Is Math culturally independent? Eleanor Robson asked this question regarding Plimpton 322. She wrote, “We tend to think of mathematics as relatively culture-free; i.e., as something that is out there, waiting to be discovered, rather than a set of socially agreed conventions. If a simple triangle can vary so much from culture to culture, though, what hope have we in relying on our modern mathematical sensibilities to interpret more complex ancient mathematics?” And yes, this was a homework question, but for some reason this question stuck with me, and I went looking a bit further. For those of you who may not know, Plimpton 322 is an ancient Mesopotamian tablet around which there is some controversy. ¹ Scholars have claimed that Plimpton 322 is anything from a set of Pythagorean Triples, to a table of reciprocal numbers, or that it is possibly a trigonometry table. The truth is, we just don’t know for sure; but whatever it is, it is definitely more complex than the tax forms or accounting forms we typically expect the Mesopotamians to have left lying around. (I just put it down a second ago, where did it go?) Robson’s comment about the triangle mentioned refers to the difference between how we normally picture or represent a triangle and the standard Mesopotamian way of representing a triangle. We have a tendency to depict a flat side facing down (for example Δ). The Mesopotamians, however, tended to represent their triangles pointing to the right similar to our play symbol. (Emblem unavailable at this time. Please consult your mp3 or video player, sorry for any inconvenience).
This question from Robson brought to my mind the idea of Musica Universalis. Musica Universalis2 is a philosophical concept that is based on some assumptions made by the Pythagoreans, namely the combination of math and theology. The Pythagoreans belived that everything had a numerical attribute,³ and they also found an appeal in certain symbols, such as the tetraktys and the Harmony of the Spheres (another name for the Musica Universalis).4 The concept of Music of the Spheres concerns the movements of the Planets, the Stars, the Moon and the Sun. (Remember, the thought at this time was that they all revolved around the Earth.) One way of interpreting this was that there was some vast Celestial Orrery or Machine that had been set into motion. This Orrery controlled not only the motion of the celestial bodies but also the affairs of men. During these millennia there was no distinction between astronomy and astrology.
Johannes Kepler is a well know and still revered astronomer. Kepler also believed there to be no distinction (at least it is not recorded) between astronomy and astrology and as an adviser and astronomer to Emperor Rudolph II he made horoscopes for not only the Emperor but also various allies and foreign leaders. Johannes Kepler believed he had worked out much of the celestial orrery in his Mysterium Cosmographicum.5 The commonly held belief of the time was that all things could be understood by observing natural motions; whether those motions were of the planets, the stars, or in some cases the patterns of other natural phenomena.
Since all patterns can be represented mathematically, math then becomes the language of the universe. This idea can also be traced back to the Pythagoreans. The concept that everything is a piece of celestial machinery that can be understood through math is still around us to this day, or at least it seems that the repercussions of it are. After all, if everything is patterns, and patterns can be interpreted wonderfully though Math, then Math must therefore be the Language of the universe. (That’s logical, that is.) This seems to be the idea that Eleanor Robson is arguing against. (Frankly, I agree with her.) This concept of a pure language of math is rather a strange convention that our society has if you really think about it. After all, the argument could be made that English (or any language really) is some sort of divine language because we can use it to so eloquently describe the world around us. Or perhaps Music is our divine language. It is pattern based, after all. So is this idea of everything being describable through math a belief we have found to be true, is it a truth that we somehow stumbled upon millennia ago, or is it a conceit of our culture?
1 A History of Mathematics by Uta C. Merzbach & Carl B. Boyer
Archetypes of Wisdom: An Introduction to Philosophy , Douglas J. Soccio