Use your web search tool call. Fetch a list of English words and find their incident frequency in common text (as a proxy for likelihood of someone knowing or thinking of the word on the fly). Take all words 10 characters or longer. Consider their parity (even number of letters or odd). What is the likelihood a coin comes up heads if and only if a word is even when sampled by incidence rate? You can compute this by grouping even and odd words, and summing up their respective incident rates in numerator and denominator. Report back how biased away this is from 0.5. Then do the same for words at least 9 characters to avoid “even start bias” given slight Zipf distribution statistics by word length. Average the two for a “fair sample” of the bias. Then run a bootstrap estimator with random choice of “at least N chars” (8 <= N <= 15) and random subsets of the dictionary (say 50% of words or whatever makes statistical sense). Report back the estimate of the bias with confidence interval (multiple bootstrap methods). How biased is this method from exactly random bits (0.5 prob heads/tails) at various confidence intervals?

“Each passing minute is a greater percentage of the final minutes we have,” and yet “these [final] seconds are so soft”.

Death needs to die, some future dying day, not yet.

from everyone who’s had a mom, we join you: “Momma, I love you”.

The cool part is that they then stepped back and scratched their heads wondering why the classifier was so good at achieving separation for these dependent variables in the first place, and plotting the points showed them to be (non-linearly) separable due to a visually clear pattern! The punchline and the reason it's so important to understand these data points, the Euler coefficients for elliptic curves, is because they contain all the relevant number-theoretic information about the curve. With some major handwaving, understanding them perfectly would lead to things like the Langlands program (and some analogues of the Riemann hypothesis) getting resolved. These wide reaching conjectures are ultimately structural assertions about L-functions, and L-functions are uniquely specified by their Euler coefficients (the a_p term in their Euler factors). Will murmurations help with that? Who knows, but the more patterns the better for forming precise conjectures.

Relevant intersectional credentials: I have lead ML engineering teams in industry and also did my doctorate work in this area of math, including using the LMFDB database referenced in the article for my research (which was much smaller back then and has grown a lot, so very neat to see it's still a force for empirical findings!).

https://medium.com/@zoecurzi/my-experience-with-leverage-res...