Wednesday, December 28, 2005

Theories are Compression Algorithms

Finished reading "Meta Math!" by Gregory Chaitin. A short (151 p plus appendices) and easy read. Basically, it's about the philosophy of math, following Godel and Turing. The main point is: all theories are about compressing information. A theory that has to detail all its results is not much of a theory. Similarly, DNA is a compression of an organism, axioms are a compression of the theorems you can prove from them.

Lots of interesting examples of this, always shown as input, processor, output:

  • encoded message -> Decoder -> original message (per Shannon and information theory)
  • scientific theory -> Calculations -> experimental data (the scientific method)
  • program -> Computer -> output (AIT, Algebraic Information Theory)
  • DNA -> Embryogenesis/Development -> organism (molecular biology)
  • axioms -> Deductions -> theorems (FAS, Formal Axiomatic System)
  • TOE (Theory of Everything) -> Calculations -> universe (physics)
  • ideas -> Mind of God -> the world (Liebniz)
A lot of his stuff he ideas he traces back to Leibniz (who we enjoyed so much in Stephenson's Quicksilver novels) in the late 17th century. Also very interesting, a semi-proposal to do away with real numbers??? Basically, real numbers (the continuum) are transcendental (not algebraic, the solution of a polynomial equation), uncomputable, random and unnameable with probability 1. Plus they give physics fits and lead to attempts to get around the difficulties such as string theory.

Also interesting discussion of randomness, per Borel. You cannot formally define maximum randomness! Any definition limits the randomness of what you define, making it not maximally random?!?!?

Numerous references to Wolfram's "A New Kind of Science". Interesting that he supports the concept of mathematics as an empirical science. The intractablilty of the real numbers indicates, you just have to get out there and explore?!?!?

The subtitle of the book is "The Quest for Omega". Chaitin's main claim to fame is that he defined the Omega number: the probability that a program of n bits will halt.

For xmas, got a 10 million candle power spotlight from my father-in-law, the king of over-the-top gifts. 91 years old and still with 95%+ of his wits about him. Also got from my oldest daughter "Ratatat", eponymous, kind of ambient trancy stuff, 2 stars, and Bloc Party, "Silent Alarm", nice peppy alterna-rock, 3 stars.

I am moving ahead in moving more 3 star songs to 2 stars. When I first got iTunes, I was thinking about how many better query front-ends I had written than its smart playlists. The star classification system is chafing me too. Maybe hack iTunes, or write my own music librarian?

Movie-wise, watched "Mr. and Mrs. Smith", fun; "A Hitchhiker's Guide to the Galaxy", more enjoyable than I expected; and "The Island", also more fun than I expected. In "The Island", tho, as with lots of pop culture, bad science is a little troubling. *** Spoiler Alert *** That clones could start to recall their original's memory has precedent in sci-fi, and what the heck, it's just entertainment, right? But, that they could not grow clones for organs and have the organs be healthy without allowing the clones to develop consciousness -- it's one of those things that could lead people to subconsciously oppose cloning -- for no good reason (not that there may not be good reasons).

The Greg Egan short story collections (last blog) had a few stories expressing his fear and mistrust of wishful, spiritualist thinking. Entertainment is good, but, for how many people is this what actually forms their opinions? Back to, need to make everybody smarter. Well, I have read, I don't remember where, that IQs are going up -- although I have seen far more stories on the ignorance of current high school graduates and college students. Still, the metacortex (ala Stross) seems to be growing individually and collectively, I think we may get there.

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