise, it must be after an infinite number of instants have elapsed since he started. This is in fact true; but the view that an infinite number of instants makes up an infinitely long time is not true, and therefore the conclusion that Achilles will never overtake the tortoise does not follow.

RussellParadox of the arrowIn the paradox of the arrow, Zeno asks us to consider an arrow in flight and argues that, in fact, the arrow must always be at rest. At each instant the arrow occupies a space equal to itself. Movement is impossible, because an instant by definition has no parts. If the arrow were capable of moving during an instant, we would contradict the definition of an instant, for the arrow would be in one position during the first part of the instant and in another position in the other part of the instant. Thus, the arrow never seems to be moving but rather, as Russell notes in his essay on infinity, "in some miraculous way the change of position has to occur between the instants, that is to say, not at any time whatever." If the arrow does not move at any given instant, how then does it make its flight?

Falleta, p.192The ship of TheseusThe ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.

Plutarch, Vita Thesei, 22-23

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Protagoras's pupilAnother paradox which has its foundation - real or legendary - in antiquity concerns the sophist Protagoras, who lived and taught in the fifth century BC. It is said that Protagoras made an arrangement with one of his pupils whereby the pupil was to pay for his instruction after he had won his first case. The young man completed his course, hung up the traditional shingle, and waited for clients. None appeared. Protagoras grew impatient and decided to sue his former pupil for the amount owed him.'For,' argued Protagoras, 'either I win this suit, or you win it. If I win, you pay me according to the judgement of the court. If you win, you pay me according to our agreement. In either case I am bound to be paid.''Not so,' replied the young man. 'If I win, then by the judgement of the court I need not pay you. If you win, then by our agreement I need not pay you. In either case I am bound not to have to pay you.'Whose argument was right? Who knows?

Northrop, p.188Sorites paradox (paradox of the heap)Suppose you have a heap of sand. If you take away one grain of sand, what remains is still a heap: removing a single grain cannot turn a heap into something that is not a heap. If two collections of grains of sand differ in number by just one grain, then both or neither are heaps. This apparently obvious and uncontroversial supposition appears to lead to the paradoxical conclusion that all collections of grains of sand, even one-membered collections, are heaps.

Sainsbury, p.23

M C Escher

Drawing hands

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Belvedere

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WaterfallMobius band

A Mobius band has just one side and just one edge. Penrose triangle

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Freemish crate

Ames room

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Geometrical paradox

 Arithmetic and algebraic paradoxes Proving that 2 = 1Here is the version offered by Augustus De Morgan: Let x = 1. Then x² = x. So x² - 1 = x -1. Dividing both sides by x -1, we conclude that x + 1 = 1; that is, since x = 1, 2 = 1.

Quine, p.5Assume thata = b.    (1)Multiplying both sides by a,a² = ab.     (2)Subtracting b² from both sides,a² - b² = ab - b² .    (3)Factorizing both sides,(a + b)(a - b) = b(a - b).    (4)Dividing both sides by (a - b),a + b = b.    (5)If now we take a = b = 1, we conclude that 2 = 1. Or we can subtract b from both sides and conclude that a, which can be taken as any number, must be equal to zero. Or we can substitute b for a and conclude

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that any number is double itself. Our result can thus be interpreted in a number of ways, all equally ridiculous.

Northrop, p. 85The paradox arises from a disguised breach of the arithmetical prohibition on division by zero, occurring at (5): since a = b, dividing both sides by (a - b) is dividing by zero, which renders the equation meaningless. As Northrop goes on to show, the same trick can be used to prove, e.g., that any two unequal numbers are equal, or that all positive whole numbers are equal.Here is another example:Proving that 3 + 2 = 0Assume A + B = C, and assume A = 3 and B = 2.Multiply both sides of the equation A + B = C by (A + B).We obtain A² + 2AB + B² = C(A + B)Rearranging the terms we haveA² + AB - AC = - AB - B² + BCFactoring out (A + B - C), we haveA(A + B - C) = - B(A + B - C)Dividing both sides by (A + B - C), that is, dividing by zero, we get A = - B, or A + B = 0, which is evidently absurd.

