Jay's Blog

Math, Teaching, Literature, and Life


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Twitter: @ProfJayDaigle

Recent Posts:

Hypothesis Testing and its Discontents, Part 1: How is it Supposed to Work?

March 31, 2022

This is the first part in a planned three-part series explaining what hypothesis testing is and how it works. In this essay I'll talk about the way hypothesis testing developed historically, in two rival schools of thought. I'll explain how these two methodologies were originally supposed to work, and why you might (or might not) want to use them.

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Why Isn't There a Replication Crisis in Math?

February 02, 2022

The replication crisis is a major problem in medicine and social science; we know that a huge fraction of the published literature is outright wrong. But in math we don't seem to have a similar crisis, despite reasonably frequent minor errors in published papers. Why not, and what can this tell us about the fields that are in crisis?

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Pascal's Wager, Medicine, and the Limits of Formal Reasoning

November 28, 2021

A back-of-the-envelope cost-benefit analysis tells us that taking ivermectin for covid might have positive expected value. If we follow that logic to its conclusion, we wind up taking twenty different supplements and this seems like it can't be wise. Resolving this apparent conflict exposes some of the deep flaws in how we often think about rationality and Bayesian reasoning. A response to a piece by Scott Alexander at Astral Codex Ten.

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More Thoughts on the Axiom of Choice

July 28, 2021

I got a lot of good, interesting comments on my recent post on the axiom of choice (both on the post itself, and in this very good Hacker News thread). I wanted to answer some common questions and share the most interesting thing I learned.

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What is the Axiom of Choice?

July 14, 2021

One of the easiest ways to start a (friendly) fight in a group of mathematicians is to bring up the axiom of choice. I'll explain what it is, why it's so controversial, and hopefully shed some light on how we choose axiomatic systems and what that means for the math we do.

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