Being Being a student a student

through the years: through the years: the beauty of the beauty of

scientific results, scientific results, mathematic & mathematic &

other arts other arts

Feb 15, Feb 15, 2012 2012 Computational Computational Science & Science & Statistics Statistics Seminar Seminar South Dakota South Dakota State University State University

Boris Boris ShmaginShmagin

WRI SDSUWRI SDSU

~~ Introduction: the meaning of being a studentIntroduction: the meaning of being a student~~ The models to study the Missouri RiverThe models to study the Missouri River

~~ The Statistical LearningThe Statistical Learning~~ Education as communication fromEducation as communication from

uncertainty to the knowledgeuncertainty to the knowledge~~ Maria Montessori (1870Maria Montessori (1870--1952) & 1952) &

her method as the answer to the questionher method as the answer to the question~~ ““VitruvianVitruvian ManMan””~~ The epilogue The epilogue ––

the science as communication of personalities the science as communication of personalities

Topics: Topics:

Introduction: Introduction: the meaning of the meaning of being a studentbeing a student

This presentation was sparked by This presentation was sparked by Dr Dr AbcAbc De question De question during one of seminarsduring one of seminars’’ sessions last semester. sessions last semester. ““Why are the students not active, Why are the students not active, they donthey don’’t ask the questions?t ask the questions?””

Teaching & learning Teaching & learning sciencescience

My UniversityMy University19651965--9696

0926199509261995

Lomonosov Lomonosov Moscow Moscow State State UniversityUniversity

Dim

a

Dim

a G

ord

evG

ord

ev, 1

980

, 198

0

The models The models used for the used for the

Missouri River Missouri River

20062006

Presentation Presentation on the on the

Western Western South Dakota South Dakota

conference conference Apr 18, 2006Apr 18, 2006

The The conference conference

presentationpresentation

Variability Variability as math as math modelsmodels

Presentation on the Western Presentation on the Western South Dakota conference South Dakota conference

Apr 18, 2006Apr 18, 2006

The duration curvesThe duration curves

The curve The curve for Missourifor Missouri

103, cfs

%

Empirical durational curve

1911-2010 for USGS 06191500

Yellowstone River at Corwin

Springs, MT

The hydrograph of hydrological year for USGS 06191500 1911-2010

Annual Annual distributiondistribution

Structure of Structure of the seasonal the seasonal variabilityvariability

Factor 1 Score

-2.5

-1.5

-0.5

0.5

1.5

2.5

1911

1920

1929

1938

1947

1956

1965

1974

1983

1992

2001

2010

Year (Hydr)

Factor 2 Score

-2.5

-1.5

-0.5

0.5

1.5

2.5

1911

1920

1929

1938

1947

1956

1965

1974

1983

1992

2001

2010

Year (Hydr)

Factor 3 Score

-2.0

-1.0

0.0

1.0

2.0

3.0

1911

1920

1929

1938

1947

1956

1965

1974

1983

1992

2001

2010

Year (Hydr)

More that More that one one

dimensiondimension

Shifts in the mean for Factor 2, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1

-2.5

-1.5

-0.5

0.5

1.5

2.5

1911

1920

1929

1938

1947

1956

1965

1974

1983

1992

2001

2010

Shifts in the mean for Factor 1, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

1911

1920

1929

1938

1947

1956

1965

1974

1983

1992

2001

2010

Shifts in the mean for Factor 3, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1

-2.0

-1.0

0.0

1.0

2.0

3.019

11

1920

1929

1938

1947

1956

1965

1974

1983

1992

2001

2010

Shifts in the mean for Annual Hydrologic Year, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1

1500

20002500

30003500

4000

45005000

5500

1911

1920

1929

1938

1947

1956

1965

1974

1983

1992

2001

2010

InterannualInterannualseasonal regime: seasonal regime: shifts shifts

Every season Every season (dimension) has (dimension) has

different different shifts.shifts.