Kasner & Newman, p. 183Proving that n = n + 1(a)   (n + 1)² = n² + 2n + 1(b)   (n + 1)² - (2n + 1) = n² (c)   Subtracting n(2n + 1) from both sides and factoring, we have(d)   (n + 1)² - (n + 1)(2n + 1) = n² - n(2n +1)(e)   Adding ¼(2n + 1)² to both sides of (d) yields(n + 1)² - (n + 1)(2n + 1) + ¼(2n + 1)² = n² - n(2n + 1) + ¼(2n + 1)² This may be written:(f)   [(n + 1) - ½(2n + 1)]² = [(n - ½(2n + 1)]² Taking square roots of both sides,(g)   n + 1 - ½(2n + 1) = n - ½(2n + 1)and, therefore,(h)   n = n + 1

Kasner & Newman, p. 184The trick here is to ignore the fact that there are two square roots for any positive number, one positive and one negative: the square roots of 4 are 2 and -2, which can be written as ±2. So (g) should properly read:±(n + 1 - ½(2n + 1)) = ±(n - ½(2n + 1)) 

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Bibliography Falletta: Nicholas L Falletta, The Paradoxicon , 1983Gamow: George Gamow, One, Two, Three...Infinity , 1967 Gardner (1): Martin Gardner, Mathematical Puzzles and Diversions , 1959 Gardner (2): Martin Gardner, Further Mathematical Puzzles and Diversions , 1969 Gardner (3): Martin Gardner, The Colossal Book of Mathematics , 2001. Gribbin: John Gribbin, In Search of Schrödinger's Cat , 1984 Hofstadter: Douglas R Hofstadter, Godel, Escher, Bach: An Eternal Golden Braid, 1979 Hughes & Brecht: Patrick Hughes and George Brecht, Vicious Circles and Infinity: an anthology of paradoxes , 1975 Jourdain: P E B Jourdain, The Philosophy of Mr B*rtr*nd R*ss*ll, 1918. Kasner & Newman: Edward Kasner and James Newman, Mathematics and the Imagination , 1940 Morris: Ivan Morris, The Ivan Morris Puzzle Book , 1972 Norththrop: Eugene P Northrop, Riddles in Mathematics , revised edition, 1961 Quine: W V Quine, The Ways of Paradox and Other Essays , revised edition, 1976 Russell: Bertrand Russell, "The Problem of Infinity Considered Historically", in Zeno's Paradoxes , edited by Wesley C Salmon, 1970Russell & Whitehead: Bertrand Russell and A N Whitehead, Principia Mathematica , 1910 Sainsbury: R M Sainsbury, Paradoxes , 2nd edition, 1995 Smullyan (1): Raymond Smullyan, What is the Name of This Book? 1978 Smullyan (2): Raymond Smullyan, Forever Undecided: A Puzzle Guide to Gödel , 1987

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Zeno's paradoxes “Achilles and the Tortoise” redirects here. For other uses, see Achilles and the Tortoise (disambiguation).“Arrow paradox” redirects here. For other uses, see Arrow paradox (disambiguation).Zeno's paradoxes are a set of problems devised by Zeno of Elea to support Parmenides' doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. It is usually assumed that Zeno took on the project of creating these paradoxes because other philosophers had created paradoxes against Parmenides' view. Thus Zeno can be interpreted as saying that to assume there is plurality is even more absurd than assuming there is only one. As such, if we are convinced by Zeno's paradoxes, we should take Parmenides' view more seriously.[1]

Several of Zeno's eight surviving paradoxes (preserved in Aristotle's Physics and Simplicius's commentary thereon) are essentially equivalent to one another; and most of them were regarded, even in ancient times, as very easy to refute. Three of the strongest and most famous—that of Achilles and the tortoise, the dichotomy argument, and that of an arrow in flight—are given here.Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum, also known as proof by contradiction. They are also credited as a source of the dialectic method used by Socrates.According to some historians of philosophy, Zeno's paradoxes were a major problem for ancient and medieval philosophers.In modern times, calculus has been widely accepted by mathematicians and engineers as at least a practical solution for calculating infinitesimal distances. Other proposed solutions to Zeno's paradoxes from past and present philosophers have included the denial that space and time are themselves infinitely divisible, and the denial that the terms space and time refer to any entity with any innate properties at all.Many philosophers still hesitate to say that all paradoxes are completely solved. Some philosophers state that these paradoxes still have modern relevance: attempts to deal with the paradoxes have resulted in intellectual discoveries, and variations on the paradoxes (see Thomson's lamp) continue to produce at least temporary puzzlement in discovering what, if anything, is wrong with the argument.The origins of the paradoxes are somewhat unclear. Diogenes Laertius says that Zeno's teacher, Parmenides, was "the first to use the argument known as 'Achilles and the Tortoise' ", and attributes this assertion to Favorinus. In a later statement, Laertius attributed the paradoxes to Zeno.

