I. Dreams of Vaccines

The other day, I was speaking with someone I'll call Steve. I will generously describe Steve as skeptical of mRNA vaccines, believing them to be dangerous and possibly part of a grand conspiracy to profit from the deaths of millions. I ask why he believes this and he cites a widely circulated video with someone talking about how dangerous new mRNA technology may be. I haven't heard of this person before but a quick search reveals that, unsurprisingly, they aren't an immunologist: they practice something I've never heard of called "osteopathy." A few more searches reveal this to be a practice that is, at best, a form of alternative medicine whose benefits largely remain empirically undemonstrated and, at worst, complete woo. Furthermore, this person has been a vocal proponent of a certain debunked claim regarding autism and vaccines.

At this point, I am sufficiently convinced that no medical claims this person makes should be taken seriously. I tell Steve as much and show him what I found. He accuses me of ad hominem and that it is my intellectual responsibility to engage with the speaker's argument seriously, to refute the speaker's points.

While the nature of Steve's claim is correct, I think this may be a teachable moment for practical epistemic rationality. I think ad hominem, bulverism, argument from authority, and similar invalid species of argument have a tight grip on ordinary thinking because, though not valid by any means, they are decent heuristics for distinguishing possibly-maybe-true things from complete horseshit.

II. The Demonic Ratio

Suppose I'm riding on the bus when a demon apparates next to me and presses an unsettling, tentacled contraption to my forehead. He wants information regarding the nature of the ratio $\frac{c i r c u m f e r e n c e}{d i a m e t e r}$ for an arbitrary circle, assuring me that a wrong answer will result in unspeakable agony for all eternity.

If I knew anything about math before, I certainly don't right now, so I frantically consult the people sitting nearby and get three competing assertions:

Alice is a research mathematician and she asserts that the ratio of a circle's circumference to its diameter is always the irrational number $π$ , which is slightly bigger than 3.
Bob is a programmer and he asserts that this ratio is always 3.14.
Charles is the local tie dye enthusiast and he asserts

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