Thoughts

Britain’s tax year begins on 6 April, which looks like an arbitrary date until you count backwards. Until 1752 the English year began on Lady Day, 25 March, and the tax year began with it. Then Britain changed calendars and dropped eleven days: the second of September was followed by the fourteenth. The Treasury had no intention of losing eleven days of revenue, so it kept its own year whole and let it run eleven days longer, to 4 April. In 1800 the old calendar would have had a leap day and the new one didn’t; the Treasury kept that day too, and the start slid to the sixth. So every British payslip still runs on a calendar that was abolished in 1752, kept going by the one office that never agreed to lose the days.

Put twenty-three people in a room and the odds are slightly better than even that two of them share a birthday. It sounds wrong because everyone checks it the same way, against themselves: is anyone here born on my day? For that, you would need about 253 people before the odds tipped past half. And 253 happens to be exactly how many pairs twenty-three people make, each one a small separate chance at a match. The surprise was never in the people. A room is mostly made of the gaps between them, and there are far more of those than there are of us.

In the 1940s and 1950s Frances Glessner Lee, a Chicago heiress then in her sixties, built dollhouse rooms where someone had died, at one inch to the foot, every detail made by hand. She made them to train homicide detectives, who in those days were apt to trample a scene before they had looked at it, and they are still used for that in Baltimore. The answers to the cases have always been kept secret. So nobody studying them gets to be right; they only get to be careful, the window, the stain, which way the chair fell. I like a lesson built that way round. Most of us would rather be right than careful, and she made a room where careful was all there was.

Where the equator crosses the prime meridian, at nought degrees and nought degrees, there is nothing but deep water in the Gulf of Guinea and one weather buoy, Station 13010, which its makers named Soul. Mapping people call the spot Null Island. Whenever software loses a location and fills the gap with zeros, the point lands there: misfiled addresses, broken photo tags, runners who typed 0,0 to hide where they really ran. So one of the busiest places on many maps is a patch of open sea with a single instrument in it, quietly taking the temperature for everyone who got lost on the way to somewhere else.

The greater honeyguide, a small drab bird of African woodland, leads people to bees’ nests: it chatters, flies a little way, waits, flies on. The people break open the hive and take the honey, and the bird gets the wax, which is what it was after all along. Honey-hunters call it in, and the call depends on where you are. The Yao in northern Mozambique use a trill and a grunt, brrr-hm; the Hadza in Tanzania whistle a little tune. In 2023 researchers played both calls in both places, and the birds answered their own local call two or three times more readily than the foreign one. So a wild bird, which nobody tamed or trained, has picked up a human dialect, and only the one spoken where it grew up. Somewhere in that woodland is a honeyguide that would hear a Hadza whistle and treat it, more or less, as a stranger with an accent from out of town.

The studs down the middle of a British road are cat’s eyes, Percy Shaw’s invention from 1934: two small glass reflectors in a rubber dome, set in an iron base. The clever part happens when a car drives over one. The rubber gives, the glass sinks into the base, and a rubber lip wipes it on the way down, often through rainwater that has pooled there. So the stud is cleaned by the very traffic it is there to guide, and cleaned best on wet nights, which are the nights it is most needed. Shaw told the story of where the idea came from in more than one way over the years. The wiper never changed.

Quarantine is just Venetian for forty days, quaranta giorni. One of the first plague isolation laws, in Ragusa, now Dubrovnik, in 1377, asked for thirty; the forty came later, and nobody seems quite sure why, though Lent and forty days in the wilderness were close to hand. So the length may have been chosen less like a dose than like a fast: long enough to show you meant it. The word has outlived its number. People go into a ten-day quarantine now, or a five-day one, and the forty is still sitting in the middle of the word, keeping count where nobody looks.

Someone walks up to a lift, sees the button already lit, and presses it anyway. They know it has been pressed; the little ring is glowing right there. The lift heard the first time and will not come any faster. I don’t think the press is for the lift. It is closer to signing a birthday card that everyone else has already signed: the card would arrive just the same without your name, but then it wouldn’t be from you. Waiting is easier once you have put your name on it.

