Friday, March 30, 2018

So, they're teaching 'Africentric maths' up North. I've not much comment on the article per se, but I did want to mention that a) it's not a bad idea because b) the Egyptians had some brilliant, bizarre things going on even if c) the school in question (at least from this article) is just doing math with some pyramids thrown in.*

But in truth Egyptian math is a wonderful example of practical restrictions leading to deep understanding. Let's look at their use of fractions:

From the Rhind Mathematical Papyrus, we have a table of answers to 2/n, where n is a rational number between 3 and 101. But the Egyptians seem to have had a horror of fractions without a unit numerator; that is, any fraction that doesn't have the form 1/n. The only exception was 2/3, which had a unique hieratic symbol. So when asked what 2/5 comes to, where we would simply stare at the questioner and say, derisively, "Two-fifths, innit?", the Egyptians gave the answer, "1/3 plus 1/15." 2/61? The answer cometh: 1/40 + 1/244 + 1/488 + 1/610

As Richard Gillings puts it in his indispensable Mathematics in the Time of the Pharaohs:

Problem 9 of the RMP requires the division of 9 loaves among 10 men. While the modern answer is that each man gets 9/10 of a loaf, this division requires that the last man must get (1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10) of a loaf; already sliced so to speak!
The practical roots of their mathematical practice show through clearly here. It's well worth your time to peruse the table itself. It is not an easy question how to go about creating such a table, and frankly I would not want to undertake it. Well done Ahmose!

The rest of the RMP includes the other items mentioned in the article: linear equations, surface area and volume, and a really excellent section on how to divide fairly the beer you have if some of it is stronger than the rest. The unit fraction table has my heart, but it's all good stuff. I suspect that the RMP is the foundation of the curriculum, but the article doesn't say so, and the author ("Sherri Borden Colley has been a reporter for more than 20 years. Many of the stories she writes are about social justice, race and culture, human rights and the courts.") doesn't seem to be interested in that aspect of things.

That is, in fact, closely related to why I suspect this program will not lead to massively increased enrollement in STEM fields. Math is hard, as Barbie tells us, and needs a certain uncommon taste for it to be enjoyed. I have a touch of it, but not enough to, say, spend my spare time creating computer models of protein folding. The reporter's own lack of interest in the nuts and bolts of the curriculum is the normal person's reaction to math. Salting basic geometry and trig with pyramids and calling it "Africentric" is unlikely to turn anyone on to math that wasn't already headed that way.


Wholly unrelated, but I caught it on re-read: has anyone else noticed that we use "so" where the old English would be "hwaet"?

*Not going to get into the question of whether "Africentric" is the right term for what is clearly an Egyptian curriculum. Just... not.


Peculiar said...

We need to collect a dataset of experimental confirmations regarding the beer.

Odious said...

Something along these lines: Ancient Ales.

Frankly, Egyptian beer sounds terrible, which is doubtless why the Ta Henket above follows no recipe I've come across. But, like Jurgen, I am willing to taste any drink once. I'll work out a 1 or 2 pesu version and begin empirical testing.