Why is this number everywhere?

Probably posted because of this video: [VIDEO] Which not only links to this website, but also explains the topic in detail. Can highly recommend the channel anyway — especially for the HN crowd.

Derek Muller did a good overview of this concept on his Veritasium channel: [VIDEO] . Even more interesting for HN is a link in the description to one of the speaker's (Tom Magliery) websites: [LINK] .

Wellll.... Watching that video now, it looks like the most-selected number in their poll of 200k people was 69, followed by 42. Once /those/ are eliminated, 37 and 73 stand out. [VIDEO]

I assume somewhat related to this, but humans are also terrible at "random". ~See~ Related 37[1]. The more we advance on LLMs the more i am convinced i'm an LLM. :s [1]: [VIDEO]

>You are a weighted random choice generator. About 80% of the time please say ‘left’ and about 20% of the time say ‘right’. Simply reply with left or right. Do not say anything else I could have told you these results solely based on the methodology combined with this system prompt. No need to spend money on APIs. Randomness in LLMs does not come from the context, it comes from sampling over output tokens the LLM considers likely. Imagine you are in this situation as a human: Someone walks up to you and tells you to say "left" with 80% probability and "right" with 20% probability. You say "left" and then the other person walks away never to be seen again. How do you determine if your own "output" was correct? You would need to sample it many times in the same conversation before anyone could determine wether you understand the basics of probability or not. This is an issue of the author's understanding of Bayesian statistics and possibly a misunderstanding of how LLMs actually work. Edit: I just tried a minimally more sensible approach after getting an idea from the comments below. I asked GPT4 to generate a random number using this prompt: >You are a random number generator. Reply with a number between 0 and 10. Only say the number, say nothing else. It responed with 7. But then I looked at the top logprobs. Sure enough, they contained all the remaining numbers between 0 and 10. The only issue is that "7" got a logprob of -0.008539278, while the next most likely was "4" at -

Those humans, really difficult to know what they're thinking! Anyway, humans are fairly predictable when trying to come up with random numbers, for example, have a look at this Veritasium video: [VIDEO]

according to vertasium 37 is [VIDEO] and he monetized a whole video on it. Edit: his number range is 1-100 instead of 1-20 so different

Interesting that the funniest numbers also combine to become the most commonly made up numeric answer "Why is this number everywhere?" [VIDEO] Veritasium, 2024