After reading the article, I have an impression that the Babylonians were stuck between the ideas of ‘pure’ and ‘applied’ mathematics. On one hand, we see that the Math problems the Babylonians had were all in the context of their daily lives back then. However, on the other hand, we also see that the numbers in these word problems were very unrealistic. We can also see that the problems themselves did not really reflect the reality as well.
These actually remind me of word problems we see in our textbooks and classes. A lot of word problems do not reflect the what is happening in the real world. We tend to take out a lot of factors like friction and air resistance and put in some ‘nice’ numbers so the problem seems easier to solve. I think we do this to focus on the topic on hand so that teachers or students do not digress. It seems like the Babylonians were doing exactly this as well to train their students.
Another reason I can think of is that due to the absence of modern algebra, the math problem seemed too complicated to be comprehended by the Babylonians. And all they could do was to use real life examples to represent the math problem itself. Metaphors and analogies had to be used to present a more suitable way for their students to learn ‘pure’ math. I still remember how my dad explained the concept of substitution to solve systems of linear equations (I was in grade 7 at that time, so I have not learnt system of equations yet). He used real life examples which employed ridiculous numbers (an orange costed $5 and an apple costed $10) so I could understand the problem without having to worry too much about the numbers since they were all ‘nice’ numbers.
These ideas showed how the ancient civilizations dealt with mathematics without modern algebra. To educate their students on more complex concepts, they had to resort to using real world problems with ‘nice’ numbers. I can see that mathematics in these civilizations originated from having to deal with real life problems. Then these problems developed into more concrete math concepts like geometry and trigonometry. However, without algebra, they had to go back to their real life to represent the problems and teach the next generations these concepts.
Brilliant and very thoughtful response! The idea of 'nice' numbers in problems is one that merits a lot more discussion. Wonderful connections with your own learning with your Dad, and on the Babylonians being betwixt and between concrete practicality and more generalized concepts.
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