I’m not sure where this month went. I mean, obviously that’s how we all feel at the end of every month. But there’s this thing with four-month-old babies where they suddenly need to re-learn how to sleep. So they sleep like newborns again – or worse, in the case of mine – except you’re back at work and nobody’s offering to bring you casseroles anymore. Parents: feel free to either give me the knowing sympathetic look or tell me how much worse it’ll get. Those who want to tell stories about how their kid always slept great can go find somebody else’s comment section.
So I literally don’t know where the month went. It’s all pretty hazy. But I did do one new thing this month: I guest lectured for a Middle Eastern Studies class. The professor asked our department chair if one of us could put something together on Middle Eastern mathematics, and due to retirements and sabbaticals I’m apparently the person on campus who knows the most about the subject. I was on the fence about accepting. It’s not like I’m low on service to the college. And I’ve been working on saying no to things with no substantive payoff. But I either wanted a change of pace or was feeling generous.
I spoke mostly about Muḥammad ibn Musa al-Khwarizmi, the man whose name gave us “algorithm,” and whose work gave us algebra – both the word and the concept. His most famous work, Hisab al-jabr w’al-muqabala, sometimes translated as The Calculation of Reduction and Completion, describes the state-of-the-art mathematical techniques of the time. So “algebra” was the latinization of “al-jabr,” meaning reduction (in the sense of reducing a fracture), which al-Khwarizmi used to refer to adding a number to both sides of an equation.
If you’ve never read any of these old texts other than Euclid, I recommend checking them out. Even the preface is illuminating: al-Khwarizmi spends a few paragraphs invoking the glory of God, and then a little less sucking up to his patron. And then he lays out his purpose for the book:
“…confining it to what is easiest and most useful in arithmetic, such as men constantly require in cases of inheritance, legacies, partition, lawsuits and trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computation, and other kinds of various sorts and kinds are concerned..”
So this text was meant to be practical, and indeed he lays out a lot of practical solutions in the book. But he also describes the basics of algebra, with proof, as a series of useful tools. And he does it all in prose, since mathematical symbols and variables hadn’t even been invented yet. Check out this solution to x²+10x=39. Vocabulary note: a root is an x term, as opposed to a square (x²) or a dirhem (number):
“The solution is this: you halve the number of the roots, which in the present instance yields five. This you multiply by itself; the product is twenty-five. Add this to thirty-nine; the sum is sixty-four. Now take the root of this, which is eight, and subtract from it half the number of the roots, which is five; what remains is three. This is the root of the square which you sought for; the square itself is nine.”
If you can fight your way through that, you’ll see that it’s basically just a very specialized version of the quadratic formula. And what’s more, Al-Khwarizmi even offers a proof, and a geometric one at that, because of course that was how you proved stuff in 840AD. In that proof, he builds a rectangle that’s x units by 10+x units, and also 39 square units. And then he moves some pieces around and literally completes the square to find x. How cool is that? Seriously, page through this thing if you have a minute.
So in my guest class, I lead a handful of humanities students through all that. And they didn’t hate it. I’m not saying this was the highlight of their week, but they liked seeing the preliminary stages of the development of something we take for granted. And I got something out of it after all, because the class had been reading a book I’ve just picked up from the library: The House of Wisdom by Jim Al-Khalili, about how Arabic science did more than just shine a heat lamp on the works of the Greeks until Europe was ready to pick them back up again. I’ll let you know how it is. Right after I get some sleep.