Triangle of Thought [Hardcover]

Alain Connes (Author), Andre Lichnerowicz (Author), Marcel Paul Schutzenberger (Author), Jennifer Gage (Translator)

Book Description

ISBN-10: 082182614X | ISBN-13: 978-0821826140 | Publication Date: January 1, 2001

Our view of the world today is fundamentally influenced by twentieth century results in physics and mathematics. Here, three members of the French Academy of Sciences: Alain Connes, André Lichnerowicz, and Marcel Paul Schützenberger, discuss the relations among mathematics, physics and philosophy, and other sciences. Written in the form of conversations among three brilliant scientists and deep thinkers, the book touches on, among others, the following questions:

Is there a "primordial truth" that exists beyond the realm of what is provable? More generally, is there a distinction between what is true in mathematics and what is provable?

How is mathematics different from other sciences? How is it the same? Does mathematics have an "object" or an "object of study", the way physics, chemistry and biology do?

Mathematics is a lens, through which we view the world. Connes, Lichnerowicz, and Schützenberger examine that lens, to understand how it affects what we do see, but also to understand how it limits what we can see.

How does a well-informed mathematician view fundamental topics of physics, such as: quantum mechanics, general relativity, quantum gravity, grand unification, and string theory?

What are the relations between computational complexity and the laws of physics?

Can pure thought alone lead physicists to the right theories, or must experimental data be the driving force? How should we compare Heisenberg's arrival at matrix mechanics from spectral data to Einstein's arrival at general relativity through his thought experiments?

The conversations are sprinkled with stories and quotes from outstanding scientists, which enliven the discourse. The book will make you think again about things that you once thought were quite familiar.

Editorial Reviews

About the Author

Alain Connes is one of the founders of non-commutative geometry. He holds the Chair of Analysis and Geometry at the Collège de France. He was awarded the Fields Medal in 1982. In 2001, he was awarded the Crafoord Prize by The Royal Swedish Academy of Sciences.

André Lichnerowicz, mathematician, noted geometer, theoretical physicist, and specialist in general relativity, was a professor at the Collège de France.

Marcel Paul Schützenberger made brilliant contributions to combinatorics and graph theory. He was simultaneously a medical doctor, a biologist, a psychiatrist, a linguist, and an algebraist.

Product Details

• Hardcover: 179 pages
• Publisher: Amer Mathematical Society (January 1, 2001)
• Language: English
• ISBN-10: 082182614X
• ISBN-13: 978-0821826140
• Product Dimensions: 8.7 x 5.8 x 0.6 inches
• Shipping Weight: 12.8 ounces (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,966,689 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

6 of 7 people found the following review helpful:

3.0 out of 5 stars A too abstract triangle, February 10, 2008

By 

Jaume Puigbo Vila "cosmos fan" (Barcelona, Spain) - See all my reviews
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This review is from: Triangle of Thought (Hardcover)

The goal of this book is "to enable a broad but enlightened audience to bridge the growing gap between the subtleties of these advances (meaning quantum mechanics, relativity and Gödel's theorem), usually accessible only to specialists, and the often unbelievably deformed images of them presented by popularized accounts".

I must disagree. Although the reader will attend an interesting dialogue between some of the top minds of the XXth century and Alain Connes is one of the greatest living mathematicians, it is difficult to follow a great part of this conversation if you are not familiar with advanced mathematics and physics. The publisher could have made the reading easier by including a lot of sidebars as Scientific American does. On the other hand I have read quite a number of books by very good scientists on the topics mentioned (therefore they could not be deformed images) and these books are much more accessible than "Triangle of Thoughts". If you have read the other Connes co-authored book, "Conversations on Mind, Matter and Mathematics", the level of accessibility of this one is similar.

That said, the book is worth reading and there are sections which are quite readable like that on Cosmology, on game theory or even on Gödel's theorem. Alain Connes introduces a distinction between primordial mathematics and axiomatic mathematics which he considers an (limited) instrument of comprehension at our disposal. Gödel affirms that any sufficiently rich axiomatic system contains truths that are not provable and it has the curious consequence that you can add a countertruth to an axiomatic system which will be free of contradiction if the former system was non contradictory.

That the book needs some editing is clear. On one hand the authors describe what a well ordering is, something that is explained in Europe in the first year of college mathematics, on the other the paragraphs such as: "The phase space is sympletic and the Hamiltonian is a function on this space that we call the `energy', and it generates the evolution of observable quantities with its Poisson bracket" give an idea of what the authors understand as "enlightened audience".
In conclusion, the book deserves 5 stars if you are part of such audience, but only three if you are a mere mortal with a good science education.