Leonardo

Technics and Praxis by Don Ihde; The Question concerning Technology and Other Essays byMartin Heidegger; William LovittReview by: Michael J. MoravcsikLeonardo, Vol. 13, No. 4 (Autumn, 1980), p. 333Published by: The MIT PressStable URL: http://www.jstor.org/stable/1578121 .

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from the point of view of graph theory see Leonardo 1, 233 (1968); 4, 51 (1971); 9, 215 (1976); 10, 148 (1977)-also in Visual Art, Mathematics and Computers: Selections from the Journal Leonardo, F. J. Malina, ed. (Oxford: Pergamon Press, 1979) pp. 51, 117, 148 and 188.)

Technics and Praxis. Don Ihde. D. Reidel, Boston, 1979. 151 pp. Paper. The Question Concerning Technology and Other Essays. Martin Heidegger. William Lovitt, trans. Harper and Row, London, 1977. 182 pp. Paper ?3.70. Reviewed by Michael J. Moravcsik*

To the perennial chagrin and dismay of philosophers, to nonspecialists philosophy has a meaning that is quite different from the professionals' view of this complex and highly technical discipline. Nonspecialists suppose that philosophy provides principles to guide human lives and gives answers to 'commonsense' types of logical, ontological, epistemological and, above all, ethical questions. In this light, I, like most readers of Leonardo, have to register a certain degree of disappointment with these two books, in that they do little to illuminate the 'philosophical' questions pertaining to tech- nology.

By far the more accessible book of the two is the one by Ihde. With a little care and concentration, any reader should be able to get through it and, from it, glean an idea of what the very embryonic specialty called 'philosophy of technology' is up to. In particular, the introductory chapter gives a historical and disciplinary overview, which is followed by three main sections. The first is on the phenomenology of instrumenta- tion, articulating for readers various features of the human- instrument relationship, none surprising, all probably in the recesses of one's personal experience, and, yet, it is mildly interesting and pleasing to see them explicitly discussed.

The second section is entitled Implications of Technology, though it treats only a few such implications and somewhat academic ones at that. Attracted by the title, I was eager to read the last chapter in this section, entitled Bach to Rock, a Musical Odyssey, but it turned out to be a somewhat labored essay on 'head music' vs. 'body music' and on 'visual' vs. 'auditory' impressions.

The third section comes probably the closest to the interest of Leonardo readers in that it deals with three types of interpretive philosophy of technology. The first chapter is on Martin Heidegger (see below), the second on a 'back-to- nature' advocate, Hans Jonas, who considers progress in technology an 'alienation' of humans from their 'natural selves', and, finally, the third is a meditation on what a true existentialist is.

All this is, as I mentioned, definitely readable, even though perhaps not very exciting for nonspecialists. In contrast, the collection of Heidegger's essays is hardly readable, even, I understand, by many philosophers. It contains five essays: The Question Concerning Technology; The Turning; The Work of Nietsche: 'God is Dead'; The Age of the World Picture; and Science and Reflection. Readers who, nevertheless, are chal- lenged to penetrate, at least to some extent, the erudite, esoteric and arcane world of Heidegger, I advise to proceed as follows: (1) Read the chapter on Heidegger in William Barrett's Irrational Man (Garden City, N.Y.: Doubleday Anchor Books, 1962); (2) Read the chapter on Heidegger in the Ihde book reviewed above; (3) Try to read the last of the five essays in the Heidegger book; (4) If your interest and ability to comprehend survive through the first three steps, read the first four Heidegger essays!

Color Theory and Its Application in Art and Design. George A. Agoston. Springer, New York, 1979. 137 pp., illus. $24.80. Reviewed by Jonathan C. Fish**

*Institute of Theoretical Science, University of Oregon,

from the point of view of graph theory see Leonardo 1, 233 (1968); 4, 51 (1971); 9, 215 (1976); 10, 148 (1977)-also in Visual Art, Mathematics and Computers: Selections from the Journal Leonardo, F. J. Malina, ed. (Oxford: Pergamon Press, 1979) pp. 51, 117, 148 and 188.)

