In the question: http://www.straightdope.com/classics/a1_125.html
there is no mention of the fact that a circle is a lot easier to divide into multiples of 3, than anything else. Using a sundial to tell time, dividing it into 10 or 20 hours would have been very dificult without some very precise measuring device. I think it was one of the reasons the Babylonians liked 12 a lot. And I believe it is the reason the 12 and 24 hour system survived all these years.
In the question: http://www.straightdope.com/classics/a1_125.html
I don’t think I understand this at all.
Obviously, it’s trivially easy to divide a circle into multiples of 2. You just draw a line through the center. Constructing perpendiculars is then just as easy for further divisions.
If you don’t know the center, isn’t the construction for halving a circle still far easier than for thirds?
But if you do know the center, it’s easier to divide it into sixths than any other fraction. And you probably do know the center, since that’s how you constructed the circle in the first place. Once you have it in sixths, about all that you can do (easily, at least) is cut the pieces in half repeatedly.
This rather misses the point – hours on a sundial are not evenly spaced, so there is no benefit to dividing its face evenly.
Ease of divisibility should have led to 64 divisions per hour. Or day, whatever.
Yes, the 60 seconds/minutes confuse me, so I’ll have to accept The Straight Dope answer on that one. But a sundial should have evenly spaced hours, the earth revolves at constant speed, and it just measures the angle between horizon and sun.
I had a pofessor who showed me how to divide a circle in to 5ths without measuring the 72 degrees, and he was the one claimed that this math didn’t exist at the time of the Babylonians, and was a reason for the twelve hour system. A ten hour system would have been more natural, what with our ten digits.
How does it do that?
At noon yesterday, on the equinox, my sundial would have measured the distance from the Sun to the horizon? It would have been the same as my co-latitude, right?
If the base of the sundial is inclined from the horizontal at the proper angle, then the hours are evenly spaced, but if you’re using a horizontal base, then they won’t be (unless you’re at one of the poles). But were they necessarily interested in the angles for marking their sundials? Maybe they just liked easily-constructible angles, or assigned some mystical significance to them.
As I see it, not being any expert on sundials, there are two angles involved, one north-south, one east-west. In measuring the time of day, north-south wouldn’t have any importance, east-west would.
The point Chronos is making, is pretty much the one I was trying to make. Cecil writes that the number 12 was somehow important to the Babylonians. I believe that in measuring time, 12 was important partly because of the 12 lunar evolutions pr year, but also because it is easy to divide a circle into 12 and 24.
Chronos, are you sure about the hours not being evenly spaced? I think I’ll have to brush up on that.
One important thing not mentioned is that the Babylonians used a base 60 number system for more than just time keeping. Although the origin of the number system may have had its genesis in astronomy, it’s natural that it would have been applied to time and angle measurement.
My guess is that when the Egyptians borrowed the twelve hour day from the Sumerians, they used it to measure 12 hours of daylight–and of course, that left 12 more hours of night. Hence our 24 hour day.
Yeah, we agree on that, it is pretty much what was written in the column. I’m trying to find out why these numbers were used, the logic behind it, and why/how they survived all these years. After all the base 60 number system died a silent death everywhere else.
Sorry to have doubted you Chronos, with a name like that I should have known you had the handle on it. I made a little drawing to show how I now think it works, here
The thing is, now I’m not really sure about the circle, but my geometry is hitting the limit. It’s the earth’s 22 odd degree tilt, I can’t see the line the sun would draw on the sky. Is it part of a circle, an elipse, or neither? Some weird sine-shape?
I must have either long fingers or short arms. I get about 9 hands straignt up at arms length from horizon to horizon. However I do get about 12 hands sideways horizon to horizon.
This makes the most sense to me because the ancients commonly used body parts for measurements eg. cubits. I was taught as a boy scout to tell time with this method. There would be 12 hands (hours) in a day.
[highjack]Think how much easier math would be if we had 6 digits per hand. Base ten sucks.[/highjack]
Actually, it would have been better to have four digits per hand, and a base of 8. It certainly would have made the advent of binary computers easier.
Well, apparently the Babylonians had 12 hands and 60 fingers.
According to historians, the Babylonians counted by going 1-2-3-4 for the fingers, -5 for the thumb, then (making a fist) and counting that as -6, then going on to the other hand and doing the same thing. Seems odd, but probably perfectly reasonable if that’s how you learned to count.
Apparently not an uncommon way of doing counting, based on the ubiquitness of measures like dozens, which are still in common use today. And, of course, 12 is mathematically an easier base to work with in many ways.
Now that is a really interesting piece of information! I didn’t know that. That actually does make a lot of sense. Do you have a reference on this?
No, I don’t have a specific cite. I heard this a long time ago, and remembered it because it seemed interesting.
But I expect some searching on the internet might find a cite; or maybe someone with more knowledge of history will be able to contribute something about this.
“Yeah, we agree on that, it is pretty much what was written in the column. I’m trying to find out why these numbers were used, the logic behind it, and why/how they survived all these years. After all the base 60 number system died a silent death everywhere else.”
I thought the logic behind base12 and base60 was generally accepted to be that they are the easiest units to sub-divide. Practical living in the earliest cities and agricultural settlements demanded trade and barter. If your measuring system is base2 you can’t easily divide by 3. Base12 is the first number that lets you divide by 2,3 and 4. Going to base60 lets you divide by 2,3,4,5 and 6.
Once this is your numbering system you have to adapt your scientific calculations to fit it.