# Tag Archives: mathematics

## Artificial Neural Networks

Of the many, many different ideas put forward to explain, model, and experiment with artificial cognition, one of the most practically successful is the Artificial Neural Network. Not because we’ve managed to actually create cognition with one, but because of … Continue reading

## Bayesian Networks

I have mentioned before that Bayesian Inference is, in general, intractable. People like Gaussians a lot because many nice results in closed-form can be derived from them, analytical treatments are in general possible and even easy to do, but for … Continue reading

## Stopping rules, p-values, and the likelihood principle

A few months ago, someone who used to be called perversesheaf came to tumblr to bash LessWrong there. Now, while there is a very large number of criticisms that can be aimed at it, both as a website and community, … Continue reading

## Confidence and Credibility

Three days ago I got slightly drunk with a few friends (two of which were mentioned in a recent post) and one of them and I were trying to explain to the other what the difference between confidence and credible intervals were. Since … Continue reading

## Learning Bayes [part 3.5]

In part 3, I discussed the problem of finding a way of drawing a posterior point estimate of a number  based on a series of point estimates that’s more “theoretically valid” than taking the median, which is the standard of the … Continue reading

## Learning Bayes [part 3]

I was talking to a friend (the same friend who inspired the two previous posts), who was talking to a friend of ours about a thing, and there’s a context but it doesn’t matter to what I want to write here. Suppose … Continue reading

## An (Intuitive?) Introduction to Entropy

There’s a concept in Probability Theory called “entropy,” which borrows a bit from the physical concept of the same name. Intuitively, it’s the degree of “surprise” of an observation, or of a probability distribution. Alternatively, it’s how much information you gain … Continue reading

## Truth, Probability, and Unachievable Consistency

What is truth? Many an author has written lengthy philosophical treatises that begin with exactly this question, but, however shaky my identification with the group may be, as a rationalist my first and foremost answer to that question – or my … Continue reading

Posted in Mathematics, Probability Theory, Rationality | | 3 Comments

## What’s logical coherence for anyway?

Time for a writeup! Or something. So I’ve written before about Logical Uncertainty in a very vague way. And a few weeks ago I wrote about a specific problem of Logical Uncertainty which was presented in the MIRI workshop. I’m gonna reference definitions and results from … Continue reading

## The Gaifman Condition and the Π1-Π2 problem

So I’m at a MIRI workshop on Logical Uncertainty, and I’m gonna make a more complete post about it later, but I wanted to talk about a thing that has been on my mind. So we’re trying to build a … Continue reading

Posted in Logic, Mathematics, Probability Theory | | 9 Comments