6174 Self-taught Indian mathematician D.R. Kaprekar (1905-1986) discovered this curious result in 1955. Take any four-digit number with at least two distinct digits, write the digits first in descending, then in ascending order, and subtract one from the other. Repeat with the resulting number, and again if necessary. Within seven iterations, you’ll always arrive at […]
Field Notes
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Superstar
This time of year, you’ll no doubt be seeing commentaries about the Star of Bethlehem, many of which will explain away the “star” as a conjunction of two planets, or as a comet, or even as a bolide (very bright meteor). Looking over my past writing, I realize I’ve been guilty of this in this […]
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Atlas and Pleione’s Kids: The Pleiades
I’ve written about the Pleiades star cluster before (“Orion and the Pleiades,” Jan. 12, 2023), in which I focused on the ancient Greek myth of the hunter Orion endlessly pursuing Mom, Dad and seven sisters across the night sky. Here, I’m going to focus on the stars themselves, and what makes them so interesting to […]
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The Lure of Immortality
We’re immortal, you and I. Well, not quite immortal as in “forever,” but if you count nearly a third of the age of the universe as forever, yes, we’re immortal. And when I say “we,” I don’t mean our bodies, what we usually think of as our selves. Along with all multicellular organisms, we consist […]
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The Magic of Photosynthesis
“How does grass make sheep?” We were walking across a field in Northern England recently, and the child-like question popped up, unbidden and unexpected, like similar ones sometimes do: “How do raindrops know to fall straight down and redwoods to grow straight up?” “How does my brain make sense of tiny squiggles on a sheet […]
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Tears in Rain: Musings on Memory
“I’ve seen things you people wouldn’t believe. Attack ships on fire off the shoulder of Orion. I watched C-beams glitter in the dark near the Tannhäuser Gate. All those moments will be lost in time, like tears in rain. Time to die.” — Roy Batty’s last words, Blade Runner Or is it “tears in the rain?”Cinephiles […]
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Bridge of Spies
“[Gary Powers] performed his duty in a very dangerous mission and he performed it well, and I think I know more about that than some of his detractors and critics know ….” — CIA Director Allen Dulles Standing on a hill recently, overlooking the Glienicke Bridge near Potsdam, Germany, several thoughts came to mind. While the […]
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Nefertiti, the Second Monotheist
Her life-sized bust rates a room of its own in the huge museum, sitting on a plinth within a 20-foot-high glass enclosure. Her discoverer, German Egyptologist Ludwig Borchardt, called her “the epitome of tranquility and harmony.” She was found (actually by an Egyptian workman under Borchardt’s supervision) on Dec. 6, 1912, in the ruins of […]
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Sketches from Humboldt’s Past
“There’s a working theory that within a year of residency, most newcomers are infected with a deep and abiding interest in this great place we call Humboldt.” So starts the introduction to Steve Lazar’s The Humboldt Project. Lazar’s passion is “deltiology,” the study and collecting of postcards. Over the past 15 years, thanks mostly to […]
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What are the Odds?!
“Players aren’t buying an investment; they’re buying permission to fantasize for a couple of days.” — Jack Murtagh, Scientific American, April 2025 Neurologists recently figured out what gamblers have known ever since a savvy Sumerian grifter invented the shell game: You don’t have to win to be a happy punter. You just have to bet […]
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The Moons of Mars
In the first volume of his Mars trilogy Red Mars, science fiction writer Kim Stanley Robinson has the larger of Mars’ two moons, Phobos, destroyed after it had been weaponized. Which would be a tragedy IRL, since Phobos may well be a stepping stone to exploring the Red Planet. It could also give us information […]
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Free Will Redux
“We are not captains of our ships. Our ships never had captains.” — Robert Sapolsky, Determined: A Science of Life Without Free Will When things get weirder — and I suspect that, politically, the weirdness is just beginning — I’m in the habit of remarking to whomever is listening, “We’re just running on a program […]