Very interesting article, despite the silly title.
Does a piano compute the inverse Fourier transform when it plays a sound? Of course, it is exactly what it does, but it is not very informative, put that way.
Some time in the late 1970s, I heard a lecture by a researcher at the Air Force Institute of Technology, who stated that if you took Fourier transforms of an optical illusion, and then reconstructed the image while progressively dropping the highest-frequency terms, the reconstructed image would eventually demonstrate the illusion.
This suggests that our sensory perceptions (and possibly, in the current research, our memories) lose fine detail in a way that can be analogized, if not explained directly, in terms of discarding or losing high-frequency information.
> This suggests that our sensory perceptions (and possibly, in the current research, our memories) lose fine detail in a way that can be analogized, if not explained directly, in terms of discarding or losing high-frequency information.
All practical analogue systems are band-limited. This applies to optical systems in the spatial domain, too.
analogies are like entries in a compression dictionary, good analogies are like succinct data structures in their ability to approach the theoretic lower bound.
I would go further, and say a piano is not calculating anything, as it is not performing symbolic manipulation. I am not sure that the case is so clear for assemblages of neurons in general (are patterns of spikes symbols?), but modeling a physical process computationally does not make the case that the process itself is a computation.
my point exactly! the "Fourier transform" is not something that you need to compute, but a trivial physical process that happens everywhere. You whistle a note, and the corresponding string of a harp nearby starts vibrating. The strings of the harp display the Fourier transform of the sound wave, but they are not computing anything. It is only when you try to simulate this process on a digital computer that it becomes somewhat difficult and interesting, but in the analog case it is a straightforward operation.
> but modeling a physical process computationally does not make the case that the process itself is a computation
IANA Mathematician, but I was under impression that it does exactly that, in a sense that if a physical process gives you results of an abstract computation, you can use this to get minimal bounds on energy requirements. Changing a bit has minimal theoretical energy cost in physical reality.
I guess it depends on if you think a computation is a manipulation of symbols. The sort of physical processes involved in a piano making sound are not symbolic manipulations, and being modelable through symbolic manipulations, or giving the same results (at whatever level of abstraction) as a symbolic manipulation, is not the same as being a symbolic manipulation.
Does a piano compute the inverse Fourier transform when it plays a sound? Of course, it is exactly what it does, but it is not very informative, put that way.