Contents1 Paradoxes of motion

1.1 Achilles and the tortoise 1.2 The dichotomy paradox 1.3 The arrow paradox

2 Proposed solutions 2.1 Proposed solutions to the arrow paradox 2.2 Proposed solutions both to Achilles and the tortoise, and to the dichotomy

2.2.1 Proposed solution using mathematical series notation 2.2.2 Proposed solution using calculus notation 2.2.3 Issues with the proposed calculus-based solution 2.2.4 Issues with the issues with the proposed calculus-based solution

2.3 Are space and time infinitely divisible? 2.4 Does motion involve a sequence of points? 2.5 Conceptual and semantical approaches 2.6 The notion of different orders of infinity

3 Status of the paradoxes today 4 Two other paradoxes as given by Aristotle

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5 Similar paradoxes presented during the Warring States Period 6 The quantum Zeno effect 7 See also 8 Zeno's paradoxes in fiction 9 Zeno's paradoxes in art 10 Zeno's paradoxes in popular culture 11 Notes 12 References 13 External links

Paradoxes of motion

Achilles and the tortoise"You can never catch up."“In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead”

—Aristotle, Physics VI:9, 239b15In the paradox of Achilles and the Tortoise, we imagine the Greek hero Achilles in a footrace with the plodding reptile. Because he is such a fast runner, Achilles graciously allows the tortoise a head start of a hundred feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run a hundred feet, bringing him to the tortoise's starting point; during this time, the tortoise has "run" a (much shorter) distance, say one foot. It will then take Achilles some further period of time to run that distance, in which said period the tortoise will advance farther; and then another period of time to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, Zeno says, swift Achilles can never overtake the tortoise. Thus, while common sense and common experience would hold that one runner can catch another, according to the above argument, he cannot; this is the paradox.

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The dichotomy paradox"You cannot even start."“That which is in locomotion must arrive at the half-way stage before it arrives at the goal.”

—Aristotle, Physics VI:9, 239b10Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.

The resulting sequence can be represented as:

This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility.This sequence also presents a second problem in that it contains no first distance to run, for any possible (finite) first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even begin. The paradoxical conclusion then would be that travel over any finite distance can neither be completed nor begun, and so all motion must be an illusion.This argument is called the Dichotomy because it involves repeatedly splitting a distance into two parts. It contains some of the same elements as the Achilles and the Tortoise paradox, but with a more apparent conclusion of motionlessness. It is also known as the Race Course paradox. Some, like Aristotle, regard the Dichotomy as really just another version of Achilles and the Tortoise. However, they emphasise different points. In the Achilles and the Tortoise, the focus is that movement by multiple objects is just an illusion whereas in the Dichotomy the focus is that movement is actually impossible.The arrow paradox"You cannot even move."“If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.”

—Aristotle, Physics VI:9, 239b5In the arrow paradox, Zeno asks us to imagine an arrow in flight. He then asks us to divide up time into a series of indivisible nows or moments. At any given moment if we look at the arrow it has an exact location so it is not moving. Yet movement has to happen in the present; it can't be that there's no movement in the present yet movement in the past or future. So throughout all time, the arrow is at rest. Thus motion cannot happen.This paradox is also known as the fletcher's paradox—a fletcher being a maker of arrows.Whereas the first two paradoxes presented divide space into segments, this paradox divides time into points.

Proposed solutionsProposed solutions to the arrow paradoxAristotle, who recorded Zeno's arguments in his work Physics, disputes Zeno's reasoning. Aristotle denies that time is composed of "nows", as implied by Zeno's argument. If there is just a collection of "nows", then there is no such thing as temporal magnitude. Therefore, if Aristotle is correct in denying that time is

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composed of indivisible "nows", then Zeno is wrong in saying that the arrow was stationary throughout its flight despite saying that in each "now" the moving arrow is at rest.According to Zeno, at any instant, the arrow must be at rest. However, this has been disputed, since being at rest is a relative term. One cannot judge, from observing any one instant, that the arrow is at rest. Rather, one requires other, adjacent instants to assert whether, compared to other instants, the arrow at one instant is at rest. Thus, compared to other instants, if the arrow is found to be at a different place than it was and will be at the times before and after, then we have reason to claim the arrow has moved.A mathematical account would be as follows: in the limit, as the length of a moment approaches zero, the instantaneous rate of change or velocity (which is the quotient of distance over length of the moment) does not have to approach zero. This nonzero limit is the velocity of the arrow at the instant.Proposed solutions both to Achilles and the tortoise, and to the dichotomyBoth the paradoxes of Achilles and the tortoise and that of the dichotomy depend on dividing distances into a sequence of distances that become progressively smaller, and so are subject to the same counter-arguments.Aristotle pointed out that as the distance decreases, the time needed to cover those distances also decreases, so that the time needed also becomes increasingly small. Such an approach to solving the paradoxes would amount to a denial that it must take an infinite amount of time to traverse an infinite sequence of distances.Before 212 BCE, Archimedes had developed a method to derive a finite answer for the sum of infinitely many terms that get progressively smaller. Theorems have been developed in more modern calculus to achieve the same result, but with a more rigorous proof of the method. These methods allow construction of solutions stating that (under suitable conditions) if the distances are always decreasing, the time is finite.

