[seandougall]

You're right, I missed that your sin(x) example was talking only about a single component.

However, cherry-picking a different reordering for each frequency component before doing an inverse FFT really isn't the same thing as playing all the sounds simultaneously.

Anyway, the thing is, we're not talking about an infinite series. This is a thread about digital audio playback, where both amplitude and phase components (I'm going to assume this site uses some sort of DCT-based codec) are quantized, and hence occupy a finite space. No amount of reordering will change that sum.

[stefco_]

Yeah for sure. I mean I was just trying to make a joke about divergent series and how "Every Noise at Once" is a deeply vague statement. But you're right that in the discrete arena it is literally a finite sum that can cancel perfectly (assuming that every sound has exactly one representable "opposite" sound in your storage format).