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News
AI is an intelligence multiplier
5+ day, 2+ min ago (257+ words) A rising tide may lift all boats, but the AI tide lifts some boats much more than others. By all accounts, the best programmers have had the biggest productivity boost from AI. And top tier mathematicians are using AI to…...
Ngram error rate
6+ day, 19+ hour ago (282+ words) “understand empathically,” 1961, an arbitrary formation by U.S. science fiction writer Robert A. Heinlein (1907-1988) in his book “Stranger in a Strange Land.” In the book it is a transliteration of a Martian word and is said to mean etymologically “to…...
Making the unnecessary easier
2+ week, 2+ day ago (353+ words) I watched a few videos this morning, looking for ideas of what I could use AI to do. In one video, someone had an agent monitor tech news sites every 30 minutes to notify him of a variety of developments. No…...
Second solutions
2+ week, 4+ day ago (239+ words) This post provides a couple examples to go along with two earlier posts. The pattern we’re illustrating is families of polynomials pn(x) that each satisfy a differential equation and a three-term recurrence. The differential equations have a second solution…...
What is the quality of software that AI writes?
2+ week, 4+ day ago (276+ words) AI-powered coding agents increase productivity for many developers. But do these agents produce good-quality code? Some say this doesn’t matter, we are heading toward dark software factories with source code never inspected, and maybe we should eliminate source code altogether…...
Three-term recurrences
3+ week, 3+ min ago (100+ words) There many examples of families of functions where each function can be computed as a linear combination of the two previous terms where a and b are functions of x but not on n. This is called a three-term recurrence formula....
Why special function terminology is arcane
3+ week, 20+ hour ago (261+ words) Special functions are special because they’re useful. They can also be shrouded in arcane terminology. These two facts are related. The more widely useful a function is, the more likely it is that the function will be discovered independently multiple…...
AI-generated ASCII diagrams
3+ week, 4+ day ago (238+ words) I like AI-generated ASCII diagrams. Because nobody would ask AI to generate ASCII diagrams, and so, it’s congruous. I like incongruity [1]. Aside from the incongruity of using a gazillion-parameter neural network to make 1970’s style ASCII art, ASCII diagrams have…...
Probability of correcting errors
4+ week, 1+ day ago (287+ words) Error correcting codes are most simply described in terms of the errors they can certainly correct. For example, the Hadamard code used for the Mariner 9 probe to Mars encoded each 6-bit pixel to a 32-bit codeword in such a way…...
Compressing a Hadamard matrix
4+ week, 1+ day ago (469+ words) Hadamard matrices are in the news following the recent announcement of a newly discovered Hadamard matrix. I’ve written three posts on Hadamard matrices recently, one as a sort of introduction and two on applications: the error correcting code used in…...