Proposed solution using mathematical series notationSeveral proposed solutions have at their core geometric series. A general geometric series can be written as

which is convergent and equal to a/(1−x) provided that |x| < 1 (otherwise the series diverges).Although these proposed solutions effectively involve dividing up the distance to be travelled into smaller and smaller pieces, it is easier to conceive of the solution as Aristotle did, by considering the time it takes Achilles to catch up to the tortoise.In the case of Achilles and the tortoise, suppose that the tortoise runs at a constant speed of v metres per second (m/s) and gets a head start of distance d metres (m), and that Achilles runs at constant speed xv m/s with x > 1. It takes Achilles time d/xv seconds (s) to travel distance d and reach the point where the tortoise started, at which time the tortoise has travelled d/x m. It then takes further time d/x²v sec for Achilles to travel this new distance d/x m, at which time the tortoise has travelled another d/x², and so on.Thus, the time taken for Achilles to catch up is

seconds. Since this is a finite quantity, Achilles will eventually catch the tortoise.Similarly, for the Dichotomy assume that each of Homer's steps takes a time proportional to the distance covered by that step. Suppose that it takes time h seconds for Homer to complete the last half of the distance to the bus; then it will have taken h/2 sec for him to complete the second-last step, traversing the distance between one quarter and half of the way. The third-last step, covering the distance between one eighth and one quarter of the way to the bus, will take h/4 sec, and so on. The total time taken by Homer is, summing from k = 0 for the last step,

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seconds. Once again, this is a convergent sum: although Homer must pass through an infinite number of distance segments, most of these are infinitesimally short and the total time required is finite. So (provided it doesn't leave for 2h seconds) Homer will catch his bus.In both cases, by moving at constant speeds (and in particular not stopping after each segment) Achilles will eventually catch the moving tortoise, and Homer the stationary bus. However, the solutions that employ geometric series have the advantage that they attempt to solve the paradoxes in their own terms, by denying the apparently paradoxical conclusions.We now give a concrete example. Suppose the tortoise starts 10 meter in advance of Achilles, and moves at 1 meter per second, while Achilles moves at 10 meters per second. Then after 1 second Achilles will reach the tortoise's earlier location, and the tortoise will be 1 meter ahead of him. After 0.1 seconds Achilles will reach this location, but the tortoise will be 0.1 meter ahead of him. After 0.01 seconds Achilles will reach this location, but the tortoise will be 0.01 meter ahead of him. It seems as if Achilles will never reach the tortoise. However even though there is infinite numbers of "steps" Achilles will have to go through, it will take him a finite amount of time to do that: The number of seconds is 1+0.1+0.01+0.001+0.0001+... = 10/9 seconds. Also, Achilles will pass the tortoise 10/9 meter past the tortoise's starting point.

Proposed solution using calculus notationZeno's paradoxes are addressed by calculus, in particular by the mathematical concept of limit, which gives a theoretical framework to deal with the problems brought up by Zeno.

d = distance between runners t = time

Issues with the proposed calculus-based solutionA suggested problem with using calculus and mathematical series to try to solve Zeno's paradoxes is that these solutions miss the point. To be precise, while these kinds of solutions specify the limit point of infinite series, they do not explain how such a series can actually ever be completed and the limit point be reached. Thus, calculus and mathematical series can be used to predict where and when Achilles will overtake the tortoise, assuming that the infinite sequence of events as laid out in the argument ever comes to an end. However, the problem lies exactly with that assumption, as Zeno's paradox points out that in order for Achilles to catch up with the Tortoise, an infinite number of physical events need to take place, which seems to be impossible in and of itself, independent of how much time such an act would require if it could actually be done.Indeed, the problem with the calculus and other series-based solutions is that these kinds of solutions beg the question. They assume that one can finish a limiting process, but this is exactly what Zeno questioned. To be precise, Zeno *started* with the assumption that a finite interval can be split into infinitely many parts, and then argued that it is impossible to move through such a landscape. For calculus and other series-based solutions to make the point that the sum of infinitely many terms can add up to a finite amount therefore merely confirms Zeno's assumption about the landscape (geometry) of space, but does nothing to answer Zeno's question of how we can actually (dynamically) move through such a space.Put a different way, when these kinds of solutions tell us that Achilles passes the tortoise 10/9 meter after the tortoise's starting point, they assume that Achilles can actually reach that point, but Zeno questioned that Achilles can actually ever get to that point. Similarly, when we are told that Achilles passes the tortoise 10/9 seconds into the race, it is assumed that time can actually flow to that point, but once again we get the same problem: If there are an infinite number of time points between t = 0 and t = 10/9, how can t = 10/9 ever be reached? How, indeed, can time flow at all if it is assumed that between any two time points there are infinitely many other time points that, at least under our naive conception of time, have to