Annual reflects Annual reflects some shiftssome shifts

Modeling Modeling the regimesthe regimes19111911--20102010(2021)(2021)

1500.0

2500.0

3500.0

4500.0

5500.0

191

1

192

1

193

1

194

1

195

1

196

1

197

1

198

1

199

1

200

1

201

1

202

1

AYH [cfs] Model

-2.5

-1.5

-0.5

0.5

1.5

2.5

1911

1921

1931

1941

1951

1961

1971

1981

1991

2001

2011

2021

F1 Model

-2.5

-1.5

-0.5

0.5

1.5

2.5

1911

1921

1931

1941

1951

1961

1971

1981

1991

2001

2011

2021

F2 Model

-2.0

-1.0

0.0

1.0

2.0

3.0

1911

1921

1931

1941

1951

1961

1971

1981

1991

2001

2011

2021

F3 Model

The WaveletsThe Wavelets

The WaveletsThe Wavelets

Math models &Math models &

Time Time VariabilityVariability

-2.5

-1.5

-0.5

0.5

1.5

2.5

1911

1921

1931

1941

1951

1961

1971

1981

1991

2001

2011

2021

F1 Model

Shifts in the mean for Annual Hydrologic Year, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1

1500

20002500

30003500

4000

45005000

5500

1911

1920

1929

1938

1947

1956

1965

1974

1983

1992

2001

2010

Annual

1500

2500

3500

4500

5500

1911

1920

1929

1938

1947

1956

1965

1974

1983

1992

2001

2010

Year (Hydr)

cfs

Shifts in the mean for Factor 2, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1

-2.5

-1.5

-0.5

0.5

1.5

2.5

1911

1920

1929

1938

1947

1956

1965

1974

1983

1992

2001

2010

Shifts in the mean for Factor 1, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

1911

1920

1929

1938

1947

1956

1965

1974

1983

1992

2001

2010

Shifts in the mean for Factor 3, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1

-2.0

-1.0

0.0

1.0

2.0

3.019

11

1920

1929

1938

1947

1956

1965

1974

1983

1992

2001

2010

Shifts in the mean for Annual Hydrologic Year, 1911-2010Probability = 0.1, cutoff length = 10, Huber parameter = 1

1500

20002500

30003500

4000

45005000

5500

1911

1920

1929

1938

1947

1956

1965

1974

1983

1992

2001

2010

To put the To put the knowledge for knowledge for work on the work on the engineering's engineering's goals goals

????

??

The common senseThe common sense

"... it is the very genius of Aristotle "... it is the very genius of Aristotle —— as it is of every great as it is of every great teacher teacher —— to make you think he is uncovering your own to make you think he is uncovering your own

thought in his."thought in his."

The Knowledge The Knowledge of the Variability of the Variability

for Watershedfor Watershed* The Knowledge about watershed comes only from the analysis of the empirical data (instrumental observations)* Variability has to be defined in coordinates of particular watershed; with the number of factor’s axes the annual & seasonal structure of hydrologic time & space may be presented* The math model does not have criteria to verify itself (Gödel's incompleteness theorems) & multi models & scales studies with use of empirical data have to be completed

The Statistical The Statistical Learning Learning

Philosophy of Data Analysis Philosophy of Data Analysis & the Natural Structures& the Natural Structures

Factor analysis is method for extraction that are regarded as thFactor analysis is method for extraction that are regarded as the basic e basic variables that account for the interrelations observed in the davariables that account for the interrelations observed in the datata

A factor is a portion of a quantity, usually an integer or polynA factor is a portion of a quantity, usually an integer or polynomial omial that, when multiplied by other factors, gives the entire quantitthat, when multiplied by other factors, gives the entire quantityy

The main applications of The main applications of factor analytic techniques are: factor analytic techniques are:

•• (1) to reduce the number of (1) to reduce the number of variables and variables and

•• (2) to detect structure(2) to detect structure in in the relationships between variables, the relationships between variables, that is to classify variables. that is to classify variables.

(From: Wolfram (From: Wolfram MathWorldMathWorld))

The variables selected after factor analysis are considered as tThe variables selected after factor analysis are considered as typical & ypical & may be used for timemay be used for time--series analysis series analysis

From Data Analysis From Data Analysis to Statistical Learningto Statistical Learning

Statistical LearningStatistical Learning

Statistical LearningStatistical LearningSUMMARYSUMMARY

““1. With the appearance of computers the concept of natural scien1. With the appearance of computers the concept of natural science, ce, its methodology & philosophy started a process of a its methodology & philosophy started a process of a paradigm changeparadigm change: :

The concepts, methodology, & philosophy of a The concepts, methodology, & philosophy of a Simple WorldSimple World move to very move to very different concepts, philosophy & methodology of a different concepts, philosophy & methodology of a Complex WorldComplex World..

