Babylonian Word Problems


Before I began this week's reading on the history of the word problem genre, I was of the view that "pure" and "applied" mathematics are somewhat interrelated, especially as many abstract concepts were borne out of practical uses of math, so it would not be appropriate to separate them into two fields.

This perspective was somewhat supported by several scholars mentioned in this chapter, including Oxford's Eleanor Robson, who argued against this kind of dichotomy in mathematics as problems can function in two levels using essentially the same idea. Like many have pointed out, some problems to the Babylonians might seem like practical subsistence problems at first, but many of them are too unrealistic and artificial for real life application. Also, resources available to the Babylonians (relative to the Greeks) may have dictated their mathematical methods, so they had no choice but to use a "unified" mathematics, using practicality as a means to reach abstraction.

The contemporary form of word problems also appears to be connected to the Babylonian texts. The algebra that we use to solve word problems can be regarded as simplified tools that replaced the ancient "rhetoric" techniques, but cannot be treated simply as "pure mathematics".


Comments

  1. Susan GerofskySeptember 30, 2019 at 12:13 PM

    Beautifully said, Jackson! I especially like your phrase, 'practicality as a means to reach abstraction'. I am very glad to see non-dichotomous conceptions of mathematics -- refreshing and thought-provoking!

    ReplyDelete

Post a Comment

Popular posts from this blog

Reflection: Presentation on Pythagorean Triples

Our group presentation on the Pythagorean Triples went as planned: we presented the theoretical background and the ancient methods of solving right triangle problems, as well as discovered an interesting extension of the 3-4-5 triangle. The reason for choosing this topic was that we found the Pythagorean Triple concept to be both very intuitive and easy to understand. To me, this extension was probably the most interesting part of our presentation, as it stretched our conventional perception of the 3-4-5 relationship even further to higher powers. However, the challenge was to understand the reasoning behind the extension, which was an idea brought up by many other mathematics scholars, and why the cubic relationship does not hold for the other Pythagorean Triples. Moreover, the Mayan number system wasn't discussed in full during the class, so it was difficult to fully grasp the link between the 3-4-5 cubic relationship to the Mayan Long Count at first. After spending some time...
Read more

Dancing Euclidean Proofs

Image
I was amazed by the creativity that the authors put into using modern dance choreography to represent mathematical proofs. Before this class, I had never thought about connecting math with arts in this fashion. As mentioned by the authors, "proofs unfold over time in a way similar to the sequential moves of a dance", and the math concepts can definitely be embodied through artistic representations. What I find interesting is how the dancers used intuition to make geometric shapes and imagining that the arms can represent equal lengths, because it's almost impossible to create precisely measured lines without any tools. At the same time, they can also be flexible and have unequal lengths to fit the parameters of a proof. I think using the body to guide the mind through geometric representations can be very helpful to the understanding of the mathematical ideas, as it provides more clarity with step-by-step movements rather than just static images on a piece of paper. ...
Read more

Word Problem With Unit Fractions

Image
The use of unit factions is convenient for everyday applications where we need to divide a set of things among an unequal number (usually larger) of individuals. For instance, suppose a group of eight friends wants to share three pies in equal portions, how can they accomplish that? A straightforward division would not solve this problem because 3 divides 8 equals 0.375, and the presence of decimals complicates things even more. I think by representing a fraction like 3/8 as a sum of two unit fractions (ie. 1/4 + 1/8) makes this kind of sharing problem much simpler. We can now infer that each person will get a quarter of a pie and one half of another quarter of a pie. Since dividing by half (or into quarters, one-eighths, etc.) is practically easy to do, this method could be useful for many similar problems, including the inheritance problem posed on the blog. If the man's inheritance is to be shared in 1/2, 1/3 and 1/12 parts among his children, then adding these unit fra...
Read more