I found this article very interesting. I had assumed that Babylonians would not have had a similar method to solve problems like algebra. I was especially impressed by the way which they were able to deal with the fractions and roots which showed up in example problems. I’m still trying to wrap my head around how they figured all this out without easily available writing materials. I suppose that a lot of what is being discussed can be drawn out in the dirt and done graphically. The method of finding an “exact” value for a square root could be understood using geometric relations. I suppose, like the Greeks, Babylonians understood the relationship between numbers and space (maybe very literally).
Me reading how babylonians did square roots:
https://blogs.sas.com/content/iml/2016/05/16/babylonian-square-roots.html
EDIT: In terms of abstractions, these algebraic differences between the modern and the Babylonian only differ in the terms used to represent the mathematics (and some other language). I still find it very impressive that the algebra done by the Babylonians was so sophisticated without the use of what we consider to be algebra. In the example 4.7, the problem is stated as a length of a rectangle exceeds its width by 7 and has a totals area of 1,0 ( 60). In modern terms this might have been written a rectangle has a length which is 7 units larger than its width and has an area of 60 units. I would have done width = x then length = x + 7. Then x(x+7) = 60 and solved this quadratic. But this is a very abstract method of doing this problem. I would like to see how this was done graphically, which is probably how Babylonians would have solved these problems.
You’ve made a thoughtful start, especially in noticing the Babylonians’ work with fractions and roots and imagining how they may have drawn their ideas in the dirt or represented them geometrically. This shows good curiosity and historical imagination. To make your reflection complete, please revisit it and expand a little more on the bigger questions from the assignment — especially how these methods connect to the ideas of generalization and abstraction, or how they shape your own view of mathematics.
ReplyDeleteThanks! This is a strong revision, Ben. You’ve now shown a much clearer comparison between Babylonian and modern algebra and demonstrated good understanding of both methods. Your recognition that the Babylonian approach was likely more geometric and your interest in seeing it graphically shows genuine curiosity and conceptual awareness.
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