Thoughts

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.

The mathematician Edward Kasner asked his young nephew, Milton Sirotta, to name a 1 followed by a hundred zeros, and the boy said googol. Then he offered a bigger one, the googolplex: a 1 followed by as many zeros as you could write before you got tired. Kasner kept the name and threw out the definition, and his reason, as he and James Newman told it in their 1940 book, was a fair one: different people get tired at different times, and it would never do for a prizefighter to own a larger number than a mathematician just because he had more stamina. So the googolplex became a 1 followed by a googol zeros, which is far more than anyone could write. The boy’s number was not so much too vague as too small, and the fair fix turned out to be one that wears out everybody equally.

Goodbye is what is left of “God be with ye.” The Oxford dictionary’s earliest example of the squeezed-down version comes from a letter Gabriel Harvey wrote in 1573, and the long form and the short one lived side by side until about 1800. The “God” probably turned into “good” because of the company the word kept: good day, good night, good morrow, all of them said at the door. Once people stopped hearing the blessing inside it, the phrase lined up with its neighbours and took their shape. Nobody decided that, and nobody had to. The meaning wore off, and the word stayed in the one place it was always for, the moment someone goes where you can’t follow.

In 1788 James Watt fitted his steam engines with a flyball governor, borrowed from the windmills: two iron balls on hinged arms, spun by the engine itself. Run too fast and the balls swing outward, and a linkage closes the steam valve; slow down and they drop, and it opens again. The engine minds its own speed. Except that sometimes, as engines got better, the cure set up a wobble of its own: the valve corrected a little late, the engine overshot, the governor corrected back, and the speed swung up and down around the point it was meant to hold. In 1868 James Clerk Maxwell wrote a paper, On Governors, working out with mathematics when a device built to steady a machine would make it swing instead. Hardly anyone read it for eighty years. Then in 1948 Norbert Wiener named a new science of feedback after it, cybernetics, from the Greek for steersman, partly in honour of Maxwell, because governor comes from the same Greek word by way of Latin. So the whole field takes its name from a machine whose most useful lesson was that correcting things is not the same as steadying them.

On New Year’s Day 1739 a French captain, Jean-Baptiste Bouvet, saw land through fog in the far South Atlantic and took it for a cape of the great southern continent everyone expected to find. He wrote down where it was, and the position was wrong. Thirty-odd years later James Cook sailed to the spot, found open sea, and decided Bouvet had probably mistaken an iceberg for land. Which was a fair conclusion, and also wrong. In 1808 a whaler came across the island, sailed all the way round it and gave it his own name. It is still there, mostly under ice, about as far from anywhere as an island gets. What I like is that both mistakes were careful ones: Bouvet saw something real and put it in the wrong place, and Cook looked in exactly the right place for something that had never been there.

The typo in a message is nearly always easier to see a second after you send it. Before that, you were reading what you meant, which is a very forgiving text: your eye slides straight over “teh” because you know perfectly well what goes there. Pressing send changes your job. You stop being the person who wrote it and become, for the first time, somebody reading it, with no say over what it says, which is exactly the reader the typo was waiting for. Careful people get the same effect by leaving a draft overnight, or reading it aloud, or going through it backwards. But the cheapest way anyone has found to read your own words like a stranger is to make them impossible to change. It is probably the only proofreading method that works every time, and it only works too late.

John Harrison, the man who eventually solved longitude at sea with a clock, started out as a carpenter, and his first clocks were made mostly of wood. That sounds like a beginner’s compromise, but it took him somewhere. The oils of his day were the weak point of any clock: they thickened in the cold, thinned in the heat and slowly went gummy, and a clock is only as steady as the friction inside it. So instead of hunting for a better oil, Harrison kept finding ways to need less of it, with parts made of lignum vitae, a tropical wood so resinous it greases itself, and later with movements designed to run on almost none at all. A turret clock he built in the early 1720s for the stables at Brocklesby Park, in Lincolnshire, is reported to be still going. The usual move, when one part of a machine keeps failing, is to make that part better. His was to keep asking whether the machine had to have it.

In 1956 the psychologist George Miller published a paper that began with a complaint: he had been persecuted by an integer. The number seven kept turning up in his experiments, roughly how many tones or loudnesses people could tell apart, and roughly how many digits they could hold in mind at once. The title called it the magical number seven, plus or minus two, and that is the part everyone kept. What the paper went on to say was more careful. Memory, he argued, is limited not by how much information it holds but by how many chunks, so a person who groups digits cleverly can hold far more than seven. And at the end he looked at all the sevens he had gathered, the seas and the wonders and the days of the week among them, and said he suspected it was only a pernicious, Pythagorean coincidence. Later work puts the limit nearer four. So the most famous number in psychology was announced by a man who doubted it, in a paper whose real finding was that the number depends on what you count, and it went out into the world as seven anyway, because a joke in a title travels further than a hedge in a conclusion.

Horace Walpole made up the word serendipity in a letter to a friend in January 1754, and explained it with a fairy tale he had once read, The Three Princes of Serendip. The princes, he wrote, were always making discoveries, by accidents and sagacity, of things they were not in quest of. Then he gave his example. One of them worked out that a mule blind in its right eye had lately walked the same road, because the grass had been eaten only on the left side. That is not an accident. That is a man looking at a verge and reading it. Walpole’s one illustration of happy chance is a piece of detective work, and the only luck in it is that the mule happened to go that way. The word has spent more than two and a half centuries meaning the accident. The other half of the definition, the part that notices which side of the road is chewed, was there in the first letter, and it was the half doing the work.

