This post presents a conjecture formulated at the Alignment Research Center in 2023. Our belief in the conjecture is at least partly load-bearing for our belief in ARC's overall agenda. We haven't directly worked on the conjecture for a while now, but we believe the conjecture is interesting in its...
Last week, ARC released a paper called Towards a Law of Iterated Expectations for Heuristic Estimators, which follows up on previous work on formalizing the presumption of independence. Most of the work described here was done in 2023. A brief table of contents for this post: * What is a...
This post presents a conjecture formulated at the Alignment Research Center in 2023. Our belief in the conjecture is at least partly load-bearing for our belief in ARC's overall agenda. We haven't directly worked on the conjecture for a while now, but we believe the conjecture is interesting in its own right.
In a recent paper in Annals of Mathematics and Philosophy, Fields medalist Timothy Gowers asks why mathematicians sometimes believe that unproved statements are likely to be true. For example, it is unknown whether is a normal number (which, roughly speaking, means that every digit appears in with equal frequency), yet this is widely believed. Gowers proposes that there is no sign of any... (read 1778 more words →)
Last week, ARC released a paper called Towards a Law of Iterated Expectations for Heuristic Estimators, which follows up on previous work on formalizing the presumption of independence. Most of the work described here was done in 2023.
A brief table of contents for this post:
In "Formalizing the Presumption of Independence", we defined a heuristic estimator to be a hypothetical algorithm that estimates the values of mathematical expression based on arguments. That is, a heuristic estimator is an algorithm that... (read 6585 more words →)