Eugene+Week+2

This week, I will be writing about Fowler’s “Early Greek Science: Thales to Plato”, specifically the mathematical aspect of it, as I found this to be the most interesting given that I am a math major. Taking a look at the whole picture, it is intriguing that the first stage in the development of math (or maybe a pre-step) is actually the “discovery of nature”. To us that seems almost implied but I guess we have to realize that someone had to have the desire to explain the phenomena in the world around him. Then the progression, if you will, of math starts like many others at first learning through practicality. Thus, I agree more with Herodotus as he speculated people began understanding measurement and geometry out of necessity. Aristotle’s theory in my opinion doesn’t really make sense because I don’t see people steering towards intense mathematics while at leisure. I feel as though leisure time would spark creativity rather than a mathematical discipline. For example, the arts always flourish during every //Golden Age// in a time of prosperity and excess leisure.

I thought the next section was odd as Fowler mention Euclid before Pythagoras when in reality, Pythagoras preceded Euclid chronologically. Pythagoras, however, is more famous for his theorem on right triangles, which every middle school student is probably required to memorize. Thus the explanations of squares, square roots, and irrationals would tie in more closely. For me, though, I don’t think Euclid is given enough credit as he had further reaching contributions, which many overlook. He is undoubtedly the father of geometry and also since he came after the Pythagorean period, he was able to build on those ideas. We now take for granted facts such as parallel lines never touch, but at one point all those claims had to be stated and proved. It is amazing to see that most of the math we learn up to and in high school was actually discovered and proven a couple thousand years ago.

The history leading up to proof for the existence of irrationals was by far the most fascinating thing on the page (for me at least). “The question is: is this list of fractions //all the numbers there are// between one and ten?” It is weird to imagine if you didn’t know irrational numbers existed and you were limited to fractions. Well, you really wouldn’t be limited because in real life a close enough approximation would suffice in any practical application. I think if today we only knew of numbers in the realm of rational numbers then I would not be the one to say “hey! I don’t think that’s all the numbers that exist; there are some we can’t write out with whole number ratios”. Strange to think about this sort of stuff but then again someone will come along and eventually stumble upon the quantity of the square root of 2.

In the grand scheme of things, it now seems appropriate that the Pythagorean idea of an irrational number comes last. The article builds up from a primitive thought of actualizing a //natural// world to a pragmatic understanding of space, area, and measurements. Finally this leads to an abstract appreciation for mathematics that is outside of the practical use for numbers. “Abstract arguments of this type, and the beautiful geometric arguments the Greeks constructed during this period and slightly later, seemed at the time to be merely mental games, valuable for developing the mind”