Technics and Praxis. Don Ihde. D. Reidel, Boston, 1979. 151 pp. Paper. The Question Concerning Technology and Other Essays. Martin Heidegger. William Lovitt, trans. Harper and Row, London, 1977. 182 pp. Paper ?3.70. Reviewed by Michael J. Moravcsik*

To the perennial chagrin and dismay of philosophers, to nonspecialists philosophy has a meaning that is quite different from the professionals' view of this complex and highly technical discipline. Nonspecialists suppose that philosophy provides principles to guide human lives and gives answers to 'commonsense' types of logical, ontological, epistemological and, above all, ethical questions. In this light, I, like most readers of Leonardo, have to register a certain degree of disappointment with these two books, in that they do little to illuminate the 'philosophical' questions pertaining to tech- nology.

By far the more accessible book of the two is the one by Ihde. With a little care and concentration, any reader should be able to get through it and, from it, glean an idea of what the very embryonic specialty called 'philosophy of technology' is up to. In particular, the introductory chapter gives a historical and disciplinary overview, which is followed by three main sections. The first is on the phenomenology of instrumenta- tion, articulating for readers various features of the human- instrument relationship, none surprising, all probably in the recesses of one's personal experience, and, yet, it is mildly interesting and pleasing to see them explicitly discussed.

The second section is entitled Implications of Technology, though it treats only a few such implications and somewhat academic ones at that. Attracted by the title, I was eager to read the last chapter in this section, entitled Bach to Rock, a Musical Odyssey, but it turned out to be a somewhat labored essay on 'head music' vs. 'body music' and on 'visual' vs. 'auditory' impressions.

The third section comes probably the closest to the interest of Leonardo readers in that it deals with three types of interpretive philosophy of technology. The first chapter is on Martin Heidegger (see below), the second on a 'back-to- nature' advocate, Hans Jonas, who considers progress in technology an 'alienation' of humans from their 'natural selves', and, finally, the third is a meditation on what a true existentialist is.

All this is, as I mentioned, definitely readable, even though perhaps not very exciting for nonspecialists. In contrast, the collection of Heidegger's essays is hardly readable, even, I understand, by many philosophers. It contains five essays: The Question Concerning Technology; The Turning; The Work of Nietsche: 'God is Dead'; The Age of the World Picture; and Science and Reflection. Readers who, nevertheless, are chal- lenged to penetrate, at least to some extent, the erudite, esoteric and arcane world of Heidegger, I advise to proceed as follows: (1) Read the chapter on Heidegger in William Barrett's Irrational Man (Garden City, N.Y.: Doubleday Anchor Books, 1962); (2) Read the chapter on Heidegger in the Ihde book reviewed above; (3) Try to read the last of the five essays in the Heidegger book; (4) If your interest and ability to comprehend survive through the first three steps, read the first four Heidegger essays!

Color Theory and Its Application in Art and Design. George A. Agoston. Springer, New York, 1979. 137 pp., illus. $24.80. Reviewed by Jonathan C. Fish**

*Institute of Theoretical Science, University of Oregon,

from the point of view of graph theory see Leonardo 1, 233 (1968); 4, 51 (1971); 9, 215 (1976); 10, 148 (1977)-also in Visual Art, Mathematics and Computers: Selections from the Journal Leonardo, F. J. Malina, ed. (Oxford: Pergamon Press, 1979) pp. 51, 117, 148 and 188.)

Technics and Praxis. Don Ihde. D. Reidel, Boston, 1979. 151 pp. Paper. The Question Concerning Technology and Other Essays. Martin Heidegger. William Lovitt, trans. Harper and Row, London, 1977. 182 pp. Paper ?3.70. Reviewed by Michael J. Moravcsik*

To the perennial chagrin and dismay of philosophers, to nonspecialists philosophy has a meaning that is quite different from the professionals' view of this complex and highly technical discipline. Nonspecialists suppose that philosophy provides principles to guide human lives and gives answers to 'commonsense' types of logical, ontological, epistemological and, above all, ethical questions. In this light, I, like most readers of Leonardo, have to register a certain degree of disappointment with these two books, in that they do little to illuminate the 'philosophical' questions pertaining to tech- nology.

