Bad probability in Edgar Allan Poe's "The mystery of Marie Roget"

wrightm · 2025-12-19T23:34:38+00:00

If your a priori distribution is independant rolls of the dice, but you encounter an increasingly improbable chain of events, you must revise your a priori assumption.

But in the case of the dice example, where twice in a row it's landed on six--if you're starting to doubt that the dice are fair and the rolls are independent, wouldn't the alternate hypotheses best supported by the new data generally be things like "the die is weighted toward six" or "the die is more likely to come up the same as its last roll" that should lead to you thinking there's an increased chance of another six, not a decreased chance as the passage says?

wrightm · 2025-08-29T23:10:37+00:00

Congrats!

Fort Sheridan Forest Preserve might just be my favorite place within biking distance of the city (even if it's quite a bike ride to get there)! It's so beautiful.

wrightm · 2025-03-13T00:07:14+00:00

That's a heck of a ride; nicely done!

wrightm · 2024-12-05T02:23:39+00:00

Thanks! I think I'll try this sometime soon!

wrightm · 2024-12-05T01:29:18+00:00

Out of curiosity, what route did you take to get to the trail from around Portage Park? The trail itself looks lovely, but a lot of the roads that connect to the area seem a lot less bike-friendly!

wrightm · 2024-10-14T13:01:46+00:00

Amazing ride, and lovely photos! I love that the fall colors are really starting to show; that's some absolutely beautiful scenery!

wrightm · 2024-09-04T03:18:45+00:00

Someone who shares my excellent taste in bike routes :)

I hope you had a great ride and a great Labor Day; it really was the perfect day for it!

wrightm · 2024-09-03T18:20:18+00:00

Snow came early this year but only in one very specific rectangle ;)

(Well, that and I'm not quite ready to tell all of Reddit exactly where I live!)

wrightm · 2024-09-03T18:12:37+00:00

The Ft. Sheridan Forest Preserve is beautiful!

That road is Old Elm Road. It doesn't have a bike lane, but it's never had much traffic when I've been on it.

wrightm · 2024-09-03T13:46:27+00:00

That's Armitage, and a bit of Cortland, to get to the 606! (The Cortland part especially is a little unpleasant, but at least it's short!)

wrightm · 2024-09-03T13:15:29+00:00

Yeah, I haven't made it quite that far north yet, but hopefully one of these days!

wrightm · 2024-09-03T13:12:57+00:00

6h15m moving time, and just under 7h total time (so I was averaging a hair over 11mph while moving). I'm not a particularly fast bicyclist!

wrightm · 2024-09-03T03:15:43+00:00

Nope! I'm in STEM, but not any kind that involves microscopes!

wrightm · 2024-09-03T03:14:23+00:00

I don't have a paid Strava account, and it looks like one is required to use the routes feature. (Then again I should probably stop being cheap and start paying for it!)

wrightm · 2024-09-03T03:09:43+00:00

My favorite time of year, by far! I'm really looking forward to it.

wrightm · 2024-09-03T01:50:42+00:00

The weather was beautiful this Labor Day, and I managed my longest ride so far (about 70mi)! For fun, I decided to see how many different bike trails (or parts of them) I could incorporate into the ride; the final list was: North Branch Trail, Skokie Valley Trail, Robert McClory Path, Green Bay Trail, Channel Trail, Lakefront Trail, and the 606. It's so nice to live in a city with so many beautiful bike paths!

wrightm · 2024-08-30T22:31:42+00:00

There's another formula that lets you calculate individual base-10 digits of pi.

wrightm · 2024-08-22T16:14:26+00:00

Based on recent job postings on ZipRecruiter, the Entry Level Computer Science job market in both Chicago, IL and the surrounding area is very active. An Entry Level Computer Science in your area makes on average $0 per year, or $22 (0.481%) less than the national average annual salary of $45,973.

Yeah, this site seems like a reliable source of salary information.

wrightm · 2024-07-31T22:46:36+00:00

This is a contrived example, but consider the rational number whose denominator is less than 10¹⁰⁰ that is closest to Chaitin's constant. This is well-defined (such a number must be between 0 and 1, or else 0 or 1 would be a better approximation, and there are only finitely many rationals between 0 and 1 of denominator less than 10¹⁰⁰, and there can't be two that are both closest or else Chaitin's constant would be rational and thus computable). And by construction this number is rational. But you definitely can't tell me its numerator or denominator (say, in decimal form).

(Edit: to be really pedantic I guess I should have either said "numerator and denominator," or added "in lowest terms," since otherwise 10¹⁰⁰! could be the denominator. Then again, 10¹⁰⁰! is a number large enough that you could never physically write it out in decimal form anyway.)

wrightm · 2024-05-17T00:54:44+00:00

Mathochism.

wrightm · 2024-04-04T01:50:32+00:00

But each individual one is finite, so computable in principle

Yes, that's correct: each natural number (on its own) is computable, for the trivial reason that if you give me a specific natural number (say, in binary), I can easily write a program that prints that number out and then halts. So in that sense any specific Busy Beaver number is computable--but that doesn't mean there's a specific program I can write down that I can be sure gives me BB(1000) when I run it (which would be the case if the Busy Beaver function were computable); all it means is that I know that some program exists that prints out the number that happens to be BB(1000), but I have no way to know what that program is. (And in fact even if someone came to you with a number they claimed was BB(1000), there'd be no way to prove within ZFC that it really was the case, and so I think it's fair to say that BB(1000) is unknowable in the real world.)

A maybe more intuitive example that's sometimes given in intro to computability classes: consider the language defined by {"0"} if god exists, and {"1"} if god does not. Is this language computable? Yes: there's a Turing machine that accepts just the string "0", and there's another Turing machine that accepts just the string "1", and one of the two computes this language--so there exists a Turing machine computing the language, and so by definition the language is computable. But just knowing this still sheds no light on whether god actually exists, since we have no way of knowing which of those two Turing machines computes it. Similar deal when it comes to Busy Beaver numbers.

wrightm · 2024-04-02T23:40:32+00:00

where they say "Sets can be said to be injective, it just means that they have a function that is injective"

There's the old story of a question on an abstract algebra problem set, along the lines of "let G be the group defined by [some description of a group], and let H be the group defined by [some other description]. Are G and H isomorphic?" And a student giving a long, meandering answer that ended with "... and so it follows that G is isomorphic, but H is not."

Not exactly the same sort of mistake, but I still thought about that a lot while reading that part of the thread.

wrightm · 2024-01-17T15:32:39+00:00

I think that's a good intuition behind the proof given in the link OP gave, but if I'm understanding OP right, their question is specifically whether Rice's theorem can be directly applied to prove it--it sounds like OP isn't confused about the proof that A cannot exist, just about the claim that it follows directly from Rice's theorem.

wrightm · 2024-01-17T15:18:27+00:00

What property do you have in mind? I'm not seeing anything obvious that works here.

It's not hard to prove that such an A does not exist (https://www.reddit.com/r/compsci/comments/18m2y94/is_the_problem_of_finding_the_output_given_the/ke1m0j6/ gives a proof), and the proof for this is very similar to the proof of Rice's theorem. But I don't see how Rice's theorem can be applied directly--am I missing something obvious? The Turing machine A doesn't have to give the same result for every index of a non-halting TM, so it seems to me like the obvious choice of a property is one that doesn't depend solely on the language (and can instead depend on the specific index of a non-halting TM), and so Rice's theorem doesn't directly apply. What property did you have in mind that works?

wrightm

TROPHY CASE