Conversations with a Mathematician: Math, Art, Science and by Gregory J. Chaitin

By Gregory J. Chaitin

G. J. Chaitin is on the IBM Thomas J. Watson study middle in big apple. He has proven that God performs cube not just in quantum mechanics, yet even within the foundations of arithmetic, the place Chaitin came across mathematical proof which are real for no cause, which are actual accidentally. This e-book collects his so much wide-ranging and non-technical lectures and interviews, and it'll be of curiosity to someone all for the philosophy of arithmetic, with the similarities and changes among physics and arithmetic, or with the artistic procedure and arithmetic as an art.
"Chaitin has placed a scratch at the rock of eternity."
Jacob T. Schwartz, Courant Institute, manhattan college, USA
"(Chaitin is) one of many nice principles males of arithmetic and laptop science."
Marcus Chown, writer of The Magic Furnace, in NEW SCIENTIST
"Finding the correct formalization is a big part of the artwork of doing nice mathematics."
John Casti, writer of Mathematical Mountaintops, on Godel, Turing and Chaitin in NATURE
"What mathematicians over the centuries - from the ancients, via Pascal, Fermat, Bernoulli, and de Moivre, to Kolmogorov and Chaitin - have found, is that it ÄrandomnessÜ is a profoundly wealthy concept."
Jerrold W. Grossman within the MATHEMATICAL INTELLIGENCER

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Extra resources for Conversations with a Mathematician: Math, Art, Science and the Limits of Reason

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My view is that science is crazier than magic. The real world is crazier than science fiction or fantasy. But to read the physics you have to understand some mathematics, and so I tried to learn some math. And there seemed to be something rather mysterious, that sort of in a way was analogous to Einstein's theory and to quantum mechanics, in math. And that was G6del's incompleteness theorem. And it fascinated me and it was very mysterious. So I was interested in that fairly young. But the idea I had at 15 was a definition of lack of structure or lack of pattern.

Besides the fact that it's my idea so obviously I'm going to be prejudiced! The reason is because program-size complexity connects with a lot of fundamental stuff in physics. You see, in physics there's a notion called entropy, which is how disordered a system is. Entropy played a particularly crucial role in the work of the famous 19th century physicist Boltzmann, Ludwig Boltzmann and it comes up in the field of statistical mechanics and in thermodynamics. Entropy measures how disordered, how chaotic, a physical system is.

Maybe a few friends of mine and I were trying to do it, and this was the best program that we came up with; nobody did any better. But how can you be sure? Well, the answer is that you can't be sure. It turns out you can never be sure! You can never be sure that a computer program is what I like to call elegant, namely that it's the most concise one that produces the output that it produces. Never ever! This escapes the power of mathematical reasoning, amazingly enough. But for any computational task, once you fix the computer programming language, once you decide on the computer programming language, and if you have in mind a particular output, there's got to be at least one program that is the smallest possible.

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