(no subject)

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.

(no subject)

[Poll #239987]

(no subject)

[Poll #240067]

It Began In Africa

Out Of Eden: The Peopling Of The World, Stephen Oppenheimer, ISBN 1841196975

This book concerns the peopling of the world by anatomically modern human beings - that is to say, us. It draws together evidence from archeology, the climate and, overwhelmingly, genetics to present an argument clear in the broad strokes but nonetheless finely detailed.

There are two kinds of genetic evidence that have only relatively recently become easy to gather, but have now been studied in sufficient detail to answer interesting questions. First is mitochondrial DNA which we inherit exclusively from our mothers; second is the Y chromosome, inherited exclusively from our fathers. By studying the variations in these two bodies of information between living people, we can construct a tree of life, and even attach rough dates to the branch points; and since people seem to be conservative about location, we can establish some of the geography of those branch points too.

Two conclusions seem to be pretty solid.

1. We are not descended from Neanderthals; indeed there is no evidence even of interbreeding. (Which doesn't mean it didn't happen at all, just that there can't have been very much.) It's too much of a coincidence to suppose that the Neanderthals coincidentally died off as our ancestors arrived in Europe; but whether we out-competed them, accidentally infected them with novel diseases, or even deliberately exterminated them, remains an unknown.

2. Modern humans evolved in Africa within the last 200K years, not all around the world, and (apart from a false start) there was only one prehistoric exodus from Africa, around 80K years ago, perhaps to what is now Yemen. Multiregionalism is dead.

The further from the root of the tree, the more speculative Oppenheimer's conclusions necessary become (as he happily admits). His story is of a rapid expansion along the coastline of southern Asia, colonizing Australia 70K years ago, a tremendous volcanic erruption temporarily dividing mankind in two and leaving a divide visible in the genetic tree to this day. From the coasts man penetrates into central Asia at various points and from there reaches Europe from 50K years ago onwards. The colonization of America becomes possible due to a major ice age starting 18K years ago.

The book is full of maps, which are generally clear, and tree diagrams, which tend not to be; the latter spend most of the available space on visually obstrucivve parallel lines, with the annotative text crammed in annoyingly small. While the subject of these diagrams is going to be inconvenient to fit on a page however presented, I do feel that it might have been possible to do better: perhaps a greater willingness to split the trees over a couple of pages. Making the lines angled rather than having every branch be a pair of right angles might have eliminated the distractive properties of the massed parallels, too (though admittedly that risks becoming inconveniently untidy in other ways).

Oppenheimer is not afraid to use abbreviations and relatively technical language. The excessively casual reader might thereby be put off, but I choose to interpret it as the author declining to insult the reader's intelligence and initiative. Similar remarks apply to the large amount of detailed argument concerning the interpretation of the genetic evidence.

He also attempts to be even-handed regarding alternative theories, though in a few cases (e.g. multiregionalism and what was at least until recently conventional wisdom concerning the colonization of the Americas) this falls through and he can't help but disagree point-blank. Clearly though there comes a point where the scales cease to balance, and while I'm not an expert in the field I didn't feel that the author had got it wrong.

As a final note, this book would be an excellent companion to Jared Diamond's Guns, Germs And Steel and I'd recommend that anyone who found one of these two books interesting should read the other.

More reviews