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occur one after the other? Thus, all these kinds of solutions presuppose that Zeno's difficulties have already been solved when trying to resolve the paradox. Which is to say, they beg the question and therefore don't resolve anything at all.An unfortunate complication among these kinds of discussions is that many treatments of Zeno's paradox present Zeno's reasoning in such a way that calculus and series-based solutions really do work as objections to that reasoning. To be precise, Zeno's reasoning is often presented as arguing that because there are an infinite number of tasks to be done, it will take an infinite amount of time to complete all these tasks, and the calculus and mathematical series based solutions are now perfectly correct in objecting to that argument by pointing out that the sum of an infinite number of time intervals can add up to a finite amount of time. However, such a presentation of Zeno's argument makes the argument into a straw man: a weak (and indeed invalid) caricature of the much stronger and much simpler argument that does not at all consider any quantifications of time. This much simpler argument simply states that for Achilles to capture the tortoise an infinite series of physical events need to be completed, which is logically impossible. The calculus and mathematical series based solutions offer no insight into this much simpler, much more stinging, paradox.[2]The following thought experiment can be used to illustrate the fact that time is irrelevant to the paradox. Imagine that Achilles notes the position occupied by the tortoise, and calls it first; after reaching that position, he once again notes the position the turtle has moved to, calling it second, and so on. If he catches up with the turtle at all, then apparently Achilles must have stopped counting, and we could ask Achilles what the greatest number he counted to was. But of course this is nonsense: there is no greatest number, and Achilles can never stop counting. So, Achilles can't catch up with the Tortoise, whether he has finite time or infinite time to do so.The situation, then, is this. Any proper variant of Zeno's paradox, such as the above thought experiment, provides a mathematical and logical account of the physical process of movement through space (or time), and argues that it is impossible for Achilles to win (or move at all). So, in order for this paradox to be resolved, one needs to either show something wrong with the math or logic (which calculus and series-based solutions do for the improper variant, but not for the proper variant), or show why this mathematical analysis cannot be used in our physical world. As suggested below, maybe space and time are not so that between any two points one can always find another point, which would indeed prevent this analysis to go through, and possibly our naive conceptions of space and time are mistaken in other ways as well. But calculus and series-based proposals do not challenge any of our conceptions of space and time in any way, as they are purely mathematical analyses that say nothing about the nature of space and time at all. Hence, these kinds of solutions do not resolve the paradox in this second way either. In short, there is nothing in calculus or series-based solutions that prevent the infinite sequences to crop up that lead to the whole paradox. So, as such, they do not resolve the paradoxes.

Issues with the issues with the proposed calculus-based solutionIf we more closely examine the thought experiment, it is clear that Achilles naming the positions "first", "second", and so forth, is a nonphysical/mathematical act rather than a physical act; as an illustration, try getting your friend to say the word "Bob" on the 1/2 second mark, then the 1/4 second mark, and so on... you just can't do it. Consequently, the "counting process" is a mathematical process, while the "catching up with the turtle" is a physical process. As with most attempts to peddle Zeno's paradoxes, the central element is the conflation of these two processes. But they are simply not to be identified. The mathematical "counting process" goes on to infinity, and this is never something one could complete. However the physical "catching up with the turtle" process is something that can be completed. This is shown by an elementary application of limiting process theory, with time as a parameter.These considerations (one must divorce the mathematical and physical processes at hand) also apply to the paradox as given in the "much more stinging" form: "for Achilles to capture the tortoise will require him to go beyond, and hence to finish, going through a series that has no finish, which is logically impossible". Here the word finish has been confusingly used for both the physical process and the mathematical process in an effort to conflate the two.The issue with the statement "Indeed, the problem with the calculus and other series-based solutions is that these kinds of solutions beg the question. They assume that one can finish a limiting process, but this /tt/file_convert/5a9fc4dd7f8b9a8e178d261f/document.doc 116/122

is exactly what Zeno questioned." is similar. They (the vast majority) do not assume that one can finish the limiting (mathematical) process, and they do not need to. To finish the physical process it is not required to finish the associated mathematical (limiting) process. The two processes are completely different in nature, and divorcing the two is essential if one is to resolve the paradox.The mention of time does not make the paradox into a strawman, and telling someone they can't mention time in their solution is extremely unfair, because the problem is posed in the form of the physical, and consideration of time is implicit in any consideration of the physical. Just because someone worded the problem without using the phrase "time" does not make it illegal to use the word "time" in the solution.Are space and time infinitely divisible?

