Astral Codex Ten

Bayes’ Theorem

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Bayes’ Theorem

Article

Bayes’ Theorem is a recurring concept in the Astral Codex Ten archive, appearing 3 times across 3 issues between November 07, 2024 and October 30, 2025. The archive places it in contexts such as “You would solve this with Bayes’ Theorem”; “part of the answer is Bayes’ theorem”; “If we want to Eganize Bayes’ theorem”. It most often appears alongside Biden, Eliezer, Trump.

Metadata

  • Category: Concepts
  • Mention count: 3
  • Issue count: 3
  • First seen: November 07, 2024
  • Last seen: October 30, 2025

Appears In

Source Context

Recovered passages from the original issue text. When the raw archive preserved outbound links inside the source passage, they are listed directly under the quote.

Congrats To Polymarket, But I Still Think They Were Mispriced
November 07, 2024 · Original source
Suppose you have a coin. You think there's a 90% chance it's fair and a 10% chance it’s biased 60/40 heads. Then you flip the coin and comes up heads. What should your new probability be? You would solve this with Bayes’ Theorem; the answer is 88% chance it’s fair, 12% chance it’s biased.
Bayes For Everyone
May 30, 2025 · Original source
It probably won’t surprise you that I think part of the answer is Bayes’ theorem. But the equation is famously prickly and off-putting:
I’ll be honest: I’ve learned something from each of these, but I think we can do even better. Specifically, I think that by using the paradigm I introduced in that book review — that of the recently-deceased philosopher Kieran Egan — we can make understanding and enjoying Bayes’ theorem a perfectly normal thing not just for quantitative geeks, but for more-or-less everyone. I’ve recently begun to test this out, and thought others might benefit from seeing what I’ve learned.
Anyhow, if we want to Eganize Bayes’ theorem, what we need to remember is that while the new tools have precision, the old tools have power. If we see Bayes’ theorem as one of the peaks of the new way of understanding, the question becomes, how can we use the old tools to secure Bayes in kids’ minds?
Links For October 2025
October 30, 2025 · Original source
27: Also Fatima-related: in the comments highlights post, I linked FLWAB’s criticism of David Hume’s argument against ever believing miracles. Joe James argues that FLWAB, myself, and other critics are misunderstanding Hume’s argument. FLWAB says no he isn’t. They continue the discussion in the comments, but neither comes off looking great, and they don’t get anywhere. I’m unfortunately still confused - there are many cases where something that never happened before happens for the first time. For example, nobody had ever seen a grizzly-polar bear hybrid until recently, so “the universal testimony of mankind” was that this didn’t happen. But when a reliable person did see it, we had little trouble imagining that we were wrong and it was simply very rare, or a new thing happening now because of climate change. If nobody has ever seen a sea part before, but then many people say they saw Moses part the Red Sea, what is different about this such that “the universal testimony of mankind” suddenly becomes a disqualifier? Hume seems to be trying to make this same distinction in his eight days of darkness example, but there it seems like he is only saying he will accept non-religious anomalies, but rule out religious ones, because religious people often lie. But then what happened to the “universal testimony of mankind” argument? I kind of get the impression that he’s groping towards Bayes’ Theorem, but hard-coding in a belief that the prior probability of lots of religious people lying is higher than the probability of a miracle. If that’s his belief, then fair enough, but I guess I expected the much-vaunted Hume’s Argument Against Miracles to be something more than this.
Inline links: criticism of David Hume’s argument against ever believing miracles., are misunderstanding Hume’s argument, no he isn’t, eight days of darkness example