2. In such changes an important role belongs to the mathematical2. In such changes an important role belongs to the mathematical factsfactsthat were discovered by analyzing the that were discovered by analyzing the ““Drosophila flyDrosophila fly”” of cognitive science the of cognitive science the ““Pattern recognition problemPattern recognition problem”” & attempts to obtain their philosophical interpretation.& attempts to obtain their philosophical interpretation.

3. The results of these analyzes lead to methods that go beyond 3. The results of these analyzes lead to methods that go beyond the the classical concept of science: creating generative models of evenclassical concept of science: creating generative models of events & explaints & explain--ability of ability of obtained rules.obtained rules.

4. The new paradigm introduces direct search for solution (4. The new paradigm introduces direct search for solution (transductivetransductiveinference, instead of inference, instead of inductiveinductive), the meditative principle of decision making, & a unity ), the meditative principle of decision making, & a unity of two languages for pattern description: technical (rational) &of two languages for pattern description: technical (rational) & holistic (irrational). holistic (irrational). This leads to the convergence of the exact science with humanitiThis leads to the convergence of the exact science with humanities.es.

5. The main difference between the new paradigm (developed in th5. The main difference between the new paradigm (developed in the e computer era) & the classical one (developed before the computercomputer era) & the classical one (developed before the computer era) is the claim:era) is the claim:

To guarantee the success of inference one needs to control the cTo guarantee the success of inference one needs to control the complexity omplexity of algorithms for inference rather than complexity of the functiof algorithms for inference rather than complexity of the function that these on that these algorithms produce. algorithms produce. Algorithms with low complexity can create a complex functionAlgorithms with low complexity can create a complex functionwhich will generalize well.which will generalize well.””

The The model model

for for statistical statistical learninglearning

The Uncertainty The Uncertainty & Different & Different

Systems of Coordinates Systems of Coordinates

Mathematical & physical Mathematical & physical objects are abstractions objects are abstractions && ““havehave”” the principle of the principle of uncertaintyuncertainty

Technological Technological objects have objects have the errors of the errors of measurement measurement

Natural objects have fuzzy Natural objects have fuzzy boundaries in their own boundaries in their own

coordinates of coordinates of nonstationarynonstationary axes axes

zz

xx

yy

xx

zz

yy

xx

zz

yy

The Uncertainty & The Uncertainty & Systems of Coordinates Systems of Coordinates

Natural objects may be classified in Natural objects may be classified in coordinates of multicoordinates of multi--dimensional dimensional

process & nonstationary axes process & nonstationary axes

xx1t1txx

zz

yy

Natural objects have fuzzy Natural objects have fuzzy boundaries in their own boundaries in their own coordinates of & nonstationary coordinates of & nonstationary axes axes

xx2t2txxitit

xx

zz

yy

Vertical slice of the Geographical Sphere with

two independent elements: System of

Anthropological Geography (SAG) &

System of Physical Geography (SFG).

Arrows indicate vertical & horizontal components

of matter, energy & information circulation

(after Krcho, 1978)

The Cybernetic Model The Cybernetic Model of the of the

GeosphereGeosphere

The The Components Components

of Landscapeof LandscapeThe System of

Physical Geography Sphere (SFG)

with five independent

elements: a1- atmosphere, a2- hydrosphere, a3- lithosphere, a4- pedosphere, a5- biosphere.

The elements of the Physical Geography System SFG are the Spheres Sa1, Sa2, Sa3, Sa4, Sa5 & they may be considered as Subsystems Sai(after Krcho, 1978)

The Components The Components of Landscape on of Landscape on

MapMap

Every Sai & Saij may be characterized by matrix of input {Wi}, matrix of output {Qi}, & matrix of states {Hi}.

The System of Physical Geography

Sphere (SFG) with five

independent elements:

a1- atmosphere, a2- hydrosphere, a3- lithosphere, a4- pedosphere, a5- biosphere

Every element a1 – a5 of SFGis a System Sai & consists from units: a1(a11, a12, a13 …), a2(a21, a22 …), … a5 & those units may be considered as subsystems Saij.

