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"There’s a common saying: “The weather has a mind of its own”. And what the Principle of Computational Equivalence tells us is that, yes, fluid dynamics in the

"There’s a common saying: “The weather has a mind of its own”. And what the Principle of Computational Equivalence tells us is that, yes, fluid dynamics in the atmosphere—and all the swirling patterns associated with it—are examples of computation that are just as sophisticated as those associated with human minds." I'm definitely not as smart as Wolfram, but in what way does the fluid dynamics of the atmosphere count as any common definition of computation?

MontyCarloHall 4y ago
One might argue that the fluid dynamics of the atmosphere are arriving at exact solutions to the Navier-Stokes equations in real time, and that this is indistinguishable from a computer doing the same thing. Thus, the atmosphere is accomplishing a feat of computation well beyond our current technological and mathematical sophistication. FWIW, I don’t agree with this definition of “computation.” I think “computation” requires the ability to artificially recapitulate a system under arbitrary boundary conditions, which is clearly not the case with the atmosphere.
- LegitShady 4y ago
  is dropping an apple solving a computation about gravity, or does the computation exist as an abstract separate from the physical forces it describes? The idea that fluid is solving the Navier-Stokes equation seems like an obvious error to me - it cannot solve the equation, it simply acts a fluid, which the equation was designed to approximate.
  - oolonthegreat 4y ago
    > The idea that fluid is solving the Navier-Stokes equation seems like an obvious error to me - it cannot solve the equation, it simply acts a fluid, which the equation was designed to approximate. that's his "Principle of Computational Equivalence", that natural processes are themselves computations. it's easy to see this is true in a "made-up" universe, say Game of Life, but whether our universe is computational is still an open question I think.
- AnimalMuppet 4y ago
  If you can physically set up those boundary conditions, the atmosphere will in fact perform the computation. (I don't agree with the argument either, by the way. The atmosphere is not solving the Navier-Stokes equation; the atmosphere is doing what the Navier-Stokes equation models. And computation includes things that we have no physical analog "computer" for.)
  - MontyCarloHall 4y ago
    >If you can physically set up those boundary conditions, the atmosphere will in fact perform the computation. The invalidity of the equivalence principle becomes much more ambiguous for me in that case. >The atmosphere is not solving the Navier-Stokes equation; the atmosphere is doing what the Navier-Stokes equation models It can sometimes be hard to distinguish the two. Analogously, you can compute a Fourier transform optically—as a simple example, the diffraction pattern of an aperture is the Fourier transform of the aperture shape (as if it were a 2D step function) [*]. Is the aperture performing the Fourier transform, or merely doing what the Fourier transform models? In the days before fast DSPs, this is exactly how Fourier transforms were computed. [*] As a more complex example, by passing collimated light through a transparency and then a lens, the image formed is the Fourier transform of the signal encoded by the transparency.

MontyCarloHall 4y ago

One might argue that the fluid dynamics of the atmosphere are arriving at exact solutions to the Navier-Stokes equations in real time, and that this is indistinguishable from a computer doing the same thing. Thus, the atmosphere is accomplishing a feat of computation well beyond our current technological and mathematical sophistication. FWIW, I don’t agree with this definition of “computation.” I think “computation” requires the ability to artificially recapitulate a system under arbitrary boundary conditions, which is clearly not the case with the atmosphere.

LegitShady 4y ago
is dropping an apple solving a computation about gravity, or does the computation exist as an abstract separate from the physical forces it describes? The idea that fluid is solving the Navier-Stokes equation seems like an obvious error to me - it cannot solve the equation, it simply acts a fluid, which the equation was designed to approximate.
- oolonthegreat 4y ago
  > The idea that fluid is solving the Navier-Stokes equation seems like an obvious error to me - it cannot solve the equation, it simply acts a fluid, which the equation was designed to approximate. that's his "Principle of Computational Equivalence", that natural processes are themselves computations. it's easy to see this is true in a "made-up" universe, say Game of Life, but whether our universe is computational is still an open question I think.
AnimalMuppet 4y ago
If you can physically set up those boundary conditions, the atmosphere will in fact perform the computation. (I don't agree with the argument either, by the way. The atmosphere is not solving the Navier-Stokes equation; the atmosphere is doing what the Navier-Stokes equation models. And computation includes things that we have no physical analog "computer" for.)
- MontyCarloHall 4y ago
  >If you can physically set up those boundary conditions, the atmosphere will in fact perform the computation. The invalidity of the equivalence principle becomes much more ambiguous for me in that case. >The atmosphere is not solving the Navier-Stokes equation; the atmosphere is doing what the Navier-Stokes equation models It can sometimes be hard to distinguish the two. Analogously, you can compute a Fourier transform optically—as a simple example, the diffraction pattern of an aperture is the Fourier transform of the aperture shape (as if it were a 2D step function) [*]. Is the aperture performing the Fourier transform, or merely doing what the Fourier transform models? In the days before fast DSPs, this is exactly how Fourier transforms were computed. [*] As a more complex example, by passing collimated light through a transparency and then a lens, the image formed is the Fourier transform of the signal encoded by the transparency.