By far the more accessible book of the two is the one by Ihde. With a little care and concentration, any reader should be able to get through it and, from it, glean an idea of what the very embryonic specialty called 'philosophy of technology' is up to. In particular, the introductory chapter gives a historical and disciplinary overview, which is followed by three main sections. The first is on the phenomenology of instrumenta- tion, articulating for readers various features of the human- instrument relationship, none surprising, all probably in the recesses of one's personal experience, and, yet, it is mildly interesting and pleasing to see them explicitly discussed.

The second section is entitled Implications of Technology, though it treats only a few such implications and somewhat academic ones at that. Attracted by the title, I was eager to read the last chapter in this section, entitled Bach to Rock, a Musical Odyssey, but it turned out to be a somewhat labored essay on 'head music' vs. 'body music' and on 'visual' vs. 'auditory' impressions.

The third section comes probably the closest to the interest of Leonardo readers in that it deals with three types of interpretive philosophy of technology. The first chapter is on Martin Heidegger (see below), the second on a 'back-to- nature' advocate, Hans Jonas, who considers progress in technology an 'alienation' of humans from their 'natural selves', and, finally, the third is a meditation on what a true existentialist is.

All this is, as I mentioned, definitely readable, even though perhaps not very exciting for nonspecialists. In contrast, the collection of Heidegger's essays is hardly readable, even, I understand, by many philosophers. It contains five essays: The Question Concerning Technology; The Turning; The Work of Nietsche: 'God is Dead'; The Age of the World Picture; and Science and Reflection. Readers who, nevertheless, are chal- lenged to penetrate, at least to some extent, the erudite, esoteric and arcane world of Heidegger, I advise to proceed as follows: (1) Read the chapter on Heidegger in William Barrett's Irrational Man (Garden City, N.Y.: Doubleday Anchor Books, 1962); (2) Read the chapter on Heidegger in the Ihde book reviewed above; (3) Try to read the last of the five essays in the Heidegger book; (4) If your interest and ability to comprehend survive through the first three steps, read the first four Heidegger essays!

Color Theory and Its Application in Art and Design. George A. Agoston. Springer, New York, 1979. 137 pp., illus. $24.80. Reviewed by Jonathan C. Fish**

*Institute of Theoretical Science, University of Oregon,

from the point of view of graph theory see Leonardo 1, 233 (1968); 4, 51 (1971); 9, 215 (1976); 10, 148 (1977)-also in Visual Art, Mathematics and Computers: Selections from the Journal Leonardo, F. J. Malina, ed. (Oxford: Pergamon Press, 1979) pp. 51, 117, 148 and 188.)

Technics and Praxis. Don Ihde. D. Reidel, Boston, 1979. 151 pp. Paper. The Question Concerning Technology and Other Essays. Martin Heidegger. William Lovitt, trans. Harper and Row, London, 1977. 182 pp. Paper ?3.70. Reviewed by Michael J. Moravcsik*

To the perennial chagrin and dismay of philosophers, to nonspecialists philosophy has a meaning that is quite different from the professionals' view of this complex and highly technical discipline. Nonspecialists suppose that philosophy provides principles to guide human lives and gives answers to 'commonsense' types of logical, ontological, epistemological and, above all, ethical questions. In this light, I, like most readers of Leonardo, have to register a certain degree of disappointment with these two books, in that they do little to illuminate the 'philosophical' questions pertaining to tech- nology.

By far the more accessible book of the two is the one by Ihde. With a little care and concentration, any reader should be able to get through it and, from it, glean an idea of what the very embryonic specialty called 'philosophy of technology' is up to. In particular, the introductory chapter gives a historical and disciplinary overview, which is followed by three main sections. The first is on the phenomenology of instrumenta- tion, articulating for readers various features of the human- instrument relationship, none surprising, all probably in the recesses of one's personal experience, and, yet, it is mildly interesting and pleasing to see them explicitly discussed.

