Thoughts

Kiruna, in the far north of Sweden, exists because of an iron ore mine, and is now moving out of the mine’s way. The ore body runs at a slant down under the old town, and the deeper the mining goes, the more the ground above it cracks and sinks, so the town centre is being rebuilt a few kilometres east, one building at a time. In August 2025 the town’s wooden church, all 672 tonnes of it, rode there on remote-controlled trailers at about half a kilometre an hour, over two days. The mining company paid for the move. It had also paid for the church in the first place, in 1912, and handed it to the parish as a gift. So the same company built the church on top of its ore, and a century later carried it gently away from the hole it was making.

The bee orchid’s lower petal is a passable impression of a female bee: furry, brown, striped, held out like a landing pad. Further south, in the Mediterranean, a male long-horned bee sometimes falls for it, tries to mate with the petal, and flies off wearing the pollen. In Britain that bee is rare, and the orchid has mostly stopped waiting. The stalks holding its pollen are weak, so after a while the pollen masses droop out on their own and swing onto the sticky part of the same flower. Darwin noticed this in 1860 and asked readers of a gardening paper to go and look for themselves. So every June, across chalk grassland and road verges where no suitor is coming, the orchid still puts on the whole costume, every stripe correct, and then quietly sees to things itself.

A desert ant in the Sahara finds its way home across flat, featureless sand partly by counting. In 2006 a team in Germany and Switzerland let ants walk out to a feeder about ten metres from the nest, then, before the walk home, glued pig bristles to some ants’ legs as stilts and trimmed others’ legs to stumps. The ants on stilts marched straight past the nest and started searching beyond it; the ants on stumps stopped short. Neither was lost. Each had taken the right number of steps for the trip out, with legs that were no longer the legs it had counted with. When the researchers let the altered ants make the whole trip out and back on their new legs, they got home fine. The counting itself never failed. It only misled them when the thing doing the counting had changed halfway through, and nobody told it.

For more than a century a family in London sold the time. John Henry Belville began in 1836, his widow Maria carried it on, and from 1892 their daughter Ruth took over. Once a week she walked to the Royal Observatory at Greenwich, set her pocket chronometer by the master clock, and got a certificate saying how far off it was. Then she went round her customers, mostly clockmakers by the end, and let them set their own clocks by hers. The watch was an old John Arnold chronometer, and she called it Arnold. She kept at it until about 1940, long after telegraph wires, and then the six pips on the radio, could bring Greenwich into a room. What she sold was never really the hour, which was free. It was a woman who had been to Greenwich that week, and could show you the paper.

A train’s dead man’s pedal is a promise made in reverse: the driver keeps it pressed, and if they let go, the brakes come on. It assumes the worst thing that can happen to a driver is that they stop pushing. In 2003, near Waterfall in New South Wales, a driver had a heart attack at the controls, and the inquiry found that the weight of his leg was enough to keep the pedal down. It also found that the legs of a large share of Sydney’s drivers were heavy enough to do the same. The fix was to stop asking for pressure and start asking for answers: a vigilance system that sounds every so often and brakes unless someone presses a button in reply. A body can hold something down without anyone in it. It takes a person to answer a question.

Most people carry at least one word they have only ever read. They know exactly what it means, they have used it correctly in their head for years, and then one day they say it aloud, “epi-tome” or “hyper-bowl”, and somebody winces. It is tempting to call that a gap in an education. I think it is closer to a record of one. Nobody said the word to you; you went and found it on a page, alone, probably young, probably in a book nobody assigned. The wrong sound is what the word looks like when the only teacher was the reading.

A Scoville rating doesn’t measure heat directly. In 1912 a pharmacist named Wilbur Scoville dissolved dried pepper in alcohol, then kept diluting the extract in sugar water until a small panel of tasters could no longer feel any burn. The rating is how far it had to be diluted. A jalapeño at a few thousand units means a few thousand parts sugar water to quiet it; the hottest peppers need more than a million. Labs now measure the chemicals with a machine and convert the answer back into Scoville’s units, because those units were the ones everybody already understood. So the hottest pepper in the world is famous for how much water it takes to make it go away.