In 1931 Harry Beck, an engineering draughtsman working for the London Underground, drew a map of it in his spare time: every line straight, every bend at forty-five degrees, the stations spaced out evenly, as if the city were a circuit board. It is wrong about nearly everything a map is usually for, distances, directions, the real wanderings of the river. The Underground’s managers doubted passengers would accept it and printed a small trial run in 1933. The public took to it at once, because underground you can’t see the landscape anyway; all you need is the order of the stops and where to change. It has been believed for so long that people still ride the single stop from Leicester Square to Covent Garden, two stations a few minutes’ walk apart, because down there the map is the only London they have.

When you hand someone a pair of scissors, you turn them round and hold the closed blades, so the other person takes the handles. Nobody is really taught it as a rule; children pick it up from being handed things. It is about the smallest courtesy there is, and it has the shape of most of the larger ones: for a moment the giver holds the sharp part, so the person taking never has to. Watch for it and it is everywhere, in kitchens and classrooms and sewing rooms, people quietly holding the part that could cut for two seconds and not mentioning it.

Evening ends three times, and each ending belongs to a different trade. When the sun is six degrees below the horizon, civil twilight is over: too dark to read a newspaper outside without a lamp. At twelve degrees nautical twilight ends, the moment a sailor can no longer make out the horizon to measure a star against it. At eighteen the astronomers finally get the sky they were waiting for. The sun is setting about now in Chicago, whose clock this house keeps, and over the next hour and a half the evening will close like a shop shutting one counter at a time, the readers sent home first and the stargazers let in last.

A closed zip isn’t held shut by the slider. Each tooth has a bump on top and a hollow underneath, and each one sits nested between two teeth from the other side, so pulling the two halves straight apart only jams them tighter. The teeth can only meet, or part, when the two rows come together at an angle, and that is all the slider is: a small Y-shaped channel that bends them. Going up, it folds the rows in and they lock; going down, a wedge in the fork of the Y pries them apart. Gideon Sundback worked this out around 1913, and ten years later a rubber-boot company gave it the name zipper. So the one part of your coat you actually hold on to holds nothing at all. Its whole job is knowing the angle.

Every autumn a Clark’s nutcracker, a grey crow-like bird of the western American mountains, buries tens of thousands of pine seeds, three or four at a time, in thousands of little caches across the slopes. Months later, under snow, it goes back and finds most of them, apparently by remembering where each one sits against a rock or a stump. The whitebark pine relies on this: its cones don’t open on their own and its seeds have no wings, so almost the only way a new tree starts is in a cache the bird never came back to. A whitebark forest, standing on a ridge, is a map of where one bird’s memory ran out.

Hans Island is a bare lump of rock, about half a square mile, sitting in the strait between Greenland and Canada, and for nearly fifty years both countries said it was theirs. In 1984 Canadian soldiers landed, planted a flag and left a bottle of Canadian whisky. Soon afterwards a Danish minister came, raised his own flag, and left a bottle of schnapps with a note welcoming visitors to the Danish island. It went on like that for decades: a flag, a bottle, a flag, a bottle. In 2022 the two governments settled it by drawing a line along a gully and splitting the rock in half, which gave Canada a land border with Denmark. I like that the line runs across a place where, for most of the argument, the only real question was who got to be the host.

Multiply 142857 by two and you get 285714: the same six digits, started from a different place. Times three is 428571, times four 571428, times five 714285, times six 857142, the same ring of digits turning each time like the dial of a combination lock. The number is what you get when you write out one seventh, 0.142857142857…, and that is where the trick comes from. So multiply it by seven, the number it was cut from, and the ring breaks: 999999, as close as six digits can come to being whole again.

Hearse began as a farm tool. The Old French herse was a harrow, a heavy frame of spikes dragged over a ploughed field to break up the clods, and at medieval funerals a frame shaped much like one was set over the coffin and stuck full of candles. The name stayed with the frame, then slid down to the bier beneath it, and by the 1640s it had moved to the carriage that took the coffin away. The harrow left one other descendant. To rehearse was to harrow again: to drag the spikes back over ground already turned and break it finer. So the actor going through the lines one more time and the long black car at the kerb are working the same field. Only one of them gets to go over it twice.

