(no subject)

[ewx]

After seeing this, I spent some time looking for web pages concerning the history of the degree as 1/360 of a circle. The most widespread answer seems to be that the Babylonians invented it, full stop. But other pages suggest that the notion of a 360-day year goes back to the Sumerians, with Greek mathematicians inventing the concept of a degree for measuring angles and Seleucid mathematicians (i.e. Mesopatamia after the Greek conquest) coming up with the further subdivison into arc-minutes and arc-seconds.

(Specifically, they called arc-minutes "the first part" and arc-seconds "the second part"; and these were translated into Latin as pars minuta prima and pars minuta secunda, hence the modern English names. The word "degree" is borrowed from Latin de gradus which allegedly derives [but see comments below] from the Arabic daraja, the Greeks using an entirely different word μοιρα.)

David Ewing Duncan, in his book The Calendar, also credits the 360-day year to the Sumerians, with the Babylonians inheriting it from them. It also notes that the Jewish calendar required months to be intercalated from time to time; and that the Egyptians had a 365-day year around 4000BCE, and even noticed their quarter-day error, but didn't incorporate it into their calendar until forced to by Augustus Caesar. This tremendous time-span with a broken calendar is long enough for any given day to have drifted through the full year twice.

In passing I also came across a rather wacky web page based on a mention in the Bible of a sundial doing something rather odd: going backwards by 10 steps. The author thinks this corresponded to a change in the Earth's orbit which changed the year from 360 days to its current length! (Never mind that other counters already had a 365-day year millenia previously or that people routinely inserted extra days and even months to make their calendars fit the solar year back then.)

Anyway. None of this gets us very close to the origin of the degree. Everything I can find just states that "the Babylonians" invented the 360-degree circle, without referring to any evidence or even usually clearly distinguishing between the Seleucids or Hammurabi's rather more ancient Babylon (though I'd normally interpret it as meaning the latter, absent any qualification). The 1936 Susa tablet, dating from around 2000BCE, relates the perimeter of a hexagon to that of a circumscribed circle, which might well have involved a numerical concept of angle, but nobody seems to report the workings.

Most of the most promising-looking references seem to go back to David Eugene Smiths's History Of Mathematics. So, I've ordered a copy of that (it looks interesting anyway, I'm not just buying it for the answer to this one question!)

My cold is somewhat better than yesterday, and I seem to have slept a bit better. Hopefuly back to work tomorrow.

Comments

Re: Calendar geekery

[ewx.livejournal.com]

I think that the source I was using there was claiming not that the word was borrowed, but rather that the use of a pre-existing word meaning 'step' to refer to a unit angle was copied from one to the other. Perhaps 'derives' is the wrong term to use to mean that.

Re: Calendar geekery

[vyvyan.livejournal.com]

Ah! I was going to comment about that in the same way. "Derivation" does imply to me (in a historical linguistic context) either genetic-style inheritance or perhaps borrowing; combined with the superficial similarity of "de gradus" and "daraja" I also assumed that was what you meant. "Semantic influence" seems to be the intended meaning, then.