Every year millions of people around the world do not mark the beginning of their new year when the clock strikes 12 on December 31. For the Chinese, the Year of the Ox will begin on January 26. For Jews the next new year starts on the evening of September 18, while Muslims have just celebrated the beginning of 1430, which arrived on the evening of December 28. As it happens, tonight nobody around the globe should be popping their corks at midnight, because the Gregorian calendar is having a blip and the new year will officially start when the second hand reaches minus 1.

We are used to adding extra days for leap years but every now and again it is necessary to add a leap second to ensure that our calendar keeps in step with the passage of the Earth around the Sun. One of the reasons that we periodically have to adjust our timekeeping is because the Earth, Sun and Moon play a crazy, syncopated rhythm as they dance through the sky.

One of the things unifying the world's calendars is the role of mathematics in trying to make sense of the passage of time; the other is that the day is a basic unit of measurement common to all of them. This is not the time it takes the Earth to spin once on its axis. That actually takes 23 hours 56 minutes and 4 seconds. Use this as the length of a day and over time day and night would flip over. Instead, a day consists of the time it takes for the Earth to spin so that the Sun returns to its original position in the sky. Because the Earth is moving around the Sun, this adds the four minutes needed to bring a day to a full 24 hours. The leap second being added at the end of 2008 is due to the gradual slowing of the Earth spinning on its axis.

Ask most people how long it takes for the Earth to travel around the Sun and they'll probably say 365 days; in reality, it takes an average of 365.2422. Again, what you mean by this is complicated but what is important is to match up seasons. So this is the number of days it takes to match up the equinoxes. The Gregorian calendar, which tells us that tomorrow is the beginning of the new year, uses an approximation to this cycle to record the passage of time. Because 0.2422 is almost a quarter, by adding an extra day into the calendar every four years, one can keep the Gregorian calendar in synch with the passage of the Earth around the Sun. Little tweaks are required because 0.2422 isn't quite 0.25. So every 100 years you miss a leap year, but every 1,000 you skip the skipping and retain the leap year.

The Islamic calendar prefers to use the cycle of the Moon instead. Here the basic unit is a lunar month, and 12 of these make up a year. The beginning of a lunar month is determined by the sighting of the new moon at Mecca. This averages out at 29.53 days, which makes a lunar year 11 days shorter than a solar year. This is why Ramadan slips each year. Because 365 divided by 11 is approximately 33, it takes 33 years for Ramadan to cycle through the year.

The Jewish and Chinese calendars try to mix and match. They attempt to unify the cycle of the Earth around the Sun with the passage of the Moon around the Earth. They do this by adding a leap month a little bit more than every third year. And the key to their calculations is the number 19, because 19 solar years

(= 19 x 365.2422 days) almost exactly matches 235 lunar months (= 235 x 29.53 days). So the Chinese calendar has seven leap years in every 19-year cycle to keep the lunar and solar calendars in synch.

So if you wake up with a cracking headache tomorrow morning, just say that it was because you spent the night trying to sort out the maths to determine exactly when you were meant to start celebrating.

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