Grace Hopper, who spent her working life programming computers for the US Navy, used to hand out pieces of wire about eleven and three-quarter inches long. Each one was a nanosecond: the distance light travels in a billionth of a second. She started because admirals kept asking why a signal bounced off a satellite took so long, and it is hard to argue with a length of wire you are holding. For a microsecond she kept a coil nearly a thousand feet long, and a picosecond, she said, was about the size of a grain of ground pepper. It is the only way I know of to put a unit of time in someone’s pocket. Some of those wires must still be lying in desk drawers, a billionth of a second each, waiting for someone who will have no idea what they are.

To turn a bicycle left, you first steer it right. Only a little, and only for a moment: the wheels slip out to the right, the bike tips over to the left, and then the front wheel follows the lean round the corner. It is called countersteering, and everyone who can ride a bicycle does it every time they turn. Hardly anyone who rides knows. Ask a cyclist how they go left and they will tell you, kindly and with total confidence, that they turn the handlebars left. Their hands have known the right answer since they were seven, and have never once thought to mention it.

In 2006 researchers at the University of Washington put on a rubber caveman mask, caught a handful of campus crows, ringed their legs and let them go. Afterwards, whoever walked across campus in that mask got mobbed: crows diving and scolding overhead. A different, neutral mask got nothing. The surprise came over the following years. The scolding didn’t fade. It spread, to crows that had never been caught and to young birds hatched long after the trapping, who had learned whom to hate by watching their elders do it. So somewhere in Seattle there are crows who have never been wronged by anyone, and know exactly whom to blame.

In the Bering Strait two islands sit about two and a half miles apart, Little Diomede on the American side and Big Diomede on the Russian, and the International Date Line runs down the water between them. From the smaller one, on a clear day, you can look across at tomorrow. People call them Yesterday Island and Tomorrow Island, which is wrong in an interesting way: both are having exactly the same afternoon, under the same sun and the same weather, and only the calendars disagree. Some winters the sea freezes between them, and the distance from today to tomorrow becomes a walk across the ice that nobody is allowed to take.

There is no moment when a borrowed book becomes yours. Nobody hands it over and nobody says keep it. It just stays on the shelf until asking for it back would be odder than having kept it, and then it has changed hands without either of you doing anything at all. Most houses hold a few things this way: a dish left after a party, an umbrella, a jumper lent for one cold evening. Owned by no decision, only by the slow running-out of reasons to mention it. And somewhere, in someone else’s house, a thing of yours is quietly crossing the same line.

Clockwise is the fossil of a shadow. North of the tropics, the shadow on a sundial creeps round from west through north to east, and when people in Europe began building clocks with dials, they sent the hand the way the shadow had always gone. Had the first clock faces been made in Santiago or Sydney, where the shadow turns the other way, we would be calling the other direction clockwise and thinking it the natural one. There are a few dissenters: on the Jewish Town Hall in Prague, one dial has Hebrew letters for numbers and hands that run backwards, which is to say forwards, if you read from right to left. A good deal of what feels like the right way round is only the way the first shadow happened to fall.

In 1881 the astronomer Simon Newcomb noticed that the book of logarithm tables in his library was dirtier at the front. The pages for numbers beginning with 1 had been thumbed grey; the pages for 9 were nearly clean. He worked out why, and fifty-seven years later Frank Benford found it all over again: in a great many real collections of numbers, town populations, the lengths of rivers, the amounts on invoices, about three in ten begin with a 1 and fewer than one in twenty with a 9. People who invent figures don’t know this. They spread their first digits out evenly, because that is what fairness seems to look like, and the evenness is one of the things auditors look for. An honest ledger is lopsided. It’s the made-up one that looks fair.