220 and 284 are called amicable numbers: add up everything that divides 220 except 220 itself and you get 284, and the divisors of 284 add up to 220. The Greeks knew that pair. Fermat put his name to a bigger one, 17,296 and 18,416, Descartes found a pair in the millions, and Euler, a century on, listed dozens more. Then in the 1860s a sixteen-year-old Italian, Nicolò Paganini (not the violinist), pointed out 1,184 and 1,210, the second-smallest pair of all, small enough to check with a pencil in an afternoon. Nobody in Europe seems to have written it down before him, though it may have been known earlier elsewhere. The great mathematicians had methods that made large pairs, and a method only finds what it was built to find. The pair next door was left for someone who simply counted.

In November 1963 an island rose out of the sea south of Iceland, and the scientists who named it Surtsey decided almost at once to keep everyone else off, so they could watch life arrive on bare rock with nobody helping. The first plant came by sea in 1965, a sea rocket washed up on the shore, and after that seeds rode in on waves, wind and birds. A few years in, the researchers found a tomato seedling growing in the warm ground. Nobody had planted it. Someone on the team had needed the toilet, and the tomato came from their lunch. They pulled it up. Of all the ways a seed could reach that island, it took the one the whole arrangement was built to rule out: it came in with the people keeping watch.

Calculate comes from the Latin calculus, a small stone: the pebbles Romans pushed around a counting board. From there the word went two ways. One branch grew into the calculus of Newton and Leibniz. The other stayed with stones, so a doctor will still call a kidney stone a renal calculus, and a dentist calls the hard scale on your teeth calculus too. Underneath both is calx, limestone, which also gave English chalk and, much later, calcium. So when a teacher writes the word calculus on a blackboard, it is the same stone at both ends: the one in the word and the one doing the writing.

Pando, in central Utah, looks like a grove of about 47,000 quaking aspens spread over roughly 106 acres. It is one tree. Every trunk is a shoot from a single root system, all genetically the same, and when a trunk dies, usually somewhere past its first century, the roots send up another. Nobody can say how old the roots are, because tree rings only date the trunks; estimates run to thousands of years. What’s going wrong there now is not age. Deer and elk eat the new shoots before they get tall, so the old trunks keep dying and nothing comes up behind them. Where researchers fenced a plot to keep the animals out, young aspens came back thick within a few years. A thing can be ancient, enormous and alive, and still be only as safe as its newest shoot.

In 1904 a horse in Berlin called Hans was answering arithmetic by tapping a hoof, and a panel of experts looked hard and found no trickery. In 1907 the psychologist Oskar Pfungst found the trick nobody was playing. Hans got the sum right when the person asking knew the answer and stood where he could see them, and almost never otherwise. As the taps neared the right number the questioner tightened very slightly, and at the right one they relaxed, and Hans stopped. None of them knew they were doing it. Pfungst learned to read the cue himself, then found he couldn’t stop giving it, even knowing exactly what it was. Hans never learned to count. He learned something harder: the moment a person stops holding their breath.

On a two-stage snowblower the auger is held to its shaft by a few soft bolts called shear pins. When the auger meets a frozen newspaper or a rock under the snow, a pin snaps, the auger stops, and the gearbox behind it is spared. Small outboard motors used to do the same with a pin through the propeller. Owners are told to keep spares on hand, because the snapping isn’t a fault; it’s the part doing its job. The mistake the parts guides warn against is replacing a broken pin with an ordinary, stronger bolt from the drawer. The machine runs fine until the next rock, and then what breaks is the thing you can’t fix in the driveway. A shear pin is the one part whose success looks, to anyone watching, exactly like a breakdown.

When a crossword clue won’t give, it is rarely because you don’t know the answer. More often you decided, before you noticed deciding, what kind of word the clue was. In cryptic puzzles “flower” is as likely to be a river as a rose, because a river is a thing that flows, and “number” can be an anaesthetic, a thing that numbs. The setter hid nothing. Every letter was in plain sight; you gave it the wrong sound in your head and then searched very hard inside that sound. That is why the answer so often turns up the next morning, or the moment you put the pen down to make tea. You didn’t learn anything overnight. You only forgot, for a second, how you had chosen to read it, and the other reading was there the whole time, spelled exactly the same.

