Meta Math - The Quest for Omega by Gregory Chaitin

By Gregory Chaitin

Gregory Chaitin, one of many world’s leading mathematicians, leads us on a spellbinding trip, illuminating the method during which he arrived at his groundbreaking theory.
Chaitin’s progressive discovery, the Omega quantity, is an exquisitely complicated illustration of unknowability in arithmetic. His investigations make clear what we will finally learn about the universe and the very nature of lifestyles. In an infectious and enthusiastic narrative, Chaitin delineates the categorical highbrow and intuitive steps he took towards the invention. he's taking us to the very frontiers of clinical considering, and is helping us to understand the art—and the sheer beauty—in the technology of math.

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Mutual Information Between X and Y The mutual information is equal to H(X) + H(Y) - H(X, Y). It's small if H(X, Y) is approximately equal to H(X) + H(Y). It's large if H(X, Y) is much smaller than H(X) + H(Y). Note that H(X, Y) cannot be larger than H(X) + H(Y) because programs are self-delimiting binary information. If two things have very little in common, it makes no difference if we consider them together or separately. But if they have a lot in common, then we can eliminate common subroutines when we calculate them at the same time, and so the mutual information will be large.

There is still some fire there," said Paracelsus, pointing toward the hearth. "If you cast this rose into the embers, you would believe that it has been consumed, and that its ashes are real. I tell you that the rose is eternal, and that only its appearances may change. " the disciple asked, puzzled. "The furnace is cold, and the retorts are covered with dust. " [Source: Jorge Luis Borges, Collected Fictions, translated by Andrew Hurley, Penguin Books, 1999, pp. 504-507. For the original La rosa de Paracelso, see Borges, Obras Completas, Tomo III, Emecé, 1996, pp.

But redundancy makes it possible to do error correction and error detection, which is very important for DNA (indeed DNA actually contains complementary base pairs, not individual bases, so that is already a form of redundancy). But unfortunately, in order for us to be able to prove theorems, we need to use a less complicated model, a toy model, one that applies well to meta-mathematics, but that does not apply well to biology. Remember: Pure mathematics is much easier to understand, much simpler, than the messy real world!

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