Main article: Planck lengthAnother proposed solution to some of the paradoxes is to consider that space and time are not infinitely divisible. Just because our number system enables us to give a number between any two numbers, it does not necessarily follow that there is a point in space between any two different points in space, and the same goes for time.If space-time is not infinitely divisible (and thus not perfectly continuous), it is "discrete" (composed of “lumps” and “jumps”, as is experimentally observed when electron orbitals jumping from one level to another in quantum physics). This means that motion is, at the smallest physical level, may be a series of jumps from one quantum space-time coordinate to the next, each occurring over distance and time intervals that are not divisible into smaller measures.Thus the total number of quantum jumps made while traversing from point A to point B would be finite, and there is no paradox.Does motion involve a sequence of points?Augustine of Hippo was the first to posit that time has no precise "moments," in his 4th century C.E. text, Confessions. In Book XI, section XI, paragraph 13, Augustine says, "truly, no time is completely present," and in Book XI, section XV, paragraph 20, Augustine says "the present, however, takes up no space."Some people, including Peter Lynds, have proposed a solution based on this ancient premise. Lynds posits that the paradoxes arise because people have wrongly assumed that an object in motion has a determined relative position at any instant in time, thus rendering the body's motion static at that instant and enabling the impossible situation of the paradoxes to be derived. Lynds asserts that the correct resolution of the paradox lies in the realisation of the absence of an instant in time underlying a body's motion, and that regardless of however small the time interval, it is still always moving and its position constantly changing, so can never be determined at a time. Consequently, a body cannot be thought of as having a determined position at a particular instant in time while in motion, nor be fractionally dissected as such, as is assumed in the paradoxes (and their historically accepted solutions).Conceptual and semantical approachesAnother approach is to deny that our conceptual account of motion as point-by-point movement through continuous space-time needs to match exactly with anything in the real world altogether. Thus, one could deny that time and space are ontological entities. That is, maybe we should acknowledge our Platonic view of reality, and say that time and space are simply conceptual constructs humans use to measure change, that the terms (space and time), though nouns, do not refer to any entities nor containers for entities, and that no thing is being divided up when one talks about "segments" of space or "points" in time.Similarly, one can say that the number of "acts" involved in anything is merely a matter of human convention and labeling. In the constant-pace scenario, one could consider the whole sequence to be one "act," ten "acts," or an infinite number of "acts." No matter how the events are labeled, the tortoise will follow the same trajectory over time, and all of the acts will be "finished" by the time the tortoise reaches the finish line. Thus, the labeling of acts is arbitrary and has nothing to do with the underlying physical process being described and that it is possible to "finish" an infinite sequence of acts.

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From the philosophical standpoint of Bergsonian space-time, the paradox is resolved as follows. The steps of the paradox as presented above can be summarised as:

There are an infinite number of positions defined by any finite movement.Let movement from one position to the next be called an 'act'.An infinite number of acts cannot be completed in a finite amount of time.An infinite number of acts cannot even be started.Thus movement cannot be started or completed.Movement is an illusion.

Moving backwards, any claims about the nature of illusions or acts are intrinsically claims about the nature of experience. According to Bergson's conception of time, all moments of time are comprised of a mixture of both a 'snap-shot' extrinsic property and a durational intensive property, which are irreducible to one another.[2]

The arrow paradox makes an argument that considers only time as a measurable, extensive, homogeneous construct that can be modeled spatially (the above diagram of it with lines being a good example). Thus a conclusion concerning the nature of experience is not warranted by an incomplete proof of only partial properties of time. The point is that 'acts' are experiential in nature.The notion of different orders of infinitySome people state that the dichotomy paradox merely makes the point that the points on a continuum cannot be counted — that from any point, there is no next point to proceed to. However, it is not clear how this comment resolves the paradox. Indeed, as one variant of Zeno's paradox would state: if there is no next point, how can one even move at all? Also, it is not clear what this comment has to do with different orders of infinity: the rational numbers are countable, i.e. of the same order of infinity as the natural numbers, but on the rational number line, there is for any rational number still no next rational number either.

