Sir, There's a Cat in Your Mirror Dimension
owl writes:
https://lcamtuf.substack.com/p/sir-theres-a-cat-in-your-mirror-dimension
A while back, we talked about the frequency domain: a clever reinterpretation of everyday signals that translates them into the amplitudes of constituent waveforms. The most common basis for this operation are sine waves running at increasing frequencies, but countless other waveforms can be used to create a number of alternative frequency domains.
In that earlier article, I also noted two important properties of frequency domain transforms. First, they are reversible: you can recover the original ("time domain" or "spatial domain") data from its frequency image. Second, the transforms have input-output symmetry: the same mathematical operation is used to go both ways. In effect, we have a lever that takes us to a mirror dimension and back. Which of the lever positions is called home is a matter of habit, not math.
Of course, in real life, the distinction matters - and it's particularly important for compression. If you take an image, convert it to the frequency-domain representation, and then reduce the precision of (or outright obliterate!) the high-frequency components, the resulting image still looks perceptually the same - but you now have much less data to transmit or store:
This makes you wonder: if the frequency-domain representation of a typical image looks like diffuse noise, if most of it is perceptually unimportant, and if the transform is just a lever that takes us back and forth between two functionally-equivalent dimensions... could we start calling that mirror dimension home and move some stuff in?
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