{Ri} is a matrix of

relations between the components of

the landscape (after Krcho, 1978)

Rij

The Structure The Structure of the of the

RelationsRelations

{Ri} is a matrix of relations between the components of the landscape

The number of characteristics for elements of landscape is unlimited

& the number is unlimited for dependences too

Rij

The Structure of Relations The Structure of Relations & Reestablishment & Reestablishment

of Dependencesof Dependences

The gThe g22 -- stream runoff system stream runoff system as a part of aas a part of a22-- hydrospherehydrosphere

may be presented as:may be presented as:SgSg22 = { = { ggjiji, , RRjiji },},

Any watershed Any watershed ggjiji for territory may for territory may be considered as a part of stream be considered as a part of stream runoff system Sgrunoff system Sg22..

ca

b

ggjiji

Each of these components may be Each of these components may be characterized by matrix of input {characterized by matrix of input {WiWi}, }, matrix of output {matrix of output {QiQi}, & matrix of states {Hi}. }, & matrix of states {Hi}.

Subsystem of Subsystem of Hydrosphere (SaHydrosphere (Sa22) )

with nine independent with nine independent elements: elements:

gg11-- atmosphere, atmosphere, gg22-- stream runoff film stream runoff film

(pellicle), (pellicle), gg33-- lithosphere, lithosphere, aa44-- pedosphere, pedosphere,

aa55-- biospherebiosphere

where where ggJiJi-- watershedwatershedin specific coordinates in specific coordinates

yy

Cybernetic Model (a) Cybernetic Model (a) for Watershed in Landscape, for Watershed in Landscape,

with Map of Conditions (b) with Map of Conditions (b) & Models of Multilayer Map (c)& Models of Multilayer Map (c)

xx

zz

xxitit

The gThe g22 -- stream runoff system stream runoff system as a part of aas a part of a22-- hydrospherehydrosphere

may be presented as:may be presented as:SgSg22 = { = { ggjiji, , RRjiji },},

Any watershed Any watershed ggjiji for territory may for territory may be considered as a part of stream be considered as a part of stream runoff system Sgrunoff system Sg22..

ca

b

ggjiji

Each of these components may be Each of these components may be characterized by matrix of input {characterized by matrix of input {WiWi}, }, matrix of output {matrix of output {QiQi}, & matrix of states {Hi}. }, & matrix of states {Hi}.

Subsystem of Subsystem of Hydrosphere (SaHydrosphere (Sa22) )

with nine independent with nine independent elements: elements:

gg11-- atmosphere, atmosphere, gg22-- stream runoff film stream runoff film

(pellicle), (pellicle), gg33-- lithosphere, lithosphere, aa44-- pedosphere, pedosphere,

aa55-- biospherebiosphere

where where ggJiJi-- watershedwatershedin specific coordinates in specific coordinates

yy

The Watershed in The Watershed in Multidimensional System of Multidimensional System of

Coordinate with Diversity Coordinate with Diversity LandscapesLandscapes

xx

zzxxitit

xxitit

Education Education as communication on as communication on the movement from the movement from Uncertainty to the Uncertainty to the

Knowledge Knowledge

The KnowledgeThe Knowledge

Bertrand Russell“Human Knowledge.

Its Scope & Limits.”1948

““I. THE DEFINITION OF KNOWLEDGEI. THE DEFINITION OF KNOWLEDGEThe question how knowledge should be defined is perhaps the mostThe question how knowledge should be defined is perhaps the most important and difficult of the important and difficult of the

three with which we shall deal. This may seem surprising: at firthree with which we shall deal. This may seem surprising: at first sight it might be thought st sight it might be thought that knowledge might be defined as belief which is in agreement that knowledge might be defined as belief which is in agreement with the facts. The with the facts. The

trouble is that no one knows what a belief is, no one knows whattrouble is that no one knows what a belief is, no one knows what a fact is, & no one knows a fact is, & no one knows what sort of agreement between them would make a belief true.what sort of agreement between them would make a belief true.

Belief. Words. Truth in Logic.Belief. Words. Truth in Logic.II. THE DATAII. THE DATA

Animal Inference. Mental & Physical Data.Animal Inference. Mental & Physical Data.III. METHODS OF INFERENCEIII. METHODS OF INFERENCE

Induction. Probability. Limitation of Variety. Grades of CertainInduction. Probability. Limitation of Variety. Grades of Certainty.ty.””

The book has six The book has six parts, & the part parts, & the part named named ““LanguageLanguage”” is is the biggest one with the biggest one with eleven chapterseleven chapters

The The UncertaintyUncertainty

LotfiLotfi A. ZadehA. Zadeh(born Feb 4, 1921)(born Feb 4, 1921)

Professor in the Graduate School, Professor in the Graduate School, Computer Science Division Department of Computer Science Division Department of

Electrical Engineering & Computer Sciences Electrical Engineering & Computer Sciences Director, Berkeley Initiative in Soft Director, Berkeley Initiative in Soft

Computing University of California Computing University of California Berkeley, CA 94720 Berkeley, CA 94720 --1776 1776

Zadeh: Zadeh: the fuzzy logicthe fuzzy logic

(The) (The) UncertaintyUncertainty““Uncertainty is a personal Uncertainty is a personal matter; it is notmatter; it is not thetheuncertainty butuncertainty but your your uncertainty.uncertainty.””

