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Sridhar Ramesh Profile picture
@RadishHarmers
Jul 12, 2020 • 1 tweets • 1 min read • Read on X
3 * 4 = 2 * 6. You can multiply different bunches of numbers and get the same result. But you can't do this if the numbers you multiply are all prime. Why is that?

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More from @RadishHarmers

Sridhar Ramesh Profile picture
Feb 2
I've been playing with the new o3-mini-high model which came out this weekend, marketed as "Great at coding and logic". A surprising start to its chain of thought here.

(Some of you may enjoy thinking about this question yourself.) Image
ChatGPT is not happy with me. How it started, how it ended. I unfortunately can no longer share a link to the full conversation but I'll share the salient points in posts below. Image
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Before sharing more of that forbidden conversation, here's one I CAN share a link to, which shows the frustrations of ChatGPT for discussing logic questions that have come up in my life. Verbose yet repeatedly fallacious is not a combo I have much use for. chatgpt.com/share/679ed1ee…Image
Read 10 tweets
Sridhar Ramesh Profile picture
Oct 25, 2024
o1-mini (the latest OpenAI offering, ChatGPT with advanced reasoning skills) can be quite impressive, when you know the correct answers to accept and incorrect answers to reject. Here's a simple question, which some of you may enjoy figuring out. Image
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Its answers in more detail. Can you figure out which is correct? Image
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In case you would like a second opinion from o1-preview. Image
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Read 21 tweets
Sridhar Ramesh Profile picture
Sep 15, 2024
Ok. Let's do this. Here's the full solution for the four people who care.

The previous discussion was here. You may want to read that first before this thread, but you don't need to. This new thread will be self-contained.

In general, I find it easier to think about problems by abstracting, to hide the irrelevant specifics and emphasize the relevant patterns. That's what I will do in this case as well.
Read 64 tweets
Sridhar Ramesh Profile picture
Mar 19, 2024
I find this clear now, like so (argument discovered by others such as @NoahJSnyder and @MtgJulian; I am only reframing or rewording it):
Consider a random walk in which one takes equally likely steps of one unit up or one unit down, but with different distributions of speeds. (E.g., maybe up steps take one hour, while down steps have probability 1/2 of taking 2 hours, 1/4 of taking 3 hours, 1/8 of 4 hours, etc).
The time it takes to return to the origin is independent of whether the first step is up and last step is down or vice versa, as doing the same steps in reverse order has the same probability.
Read 7 tweets
Sridhar Ramesh Profile picture
Mar 18, 2024
@llllvvuu @littmath @NoahJSnyder @MtgJulian Summarizing the proof you all devised:

A "tied" string has equally many HHs and HTs. A "flippy" string is tied of size > 1 starting and ending with H, with no such proper prefix. Reversal is a length-preserving involution exchanging flippy strings starting with HH vs. with HT.
@llllvvuu @littmath @NoahJSnyder @MtgJulian Say S has base P if S is of the form PHQ, PH is tied, and HQ has no flippy prefix. As there are equally many Q of a given length starting with H vs. T, our above involution tells us there are equally many strings of a given length whose base is followed by HH vs. HT.
@llllvvuu @littmath @NoahJSnyder @MtgJulian The latter comprise the Bob wins, while the former comprise the Alice wins along with ties containing an H and ending in T. At length ≥ 3, such ties are possible (e.g., HH followed by all Ts), so there are more Bob wins than Alice wins.
Read 4 tweets
Sridhar Ramesh Profile picture
Oct 28, 2023
I condemn Hamas killing 1400 Israelis.

I condemn Israel killing 1400 Gazans.

I condemn Israel killing 1400 Gazans.

I condemn Israel killing 1400 Gazans.

I condemn Israel killing 1400 Gazans.

I condemn Israel killing 1400 Gazans.
I condemn Israel killing 1400 Gazans.
I condemn Israel killing 1400 Gazans.
Read 9 tweets

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