All of MyrddinE's Comments + Replies

An Intuitive Explanation of Solomonoff Induction

I am a bit confused... how do you reconcile SI with Gödel's incomleteness theorum. Any rigid symbolic system (such as one that defines the world in binary) will invariably have truths that cannot be proven within the system. Am I misunderstanding something?

6Eliezer Yudkowsky10yThere are things Solomonoff Induction can't understand which Solomonoff Induction Plus One can comprehend, but these things are not computable. In particular, if you have an agent with a hypercomputer that uses Solomoff Induction, no Solomonoff Inductor will be able to simulate the hypercomputer. AIXI is outside AIXI's model space. You need a hypercomputer plus one to comprehend the halting behavior of hypercomputers. But a Solomonoff Inductor can predict the behavior of a hypercomputer at least well as you can, because you're computable, and so you're inside the Solomonoff Inductor. Literally. It's got an exact copy of you in there.
5shokwave10yThe post covers that, though not by that name: When Solomonoff induction runs into a halting problem it may well run forever. This is a part of why it's uncomputable. Uncomputable is a pretty good synonym for unprovable, in this case.
But Somebody Would Have Noticed

Caffeine addiction. For years nobody had actually tested whether caffeine had a physical withdrawal symptom, and the result was patients in hospitals being given (or denied) painkillers for phantom headaches. It was an example of a situation that many people knew existed, but could not easily communicate to those whose belief mattered.