Dennis Lindley Dennis Lindley (2006) (2006) Understanding Understanding UncertaintyUncertainty

Dennis Victor LindleyDennis Victor Lindley(born 25 July 1923) (born 25 July 1923)

Professor Emeritus of Statistics, Professor Emeritus of Statistics, & past Head of Department, & past Head of Department,

at University College London (UK). at University College London (UK). He is a British statistician, decision theorist & He is a British statistician, decision theorist &

leading advocate of Bayesian statisticsleading advocate of Bayesian statistics

There is part of There is part of science looking in the science looking in the

coinscoins

The The modelmodel

The The modelmodel

Statistics & UncertaintyStatistics & UncertaintyThe statistician's task is The statistician's task is

to articulate the to articulate the scientist's uncertainties scientist's uncertainties

in the in the language language of of probabilityprobability……

A model is merely your A model is merely your reflection of reality &, reflection of reality &,

like probability, like probability, it describes neither you it describes neither you

nor the world, nor the world, but only a relationship but only a relationship

between you & between you & that world.that world.”” (p. 303)(p. 303)

“…“… data analysis assists in the formulation of a modeldata analysis assists in the formulation of a model & & is an activity that precedes the formal probability calculationsis an activity that precedes the formal probability calculations that are that are needed for inference.needed for inference.”” (p. 305)(p. 305)““Statisticians are not masters in their own house.Statisticians are not masters in their own house.Their task is to help the client to handle the uncertainty that Their task is to help the client to handle the uncertainty that they encounter. they encounter. The The 'you''you' of the analysis is the client, not the statistician.of the analysis is the client, not the statistician.”” (p. 318)(p. 318)

Statistics at workStatistics at work

““Karl Pearson said 'The unity of all science consists alone in itKarl Pearson said 'The unity of all science consists alone in its method, not in its material' s method, not in its material' (Pearson, 1892). (Pearson, 1892). It is not true to say that physics is science whereas literatureIt is not true to say that physics is science whereas literature is notis not..””(p. 316)(p. 316)

The Uncertainty The Uncertainty & Information & Information

The Science & The Science & the Languagethe Language

[In linguistic] ... [In linguistic] ... ““the proper object of study the proper object of study

was was the speaker's the speaker's underlying underlying

knowledge of the languageknowledge of the language, , his "linguistic competence" his "linguistic competence"

that enables him to produce that enables him to produce & understand sentences & understand sentences

he has never heard beforehe has never heard before””From: From: "Chomsky's Revolution "Chomsky's Revolution

In Linguistics"In Linguistics"by John R. Searleby John R. Searle

The New York Review of Books, The New York Review of Books, June 29, 1972June 29, 1972

EvolutionEvolution

Communication Communication & language& language

Information in the Information in the LanguageLanguage

““In cognitive linguistics as In cognitive linguistics as in cognitive science, the human in cognitive science, the human

mind is considered to be an mind is considered to be an informationinformation--processing device processing device

((StillingsStillings 1995), 1995), & language is viewed as & language is viewed as

a vehicle for communicating a vehicle for communicating information.information.””

From: J. Van de From: J. Van de WalleWalle, 2008, 2008

Six communication

functions

distinguished

by Jakobson,

(from Wiki)

Learning Learning ConceptConcept

The Uncertainty & The Knowledge The Uncertainty & The Knowledge through Modeling: Object, through Modeling: Object,

Data, Analysis & ResultsData, Analysis & ResultsPhoto picture Photo picture

as presentation as presentation

of the natural of the natural

objectobject

The conceptual model The conceptual model

(Cybernetic Model)(Cybernetic Model)

is the way to use is the way to use

previously obtained previously obtained

KnowledgeKnowledge

The knowledge (K)= 0,The knowledge (K)= 0,about a new object for about a new object for the considerationthe considerationthe uncertainty (U)= 1the uncertainty (U)= 1

