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Triangle of Thought, by Alain Connes, Andre Lichnerowicz, Marcel Paul Schutzenberger
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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, Andre Lichnerowicz, and Marcel Paul Schutzenberger, 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 Schutzenberger 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. Alain Connes is one of the founders of non-commutative geometry. He holds the Chair of Analysis and Geometry at the College 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. Andre Lichnerowicz, mathematician, noted geometer, theoretical physicist, and specialist in general relativity, was a professor at the College de France. Marcel Paul Schutzenberger made brilliant contributions to combinatorics and graph theory. He was simultaneously a medical doctor, a biologist, a psychiatrist, a linguist, and an algebraist.
- Sales Rank: #2460191 in Books
- Published on: 2001-01-01
- Original language: English
- Dimensions: 9.00" h x 6.00" w x .50" l, .80 pounds
- Binding: Hardcover
- 179 pages
About the Author
Alain Connes, College de France, Paris, France,
Most helpful customer reviews
0 of 0 people found the following review helpful.
like in the most intriguing novel
By Marcial Losada
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.
0 of 0 people found the following review helpful.
Phenomenal discourse!
By Kevin Roberge
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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