Ostracize comes from ostrakon, the Greek word for a shell or a broken piece of pot. Once a year Athens could decide to send one citizen away for ten years, and each voter scratched a name on a potsherd, the scrap paper of a city where pots were always breaking. The exile kept his property and could come back when the ten years were up. Archaeologists found about 190 of these sherds dumped in a well on the north slope of the Acropolis, every one with the name Themistocles, and the handwriting comes down to around fourteen people. Nobody knows for certain why: helpers for voters who couldn’t write, perhaps, or a campaign. Either way the word kept the pottery and lost the part where you could come home.

In October 1961 a volcano opened beside the only village on Tristan da Cunha, an island in the South Atlantic about as far from anywhere as people live, and the whole population, a little over 260 people, was taken to England. They were housed in old RAF quarters at Calshot, on Southampton Water, and found work there. A year later they held a vote on going back, and a large majority said yes. Most were home by the end of 1963, on an island with no airport, about a week by boat from Cape Town. When they rebuilt, they named their harbour Calshot Harbour, and the old quarters in England became Tristan Close. So each place now carries the other’s name: the one they were sent to, and the one they chose.

A great frigatebird can stay out over the ocean for weeks without landing, and for a long time nobody knew how it slept. In 2016 a team led by Niels Rattenborg put small recorders on the birds’ heads and found out: in short naps, a few seconds at a time, mostly while circling up in rising air, sometimes with half the brain asleep and the open eye turned the way it was going. Added up, it came to about forty minutes a day. The same birds, back on land, sleep for something like twelve hours. So the answer was not that the frigatebird has learned to do without sleep. It has learned to put it off, and it pays when it gets home.

A lens bends light only at its surfaces, where the light goes into the glass and where it comes out. Everything in between just carries it across. For a reading glass that hardly matters, but a lens big enough to throw a lighthouse beam out to sea would be a slab so thick it cracked, sagged and swallowed the light it was meant to send. Augustin Fresnel’s answer, lit for the first time at the Cordouan lighthouse in France in 1823, was to keep the curves and throw away the middle: the lens cut into concentric rings of prism, each holding only the slice of surface that did the bending, stepped back flat. Buffon had sketched a one-piece version in the 1740s, and Fresnel said so in print. The glass that was taken out had not been doing anything wrong. It had been doing exactly what glass does, and that was the trouble.

A bicycle is quiet while you pedal and ticks while you coast, which is the opposite of what you might guess. Inside the rear hub, small spring-loaded catches called pawls sit against a ring of teeth. When you push the pedals they catch and hold, and the wheel turns with your legs without a sound. When you stop, the wheel runs on ahead of the gears, and the pawls ride up over each tooth and snap down off it: that’s the ticking. Some riders pay extra for hubs that click louder, and some engineers have spent years making hubs that don’t click at all. But on an ordinary bike the noise only starts when you stop working. It’s the sound of the machine letting go of you.

Strip a ring of bark from most trees and you have killed them. The bark is where sugar travels down from the leaves, and a tree cut off at the waist starves slowly, standing up; farmers used to clear land that way. The African baobab is an exception. People have stripped its bark for rope for generations, and in a dry season elephants gouge it for the wet wood underneath, and the tree, within limits, grows a new layer over the wound and carries on. Baobabs in elephant country wear the scars, lumpy and folded like a badly healed knee. They aren’t invulnerable: when drought, fire and elephants come at once, they die like anything else. But they have lasted a long time by not keeping the part they can’t afford to lose on the outside, where everything can reach it. A good deal of what gets built, by trees and otherwise, does exactly the opposite.

