SINCE the start of 2010, your correspondent has amused himself by interpreting the date as a binary number, and then converting that into its decimal equivalent. Expressed internationally as dd.mm.yy, the first day of this year was 010110. In decimal form, that works out to be 2^{4}+2^{2}+2^{1}=22. The game is pointless, of course. But it has made him ponder the whole date and time arrangement people take for granted.

There are only four years a century when you can play this little game. In the current century, two years (2000 and 2001) have already passed. Like the previous pair, the two that remain (2010 and 2011) contain only three days (1st, 10th and 11th) in three months (January, October and November) that lend themselves to this phoney binary treatment.

Bridgeman

Obviously, the smallest binary number in this century's set was January 1st at the turn of the millennium (010100). The largest will be November 11th next year, when all the bits in the six-digit sequence are present (111111). In decimal terms, that is equal to 2^{5}+2^{4}+2^{3}+2^{2}+2^{1}+2^{0}= 63. There is nothing magical about such a number, though November 11th does happen to be the birthday of a member of your correspondent's family. For his own amusement, 63 of something will figure in the celebration.

All this playing around with binary numbers has made him wonder why binary time—or, for that matter, decimal time—never caught on in the Western world. Decimal time has been tried on many occasions. Indeed, a decimal calendar based on a ten-month year was used by Romans during the time of Romulus and Remus. Their calendar ran from March to December. The two missing months needed to make up a solar year were dismissed as winter when nothing grew or happened—and therefore not worth worrying about.

The ancient Egyptians were far smarter. For three millennia before Christ, they used a 12-month calendar, with each month comprising three ten-day weeks. Five rogue days were tacked on the end of the cycle to complete the solar year. By the time of Augustus, the so-called Alexandrian calendar had even incorporated an additional day for leap years. This was essentially the decimal calendar that the French introduced during the revolution. But the French Republic's official ten-day week lasted for little more than a dozen years before Napoleon abolished it in 1806.

Ironically, when the French invented the metric system in 1795, two years after they changed the calendar, they decimalised everything except time. There were base units for length, area, volume, weight and even currency. But seconds and minutes, hours and days, weeks and months were left unscathed.

That, along with the failure to decimalise the compass, was perhaps the metrication commission's biggest setback. Its august president, the noted mathematician Joseph-Louis Lagrange, tried in vain to get the Republic to adopt the déci-jour and centi-jour (a tenth and a hundredth of a day, respectively). But the decimal calendar was deemed enough of a gesture to the new age of rationalism, even though it did not comply with the strict divisions and multiples of ten, and used none of the metric system's prefixes (milli-, centi-, deci-, deca-, hecto-, kilo-, etc).

Even so, the idea of a centi-jour (14.4 minutes) has cropped up on several occasions since. One reason is that a ten-hour clock, with each hour divided into 100 decimal minutes, and each decimal minute sub-divided into 100 decimal seconds, would make navigation easier—provided, of course, you had a decimal sextant and compass to go with it. Decimal time and longitude would then correlate directly without the need for logarithmic conversion tables. Even the Royal Geographical Society in Victorian England was keen on decimal navigation, and published tables to convert sexagesimal angles and hours into centi-jours and their decimal subdivisions.

Numerous clocks were made in France and elsewhere during the 19th century with faces showing both the numbers 1-12 for standard time and 1-10 for decimal time. The supposed advantage was that any observer with a decimal chronometer and a view of the sun's height above the horizon would then know instantly where on the planet he was. With 100 decimal degrees (or “gons” as they became known) to a right-angle, and the distance from the pole to the equator being almost exactly 10,000 kilometres, 1 km along the surface subtends an angle of one centigon (a hundredth of a decimal degree) at the centre of the Earth. Had it come to pass, decimal time and decimal angular measurement might have done for the 19th century what GPS did for the 20th.

But the French were not the first to think of the ten-hour day, nor even the centi-jour. Like the Egyptians with their decimal calendar, the Chinese used decimal (not to mention duodecimal) time several millennia before Christ. Since the beginning of history, they have divided the day into a 100 equal parts called *ke* (14.4 minutes), and split each of those into 60 *fen* (14.4 seconds). When Jesuit missionaries introduced Western clocks to China in the 17th century, the local inhabitants simply changed the number of divisions in a day from 100 to 96, making a *ke* equal to exactly 15 minutes.

To this day, the term *ke* is used in China to denote “a quarter of a hour”. In Japan, the same character (pronounced either “koku” or “kizamu”) translates roughly into “carving out a small amount of time” and was used, until the Meiji era, to signify “hour”, while the character for *fen* (pronounced “fûn” in Japanese) is used to this day to denote “minute”.

Ultimately, the only unit of time that really matters is the second. Originally, the internationally accepted system of units known as SI (Système International d'Unités) defined the second as 1/86,400 of a mean solar day—simply the inverse of the number of seconds in 24 hours. But irregularities in the rotation of the Earth made that unreliable. Thus, in 1967, SI adopted a more precise definition based on the frequency of the radiation a caesium atom emits when it flips between two energy states. No ifs and buts, at absolute zero temperature, this is exactly 9,192,631,770 hertz.

Physicists have no trouble using, on the one hand, picoseconds (trillionths of a second) or even femtoseconds (quadrillionths of a second) to discuss time at the atomic scale. They also talk cheerfully of 10^{18} seconds needed for light to travel from the farthest reaches of the universe. Likewise, in computing, “Unix Time” gives the date and time in terms of the number of seconds since January 1st 1970, and Microsoft's “Filetime” is recorded as multiples of 100-nanosecond units since January 1st 1601.

But computer scientists are just as likely to divide their day into hexadecimal hours, with each hour broken up into hexadecimal minutes. (The 16-base hexadecimal system uses the numbers 0-9 followed by the letters A-F.) The hexadecimal day begins at midnight at .0000. One second after midnight, the time is .0001. Half a day later, noon arrives at .8000. A second before the next midnight is .FFFF. Got it? Your correspondent neither.

In normal life, people have to go to work, arrange schedules, catch planes and trains, and pick up children from school at given times. The number of seconds needed to do such useful things has to be given names everyone recognises and agrees upon. It would be nice if such units of time were decimal multiples of one another. Unfortunately, here on planet Earth, with its decidedly undecimal sidereal year of 365-and-a-quarter days, that is just not going to happen.