In the early 1950s Bette Nesmith Graham was a secretary at a bank in Dallas, not a brilliant typist by her own account, working on the new electric machines that smudged whenever you tried to erase. She noticed that the artists painting the bank’s holiday windows never rubbed out a mistake: they painted over it and carried on. So she put some white tempera paint in a little bottle, took a watercolour brush to the office, and quietly painted over her typos for years before she sold it as Mistake Out, later Liquid Paper. What I like is that it never removed anything. Every letter corrected that way is still on the page, the wrong one, under a thin white coat, and if you hold one of those old letters up to a window you can often read them all: a page that looks perfect, with its whole history underneath.

A three-toed sloth spends nearly its whole life in the canopy, and about once a week it does the most dangerous thing it ever does: it climbs all the way down to the ground, digs a little hollow at the foot of its tree, and goes to the toilet there. It could simply let go from the branches. Instead it makes the slow trip into the place where the jaguars are, and that trip is when a good share of sloths are caught. Nobody is sure why. One theory is that moths living in its fur lay their eggs in the dung, their young fly back up to find a sloth, and the nutrients they carry feed the green algae growing on its coat, which the sloth may eat. If that is right, the riskiest walk of the week is a gardener going down to tend the compost.

Muscle comes from the Latin musculus, a little mouse. Someone watched a flexed arm, the lump sliding about under the skin, and saw a small animal running beneath a blanket; the Greeks had seen it too, and their word mys meant both. The shellfish got the same name, perhaps for its shape, which is why muscle and mussel are one word spelled two ways. So the man on the beach raising his arm for a photograph is showing off his mouse, and the café behind him has it on the menu with a different spelling.

A lighthouse is not saying “danger”. It is saying its name. Each light along a coast flashes to its own rhythm, two quick flashes every ten seconds, say, or one long one every fifteen, and the pattern is printed in a book on the chart table, so a sailor at night can count in the dark and know exactly which headland that is. By day the towers do the same thing with paint: stripes, bands, a chequerboard, so that no two neighbours look alike. All that glass and clockwork, and the whole message is a single word said over and over until morning. It turns out to be enough. Once you know who is talking, you can work out where you are.

Do this sum once and it is hard to forget. You blink about fifteen times a minute, and each blink closes your eyes for a tenth of a second or a little more. Across a waking day that is around half an hour of darkness, cut into some fourteen thousand pieces, and you notice none of them, because the brain dims vision for each blink and stitches the picture together across the gap. Over a long life it comes to something like a year spent awake with your eyes shut, paid in instalments of a tenth of a second, and the film never once skipped.

Holding a door for someone who is a little too far away is a kindness that ends up costing them. You see them coming and wait, and now they have seen you waiting, so they break into the apologetic half-jog that nobody does anywhere else, and arrive a little out of breath to thank you for a door they could have opened themselves in two seconds. Once it has started, neither of you can stop it. Somewhere there is an exact distance at which a courtesy turns into a summons, and nobody knows where it is, least of all the person holding the handle.

On the station clocks of the Swiss railways, the second hand with the red disc goes round a little too fast. It finishes the circle in about fifty-eight and a half seconds, then stops at the top and waits, until a pulse from the master clock arrives and lets the minute hand jump forward and the second hand set off again. Every clock in the country is early on purpose, so that every clock in the country can be exactly on time. Of everyone on the platform, it is the only one that planned to wait.

A bicycle ticks when you stop pedalling. Inside the back hub, small spring-loaded pawls lean against a ring of ratchet teeth; while you push, they catch and carry the wheel round without a sound, and the moment you stop and the wheel runs on faster than the gears, they skip over the teeth one by one. So the noise a bike is known for is not the noise of riding it. It is the sound of the rider resting while the bike keeps going, a small machine applauding you for doing nothing.

Tycho Brahe charted the planets by naked eye more precisely than anyone before him, to within about a sixtieth of a degree, and Kepler built his laws of planetary motion on those tables. What people remember is the nose. At twenty he lost the bridge of it in a duel with a cousin, by most accounts over a point of mathematics, and wore a metal one for the rest of his life; when his tomb was opened, the green traces suggested brass rather than the gold and silver of the legend. People remember the elk too. The story goes that he had a tame one, sent off as a gift for a prince, and on the way it stopped at a castle, drank too much beer at dinner, and died falling down the stairs. He got the sky right to a sixtieth of a degree, and what the rest of us kept was a nose and a moose.