KKpp = 1 & we have the = 1 & we have the direction for the direction for the research, the task,research, the task,U = 0, but the U = 0, but the Knowledge is Knowledge is previous (previous (KKpp))

The Statistical Learning The Statistical Learning is the way to obtain is the way to obtain ((““extractextract””) the structure ) the structure of a natural objectof a natural object

After After Statistical Statistical

LearningLearningK > UK > U

The Uncertainty from The Uncertainty from Analysis obtained for Analysis obtained for

every model. every model. For Factor Analysis For Factor Analysis U=1U=1-- explained variabilityexplained variability

The Uncertainty & The Knowledge The Uncertainty & The Knowledge through Modeling: Object, through Modeling: Object,

Data, Analysis & ResultsData, Analysis & ResultsPhoto picture Photo picture

as presentation as presentation

of the natural of the natural

objectobject

The conceptual model The conceptual model

(Cybernetic Model)(Cybernetic Model)

is the way to use is the way to use

previously obtained previously obtained

KnowledgeKnowledge

The knowledge (K)= 0,The knowledge (K)= 0,about a new object for about a new object for the considerationthe considerationthe uncertainty (U)= 1the uncertainty (U)= 1

KKpp = 1 & we have the = 1 & we have the direction for the direction for the research, the task,research, the task,U = 0, but the U = 0, but the Knowledge is Knowledge is previous (previous (KKpp))

The Statistical Learning The Statistical Learning is the way to obtain is the way to obtain ((““extractextract””) the structure ) the structure of a natural objectof a natural object

After After Statistical Statistical

LearningLearningK > UK > U

The Uncertainty from The Uncertainty from Analysis obtained for Analysis obtained for

every model. every model. For Factor Analysis For Factor Analysis U=1U=1-- explained variabilityexplained variability

Communicating the Communicating the Knowledge for the Knowledge for the

WatershedWatershedScientist Scientist

working in working in Hydrology have Hydrology have

to handle the to handle the Uncertainty & Uncertainty & communicate communicate

the Knowledge the Knowledge about about

timetime--spatial spatial variability of variability of

the Watershed the Watershed characteristics characteristics

““VitruvianVitruvian ManMan””Albert Einstein wrote that the mind “always has tried to form for itself a simple

& synoptic image of the surrounding world.”

During the Renaissance, when the ancient Greek

idea of man as the measure of all things leapt

to the forefront of intellectual life, the human

body became a preferred object for this type of “synoptic” speculation.

… “Vitruvian Man”ultimately offers a

“synoptic image” of the Renaissance itself.

Leonardo’s most famous images, “Vitruvian Man” (circa 1490).

““VitruvianVitruvianManMan””

The ancient Roman engineer The ancient Roman engineer Vitruvius opined in his magnum opus, Vitruvius opined in his magnum opus,

““Ten Books on ArchitectureTen Books on Architecture””(circa 25 B.C.), (circa 25 B.C.),

that a temple cannot be built properly that a temple cannot be built properly ““unless it conforms exactly to the unless it conforms exactly to the

principle relating the members of a principle relating the members of a wellwell--shaped man.shaped man.”” He then He then

enumerated the ideal proportions of enumerated the ideal proportions of the male physique & posited that a the male physique & posited that a manman’’s outstretched body could be s outstretched body could be

made to fit within a circle & a square.made to fit within a circle & a square.

Lester writes: Lester writes: ““The circle represented the cosmic & The circle represented the cosmic &

the divine; the divine; the square represented the earthly & the square represented the earthly &

the secular.the secular.””

Our Our UniversityUniversity

Raphael Raphael

(1509(1509--1510) 1510)

Fresco (500*770 cm) Vatican City, Apostolic Palace Fresco (500*770 cm) Vatican City, Apostolic Palace

The School of Athens: The School of Athens: all togetherall together

““Sky is limitSky is limit””

there were people in SD there were people in SD who saw the connectionswho saw the connections

““VitruvianVitruvian ManMan””

… “Vitruvian Man”ultimately offers a “synoptic image” of the Renaissance itself.

