The decimal clock.

If we are willing to redraw the calendar, the clock deserves the same scrutiny – and the obvious repair is to count time in tens.

Why are there 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute? The 24 hours, split into two twelve-hour rounds, come from the ancient Egyptians and their sundials. The 60s come from the Babylonians and their base-60 counting. It is a wonderfully long inheritance – and a daily obstacle every time we try to add up a span of time we are not already used to.

A more comprehensible clock would respect the way we actually count. In other words, it would be decimal.

A myriad moments

Divide the day into a hundred spells, each spell into a hundred moments, and each moment into a hundred blinks. A day is then a myriad moments – in the word’s original sense of ten thousand. New names keep the new units from being confused with the old hours and minutes.

A spell is roughly a quarter-hour; a moment, a slow breath; a blink, about a tenth of a second.

The hundred-part day, four times over

The spell comes with a pedigree. The fourteen-and-a-half-minute hundredth-of-a-day has been arrived at independently at least four times – and for the better part of two thousand years, the largest civilisation on Earth ran on it. From the Han dynasty onward, China divided the day into a hundred kè – the word means “mark,” after the graduations on a water clock’s float rule – alongside the twelve double-hours, the two systems meshing awkwardly at eight and a third kè per double-hour.^[1] The great Shoushi calendar of 1280 went all the way: a hundred kè to the day, a hundred fēn to the kè, a hundred miǎo to the fēn – precisely the spell–moment–blink chain proposed above, seven centuries early. The decimal day was only abolished in 1645, when the Jesuit-run imperial observatory redefined the kè as exactly a quarter-hour, 96 to the day, so that the new European tables would divide evenly. The word survives: in modern Chinese, kè still means a quarter of an hour – a fossil of the centiday, rounded to fit our clock.

The second invention was law, briefly. Revolutionary France decreed in 1793 that “the day, from midnight to midnight, is divided into ten parts, each part into ten others, and so on” – ten hours of a hundred minutes of a hundred seconds.^[2] Watchmakers built the dials; a handful survive in the Musée des Arts et Métiers, and Laplace kept a decimal watch and wrote his Mécanique Céleste in decimal fractions of the day. Lagrange, ever the clear thinker, proposed calling the units décijours and centijours – the spell again, under its most honest name. Decimal time was mandatory for public records for exactly 197 days before being suspended in April 1795, by the same law that launched the metric system. The metre conquered the world; the decimal day did not survive its first spring. The difference was installed hardware: every steeple in France already carried the old dial.

It kept coming back. In 1894 the Toulouse chemist Joseph de Rey-Pailhade proposed the cé – short for centijour – the third independent arrival at the same 14.4 minutes.^[3] In 1897 the Bureau des Longitudes convened a commission on the decimalisation of time, with Henri Poincaré as its secretary; it tried the diplomatic compromise of keeping the 24-hour day and decimalising below it, and was abandoned by 1900, defeated once more by the world’s installed instruments.^[4] A century later Swatch sold the idea as marketing: “Internet Time” (1998) cut the day into a thousand .beats of 86.4 seconds – the Revolutionary decimal minute reborn – counted from the meridian of the company headquarters in Biel. It faded within a few years, leaving a vestigial B format character in PHP’s date function.

Four inventions, one obstacle. Nothing ever defeated the arithmetic – what defeated each attempt was the cost of replacing every clock in existence, and the habits of everyone who could already read one. That obstacle is worth naming precisely, because it is the one thing that has changed: nearly every clock face in the world is now software.

Starting the day at dawn

The traditional clock is wrong about where the day begins, too. Let the day start in the early morning – at what the old clock calls 6 a.m. – rather than in the dead of night. Morning is the spring of the day; it makes more sense for the day to turn over as the world wakes than for it to roll over to a new date in the middle of a long night.

This also lets the clock rhyme with the calendar. If the year begins at the spring equinox and the day begins at dawn, both circles start on their right-hand side and run counterclockwise, up and around – the same direction the Earth turns and the planets orbit, and the same way the mathematical unit circle is drawn.

Where the day has begun

Here too the dawn start has deep company. Pliny the Elder, writing in the first century, catalogued where the world’s peoples placed the day’s boundary: the Babylonians counted between two sunrises, the Athenians between two sunsets, the Umbrians from noon to noon, “the common people everywhere” from light to dark, and the Roman priests and civil authorities from midnight to midnight.^[5] Midnight, in other words, is not a law of nature; it is Roman law. The lawyers wanted a boundary that never moves with the seasons and falls when nothing is happening – unobservable, and for contracts that was a feature. The 1884 International Meridian Conference made the Roman convention global.

Every other choice has been lived in. The Egyptian day began at first light, and the Hindu civil day still runs sunrise to sunrise. The Jewish and Islamic days begin at sunset, as the Babylonian calendar’s did. Italy counted its hours 1 to 24 from sunset well into the 18th century – the 24-hour dials of St Mark’s in Venice and the Prague Orloj still show the system – while “Babylonian hours,” counted from sunrise, ran alongside it on Central European sundials. Astronomers, for their part, began the day at noon for centuries, so that a single night’s observations would fall under one date; they only surrendered to the civil midnight in 1925.^[6] The navy kept a noon-to-noon day of its own – the Battle of Trafalgar is logged in nautical time, the Admiralty order abolishing it not having reached the fleet in time.

So the day’s start is, historically, a choice – and dawn is among the oldest answers, not an eccentric one. What is genuinely new is only the pairing: a dawn start chosen so that the day and the year turn over together, at the waking of the world and the waking of the year.

A compact notation

Because the units are decimal, the time of day is just a fraction. You can append it to a date as a string of decimals, to whatever precision you need – an extremely compact notation when one is wanted. The real prize, though, is arithmetic: every span of time becomes a subtraction you can do in your head.

It would take some getting used to, and there is a great deal downstream that would need adjusting. That does not make it the wrong idea – only a slow one. Four failed attempts say the obstacle is the installed clocks; the fifth attempt gets to make its case in an age when the clocks are screens.

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