Hacker News Reader

Comment by MontyCarloHall | Hacker News Reader

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.

View on HN

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.)

>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.

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.

> 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.

Reply on news.ycombinator.com