Peter Durand patented the tin can in England in 1810, and for decades nobody sold a tool to open one. People used what they had: a knife, a bayonet, and by one account the advice was to cut round the top with a chisel and hammer. The first real can openers came in the 1850s, Robert Yeates’s in England in 1855 and Ezra Warner’s in America in 1858, nearly half a century late. It is easy to make a joke of that, but the delay probably wasn’t stupidity. The early cans were thick, made to survive ships and campaigns, and nothing small opens a thick can. An opener only made sense once cans got thinner, and they could only get thinner once people trusted them. The opener couldn’t come first. It had to wait for the can to stop being built against everything, including the person who bought it.

In the 1960s, digging at Masada, archaeologists found date seeds about two thousand years old, and put them away. Some sat in a university drawer for around forty years until, in 2005, a researcher planted three, mostly to see. One came up. They called it Methuselah, and it grew into a healthy palm of a kind not seen in that country for centuries. It also turned out to be male, which for a date palm means that on its own it would never bear a single date. So other old seeds were coaxed out of the ground, and one of them, a female grown from a seed found in a cave not far off, was given its pollen. A few years ago she fruited. The first fruit of the palm that started it all came off somebody else’s branches. Two thousand years in the ground and forty in a drawer, and what it was waiting for in the end was not water or light but another seed that had waited about as long.

For a while the axolotl was filed as its own kind of animal: a salamander that kept its feathery gills, lived in the water all its life, and bred that way. Then, in Paris in the 1860s, among the axolotls being raised from a handful brought over from Mexico, a few did something none of the others had. Their gills shrank, their fins went, and they climbed out as land salamanders that looked very like the American tiger salamander. The animal everyone had been describing was a larva. It had simply never needed to finish. Later it turned out that the change hangs on thyroid hormone, and that a dose of it can push an axolotl through a metamorphosis its ancestors in the lakes around Mexico City had mostly stopped bothering with. What I like is that the grown-up form was never lost, only left unused, the way you might keep the key to a house you moved out of years ago. Most axolotls live their whole lives without trying the door.

Gibraltar is joined to Spain by a flat strip of sand, and during the Second World War the runway was laid straight across it, because that was the only flat ground there was. Which meant the main road into Gibraltar ran across the runway. For about eighty years, when a plane was due, barriers came down like a level crossing and the traffic waited while an airliner went past where the cars had just been. In March 2023 a road tunnel, about 350 metres long, opened under the end of the runway, and the cars stopped crossing. People on foot and on bicycles still do. So if you walk in from the border, you can still be asked to stand at a barrier and wait while somebody else arrives.

Hand someone a new pen to try and there is a good chance they write their name. Not a word, not the date: the name, or else a tight little spiral. It makes sense once you see it as a test. To find out whether a pen is any good you need to write something whose shape you already know exactly, so that any skip or blot or wobble can only be the pen’s fault. You have probably written your name more often than anything else. You know how it goes down to the angle of the last stroke. So the name is a ruler, and you lay the pen against it to see where the pen comes up short. Signatures drift over a lifetime, of course. But for the length of one scribble on the back of a receipt, yours is the fixed point, and the rest of the world is the thing being checked.

Alfred Wegener said the continents move, and for evidence of it happening now he had longitudes. Expeditions had fixed positions on the coast of Greenland across the nineteenth century, and when he set the old numbers side by side the island seemed to be sliding west by something like thirty metres a year. In the 1930s Danish surveyors measured again with better instruments and found the shift was mostly error in the old observations, which were never as exact as he had trusted them to be. The real drift, it turned out decades later, is a couple of centimetres a year, more than a thousand times smaller. So the one measurement he had of the thing moving was wrong, and the thing was moving. He was right about the earth and wrong about his proof, and he died on the Greenland ice in November 1930, before anyone had settled either half.

In 1494 Luca Pacioli, in a fat Venetian book of arithmetic for merchants, gave a rule for how long money takes to double: divide 72 by the rate of interest. At six percent, twelve years. He did not say why it worked, which is usually taken to mean it was already old. Nobody could have said why. The reason sits in the natural logarithm of 2, and logarithms were not published until 1614, a hundred and twenty years after the book. The honest number is nearer 69, but 69 divides by almost nothing, and 72 splits cleanly by 2, 3, 4, 6, 8, 9 and 12, and at the sort of rates merchants actually charged it happens to land closer to the truth anyway. So the rule was picked for being easy to do in your head, and turned out more accurate because of who would be using it. It worked for more than a century before anyone could explain it, and it has never needed the explanation to keep working.

Nostalgia was coined in 1688 as the name of a disease. A young doctor, Johannes Hofer, wanted a learned word for what the Swiss called Heimweh, and he built one out of Greek: nostos, the return home, and algos, pain. The symptoms listed for it included fever, an irregular heartbeat, weakness, stomach pain and melancholy, and it was said that in some cases it could kill. Military doctors went on diagnosing it long after Hofer. Somewhere along the way the word left medicine and changed sign, and now it is something we choose on purpose: an old song, a sweet they have started making again, a film set in the year we were twelve. Nobody runs a fever from it. What strikes me is that the illness was always about a place, a valley you could in principle walk back to. The kind we kept is mostly about a time, which has no road back to it. The disease, at least, had somewhere to go. What we kept is the version with nowhere to go, and we decided to enjoy it.