Monday, September 18, 2023

Impossibility of Solomonoff Induction Refuted by Greeks

Solomonoff induction is the proven guaranteed-truth machine. SI is Sherlock Holmes reasoning: if you eliminate the impossible, wisdom remains, no matter how seemingly improbable.

"Obviously Solomonoff Induction is impossible to do in the real world." 


Allegedly, Solomonoff induction doesn't work because the search space is too big: any search strategy using less than infinite resources has a 0% chance of stumbling across the correct hypothesis, and thus all your guesses will die during the pruning phase. There's just too many false hypotheses to find the truth in this haystack. This is indeed true if you're talking about silicon machine intelligence.

Reality: Anaximander's theory of evolution. Hero's steam engine. Democritus' theory of atoms and the void.

The Greeks could have derived the entirety of the modern world had they taken Solomonoff induction seriously. The only thing stopping them from inventing semiconductors and conquering the entire world was their unwillingness to engage in a pruning phase. All they had to do was eliminate non-Hero engines, and then look more deeply into Hero's engine. Reminds me of the time I searched all over my desk and couldn't find my glasses, because they were on my forehead. 

Despite endless proofs that you cannot successfully carry out a Solomonoff search phase, empirically, you can and do. Sorry, a strategy does exist. However. It's not a material strategy. Can't implemented Solomonoff search on an unconscious thinking machine. 

It's not only possible, you already know how to do it. Think up all the possibilities. Okay, now realize you missed some and think those up too. Yes, really, all the possibilities. Everything that hasn't already been eliminated, no matter how weird. Okay now you're done. You're good, go prune. 

Compared to the profits the method cannot be called even remotely hard, never mind [impossible]. (P.S. This is why it's a good idea to attempt 'impossible' things.) At worst, you end up pruning every possibility and realize you didn't quite finish the search, meaning the method is absurdly robust: if you do it wrong, the method itself tells you what you did wrong.


P.S If the Greeks were truly intelligent, they would have also derived the profanity of Fascism thus discarding it, resulting in all the benefits of the modern world without any of the downsides. Techno-Amish.

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