[slimscsi]

My point is, I am comparing temporal dimension to temporal dimension regardless of how many special dimensions there are. And I don’t understand the argument that an audio sample is more analogous to a pixel that it is a frame on a time line.

[kragen]

It's analogous to both, from different valid points of view.

[lonelappde]

In particular, in data processing, all dimensionality is equivalent, since and infinite set S the same cardinality as S^n for any whole number n, and any finite set is smaller than the 1-dimensional set of naturals.

[kragen]

Yeah, at least if Hilbert spaces can fuck off, which is why we can approximate signal processing on digital computers at all. And, because of space-filling curves, in some sense ℝⁿ is equivalent to ℝ. But, to understand signal processing, a much more useful point of view is that ℝⁿ is significantly different for different values of n, but not completely unrelated; and ℤⁿ is a useful approximation of ℝⁿ, as is (ℤ/mℤ)ⁿ.