Status of the paradoxes todayMathematicians thought they had done away with Zeno's paradoxes with the invention of the calculus and methods of handling infinite sequences by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century, and then again when certain problems with their methods were resolved by the reformulation of the calculus and infinite series methods in the 19th century. Most philosophers, and certainly scientists, generally agree with the mathematical results.Zeno's paradoxes are still hotly debated by philosophers in academic circles. Infinite processes have remained theoretically troublesome. L. E. J. Brouwer, a Dutch mathematician of the 19th and 20th century, and founder of the Intuitionist school, was the most prominent of those who rejected arguments, including proofs, involving infinities. In this, he followed Leopold Kronecker, an earlier 19th century mathematician. Some claim that a rigorous formulation of the calculus (as the epsilon-delta version of Weierstrass and Cauchy in the 19th century or the equivalent and equally rigorous differential/infinitesimal version by Abraham Robinson in the 20th) has not resolved all problems involving infinities, including Zeno's.

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Two other paradoxes as given by AristotleParadox of Place:

"… if everything that exists has a place, place too will have a place, and so on ad infinitum". (Aristotle Physics IV:1, 209a25)

Paradox of the Grain of Millet:"… there is no part of the millet that does not make a sound: for there is no reason why any such part should not in any length of time fail to move the air that the whole bushel moves in falling. In fact it does not of itself move even such a quantity of the air as it would move if this part were by itself: for no part even exists otherwise than potentially." (Aristotle Physics VII:5, 250a20)

For an expanded account of Zeno's arguments as presented by Aristotle, see: Simplicius' commentary On Aristotle's Physics.

Similar paradoxes presented during the Warring States PeriodIn the 21 paradoxes of Hui Shi (惠施) (380 BCE? -305 BCE?) a member of the Ming Jia (名家) school of philosophy, also mentions two very similar paradoxes:

16. An arrow is flying so fast that there are moments when it is neither in motion nor at rest. 21. Take a stick one chǐ long and cut it in half every day and you will never exhaust it even after

ten thousand generations

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The quantum Zeno effectRecently, physicists studying quantum mechanics have noticed that the dynamical evolution (motion) of a quantum system can be hindered (or even inhibited) through observation of the system. This effect is usually called the quantum Zeno effect as it is strongly reminiscent of (but not fundamentally related to) Zeno's arrow paradox.

See alsoWikiquote has a collection of quotations related to: Aristotle

Supertask Zeno machine 0.999... Gödel, Escher, Bach What the Tortoise Said to Achilles

Zeno's paradoxes in fiction Terry Pratchett in the book Pyramids combines the "Achilles and the tortoise" paradox and the

arrow paradox to create the paradox of the arrow chasing the tortoise. [1] The concept of "nows" in the fletcher's paradox is also explored in Thief of Time.

Dilbert has claimed that "No one ever wants to take more than half of what's left of the last doughnut. That's why I call it Xeno's doughnut" (2005-08-13).

Umberto Eco in his 2004 novel (English language version 2005), The Mysterious Flame of Queen Loana, has the narrator (trying to recover from amnesia by going through old books and possessions) look at a recursive image and remark: "... Chinese boxes or Matrioshka dolls. Infinity, as seen through the eyes of a boy who has yet to study Zeno's paradox. The race towards an unreachable goal; neither the tortoise nor Achilles would ever have reached the last..."

In Beyond Zork, there is a bridge named "Zeno's Bridge". It is impossible to fully cross this bridge, as you can only go a fraction of the distance to the destination.

Phillip K. Dick , in his 1953 short story "The Indefatigable Frog", uses Zeno's paradoxes as a basis for an experiment that places a shrinking frog in a tunnel, thus always increasing the length of the tunnel relative to the frog.

Jorge Luis Borges explores various implications of Zeno's paradoxes in several of his stories and essays. In Avatars of the Tortoise (1932) he discusses how the argument of "Achilles and the tortoise" has manifested itself in the writings of Plato, William James, Lewis Carroll and many others, and goes on to argue that the paradox demonstrates the unreality of the visible world.

Tom Stoppard in his play Jumpers references Zeno's paradox via the philosopher George; George manages to kill his tortoise Thumper while attempting to disprove Zeno's paradox.

