This article also made me consider how motivations for the evolution of mathematical though has changed since its' infancy. It seems that the primary motivation for the Egyptian and Babalyonians was to solve basic problems related to measurement and construction (essentially geometry and algebra). Nowadays, the study of mathematics need not have any particular set of applications in mind outside of explaining certain phenomena within a mathematical system. So it seems that the motivations underlaying the study of mathematics have drifted beyond mere utility. I am left to wonder if utility was the prime motivation for other human intellectual endeavors? Is the move away from solely utilitarian grounds reflect a shift from primal needs to intellectual ones? Or is such a shift towards abstraction natural and would occur regardless if primal needs still remained central to everyday life?
Monday, September 3, 2012
Multi-what?
While reading this article my thoughts seemed to drift quickly to how "unintuitive" the methods of solution for simple arithmetic and geometric problems appeared in Egyptian and Babylonian mathematics. But I quickly realized that it was not the case that these methods of solution were truly unintuitive but rather that they constructed at a time when the basic frameworks we all take for granted were in their infancy. As such, the choice of operations was relatively unrestricted, after all, there really didn't exist systems of multiplication, counting or division that were a part of the norm. So, counting in base 60, using only 'unit' fractions and multiplication based solely on doubling were chosen for their understandability within existing frameworks. This, I find, is an excellent example of how human understanding of concepts grows with their use over time. It is often the case that we may have a hunch that a certain state of affairs is true but lack the means to covey it in a formal way. As such, we can construct examples to build upon an intuitive grasp on a given concept, thus flushing out important details that are otherwise obscured from intuition.
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I like your discussion of the motivation for intellectual endeavors in the second paragraph. I think the article "Necessity's Mother" that we discussed last week has some relevance to this idea. What causes mathematical development? Is it necessity (i.e., the need to measure heights of pyramids during construction, or the need to determine the amount of material to fill a given area) or is it curiosity of abstract ideas, regardless of practicality, perhaps with practical uses to be found later.
ReplyDeleteNowadays, unlike during the time of the Babylonians and Egyptians, mathematics is not restricted to areas with practical application. Indeed, some areas of mathematics today have no known practical application; however, that is not to say that some application may not be found for these mathematical developments in the future. In the time of the Ancient Egyptians and Babylonians, "necessity"(needs in architecture, commerce etc.) provoked the development of a mathematical system, and the people using this system at the time had neither the mathematical "tools" nor the need to consider those ideas which did not have representations in the natural world.
Your comments on motivation reminded me on page 34 how this development is all based off "mathematics" and how different cultures may take what has been known and expand off/reconstruct certain aspects. I think it is based off of necessity and connivence, we can develop new symbols the represent numbers in different ways so it doesn't take/have so many numbers. For example our symbol for pi, using the square root, numbers to the nth power. We know how to use these now, and instead of having to write out 100 we can just right 10 to the 2nd power. (I don't think I can type it how I want, but I hope you get the point I am trying to get at!)
ReplyDeleteThis also made me think back to one of my Elementary Education classes and how we are told as educators to encourage kids to learn math through the symbols that different cultures use, and the history behind them. How as teachers we spend all this time trying to encourage students to learn about mathematics in any way that can be interesting to them, and applying other mathematical systems to ours will help them understand our system better.
I had always wondered why the Pythagorean theorem worked. I found it interesting that the oldest usage of the Pythagorean theorem by the Egyptians was after the “Greek” mathematics were established and when they explained the Pythagorean theorem in the Mesopotamian article it made a lot of sense.
ReplyDeleteIt still seems kind of strange to me that the Mesopotamian mathematics used base 60, but I do understand what you mean about concepts. We basically built a system to understand the geometric shapes of our world.
When they mentioned the natural phenomenon of the stars, I was wondering: what are those 5 wandering stars they were talking about in the last one?