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Triangle of Thought

4.3 out of 5 stars 3 customer reviews
ISBN-13: 978-0821826140
ISBN-10: 082182614X
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About the Author

Alain Connes, College de France, Paris, France,

Product Details

  • Hardcover: 179 pages
  • Publisher: Amer Mathematical Society (January 1, 2001)
  • Language: English
  • ISBN-10: 082182614X
  • ISBN-13: 978-0821826140
  • Product Dimensions: 0.5 x 6 x 9 inches
  • Shipping Weight: 12.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #2,470,324 in Books (See Top 100 in Books)

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Format: Hardcover Verified Purchase
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.
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Format: Hardcover Verified Purchase
This is now one of the few printed books that I keep in my shelf (I am now a Kindle-converted reader, which I though I would never be).

I have read this book at least three times. Not because it is hard to understand, but for the depth of thinking that characterizes the book. There are no equations here, just profound thoughts that keep you interested all the time, like in the most intriguing novel.

I have often wondered, like countless others, about the "unreasonable" power of mathematics. My field is human interaction processes (social psychology) and I have found that many mathematical structures (functions, abstract spaces, group symmetry) often shed a bright light into the complexity of human interaction. I remember a talk I gave at Los Alamos National Laboratory, where one of the mathematicians there told me: "your are dealing with the 8-body problem" referring to the number of the team members I often worked with. If it weren't for mathematics, these almost intractable problems could not be even approached successfully.

Herein lies my unending interest in Triangle of Thoughts. This book in conjunction with Changeux and Connes's Conversatons on Mind, Matter and Mathematics, should be mandatory reading for graduate students in social psychology who might want to venture into the very reasonable power of mathematics to unveil the dark corners of human interaction where many unexpected findings await them.
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Format: Hardcover
This sort of casual conversation that wanders across these three passions of mine: physics, philosophy and mathematics, is rare. As you read these great minds jump all over deep topics and the history of their development. The conversation is inspiring for its depth and breadth and I recommend reading this along with your cup of coffee. To appreciate all the references, at least in passing, it would be helpful to have some graduate work in physics or mathematics coupled with a broad interests. The layperson is likely to find many references that are unfamiliar to them. However you can gloss over those passages or pause and do a little background research in the meantime before returning to the passage. This is just another example of why Alain Connes is one of my new mathematical heroes.
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