
Fixed Point Theorems
 2592 wordsFixed Point Theorems Introduction A fixed point of a function \(f(x)\) is a point such that \(f(x) = x\). Fixed point theorems are theorems that that show that various types of functions have fixed points. Sometimes, they even give you a method for finding those fixed points. Fixed point theorems...

The Solomonoff Prior is Malign
 5089 wordsCross posted from LessWrong. This argument came to my attention from this post by Paul Christiano. I also found this clarification helpful. I found these counterarguments stimulating and have included some discussion of them. Very little of this content is original. My contributions consist of fleshing out arguments and constructing...

Death is Bad
 563 wordsWhen I was about 13, I was at a birthday party. Someone started clapping and said: “every time I clap, someone in the world dies.” Someone else called out: “then stop clapping your hands!” Laughter ensued, and the incident was quickly forgotten. While you are reading this sentence, someone in...

Stories of my Life
 392 wordsYesterday was my 22nd birthday, marking the end of my 22nd year on Earth. In honor of this, here are 22 stories of my life: When I was one, I locked myself inside the bathroom. My mother once took me shopping and I hid inside a circular clothes rack. Afterwards,...

How to Construct Bets
 483 wordsSuppose I think event \(E\) is going to happen with 50% chance and my friend thinks that it’s going to happen with 70% chance. Clearly, we should bet on it, but how do we do that? Simple algebraic manipulations suffice to show that a fair bet assuming \(E\) happens at...