okay I actually took some _off-list notes_ (omigod right) to try to hold these different things in my mind at once
the 300 degree/sample signal is already destructively interfering with itself, so unrotating it by 300 degree/sample removes the interference, making it aligned and turning it into a peak. The result is actually correct. If we were to instead unrotate by 180 degree/sample, we should see the other signal harmonize with itself and become a peak, summing to 6.0 because there are 6 samples. 0800 >>> np.abs(removed_180), np.angle(removed_180)*180//np.pi (array([2., 1., 1., 2., 1., 1.]), array([ 0., 59., -61., -1., 59., -61.])) >>> np.sum(removed_180) (5.999999999999999-1.1102230246251565e-15j) This does indeed work. Given the environment is one of complete destructive self interference of spinning components, components can be isolated by further spinning at the rate that opposes them, and they stop destructively interfering. Somehow, the other components keep on destructively interfering. Why is it that the other components still destructively interfere after the rate change? And, how does this work if none of the components are destructively interfering? Thinking of the latter question, you'd indeed be able to produce a sum with one component removed, although others might be included. It's a little complex there. More challenges than I was hoping for. Comprehending it better could help me grapple with it. - I'm spending a little time skipping by the detailed comprehension and daydreaming on the larger part of the problem. We can consider these spirals as individual points in a larger-dimensioned space composed of complex spirals. Addition in this space would be multiplication of the spirals, kind of roughly. The importance is the use of it. If we have a spiral at 300 degrees, we can remove this from data to remove the 300 degree component .. actually i confused myself typing the space up a little, and i'm bopping back to the more detaile dunderstand .. [ basic idea is data contains many spirals. we can remove a spiral. this adjusts the other spirals. we can consider the parts of the problem in this space to simplify and summarise it. but it got somewhat corrupt. freq_300 and freq_180 would be components of this space: they add a 300 deg/sec and 180 deg/sec rotation to data summing is kind of an evaluation of a point in the space. it shows whether the signals combine or not. the fourier frequencies are all components in this space. we're considering the one at 120 deg/sec . so are the original signals. they are at 60 deg/sec and 180 deg/sec . when we sum the original signals, this operation unfortunately was lost in the transformation to language. the 60 deg/sec and 180 deg/sec components are combined with the 120 deg/sec component. this makes combined infomration that has its own deg/sec property, but has peaks and things that show it contains two underlying waves. This combination is formed by summation, before or after product. Since summation is [commutative? transitive?] with multiplication, operations on the unaccelerated waves can be considered identical to operations on the accelerated waves (by 120 deg/sec). Now, consider the final summation wave, which consists of both 60 deg/sec and 180 deg/sec components, both of them accelerated by 120 deg/sec to 180 deg/sec and 300 deg/sec . When we decelerate them by 300 deg/sec, this applies to both waves separately, although they are in a combined space. the 60 deg/sec wave is now at 180 - 300 = -120 deg/sec, which is 240 deg/sec accoridng to calculator the 180 deg/sec wave is not at 300 - 300 = 0 deg/sec. So it harmonizes! Meanwhile, the 240 deg/sec wave is self-interfering because of how 240 deg/sec aligns with the sampling count of 6. ] [ok that was quite helpful and simplifying in the end. it really slowed the idea down to type out all the space and then translate to normativeness of waves. i think spacially.]
