RE: virus: What you call this thing?

TheHermit (
Thu, 13 May 1999 03:34:36 -0500

This is really funny as one of my previous posts - to another Eric, ERiC Boyd actually, was on exactly this subject. So here it is, with some slight corrections.

The Babylonians laid the foundations of the place-value system the number system they borrowed from the Sumerians, we see two basic "large ones": ten and sixty, from the most ancient clay tablets which have come down to us, dating to the beginning of the third millennium B.C.E. We can only guess where the number sixty was taken from. The well-known historian of mathematics O. Neigebauer believes that it originated in the relation between the basic monetary units in circulation in Mesopotamia: one mana (in Greek mina was sixty shekels). Such an explanation does not satisfy our curiosity because the question immediately arises: why are there sixty shekels in a mana? Isn't it precisely because a system based on sixty was used? After all, we don't count by tens and hundreds because there are 100 kopecks in a ruble! F. Thureau-Dangin, an Assyriologist, gives linguistic arguments to show that the number system was the primary phenomenon and the system of measures came second. Selection of the number sixty was apparently a historical accident, but one can hardly doubt that this accident was promoted by an important characteristic of the number sixty, namely that it has an extraordinarily large number of divisors 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30). This is a very useful feature both for a monetary unit (since its existent money has been evenly subdivided) and for establishing a system of counting (if we assume that some wise man introduced it, guided considerations of convenience in calculation).

The mathematical culture of the Babylonians is known to us from texts dating from the Ancient Babylonian (1800-1600 B.C.E.) and the Seleucidae epoch (305-64 B.C.E.). A comparison of these texts shows that no radical changes took place in the mathematics of the Babylonians during this time.

The Babylonians computed the circumference and area of a circle using a value of [pi]=3, which is much worse than the Egyptian approximation.

The Egyptians calculated the area of a circle by squaring 8/9, of its diameter, a difference of about 1 percent from the value of pi. (from the Moscow Papyrus which refers to this knowledge as being "common" by around 3,700 B.C.E.).

The reason for 360 divisions is simple, it is based on the physical measuring instruments which were available to them. In other words, at the time that the division of the circle became a convention, they could represent each sixth of the circle with sixty divisions. To go beyond that to 120 divisions was beyond the limits of their technology. Try it for yourself sometime - even on a really big sheet of paper... and they used clay tablets the size of bricks....

Having familiarized themselves with both the Egyptian and the Babylonian systems of writing fractions and performing operations on them, the Greeks selected the Babylonian system for astronomical calculations because it was incomparably better, but they preserved their own alphabetic system for writing whole numbers. Thus the Greek system used in astronomy was a mixed one: the whole part of the number was represented in the decimal nonpositional system while the fractional part was in the 60-base positional system--not a very logical solution by the creators of logic! Following their happy example we continue today to count hours and degrees (angular) in tens and hundreds, but we divide them into minutes and seconds.

The above is in part derived from chapter 9 of the "The Phenomenon of Science" by Valentin F. Turchin and the balance from Lancelot Hogben's Mathematics for the millions.

> -----Original Message-----
> From:
> []On Behalf
> Of Erik
> Sent: Thursday, May 13, 1999 3:09 AM
> To:
> Subject: Re: virus: What you call this thing?
> Please not to all started off with couple of
> copulating rabbits!
> Now, can anyone tell me why a circle has 360 degrees (please,
> I will not
> sneeze say Mr. Weakintheknees).
> eEc