Fortunately these days I have a very patient interlocutor named ChatGPT blessed with an infinite tolerance for half-baked questions and a soothing lack of judgmentality.
I know it’s popular to say AI is overhyped or not actually useful, but I think one area where it’s unquestionably a massive improvement is in asking stupid questions. I ask ChatGPT so many questions that I’ve started looking for ways to automatically send me a daily summary of questions and answers, to add to Anki.
I used to post a lot of these types of questions on subreddits that are Ask-related. Ask Philosophy and Ask Historians, for example. Unfortunately the mod teams for many subreddits like this have gone overboard, deleting anything that doesn’t fit their specific idiosyncratic rules.
Needless to say I have almost entirely stopped asking questions on Reddit.
> Toss a fair coin until the number of heads exceeds the number of tails. This determines a stopping time. What is the probability that this stopping time is even?
Claude Code did pretty well:
> Zero.
>
> The stopping time always falls on an odd toss. Here's why: after >n tosses, heads minus
> tails equals S_n = X₁ + X₂ + ... + X_n where each X_i takes >value +1 or −1. The sum
> of n odd numbers shares parity with n. For S_n = 1 (the first >time heads exceeds
> tails), we need n odd.
>
> No even stopping time exists. The probability equals exactly 0.
>
> Cogitated for 38s
Fortunately these days I have a very patient interlocutor named ChatGPT blessed with an infinite tolerance for half-baked questions and a soothing lack of judgmentality.
I know it’s popular to say AI is overhyped or not actually useful, but I think one area where it’s unquestionably a massive improvement is in asking stupid questions. I ask ChatGPT so many questions that I’ve started looking for ways to automatically send me a daily summary of questions and answers, to add to Anki.
I used to post a lot of these types of questions on subreddits that are Ask-related. Ask Philosophy and Ask Historians, for example. Unfortunately the mod teams for many subreddits like this have gone overboard, deleting anything that doesn’t fit their specific idiosyncratic rules.
Needless to say I have almost entirely stopped asking questions on Reddit.
https://math.mit.edu/~apost/courses/18.204-2016/18.204_Jon_L... doesn't this paper demonstrate the same thing like a decade before?
> Toss a fair coin until the number of heads exceeds the number of tails. This determines a stopping time. What is the probability that this stopping time is even?
Claude Code did pretty well:
> Zero. > > The stopping time always falls on an odd toss. Here's why: after >n tosses, heads minus > tails equals S_n = X₁ + X₂ + ... + X_n where each X_i takes >value +1 or −1. The sum > of n odd numbers shares parity with n. For S_n = 1 (the first >time heads exceeds > tails), we need n odd. > > No even stopping time exists. The probability equals exactly 0. > > Cogitated for 38s