In Knight Rider Season 1 - Episode 09 Trust Doesn't Rust - 0:24:00 until 0:24:38 - a reference was made by KITT to an upcoming duel between him (KITT) and KARR (his earlier prototype). Kitt says: "...however since KARR is as powerful and as nearly indestructible as myself, Zeno's paradoxes should be affected." Devon Miles then explains who Zeno is. Kitt continues: "Zeno first postulated a question which my twin would most certainly be aware of: To wit; what would happen if an irresistible force met an immovable object?" In a later head-on-collision scene with KITT vs. KARR, Michael says: "..remember Zeno and that immovable object thing? We are about to find out the answer." Scholars do not attribute the irresistible force paradox to Zeno, and its origin is uncertain.

In Harry Turtledove's novel Wisdom of the Fox, the character Rihwin employs the dichotomy paradox to trick a demon into carelessly halving its distance to him and thus leaving itself vulnerable.

In the movie I.Q. (1994), Catherine Boyd (played by Meg Ryan), poses Zeno's dichotomy paradox to her love interest, Ed Walters (Tim Robbins), as a flirtingly jocular explanation as to why it is

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impossible for her to approach and dance with him. In Frank and Ernest (comic strip), Zeno's dichotomy paradox is stated and said to be used as an

excuse for the reason one character did not get to work on time.

Zeno's paradoxes in artZeno's paradox on a 1990 Croatian election poster

A political party in Croatia in 1990 used Zeno's paradox of Achilles and the tortoise to encourage voters to choose the path of slow and clever civilian initiatives (the tortoise) rather than militant nationalism (Achilles as an armored warrior). Croatian voters decided that Achilles would win the race.

Artist Mark Tansey created a painting titled Achilles and the Tortoise which shows the plume from a rising rocket, around which there are observers, which mimics the appearance of a nearby evergreen tree, with the rocket just short of passing the height of the tree. In the foreground are a group of people finishing the activity of planting a new tree. The image, suggesting the rocket as shown will not ever pass the height of the tree, and tantalizing the viewer with the idea that this has something to do with the processes being shown and that the new tree may or may not pass the rocket first--raises questions about how much static representations can have you understand what's being represented. Tansey is

alluding to Zeno's own logic as a representation of what he's describing.

Zeno's paradoxes in popular culture In the Microsoft/Ensemble Studios game, Age of Mythology: The Titans, the phrase ZENO'S

PARADOX in capitals in the chat menu assigns a random selection of god/titan powers. On the CD How Can You Be in Two Places at Once When You're Not Anywhere at All by The

Firesign Theatre, a track called Zeno's Evil features a series of road signs saying "Antelope Freeway, 1 mile", "Antelope Freeway, 1/2 mile", "Antelope Freeway 1/4 mile", "Antelope Freeway, 1/8 mile", "Antelope Freeway, 1/16 mile" and so on.

The UK synthpop band Spray's first album contained a track titled "So Close," applies the fletcher's paradox to romance, including the telling line, "How close can I get when Cupid's arrow is always doomed to stall halfway to your heart?"

Notes1. ̂ Plato, Parmenides, 128c; Kirk, p. 277. 2. ̂ see Borradori at http://faculty.vassar.edu/giborrad/the_temporalization.htm 3. ̂ "A source book in Chinese philosophy"

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References Plato . Plato: Cratylus. Parmenides. Greater Hippias. Lesser Hippias, H. N. Fowler (Translator),

Loeb Classical Library (January 1, 1926). ISBN 0674991850. Kirk, G. S., J. E. Raven, M. Schofield. The Presocratic Philosophers: A Critical History with a

Selection of Texts. Cambridge University Press; 2 edition (February 24, 1984). ISBN 0521274559. Sainsbury, R.M., Paradoxes, Second Ed (Cambridge UP, 2003). ISBN 0521483476. Solvitur ambulando "A Source Book In Chinese Philosophy", Chan, Wing-Tsit, Princeton University Press, 1969.

ISBN 0691019649

External links Some paradoxes - an anthology http://www.mathacademy.com/pr/prime/articles/zeno_tort/index.asp Modernity of Zeno's paradoxes Zeno's Paradoxes: A Timely Solution by Peter Lynds Zeno's Paradox, A Solution at Myriaden Zeno's Paradoxes of Motion: a section from Kevin Brown's book Reflections on Relativity BBC article on shortest time measured as of 2004 : 10−16 seconds. Stanford Encyclopedia of Philosophy entry Zeno meets modern science Sankhya Philosophy Zeno's Paradoxes The Stanford Encyclopedia of Philosophy The all or nothing dichotomy

This article incorporates material from Zeno's paradox on PlanetMath, which is licensed under the GFDL.Retrieved from "http://en.wikipedia.org/wiki/Zeno%27s_paradoxes"

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