The Design of our Calendar

Have you ever wondered…

  • why are there 60 minutes in an hour?
  • why are there 24 hours in a day?
  • why are there 7 days in a week?
  • why are there 28, 29, 30 or 31 days in a month?
  • why are there 12 months in a year?

Can you find the logic in those facts?

Some aspects of our calendar system, which is the Gregorian calendar, are linked to scientific facts from our universe:

  • One day is the time it takes the earth to spin 360° (approximately).
  • One year is the time it takes the earth to revolve around the sun.

Having these concepts linked provides quite some conveniences. More specifically, in each day the position of the sun is at its highest point at noon (well sort of, but that’s another story). And each year starts in exactly the same season. As a result, agriculture can actually use the calendar to plan their activities.

As a result of the facts that the duration of a day and a year are linked to the movements in our solar system, the exact number of days that fit in a single year cannot be freely chosen, it’s 365.24 days. However, all the other time units that men has invented over thousands of years are more or less arbitrary.

The most well known arbitrary system in the Western world is the decimal system. We all basically think in powers of 10. In the decimal system, each unit consists of 10 smaller units. Eg. one meter has 10 decimeter, which has 10 centimeters, … We came accustomed to this when we started using Roman numerals which are also based on powers of ten. It turns out that people are very good at calculating with multiples and powers of 10.

So why are there not 10 months in a year? Well, at the time, there actually were ten months in the calendar. But because there are approximately 12 lunar cycles in a year, the months of January and February were added to the calendar and the original fifth and sixth months were renamed July and August in honour of Julius Caesar and his successor Augustus. This can still be seen in the names of the months September (from Latin septem, “seven”), October (from Latin octō, “eight”), November (from Latin novem, “nine”) and December (from Latin decem, “ten”).

In the end, what have we won by using 12 months instead of ten in a single year? At least the financial systems in the world make use of the division in twelve months, as they’re mostly using quarters to report on results. Luckily, 12 can easily be divided by four whereas 10 can’t. But our calendar is still not in sync with the movement of the moon, which was the purpose in the first place. One lunar cycle takes 29.53 days, which is not a full number of days and doesn’t align to a year (365.24 divided by 29.53 is 12.37). Unless you invent some sort of exception, you won’t be able to align a calendar system to both the seasons (a year) and the lunar cycle. We should ask ourselves if both are needed, or if one is more important than the other.

Ok, we’re stuck with 12 months in a year, but why is the length of each month different? This has resulted from a compromise. Initially, months were mostly 29 days long and the average length of a month was 29.5 days which is the time taken by the Moon to orbit the Earth (see previous paragraph). However, this resulted in a year of only 354 days while the orbital period of the Earth is 365.2422 days. As a result, the calender became out of sync with seasons which was bad. This was initially corrected in an arbitrary way by adding a 13th month, but soon the calender was thrown into severe confusion. In 46 B.C., Julius Caesar reformed the calender by ordering the year to be 365 days in length and to contain 12 months. This forced some days to be added to some of the months to bring the total from 354 up to 365 days. To account for the extra 0.2422 days, every fourth year was made a leap year. This made the average length of a year to be 365.25 days.

The next unit of our calendar, which surprisingly doesn’t fit with the other units, is the number of days in a week. The number of days in a year is simply not a multiple of 7, then why do we have seven days in a week? It was associated with the seven heavenly bodies; the Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn. For this reason, some believe, marking rituals every seventh-day became important. A seven-day week based on these same celestial bodies was adopted as far away as Japan and ancient China.

As mentioned before, the duration of a day is simply the time it takes the earth to face the Prime Meridian back to the sun. But how you split this up into units is completely up to … well, men. Today we might choose 10 hours for a single day, but the ancient Egyptians made it a bit more complex. They divided day-time into 10 hours, which they measured with devices such as shadow clocks. But then the Egyptians added a twilight hour at the beginning and another one at the end of the day-time. Night-time was divided in 12 hours, based on the observations of stars. The result is a day of 24 hours.

Personally, I might prefer 100 minutes in an hour, but the Babylonians used a sexagesimal system for mathematics and astronomy. This means that they counted in multiples of 60. It’s a system that they derived from the Sumerians who were using it as early as 3500 BC. They used this to their convenience and split an hour into 60 minutes. 60 is not a power of 10, but it has another mathematical convenience. It is divisible by a large number of smaller numbers without a remainder: 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. The same is true for the number of seconds in an hour.

With the current solution, there are 1440 minutes or 86400 seconds in a day. If we would’ve had 10 hours in a day, 100 minutes in an hour and 100 seconds in a minute, we would’ve had 1000 minutes or 10 000 seconds in a day. It calculates much easier, and you only need to make make a second 14% shorter in time to make it happen.

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