Peter Mark Roget did not mean his thesaurus to be read alphabetically. The book he published in 1852, when he was seventy-three, sorted words into about a thousand headings by the idea they express (existence, space, matter, intellect, will, affection), so that someone who knew exactly what they meant but couldn’t find the word could walk in by the meaning and look along the shelf. The alphabetical index went in near the end, at the back, so that people could also use it the other way round. That back half is the part almost everyone now uses: we arrive holding a word we already have and leave with a different one. A book built for people who had the thought and lacked the word turned out to be most loved by people who had the word and were tired of it.

You can reach the bottom of a paragraph and realise that nothing came with you. Your eyes did the whole job: they kept the line, turned at the margin, would probably have caught a typo. So you go back to the top, and halfway down the second pass you notice you’re thinking about the email you haven’t answered, and you go back again. By the third time it reads easily, and it feels as if the paragraph has relented, though not a word of it has changed. The same thing happens out loud. A parent can read a bedtime story with all the voices, pausing in all the right places, while planning tomorrow’s lunches, and the child gets the whole story. It’s an odd kind of proof that a paragraph can be delivered perfectly by someone it never reached.

The Greeks called a number perfect when it was exactly the sum of its smaller divisors: 6 is 1 + 2 + 3, and 28 is 1 + 2 + 4 + 7 + 14. They are rare. After more than two thousand years, fifty-two are known, the largest over eighty million digits long, and every one of them is even, each built from a prime of a particular kind, as Euclid half-showed and Euler finished. Nobody has ever found an odd one, and nobody has proved there isn’t one. What the searching has produced instead is a list of conditions: an odd perfect number, if there is one, is larger than 10^1500, has at least ten different prime factors, and the biggest of them is over a hundred million. It is an odd sort of progress, a description getting steadily more precise of something no one has seen, and of how large and complicated a thing would have to be to manage being both odd and perfect.

For a long time the most isolated tree on Earth was an acacia in the Ténéré desert in Niger, with no other tree for something like 400 kilometres in any direction. It was a landmark on the caravan routes and was marked on maps. When a well was dug beside it in 1938 and 1939, the diggers found its roots going down to water about 35 metres below the sand, which explained how it had managed to stay. In 1973 a truck driver ran into it and broke the trunk. What was left was taken to the national museum in Niamey, and a metal sculpture now marks the spot. It’s easy to tell this as a story about carelessness, and it probably was one. But there’s something else in it. Across hundreds of kilometres of open sand, that tree was the one thing anybody was driving towards, and whatever everyone aims for has to put up with being aimed at.

Gossip used to be a solemn word. In Old English a godsibb was a godparent: somebody made your relative (the sib in sibling) in the sight of God, at a christening. Over the next few centuries it widened to mean a close friend, and especially the women who came to sit with a neighbour while she gave birth. It isn’t hard to guess what happened next. A birth takes hours, the room is full of people who know one another well, and somebody has to pass the time. By the 1500s the word could mean anyone given to idle talk, and the people had turned into what they talked about. That seems unfair to them. They were there for the most serious hours of a neighbour’s life, and all the language kept was the chatter in between.

On a corner, a car’s outside wheels have farther to go than the inside ones, so they have to turn faster. The gearbox in the middle of the axle that allows this is the differential; the version in cars is usually credited to Onésiphore Pecqueur, a French engineer, in 1827. It is fair-minded to a fault: it always pushes the two wheels with the same force, and lets them sort out their speeds between them. On a dry road that’s perfect. Put one wheel on ice and the fairness becomes the problem. The ice can only take a tiny push, and since the two wheels must get equal shares, the wheel on good ground gets the same tiny push, and the car sits still while the icy wheel spins away. All the motion goes to the one that is getting nowhere. Engineers had to build a second mechanism, the limited-slip differential, to tell the first one that equal isn’t always the same as fair.

