Have you ever wondered why we have 24 hours in a day when the rest of our math is based on the decimal system – base 10. Where did the 24 come from?

One of my passions is history; I’m not a real historian - I just watch one on TV.

It turns out that the Sumerians used **base 12**, not base 10. Each finger has three segments for a total of twelve segments on each hand. It’s even convenient to touch the thumb to each segment for counting. Combine both hands and you have a two-digit hand-based abacus. The Sumerians also believed that twelve was a special number – it can be divided by 2, 3, 4, or 6, while 10 can only be evenly divided by 2 and 5. So they divided the day into twelve segments – each being two modern hours long.

The 60 minutes to an hour and 60 seconds to a minute come from the Babylonians who used a base 60 mathematical system.

Finally, the Egyptians split the 12 segment day into 24 segments and standardized the hours.

(and if you know more details to this moment of history - *please* don't hesitate to add your knowledge as a comment.)

## Comments

## snuh said:

I had a great high school history teacher who'd shout out "history lives!" with a huge grin on his face when something like this came up - the enthusiasm was infectious. There are some great and accessible books on the history of mathematics - you might like The Universal History of Numbers: From Prehistory to the Invention of the Computer

## Stephen Morris said:

on a similar note, take a look at the french revolutionary calendar with 10 day weeks :-

http://en.wikipedia.org/wiki/French_Republican_Calendar

seems outlandish now but interesting to remember how many of the other reforms from the French revolution are accepted standards today (kilograms, grams, kilometres, metres etc)

## Dave Jermy said:

It's not just time that uses non-metric measurements, at least in the UK and US. What about distance (inches, feet, yards, furlongs and miles), weight (ounce, pounds, stones (UK only, I think)) and capacity (fl ounce, pint, gallon)? There are various different bases being used in those, none of them base-10.

All right, all of them have metric equivalents but there's a good reason why the non-metric versions are still so widely used: in many ways they are much easier to work with, given that bases of 12, 16, 24 etc. have so many more divisors than base-10.

It's less than 40 years since the UK switched to decimal currency and before that it used base-240, with 1 pound equal to 240 pennies. The reason for base-240? Well, it can be divided by 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, 60, 80 & 120 so it is extremely versatile.

I think switching to metric measurements is one of the reasons for declining standards in mathematics: using base-10 for everything means that people learn to rely on calculators much more than they would have to with more useful bases. If everything was base-12 then we would have a much better innate understanding of numbers and how they all work.

## Denis Gobo said:

@Dave

>>there's a good reason why the non-metric versions are still so >>widely used: in many ways they are much easier to work with

I disagree with that. For example take a liter of water how much does it weigh? Easy a kilo, it fits in a cubic decimeter boils at 100 degrees Celcius freezes/thaws at 0 degrees celcius

Take a gallon of water how much does it weigh? ask 10 people see if you get the correct answer, I just asked a bunch of people not one of them could answer it.

height is also more precise, If your height is 1.78 meters, what is that in inches feet? About 5 feet and 10 inches and then you get into half and quarter inches. When working with the decimal system you actually don't need a calculator because everything is divisible by 10, you can go from Kilometer to Hectometer and all the way down to Nanometers

Of course for someone who grew up with the metric system it is always easier to say that the metric system is easier to use :-)

## AaronBertrand said:

I agree that metric is much more intuitive and logical. (I'm not sure why base-10 would require calculators more than base-240?)

But even in countries like Canada, where the metric system is obviously quite prevalent, I still grew up measuring my height in feet+inches, and my weight in pounds. Since moving away, however, I really do miss measuring the temperature in Celsius.

## Denis Gobo said:

>>an intesting aside to celsius temp is that the boiling pint of water is depdendent on the barometric pressure or altitude.

same with your ability of polishing of that bottle of Glenmorangie high up on the mountain :-)

## Paul Nielsen said:

An interesting aside on Celsius temperatures is that the boiling point of water is dependent on the barometric pressure or altitude. Where I live in Colorado, water boils at 93.5 degrees Celsius, and it’s difficult to make a good chocolate soufflé – but that’s a topic for a different blog.

## Denis Gobo said:

BTW by polishing the bottle I mean drinking what is inside not cleaning the outside :-)

## Denis Gobo said:

Paul, you can't correct your spelling mistakes I already copied and pasted them :-) BTW you still have to correct celsius :-)

## Paul Nielsen said:

Yes, I saw that - Drats! pwned by the Denis! You're just too fast for me, and while you're thinking about Glenmorangie high up on the mountain too. I was dreaming of chocolate soufflé - that's my excuse.

## Denis Gobo said:

Paul, if water boils faster at high altitude, would it also mean that writing SQL Server 2008 Bible will be faster? Just a thought, albeit silly :-)

## Hugo Kornelis said:

Denis,

If he's polishing those bottles up there, I think it'd be slower rather than faster. (And what he wrote would never get past tech edit <g>).

## Eric said:

Wasn’t it the Sumerians who worshipped Gozer? A practice we all know led to the whole keymaster/gatekeeper fiasco and the summoning of the Stay-Puft Marshmallow man in New York in the late 80’s?