Understanding two of the weirdest theorems in math: Gödel’s incompleteness

November 17, 2023

Gödel's incomplete theorems are famously profound, strange, and interesting pieces of math. But it's hard to understand them, and especially hard to understand why they are true. I've never been quite satisfied with the explanations I've seen for the general public, so I wanted to take a crack at explaining what these theorems say and give a flavor of why they hold. See what you think: Incompleteness Theorem 1 is about whether all mathematical truths can be proven. The first inco...

Three big reasons we struggle to find the truth

June 3, 2021

As I see it, there are three main causes for our struggles to see the truth on any particular topic: 1. Mimicry: when our in-group promotes falsity that we copy 2. Incentives: when we predict that knowing the truth would feel bad or harm our objectives 3. Complexity: when the truth is hard to figure out Examples: 1. Mimicry • Some are Christians because all their friends and family are, too; some are atheists for the same reason. • Some think that it makes sense to ...

Hypothesis about America: people are coming to realize society is messed up

September 1, 2020

I've been coming to think that the following hypothesis may be true about America: Increasingly, people in the U.S. are concluding that society is really F'd up. But the reasons are subtle, hidden, and complex, so each group picks their favorite simple enemy to blame. Problems go unfixed. Points in favor of the claim that people are increasingly coming to this realization: 1. This helps explain Trump's election in 2016. Many rural Republicans and disaffected independents believed s...