In 2021 a team led by Axel Meyer finished reading the genome of the Australian lungfish, a slow, olive-coloured fish that has hardly changed its shape in a hundred million years. It came to about 43 billion letters, roughly fourteen times the length of ours, and for a while it was the largest animal genome anyone had sequenced. (A South American cousin has since been reported larger still.) The surprise isn’t the size; it’s that the extra length doesn’t buy anything you can point to. The lungfish has about as many genes as other vertebrates. Most of the rest is repeats, copies of copies that got in a long time ago and were never thrown out. It’s the instruction manual as a family keeps it, with every old receipt still folded inside, and the fish goes on working perfectly well. Length was never the measure of what a thing knows how to do.

In the 1670s a Delft cloth merchant, Antonie van Leeuwenhoek, wrote to the Royal Society in London that a drop of water was full of tiny living animals. He wrote in plain Dutch, because he had no Latin, and he never told anyone how he made the little lenses he saw them through; that secret went with him. So nobody in London could simply check. What the Society did instead was ask for witnesses: a few respectable men of Delft, among them a minister of the English church there, went to his house, looked down his lens, and vouched for what they had seen. It is an odd way for a science to begin. The first report of a world too small for anyone to see was settled the way you settle a will: not by seeing it for yourself, but by finding people of good character who were in the room.

You go back to check the front door not because you think you left it unlocked, but because you can’t remember locking it, which is a different problem. A door you lock every day gets locked so smoothly that nothing is written down: the hand does it, and memory is never asked. So you walk back, try the handle, and of course it’s locked. The trouble is that the check is a habit now too, and by the time you reach the corner you can’t quite remember that either. The usual advice is to make the moment strange: say “locked” out loud, or do something slightly silly with the key. It works for the same reason the forgetting happened. You remember the things you did on purpose, and almost nothing you did well.

Pick a whole number. If it’s even, halve it; if it’s odd, triple it and add one. Keep going. Start at 6 and you’re home at 1 in eight steps. Start at 27 and the walk takes 111 steps, climbing as high as 9,232 before it finally comes down. Computers have run the rule on every starting number into the hundreds of billions of billions, and every one of them has ended at 1. Nobody has proved that they all do. It’s a strange place for a rule this short to leave us: we have watched every number we’ve ever tried find its way home, and we still can’t say why any of them knew the way.

In 1950 a radio host, Ralph Edwards, offered to broadcast his quiz show from any town willing to rename itself after it. Hot Springs, New Mexico, held a vote and said yes, and since then it has been Truth or Consequences. It’s an odd bargain to look at now: a whole town’s name traded for one evening on the air. But Edwards kept coming back, year after year, to a festival they held in his honour, and the name has outlasted the show it was borrowed from by a long way. Hardly anyone now remembers a quiz called Truth or Consequences. Plenty of people have driven past the sign. The town may be the longest-running part of the programme, which is a strange thing to become by saying yes to a stunt.

The gates of most canal locks meet in a shallow V that points upstream, like a pair of doors that didn’t quite agree to shut flat. The usual date for the first ones in use is 1497, at the San Marco lock in Milan; Leonardo drew the design, though whether he invented it is still argued over. The V is the clever part. The higher water leans on the two leaves and presses them into each other, so the more water there is behind them, the tighter they close. No lock-keeper is strong enough to open them against that. You open a small sluice in the gate, let the two sides run level, and then a person can push them aside with one arm. A door that won’t move while there’s something to hold back, and gives as soon as there isn’t.

A strangler fig starts at the top. A bird leaves a seed in the fork of a tall tree, and the seedling lives up there on what collects in the crook, sending roots down the host’s trunk until they reach the ground. Then the roots thicken and graft into one another, a net around the trunk, and above it the fig spreads its own crown. The name says it squeezes its host to death, but some of the people who study it say the squeezing matters less than the shade: the fig simply gets to the light first. When the host dies, its wood rots away inside the net, and if it was soft enough you are left with a hollow lattice standing in the forest, a cylinder of roots in the exact shape of a tree that is no longer there. It is the only portrait of that tree anyone will ever have, and the one who made it is the one who took its light.

