Earlier this year Matt Welsh announced the end of programming. He wrote, in Communications of the ACM: I believe the conventional idea of “writing a program” is headed for extinction, and indeed, for all but very specialized applications, most software, as we know it, will be replaced by AI systems that are trained rather than programmed. In situations where one needs a “simple” program (after all, not everything should require a model of hundreds of billions of parameters running on a cluster of GPUs), those programs will, themselves, be generated by an AI rather than coded by hand. A few w ..read more

John von Neumann was a prodigy and a polymath. He made notable con­tri­bu­tions in pure mathematics, physics, game theory, economics, and the design of computers. He also came up with the first algorithm for generating pseudo­random numbers with a digital computer. That last invention, however, is seldom counted among his most brilliant accomplishments. For example, Don Knuth leads off Vol. 2 of The Art of Computer Programming with a cautionary tale about the von Neumann scheme. I did the same in my first column for American Scientist, 30 years ago.To the extent his random-number work is remem ..read more

A day or two after publishing my TL;DR on Wordle algorithms, I stumbled on a remarkable paper that neatly summarizes all the main ideas. The remarkable part is that the paper was written 50 years before Wordle was invented! The paper is “Information Theory and the Game of Jotto,” issued in August of 1971 as Artificial Intelligence Memo No. 28 from the AI Lab at MIT. The author was Michael D. Beeler, known to me mainly as one of the three principal authors of HAKMEM (the others were Bill Gosper and Rich Schroeppel). Beeler later worked at Bolt, Baranek, and Newman, an MIT spinoff. Wikipedia tel ..read more

When the Wordle wave washed over the world some months ago, I played along like everybody else, once a day collecting my rows of gray and gold and green letters. But my main interest was not in testing my linguistic intuitions; I wanted to write a computer program to solve the puzzle. Could I create something that would play a stronger game than I do? It’s now clear the answer to that question is yes, but I can’t say whether it’s because I’m such a hotshot programmer or such a mediocre Wordler. I hasten to add that my motivation in this project is not to cheat. Josh Wardle, the creator of Word ..read more

Lately I’ve been thinking about the number 60. Babylonian accountants and land surveyors did their arithmetic in base 60, presumably because sexagesimal num­bers help with wrangling fractions. When you organize things in groups of 60, you can divide them into halves, thirds, fourths, fifths, sixths, tenths, twelfths, fifteenths, twentieths, thirtieths, and sixtieths. No smaller number has as many divisors, a fact that puts 60 in an elite class of “highly composite numbers.” (The term and the definition were introduced by Srinivasan Ramanujan in 1915.) There’s something else about 60 that I nev ..read more

Figure 1 Peaks and troughs, lumps and slumps, wave after wave of surge and retreat: I have been following the ups and downs of this curve, day by day, for a year and a half. The graph records the number of newly reported cases of Covid-19 in the United States for each day from 21 January 2020 through 20 July 2021. That’s 547 days, and also exactly 18 months. The faint, slender vertical bars in the background give the raw daily numbers; the bold blue line is a seven-day trailing average. (In other words, the case count for each day is averaged with the counts for the six preceding days.) I stru ..read more

As a kid I loved magnets. I wanted to know where the push and pull came from. Years later, when I heard about the Ising model of ferromagnetism, I became an instant fan. Here was a simple set of rules, like a game played on graph paper, that offered a glimpse of what goes on inside a magnetic material. Lots of tiny magnetic fields spon­taneously line up to make one big field, like a school of fish all swimming in the same direction. I was even more enthusiastic when I learned about the Monte Carlo method, a jauntily named collection of mathematical and computational tricks that can be used to ..read more

Packing up the household for a recent move, I was delving into shoeboxes, photo albums, and file folders that had not been opened in decades. One of my discoveries, found in an envelope at the back of a file drawer, was the paper sleeve from a drinking straw, imprinted with a saccharine message: This flimsy slip of paper seems like an odd scrap to preserve for the ages, but when I pulled it out of the envelope, I knew instantly where it came from and why I had saved it. The year was 1967. I was 17 then; I’m 71 now. Transposing those two digits takes just a flick of the fingertips. I can blith ..read more

The Thanksgiving holiday is upon us, but Anthony Fauci and the CDCand 79 percent of epidemiologists are urging us to forgo the big family gathering this year. I’m sure that’s sound advice, but I haven’t seen much quantitative analysis to back it up. How serious is the risk when we go over the river and through the woods to grandmother’s house? What are the pubic health consequences if the whole country sticks to the familiar ritual of too much food and football? The tableau presented below is a product of my amateur efforts to address these questions. It’s a simple exercise in the mechanics of ..read more

A few weeks ago, after taking a walk in the woods, I wrote about the puzzling diversity of forest trees. On my walk I found a dozen species sharing the same habitat and apparently competing for the same resources—primarily access to sunlight. An ecological principle says that one species should win this contest and drive out all the others, but the trees haven’t read the ecology textbooks. In that essay I also mentioned three other questions about trees that have long been bothering me. In this sequel I want to poke at those other questions a bit more deeply. Question 1: Why do the leaves of t ..read more