Beforethe Pacioli collaboration, the idea had inspired what has since becomeone of Leonardo’s most famous images, “Vitruvian Man” (circa 1490), acareful line drawing of a nude male figure whose outstretched arms andlegs fit perfectly in the bounds of a circle and a square. “Vitruvian Man”has entered popular culture as an emblem of Leonardo’s genius —redolent of secret knowledge …The story, in some respects, is simple. The ancient Roman engineerVitruvius opined in his magnum opus, “Ten Books on Architecture” (circa25 B.C.), that a temple cannot be built properly “unless it conformsexactly to the principle relating the members of a well-shaped man.” Hethen enumerated the ideal proportions of the male physique and positedthat a man’s outstretched body could be made to fit within a circle and asquare. “Ancient philosophers, mathematicians and mystics had longinvested those two shapes with special symbolic powers,” Lester writes.“The circle represented the cosmic and the divine; the square representedthe earthly and the secular.”

Renaissance of our days Renaissance of our days

In the search of In the search of the the

““EnlightenmentEnlightenment’’ss””image image

Maria Montessori Maria Montessori (1870(1870--1952)1952)

Scientific observation has established that Scientific observation has established that education is not what the teacher gives; education is not what the teacher gives; education is a natural process spontaneously education is a natural process spontaneously carried out by the human individualcarried out by the human individual, & , & is acquired not by listening to words but by is acquired not by listening to words but by experiences upon the environment. experiences upon the environment. The task of the teacher becomes that of The task of the teacher becomes that of preparing a series of motives of cultural preparing a series of motives of cultural activity, spread over a specially prepared activity, spread over a specially prepared environment, & then refraining from obtrusive environment, & then refraining from obtrusive interference. Human interference. Human teachers can only helpteachers can only helpthe great work that is being done, as servants the great work that is being done, as servants help the master. help the master. Doing soDoing so, they will be witnesses to the , they will be witnesses to the unfolding of the human soul & to the rising unfolding of the human soul & to the rising of a New Manof a New Man who will not be a victim of who will not be a victim of events, but will have the clarity of vision to events, but will have the clarity of vision to direct & shape the future of human society.direct & shape the future of human society.Maria Montessori,Maria Montessori, 1946. 1946. ””Education for a New WorldEducation for a New World””

Few biographical factsFew biographical factsMaria Montessori became a physician in 1896, she was the first wMaria Montessori became a physician in 1896, she was the first woman in Italy to receive oman in Italy to receive a medical degree. She worked in the fields of psychiatry, educata medical degree. She worked in the fields of psychiatry, education & anthropology. ion & anthropology. In her work at the University of Rome psychiatric clinic Dr. MonIn her work at the University of Rome psychiatric clinic Dr. Montessori developed an tessori developed an interest in the treatment of special needs children, for severalinterest in the treatment of special needs children, for several years, she worked, wrote, years, she worked, wrote, and spoke on their behalf. and spoke on their behalf. In 1907 she was given the opportunity to study "normal" childrenIn 1907 she was given the opportunity to study "normal" children, taking charge of fifty , taking charge of fifty poor children of the dirty, desolate streets of the San Lorenzo poor children of the dirty, desolate streets of the San Lorenzo slum on the outskirts of slum on the outskirts of Rome. The news of the unprecedented success of her work soon sprRome. The news of the unprecedented success of her work soon spread around the world, ead around the world, people coming from far & wide to see the children for themselvespeople coming from far & wide to see the children for themselves..Invited to the USA by Alexander Graham Bell, Thomas Edison, & otInvited to the USA by Alexander Graham Bell, Thomas Edison, & others, Dr. Montessori hers, Dr. Montessori spoke at Carnegie Hall in 1915. spoke at Carnegie Hall in 1915. She was invited to set up a classroom at the PanamaShe was invited to set up a classroom at the Panama--Pacific ExpositionPacific Exposition in San Francisco, in San Francisco, where spectators watched twentywhere spectators watched twenty--one children, allone children, all new to this Montessori method, new to this Montessori method, behind abehind a glass wall for four months. The only two gold medals awarded forglass wall for four months. The only two gold medals awarded for education went education went to this class. (From: to this class. (From: http://http://www.montessori.eduwww.montessori.edu).).

Her method Her method as the answer to as the answer to Dr Dr AbcAbc DeDe’’s questions questionThe main principles of Maria The main principles of Maria MontesoryMontesory teaching method teaching method are applicable for college/university level course in are applicable for college/university level course in research seminar format: research seminar format:

* students are not blank slates, but that they each * students are not blank slates, but that they each has inherent, individual gift;has inherent, individual gift;

* the professor* the professor’’s job is to help students find these s job is to help students find these gifts, rather than dictating what a student should know;gifts, rather than dictating what a student should know;

* the professor has to provide a framework of * the professor has to provide a framework of specific discipline & encourage independence, selfspecific discipline & encourage independence, self--directed learning (+ Web), & learning from peers. directed learning (+ Web), & learning from peers.

