This blog started life with an exercise in taking the fake arxiv-like abstracts generated by snarxiv.org, and looking for meaningful interpretations. Nine years later, it's the age of GPT-3, the AI that can write a small essay given an appropriate "prompt". Could GPT-3 be tuned to produce an entire fictitious physics paper, given a snarxiv abstract as prompt?

In the previous post, I posed the question, why is 𝜋 near the number 3? We may actually have the beginning of an answer. As John Baez discusses, the geometric mean of e and 𝜋 is very close to 3; and Ramanujan proposed an exact formula for that mean, the sum of an infinite series and an infinite continued fraction, which derives in part from the properties of Gaussian distributions. So there may be a deep reason after all.

Note a Koide-like relation, between e, pi, and Khinchin's constant from the theory of continued fractions: https://math.stackexchange.com/questions/1662442/something-similar-to-the-bizarre-koide-formula

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