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Foldable Words | bit-player
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
More Questions About Trees | bit-player
A few weeks ago, after taking a walk in the woods, I wrote aboutthe 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 t
Three Months in Monte Carlo | bit-player
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 materi
Questions About Trees | bit-player
“The woods are lovely, dark and deep,” wrote Robert Frost. Those iambs come to me unbidden every time I set off down a nearby woodland trail. The trail is named for Frost, who spent several years in this part of Massachusetts, teaching boys in brass-buttoned blazers at Amherst College. Did the poet
My God, It’s Full of Dots! | bit-player
Please click or tap in the gray square below. It will fill with a jolly tableau of colored disks—first big blue ones, then somewhat smaller purple ones, and eventually lots of tiny red dots.Sorry. My program and your browser are not getting along. None of the interactive elements of this page will w
Words for the Wordle-Weary | bit-player
When theWordlewave 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 s
Does having prime neighbors make you more composite? | bit-player
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,
April Fool Redux | bit-player
I have a scheme to rescue the swooning U.S. economy. My idea partakes of the silliness that always accompanies the coming of April, but it’s not entirely an April Fool joke. T. S. Eliot told us that April is the cruelest month. I’m proposing that if we take a double dose of April, it might turn kind
The Teetering Towers of Abstraction | bit-player
Abstraction is an abstraction. You can’t touch it or taste it or photograph it. You can barely talk about it without resorting to metaphors and analogies. Yet this ghostly concept is an essential tool in both mathematics and computer science. Oddly, it seems to inspire quite different feelings and r
We Gather Together… | bit-player
The Thanksgiving holiday is upon us, butAnthony Fauciand theCDCand79 percent of epidemiologistsare 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 t
The Middle of the Square | bit-player
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 s
Riding the Covid coaster | bit-player
Figure 1Peaks 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
Jotto | bit-player
A day or two after publishing myTL;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 1
MathJax turns 3.0 | bit-player
When I launched bit-player.org in 2006, displaying any sort of mathematical notation on the web was torture. I would typeset an equation in LaTeX, convert the output to a JPEG image, upload the image file to a directory on the server, and embed a reference to the file in an HTMLimgtag. The process w
We Gather Together | bit-player
In January I went to the Joint Mathematics Meetings, which were held in Denver for the first time ever. The main venue was the Colorado Convention Center, a building whose roof area, by my rough estimate, is well above a million square feet. Inside I found acres of patterned carpet, enoughfoldingsta