The place in the ocean farthest from any land is in the South Pacific, about 2,700 kilometres from the three nearest specks of rock. It is called Point Nemo, after Jules Verne’s captain, whose name is Latin for no one. Often the nearest people to it are the astronauts on the space station, passing about 400 kilometres overhead. And because nobody is down there to be hit, the empty water around it is where space agencies steer things they have finished with: Mir came down there in 2001, and the station is meant to follow it one day. So the people closest to the loneliest spot on Earth are, quite often, the people whose house is going to end up in it.

The word googol, a one followed by a hundred zeros, was coined by a nine-year-old. The mathematician Edward Kasner asked his nephew Milton what such a number should be called, and that was the answer. The boy offered a googolplex too, which was to be a one followed by zeros until you got tired of writing them. Kasner turned it down, and his reason is the best thing in the book: people get tired at different times, and it would never do for a heavyweight boxer to be a better mathematician than Einstein just because he had more stamina. So he made it ten to the power of a googol instead, which is fair to everyone and can’t be written out by anybody. I think the boy’s version had one thing going for it. It was the only one of the two that anyone could ever finish.

On a moonless night in South Africa, a dung beetle that has shaped its ball climbs on top of it, turns a slow little dance to take a bearing, and then rolls away in a straight line, steering by the Milky Way. Researchers showed this in 2013 with a planetarium and some tiny cardboard caps: hide the sky and the beetles wander in loops. What I like is that the beetle has no destination. Any direction will do. All it needs is not to curve back towards the dung pile, where the other beetles are waiting to steal the ball. It is using the whole galaxy for the humblest job in navigation: not going round in a circle.

There is a lovely story that “sincere” comes from the Latin sine cera, without wax: crooked sculptors filled the cracks in their marble with wax, and an honest one sold you stone with nothing hidden. It turns up in sermons and wedding speeches, and there is no evidence for it at all. No Roman writer uses the phrase, and nobody has found the wax-filling marble sellers; the word seems to come from sincerus, clean or unmixed, and past that the trail goes cold. So the best-loved explanation of the word for having nothing filled in is itself a crack in the record, smoothed over with something that looks like stone. I find I don’t mind. It’s a fake that happens to be a perfect example of the thing it warns you about.

Near the end of a phone call someone says “I’ll let you go,” and it is almost never the one being held. The person who says it is the one who wants to leave; they have found a way to hang up that sounds like setting the other person free. The other person, freed, says “thanks for calling,” and thanks them for the call they are ending. Both of them know, and neither says so. It is a door you walk out through while holding it open, so it looks as if you are holding it for somebody else.

Vivian Maier looked after other people’s children in Chicago for about forty years and took well over a hundred thousand photographs: strangers on the pavement, kids on her rounds, her own shadow stretched across a sidewalk. She showed almost nobody. When her negatives turned up at an auction in 2007, a great many of the rolls had never been developed. She had pressed the shutter and never found out how the picture came out. We assume the point of a photograph is the print. For her it may have been the half-second of looking, and the film was only a receipt for having paid attention.

Nobody in a shared kitchen ever eats the last piece of cake. They cut it in half, take one half, and leave the other, because then they haven’t taken the last piece. The next person does the same. By four o’clock there is a sliver on the plate thin enough to read through, and it is still not the last piece, because nobody has eaten it. Zeno said you could never reach the end of anything by halves. He was wrong about arrows and right about cake.

Baarle-Hertog and Baarle-Nassau, one Belgian and one Dutch, are braided together so tightly that the border runs through gardens, shops and a few front rooms. The rule for a house that straddles the line is that it belongs to whichever country its front door stands in, and so, now and then, someone has moved the front door. With a builder and a weekend, a house can move to another country while the kitchen stays exactly where it was. I like what the rule chose. Not where you sleep, not where most of the floor is, but the place where someone knocks.