The second section is entitled Implications of Technology, though it treats only a few such implications and somewhat academic ones at that. Attracted by the title, I was eager to read the last chapter in this section, entitled Bach to Rock, a Musical Odyssey, but it turned out to be a somewhat labored essay on 'head music' vs. 'body music' and on 'visual' vs. 'auditory' impressions.

The third section comes probably the closest to the interest of Leonardo readers in that it deals with three types of interpretive philosophy of technology. The first chapter is on Martin Heidegger (see below), the second on a 'back-to- nature' advocate, Hans Jonas, who considers progress in technology an 'alienation' of humans from their 'natural selves', and, finally, the third is a meditation on what a true existentialist is.

All this is, as I mentioned, definitely readable, even though perhaps not very exciting for nonspecialists. In contrast, the collection of Heidegger's essays is hardly readable, even, I understand, by many philosophers. It contains five essays: The Question Concerning Technology; The Turning; The Work of Nietsche: 'God is Dead'; The Age of the World Picture; and Science and Reflection. Readers who, nevertheless, are chal- lenged to penetrate, at least to some extent, the erudite, esoteric and arcane world of Heidegger, I advise to proceed as follows: (1) Read the chapter on Heidegger in William Barrett's Irrational Man (Garden City, N.Y.: Doubleday Anchor Books, 1962); (2) Read the chapter on Heidegger in the Ihde book reviewed above; (3) Try to read the last of the five essays in the Heidegger book; (4) If your interest and ability to comprehend survive through the first three steps, read the first four Heidegger essays!

Color Theory and Its Application in Art and Design. George A. Agoston. Springer, New York, 1979. 137 pp., illus. $24.80. Reviewed by Jonathan C. Fish**

*Institute of Theoretical Science, University of Oregon,

and exclamation marks towards the end of the book, will encourage his readers to persist. Moreover, if readers remem- ber to read at least in some degree 'as poets'-that is, responding to the striking imagery of black holes, wave packets, quarks, and baryon binding, rather than struggling with each and every equation-then they will find the book rewarding.

Physics for Poets was first published in 1970. The 1978 revised version, which includes nearly 30% new material, seems to have been designed primarily to make it more accessible by cutting down on the mathematics that made the first edition harder going. It ends with a series of questions suitable for students embarking on their first serious course in physics.

Dots and Lines. Richard J. Trudeau. Kent State Univ. Press, Kent, Ohio, U.S.A., 1978. 203 pp., illus. Paper, $6.50. Reviewed by Arthur L. Loeb*

This is a book on graph theory, the mathematical treatment of configurations; the four-color problem and the problem of the Koenigsberg bridges, for example, fall within its scope. One of the principal difficulties facing one unfamiliar with the subject is the large number of special terms; unless one has used them or has visual analogs to which to tie them, it is difficult to grasp the theorems and proofs and the concrete meaning of results obtained.

I found Trudeau's text a splendid and delightful introduc- tion to graph theory. There are numerous illustrations for each topic discussed and he proceeds patiently from simpler to more complex abstractions that have considerable power. For example, in an exercise at the conclusion of Chapter 2, using only elementary properties of rather simple graphs, one is asked to prove that in any gathering of six people there are three people who are and three people who are not mutually acquainted. This example of the interplay between graph theory and its application to problems of logic convincingly presents the value of this branch of mathematics.

Topics covered are Planar Graphs, Euler's Formula, Plato- nic Graphs, Coloring, Graphs of Genus Higher than Zero, Euler and Hamilton Walks. An Afterword deals with the solution of the four-color problem that had been announced just as the book was going to press. Rigor is stressed, and, in the rare instance when a theorem is not proven, the reason is pointed out explicitly as a demonstration of some of the idiosyncrasies of mathematics. One instance is Jordan's theorem: 'If C is a continuous simple closed curve in a plane, then C divides the rest of the plane into two regions having C as their common boundary. If a point P in one of these regions is joined to a point Q in the other by a continuous curve L in the plane, then L intersects C.' Trudeau points out that this theorem, seemingly so obvious, could not be proven by Jordan himself, and decades passed before a proof was found.

