Saturday, January 8, 2022

Algebra as translation-aid

To follow up on Islam as the religion of mathematicians, lately I stumbled upon an Andalusi known as Ibn Badr. As the son of an Ismail, he's been deemed an Arab heir to Euclid. He was one of those guys whom the Andalus spat out, like Ibn Hazm and Maimonides; we can read about that elsewhere. Looking abroad I came across Jeffrey A. Oaks, "Medieval Arabic Algebra as an Artificial Language". It seems that the Muslims invented algebra and... didn't use it.

Rather, the Muslims didn't use it as we use it, for mathematical proof directly. They did use it for solving equations. Oaks says, also, that algebra was a constructed language. That piques my curiosity.

The king of mathematical proof, before algebra was known, was geometry. You state in Middle Egyptian how to bisect an angle (say), and then you illustrate that according to your instructions. Then some Greek like Euclid comes along and states the same thing in his language; followed by some Syrian, and finally an Arab.

As time went on, especially out east, not all Muslims wanted Arabic. An Arab-reading Choresmian is sick of translating all this stuff, and also finds the longhand to be a chore and a waste of good parchment. He sees that the illustrations haven't changed in three thousand years. So he puts most of the verbiage down in a few common symbols.

This means the maths can be speed-read in Arabic ... or Middle Persian ... or Sanskrit. Parchment is conserved, as well. (Paper is on its way, but I am unsure - until AD 1600 - how cheap that ever was along the Silk Road between Gansu and Araby.)

Yet even with good mathematical notation, the Ibn Badrs out west stuck with Euclid's method which was geometry. Oats says: so did the Europeans, until the 17th century AD. That's ... exactly when Kepler came to Prague.

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