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Originally Posted by Nachtwolf
Sorry, this is ridiculous. While the symbols we use for numbers are of purely human origin, the symbol is not the number, but rather a means of representing mathematical aspects of nature. Take a physics course.
I've completed one semester of Differential Equations, and while there is still much higher math for me to explore, I would be surprised if this were insufficient for the purposes of our discussion.
It's clear enough - but it's also clear from your explanation (assuming for the moment that it is true) that Phi is not the only possible "base" for a musical system. Yet the Neanderthals used it, the Chinese used it, the Greeks used it, and we use it, when to my knowledge no musical systems on earth have been based on either e or v2. Your claim was that "harmonic systems based on Phi outperform non-harmonic systems or systems based on some other harmonic," but here you write that both e and v2 could be used, when, to my knowledge, they never were. (It is interesting to speculate on what such music would sound like. I hypothesize that, even though the wave forms would combine appropriately, humans would still find them unappealing.)
Additionally, why do you think that Phi so appealing to humans on a purely visual level? Conflicting wavelengths of light are not an issue, here. Humans did not evolve alongside pentagrams and golden rectangles, after all; assuming that natural selection programmed this aesthetic into human beings, how do you believe that it did so? What is so interesting to me is that Phi seems to underlie human aesthetics in general, not merely the aesthetics of a single area. I'll expound on this further, but I want to see your response first.
--Mark
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No Offense, but one semester of differential equations means nothing in the long run. I'm an engineering physics major. I've taken calculus, differential equations, linear algebra, complex analysis and group theory. Woohoo, big deal. Mathematics is far more than just one semester of diffential equations. How about number theory? Set theory?
Riddle me this. How do you know that human aesthetics is underlined by phi? Nono, I don't want a bunch of links, that's not my question. My question is this:
Phi is irrational. There are an infinite number of digits in phi. In order to prove that human aesthetics is underlined by phi, you would need to measure "aethetic" qualities (whatever that means) out to an infinite precision. In actuality, I would say that any measurement you make can be argued, and it's accuracy debated. Why do you measure from the fish's eye to it's tail. Where on the eye? The pupil? The center of the pupil? To where on the tail? What counts as the end of the tail? How exact are your measurements? Down to the centimeter? To the milimeter? To the nanometer?
It seems kind of ... irational, to me to say that phi exists in nature, when it is impossible to measure such things with the infinite precision necessary to prove the point. Maybe the ratios are acutally 1.61803398. Not a huge difference between that and Phi, but nonetheless, it isn't phi.
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Humans did not evolve alongside pentagrams and golden rectangles, after all; assuming that natural selection programmed this aesthetic into human beings, how do you believe that it did so?
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Because Phi is the convergence of a ratio of a geometric series. Cellular reproduction occurs by binary division. A geometric series. DNA replicates by binary division. I'm sure there are many possible explinations, but I'm no biologist. Phi may simply represent the most efficient (energy wise, time wise, or cell count wise) way of producing biological structures.
The human cochlea is shaped much like a conch shell. Perhaps the shape of the cochlea is also based on phi, so it makes sense that our music system may in some way also be based on phi.