Mathematics for AIXI and Gödel machine

post by Faustus2 · 2015-07-22T18:52:21.121Z · LW · GW · Legacy · 6 comments

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6 comments

Just a quick question, does anyone know which math topics I'd have to learn to understand the work on AIXI and the Gödel machine? Any pointers or suggestions would be appreciated. 

6 comments

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comment by MrMind · 2015-07-23T13:12:21.783Z · LW(p) · GW(p)

Classical logic up to Goedel's theorem.
Fairly standard Bayesian probability.
A little bit of coding (up to Kraft's inequality).
Computability and algorithmic complexity.
Solomonoff induction.

It's all pretty basic stuff, but taken from a variety of disciplines.

comment by Manfred · 2015-07-22T19:45:30.796Z · LW(p) · GW(p)

The things you directly need are algorithmic complexity theory (Classic textbook: Li and Vitanyi) and some way of understanding proofs (Probably start with regular mathematical logic / model theory, not sure of a standout textbook here, maybe Manin?, then look into modal logic, classic textbook by Boolos).

Prerequisites for those are mathematical logic, set theory, probability theory, and some amount of discrete math.

Replies from: Faustus2
comment by Faustus2 · 2015-07-22T20:23:41.932Z · LW(p) · GW(p)

Thank you, I'm grateful for your time.

comment by Gunnar_Zarncke · 2015-07-23T06:48:19.431Z · LW(p) · GW(p)

What (parts of) the areas mentioned in the other posts do you already know? That may significantly affect the specific recommendation and approach.

comment by V_V · 2015-07-22T20:39:14.616Z · LW(p) · GW(p)

Elementary probability theory, elementary theoretical computer science, Solomonoff's theory of inductive inference, reinforcement learning.

comment by Thomas · 2015-07-22T19:36:17.835Z · LW(p) · GW(p)

I think you have to invent, not just to learn this.