Each chapter contains from 18 to 40 stimulating exercises, and they are frequently referred to in subsequent chapters. I found that some of the exercises were not adequately pre- sented. For example, in Exercise 12 on page 94 the 'pigeon hole principle' is stated as follows: 'If m objects are distributed into n boxes and m is larger than n, then at least one box contains min of the objects.' Does Trudeau mean 'exactly mln' or 'at least m/n'? Perhaps this uncertainty was left intentional- ly in view of an appended exercise, but I think the uncertainty should have been avoided. I also find it unfortunate that, in such an otherwise beautifully designed book, chapter numbers are not indicated at the head of at least every other page, in order to facilitate checking the numerous cross-references.

My criticisms of the book are trivial, and I highly recom- mend it to those interested in design configurations as well as to those who delight in mathematical games. I hope that Trudeau will bring his same approach to group theory, which may be considered complementary to graph theory in the mathematics of configurations. (For discussions of visual art

and exclamation marks towards the end of the book, will encourage his readers to persist. Moreover, if readers remem- ber to read at least in some degree 'as poets'-that is, responding to the striking imagery of black holes, wave packets, quarks, and baryon binding, rather than struggling with each and every equation-then they will find the book rewarding.

Physics for Poets was first published in 1970. The 1978 revised version, which includes nearly 30% new material, seems to have been designed primarily to make it more accessible by cutting down on the mathematics that made the first edition harder going. It ends with a series of questions suitable for students embarking on their first serious course in physics.

Dots and Lines. Richard J. Trudeau. Kent State Univ. Press, Kent, Ohio, U.S.A., 1978. 203 pp., illus. Paper, $6.50. Reviewed by Arthur L. Loeb*

This is a book on graph theory, the mathematical treatment of configurations; the four-color problem and the problem of the Koenigsberg bridges, for example, fall within its scope. One of the principal difficulties facing one unfamiliar with the subject is the large number of special terms; unless one has used them or has visual analogs to which to tie them, it is difficult to grasp the theorems and proofs and the concrete meaning of results obtained.

I found Trudeau's text a splendid and delightful introduc- tion to graph theory. There are numerous illustrations for each topic discussed and he proceeds patiently from simpler to more complex abstractions that have considerable power. For example, in an exercise at the conclusion of Chapter 2, using only elementary properties of rather simple graphs, one is asked to prove that in any gathering of six people there are three people who are and three people who are not mutually acquainted. This example of the interplay between graph theory and its application to problems of logic convincingly presents the value of this branch of mathematics.

Topics covered are Planar Graphs, Euler's Formula, Plato- nic Graphs, Coloring, Graphs of Genus Higher than Zero, Euler and Hamilton Walks. An Afterword deals with the solution of the four-color problem that had been announced just as the book was going to press. Rigor is stressed, and, in the rare instance when a theorem is not proven, the reason is pointed out explicitly as a demonstration of some of the idiosyncrasies of mathematics. One instance is Jordan's theorem: 'If C is a continuous simple closed curve in a plane, then C divides the rest of the plane into two regions having C as their common boundary. If a point P in one of these regions is joined to a point Q in the other by a continuous curve L in the plane, then L intersects C.' Trudeau points out that this theorem, seemingly so obvious, could not be proven by Jordan himself, and decades passed before a proof was found.

Each chapter contains from 18 to 40 stimulating exercises, and they are frequently referred to in subsequent chapters. I found that some of the exercises were not adequately pre- sented. For example, in Exercise 12 on page 94 the 'pigeon hole principle' is stated as follows: 'If m objects are distributed into n boxes and m is larger than n, then at least one box contains min of the objects.' Does Trudeau mean 'exactly mln' or 'at least m/n'? Perhaps this uncertainty was left intentional- ly in view of an appended exercise, but I think the uncertainty should have been avoided. I also find it unfortunate that, in such an otherwise beautifully designed book, chapter numbers are not indicated at the head of at least every other page, in order to facilitate checking the numerous cross-references.

