Tuesday, May 31, 2016

Compression, Randomness, a theory of everything, and a 200TB proof

If the universe is describable (and I think it is if we allow neologisms), will its description fit in 1,000 pages? There is a computer that in two days apparently churned out a 200 TB proof yet my assumption is that the code is probably less than one GB. 200000GB to 1 GB is a mighty high compression ratio. Lossless compression at that. That 200 TB proof contains enough structure to be a proof. One could call the code that produced it a description of the proof.

In fact, 200,000:1 is exceptional levels of structure.

I tried using winRAR to compress various types of things. I attempted to compress white noise, speech, and a perfect 440Hz. I also compressed the output of a random number generator, plainext, and ciphertext. Finally images.

None of them is as high a compression ratio 200000:1 but that pales in comparison to infinite compression:

A sequence of all ones.

That description is a lossless compression of an infinite string to a finite string. So infinite to finite compression is attainable.

The question is will we ever find it?

Imagine the totality of all descriptions. This is included in the so called hyperwebster. Since the universe is describable, the hyperwebster contains that description.

Is that close?

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