Proof isn't always possible

Recursion as a principle shows up in Statistics and object oriented programming. In programming it might be memory intensive and intricate, but in the abstract, these solutions have the beauty and allure of elegance. A recursive application of modulo division is another solution in search of an application in mathematics. Fibonacci wrote a whole book about the Fibonacci series, on the slender basis of a use in censuses. So to contrive an application of recursive modulo division, we assert the smoker who collects cigarette butts. For every seven butts he collects, he can roll one supplemental cigarette. Recursion becomes useful when he smokes these, but remembers to collect these butts as well, revisiting his solution. Note: as a practical matter, we add the resulting tally of butts to the modulo remaining unused butts, for a new arithmetical exercise. Ex: At the observatory a scientist collects as many butts as there are three digit primes. He performs his experiment on these, as ...

The first number we learn is one, or identity. Then, we encounter zero or null. So when we want to count, it makes sense to take an empty set and put elements into it. We readily identify one. When we add another, we think we have come to two, because it is “not one.” But if we add yet another, we encounter a new consideration: what makes our “count” go from “two” to “three,” rather than continuing to be an exotic “not one?”

In an entry to one of my 65535sec student research blogs, I observed that one strategy for analysis is to represent the cryptogram as a matrix A. The perform a differential analysis on A x A^T and the differing A^T x A. By mentally imagining using such a procedure against Vigenere, I infer a question. The key material of Vigenere has a periodicity. I can suppose the A x A^T vs A^T x A would also exhibit a period, but I would be surprised if it reduced to a one to one simple substitution. As such, I suppose it would be worth asking what can usefully be said about the data for differential analysis?

 There are various standards of randomness. We can distinguish between a square distribution and the bell curve. Beyond that, some tests calculate probability of a number repeating, two and three times, for cryptographically random. In the same family of tests, we can test for localized order, or surges of bell curve fitting data interspersed by data that displays higher entropy. With these thoughts in mind, most people are willing to accept series of range 0 - 9, from ten sided dice when they are cast in groups. This rule is to compensate any tendency to repeat a “side,” like a similar problem that attends coin flips.  To be vigilant against human interference, we can plan to cast five ten-sided dice repeatedly, and line the resulting group up in a row. This prevents the transcriptionist from choosing orders from the available five choices (sometimes in an effort to avoid that very failing).  The strategy of lining the experiment up in a line is a good rule to have fo...

Counting is axiomatic. We suppose there is no way to compute the cardinal number of a set. When we begin to count, we observe one, or unity. Then we come to two, because it is not null, but also not one. However, when we come to three, what makes it three? Why doesn’t it just go on being “more than one?”

Rather than having been a waste of time, an education can make ChatGPT be far more helpful or specific. “When you have an education ChatGPT does way more for you!” I used a ChatBot to develop the following joke. The written prompt ideas were preparatory, but accumulated during the process. Make sorting x and y Cartesian coordinates ascending on a regression dataset, both humorous AND relatable to a wide audience. Step one, we are gonna NUMBER every x,y pair, 1-50. Somehow the x’s and y’s are going to keep their numbering, and this is how we discover they have been re-associated. R value < 0.5 is the bomb!  Building comments: r value is kind of like pass/fail in school. It is not on a continuum. A continuum represents How ripe a tomato is; a watermelon has a handy double entendre. R values are more like pregnant or not pregnant. So Darren, what have you been doing with yourself lately? We’ve been doing regression analysis on data sets for an AI model. Sounds like a cross between ...