My criticisms of the book are trivial, and I highly recom- mend it to those interested in design configurations as well as to those who delight in mathematical games. I hope that Trudeau will bring his same approach to group theory, which may be considered complementary to graph theory in the mathematics of configurations. (For discussions of visual art

and exclamation marks towards the end of the book, will encourage his readers to persist. Moreover, if readers remem- ber to read at least in some degree 'as poets'-that is, responding to the striking imagery of black holes, wave packets, quarks, and baryon binding, rather than struggling with each and every equation-then they will find the book rewarding.

Physics for Poets was first published in 1970. The 1978 revised version, which includes nearly 30% new material, seems to have been designed primarily to make it more accessible by cutting down on the mathematics that made the first edition harder going. It ends with a series of questions suitable for students embarking on their first serious course in physics.

Dots and Lines. Richard J. Trudeau. Kent State Univ. Press, Kent, Ohio, U.S.A., 1978. 203 pp., illus. Paper, $6.50. Reviewed by Arthur L. Loeb*

This is a book on graph theory, the mathematical treatment of configurations; the four-color problem and the problem of the Koenigsberg bridges, for example, fall within its scope. One of the principal difficulties facing one unfamiliar with the subject is the large number of special terms; unless one has used them or has visual analogs to which to tie them, it is difficult to grasp the theorems and proofs and the concrete meaning of results obtained.

I found Trudeau's text a splendid and delightful introduc- tion to graph theory. There are numerous illustrations for each topic discussed and he proceeds patiently from simpler to more complex abstractions that have considerable power. For example, in an exercise at the conclusion of Chapter 2, using only elementary properties of rather simple graphs, one is asked to prove that in any gathering of six people there are three people who are and three people who are not mutually acquainted. This example of the interplay between graph theory and its application to problems of logic convincingly presents the value of this branch of mathematics.

Topics covered are Planar Graphs, Euler's Formula, Plato- nic Graphs, Coloring, Graphs of Genus Higher than Zero, Euler and Hamilton Walks. An Afterword deals with the solution of the four-color problem that had been announced just as the book was going to press. Rigor is stressed, and, in the rare instance when a theorem is not proven, the reason is pointed out explicitly as a demonstration of some of the idiosyncrasies of mathematics. One instance is Jordan's theorem: 'If C is a continuous simple closed curve in a plane, then C divides the rest of the plane into two regions having C as their common boundary. If a point P in one of these regions is joined to a point Q in the other by a continuous curve L in the plane, then L intersects C.' Trudeau points out that this theorem, seemingly so obvious, could not be proven by Jordan himself, and decades passed before a proof was found.

Each chapter contains from 18 to 40 stimulating exercises, and they are frequently referred to in subsequent chapters. I found that some of the exercises were not adequately pre- sented. For example, in Exercise 12 on page 94 the 'pigeon hole principle' is stated as follows: 'If m objects are distributed into n boxes and m is larger than n, then at least one box contains min of the objects.' Does Trudeau mean 'exactly mln' or 'at least m/n'? Perhaps this uncertainty was left intentional- ly in view of an appended exercise, but I think the uncertainty should have been avoided. I also find it unfortunate that, in such an otherwise beautifully designed book, chapter numbers are not indicated at the head of at least every other page, in order to facilitate checking the numerous cross-references.

My criticisms of the book are trivial, and I highly recom- mend it to those interested in design configurations as well as to those who delight in mathematical games. I hope that Trudeau will bring his same approach to group theory, which may be considered complementary to graph theory in the mathematics of configurations. (For discussions of visual art

and exclamation marks towards the end of the book, will encourage his readers to persist. Moreover, if readers remem- ber to read at least in some degree 'as poets'-that is, responding to the striking imagery of black holes, wave packets, quarks, and baryon binding, rather than struggling with each and every equation-then they will find the book rewarding.

