I'm supposed to be doing something entirely different, but what the hell.
Right, so. Like. You're a floating consciousness that doesn't really do anything, and wastes all day imagining waves of various amplitudes and frequencies, let's say in the range of 30Hz to 20,000Hz. So, one day you're all like, "hey, it'd be really funny if there was more to existence that floating in nothingness and imagining waves, like it'd be really cool if there were other conscious beings around, and I'd be really stoked if they could appreciate all those waves". Except waves are pretty much all you ever imagine, so you'd really like those hypothetical conscious folks to appreciate certain patterns of waves over others, to give the set of all possible experiences some much needed variety. Exactly what patterns? Leave it to evolution, I guess? Maybe it'll have something to do with ratios of small numbers and their powers? Dunno. What is a small number anyway? 6?
No, more like 1, 2, 3, 5. Let the engines run. And you don't really care about the details anyway. You just want a universe with waves and with conscious beings finding patterns in those waves, along the lines of:
- The sum of squares (or really, any similar metric) of the amplitudes of the sum of the waves in a given range of time will be proportional to how much attention the perception of the waves will grab in the perceiver's consciousness in that range of time.
- When something generates a wave, the amplitudes of the generated wave will generally increase at first and then decrease with time
- Any two waves with a frequency ratio of 2n:1 where n is a natural number will seem the same, even though their frequencies and amplitudes are demonstrably different and there's nothing else to those waves (did I tell you that all those waves are sines already? I mean, we could do this with any other kind of wave too, but sines are simple and fun). Culture might override this, or maybe not.
- Given four waves A, B, C and D, A will be perceived to be exactly as far apart from B as C is from D if and only if the frequency ratio of A to B is equal to the frequency ratio of C to D.
- Things that will generate waves will generally generate multiple. Specifically, usually they will generate one main wave with a high amplitude, and other waves with lower amplitudes and frequencies that are whole multiples of that of the main wave. Waves generated together like this will be perceived to be a whole - a one big indivisible complicated wave with the frequency of the main wave - and the exact amplitude of each multiple of the main wave and the exact pattern at which each one rises in, maintains, and falls in amplitude will be characteristic of the thing that generated those waves (as in, similar things will be able to generate similar patterns of waves), along with some other less important things like generated waves that are not the multiples of the main wave, or special cases where the perceived frequency is not the frequency of the main wave.
- Waves with frequencies so close that their difference is below about 30 will feel eerie when perceived together, largely due to the fact that their sum will regularly fluctuate in the local sums of squares of amplitudes and thus in the attention-grabbing property of the perception of the waves.
- None of this actually matters, because it's all in your head.
What's a head? Actually, nah.
*I'm not actually gonna number the rest, if I ever decide to come back to this site again.
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