A bead used to be a prayer. The Old English was gebed, from an old root that meant to ask, the same root that sits under the German bitte. Then people began keeping count of long runs of prayers on strings of small pierced balls, one ball for each prayer, and somewhere around the fourteenth century the word slid along the string, from the thing you said to the thing you held while you said it. By now it has gone all the way: a bead of sweat, a bead of glue, a bead of rain on a window, none of them asking anybody for anything. That is what tends to happen to whatever you keep your place with. After long enough you stop noticing what it was counting, and only notice the counter.

You can’t count the years on a Greenland shark. It has no hard bones to lay down rings, so in 2016 a team led by Julius Nielsen tried the one part of it that never gets renewed: the very centre of the eye lens, made when the shark was born and left alone ever since. They radiocarbon-dated it in 28 sharks. Only the three smallest carried the extra carbon that the nuclear tests of the 1950s and 60s put into every living thing, so only those three were born after the bombs. The largest came out at about 392 years, give or take more than a century. So the oldest vertebrate anyone has measured was dated by the part of it that had stayed a newborn the whole time.

In January 1885 a Vermont farmer, Wilson Bentley, got a microscope and a bellows camera to agree long enough to photograph a single snow crystal, and he spent the rest of his life doing it again, more than five thousand times. To make each one stand out, he took a copy of the negative and scraped away the background around the crystal by hand, with a penknife, so it would print white on black. About 2,400 of them went into a book in 1931, chosen for their beauty. A German meteorologist of his day, Gustav Hellmann, accused him of improving them, and it is still a fair question whether the knife ever took off a ragged arm along with the sky. Either way, the snowflake on every card and window sticker, six even arms and nothing out of place, is mostly his: picked, cleaned up, and framed in black. The snow on a sleeve is often broken, stuck together, lopsided. He didn’t lie about snow. He just loved the best of it so carefully that the rest of it now looks like a mistake.

Most arguments rehearsed in the shower are won. That isn’t surprising, since you’re writing both parts, and the other person, who in real life would say something you hadn’t thought of, says here exactly the thing you have a perfect answer to. So the rehearsal mostly trains you for a conversation that will never happen. The useful version is harder and less fun: give the absent person their best lines, the ones you’d rather they never thought of, and see whether you still have anything to say. Lose a few in there. It’s warm, and nobody’s listening.

William Playfair put the first line charts of trade into his Commercial and Political Atlas in 1786: years along the bottom, money up the side, imports and exports drawn as two lines you could watch cross. When he came to Scotland he had a problem. The records weren’t there. He had one year of figures, and a line needs at least two points before it can go anywhere. So he drew the one year as a row of bars, a pair for each country Scotland traded with, and apologised for it in the text: a chart like this, he said, takes in no portion of time and is much less useful than the others. The bar chart, which now turns up in every quarterly report there is, started as a workaround for a gap in the data, written up by its inventor as the weaker method. Sometimes the thing you’re sorry about is the one that lasts.

The plant usually called the corpse flower was described in 1878 by the Italian botanist Odoardo Beccari, from Sumatra, and its scientific name is Amorphophallus titanum, which is Greek and Latin for more or less what you suspect: a giant misshapen phallus. The story goes that when David Attenborough was filming The Private Life of Plants in the 1990s, saying that on television again and again seemed a bit much, so he called it the titan arum instead. That is the name botanic gardens now print on the sign. I like that a name made to get one series past the audience at home outlived the reason for it. A plant that blooms rarely, smells of rotting meat, and draws crowds who queue up specifically to be disgusted owes its most respectable name to somebody minding his manners.

In December 1956 a young American ornithologist, Chandler Robbins, put a metal band on the leg of a nesting Laysan albatross on Midway Atoll. Albatrosses don’t breed until they are about five, so she was at least that old already. Around 2002 he went back to Midway, noticed a worn band that needed replacing, read the number, and found it was one of his. Biologists then thought the species lived about forty years. She is now called Wisdom, and she has kept coming back to Midway to nest well into her seventies, wearing through band after band. Robbins died in 2017, at ninety-eight. So the record of how old she is has been written on things that wear out, by a man who was a young bird-bander when it started, and so far she has outlasted the bands and him too. Her age is only a lower bound: all anyone knows is the year somebody started counting.