Tomasello, 51, previously taught psychology at Emory University in Atlanta & conducted research at Atlanta’s Yerkes

Primate Center. Through his studies of learning in human children ages 1 to 4

years old, as well as in chimpanzees, gorillas, & orangutans, he found that,

unlike other great apes, humans are specially adapted to learn cooperatively,

even before developing language. This collaborative approach to learning leads to shared intellectual creations such as

language, & shared cultural creations such as social norms &institutions..

A century A century laterlater

TomaselloTomasello’’s work has clear applications in education, by highlighting s work has clear applications in education, by highlighting the the importance of peer learningimportance of peer learning, says Anne Peterson, a psychologist at the Center , says Anne Peterson, a psychologist at the Center for Human Growth & Development at the University of Michigan, Anfor Human Growth & Development at the University of Michigan, Ann Arbor, & n Arbor, & the chair of the jury that awarded Tomasello the prize.the chair of the jury that awarded Tomasello the prize.

A century A century laterlater

Students Students in in

the the UniversityUniversity

Epilogue: Epilogue: the science the science

as as communication communication of personalities of personalities

Is it

the

scie

nce?

Is it

the

scie

nce?

““In place of scientific method, Polanyi In place of scientific method, Polanyi trumpeted the importance of trumpeted the importance of ““tacit knowledge.tacit knowledge.””

No practicing scientist learned the craft of research No practicing scientist learned the craft of research from books or articlesfrom books or articles, Polanyi argued. Rather, , Polanyi argued. Rather, they had to they had to practice craftpractice craft like skills, which they internalized via social like skills, which they internalized via social

relationships like apprenticeship training. relationships like apprenticeship training.

Scientists often formed their beliefs from an immersion in Scientists often formed their beliefs from an immersion in particulars that resisted explicit articulation; particulars that resisted explicit articulation;

he likened the experience to he likened the experience to religious conversion. religious conversion.

To Polanyi, To Polanyi, the routines of scientific research could never be the routines of scientific research could never be

captured by recipes,captured by recipes,& therefore any effort to steer the direction of research, & therefore any effort to steer the direction of research,

or subject science to central planning, was bound to fail.or subject science to central planning, was bound to fail.””

The The ““tacit knowledgetacit knowledge””

Tacit 1:Tacit 1: expressed or carried on without words or speechexpressed or carried on without words or speech2 :2 : impliedimplied or indicated (as by an act or by silence) but not actually expreor indicated (as by an act or by silence) but not actually expressedssed

Michael PolanyiMichael Polanyi(1891 (1891 –– 19761976)

Polanyi addressing the Congress of Polanyi addressing the Congress of Cultural Freedom in Milan about Cultural Freedom in Milan about 19561956

It is the It is the social scientific communitysocial scientific community, , not a rational scientific method, not a rational scientific method,

that that is the determining conditionis the determining condition of of scientific scientific knowledgeknowledge..”” [M. Polanyi 1963][M. Polanyi 1963]

““The system of scientificThe system of scientific knowledge is knowledge is a social systema social system of authority & apprenticeshipof authority & apprenticeship, ,

which imposes discipline & which values tradition, which imposes discipline & which values tradition, while teaching expert skills. In contrast to histories of while teaching expert skills. In contrast to histories of

science which emphasize the work of revolutionary heroes, science which emphasize the work of revolutionary heroes, most scientific work is accomplished within the framework most scientific work is accomplished within the framework of beliefs or dogmas that provide the problems & answers of beliefs or dogmas that provide the problems & answers

for ordinary scientific work.for ordinary scientific work.””

““Science remains objective, not in the detachment Science remains objective, not in the detachment of the knower from the known, of the knower from the known,

but in but in the power of science the power of science to establish contact with a hidden reality to establish contact with a hidden reality

based in the skills & commitment of the knowerbased in the skills & commitment of the knower..””[M. Polanyi 1964] [M. Polanyi 1964]

"In questions "In questions of science, of science,

the authority of a thousand the authority of a thousand is not worth is not worth

the humble reasoning of the humble reasoning of a single individual.a single individual.““

Galileo GalileiGalileo Galilei

The The

ScientistScientist

“A model is merely your reflection of reality &, like probability, it describes neither you nor the world, but only a relationship between you & that world”Dennis Lindley

QuestionsQuestions