Physics for Poets was first published in 1970. The 1978 revised version, which includes nearly 30% new material, seems to have been designed primarily to make it more accessible by cutting down on the mathematics that made the first edition harder going. It ends with a series of questions suitable for students embarking on their first serious course in physics.

Dots and Lines. Richard J. Trudeau. Kent State Univ. Press, Kent, Ohio, U.S.A., 1978. 203 pp., illus. Paper, $6.50. Reviewed by Arthur L. Loeb*

This is a book on graph theory, the mathematical treatment of configurations; the four-color problem and the problem of the Koenigsberg bridges, for example, fall within its scope. One of the principal difficulties facing one unfamiliar with the subject is the large number of special terms; unless one has used them or has visual analogs to which to tie them, it is difficult to grasp the theorems and proofs and the concrete meaning of results obtained.

I found Trudeau's text a splendid and delightful introduc- tion to graph theory. There are numerous illustrations for each topic discussed and he proceeds patiently from simpler to more complex abstractions that have considerable power. For example, in an exercise at the conclusion of Chapter 2, using only elementary properties of rather simple graphs, one is asked to prove that in any gathering of six people there are three people who are and three people who are not mutually acquainted. This example of the interplay between graph theory and its application to problems of logic convincingly presents the value of this branch of mathematics.

Topics covered are Planar Graphs, Euler's Formula, Plato- nic Graphs, Coloring, Graphs of Genus Higher than Zero, Euler and Hamilton Walks. An Afterword deals with the solution of the four-color problem that had been announced just as the book was going to press. Rigor is stressed, and, in the rare instance when a theorem is not proven, the reason is pointed out explicitly as a demonstration of some of the idiosyncrasies of mathematics. One instance is Jordan's theorem: 'If C is a continuous simple closed curve in a plane, then C divides the rest of the plane into two regions having C as their common boundary. If a point P in one of these regions is joined to a point Q in the other by a continuous curve L in the plane, then L intersects C.' Trudeau points out that this theorem, seemingly so obvious, could not be proven by Jordan himself, and decades passed before a proof was found.

Each chapter contains from 18 to 40 stimulating exercises, and they are frequently referred to in subsequent chapters. I found that some of the exercises were not adequately pre- sented. For example, in Exercise 12 on page 94 the 'pigeon hole principle' is stated as follows: 'If m objects are distributed into n boxes and m is larger than n, then at least one box contains min of the objects.' Does Trudeau mean 'exactly mln' or 'at least m/n'? Perhaps this uncertainty was left intentional- ly in view of an appended exercise, but I think the uncertainty should have been avoided. I also find it unfortunate that, in such an otherwise beautifully designed book, chapter numbers are not indicated at the head of at least every other page, in order to facilitate checking the numerous cross-references.

My criticisms of the book are trivial, and I highly recom- mend it to those interested in design configurations as well as to those who delight in mathematical games. I hope that Trudeau will bring his same approach to group theory, which may be considered complementary to graph theory in the mathematics of configurations. (For discussions of visual art

*Dept. of Visual and Environmental Studies, Harvard Univer- sity, Cambridge, MA 02138, U.S.A. *Dept. of Visual and Environmental Studies, Harvard Univer- sity, Cambridge, MA 02138, U.S.A. *Dept. of Visual and Environmental Studies, Harvard Univer- sity, Cambridge, MA 02138, U.S.A. *Dept. of Visual and Environmental Studies, Harvard Univer- sity, Cambridge, MA 02138, U.S.A.

Eugene, OR 97403, U.S.A. **21 College Road, Cheltenham, Gloucester GL53 7HY, Eng- land.

Eugene, OR 97403, U.S.A. **21 College Road, Cheltenham, Gloucester GL53 7HY, Eng- land.

Eugene, OR 97403, U.S.A. **21 College Road, Cheltenham, Gloucester GL53 7HY, Eng- land.

Eugene, OR 97403, U.S.A. **21 College Road, Cheltenham, Gloucester GL53 7HY, Eng- land.

Books Books Books Books 333 333 333 333

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