I've been contemplating the possibility of our universe and physics being a big computer simulation. But unlike the writer of this Oxford paper, I have in mind the simulation not being later humans or advanced being simulating their own galaxy's history, but rather an entity in an environment not within our universe, simulating our reality and all of its physics, in some environment where computing such a a large simulation might be possible.

So my curiosity is whether additional spacial dimensions might make for better computers.

For a simplified example, our computers in 3D space are more easily capable of simulating 2 dimensions than 3. Perhaps a 4D computer, then, might simulate more easily a 3D space. Or a 5D computer, etc etc assuming that such a universe exists.

  • What exactly is the reason that you're suggesting this world is a simulation in 4D? I find that 'the fourth dimension' is often used for just 'something we can't understand' - so please confirm that this is not like that. – user2953 Dec 28 '14 at 17:13
  • @Keelan we actually do understand the fourth dimension to a pretty interesting extent. It's mysterious, at least to me, because I don't understand the setting or context where a 4D world can / would exist, but I do understand that there is an extra axis onto which space can be observed and filled. That fact alone would seemingly have very interesting and complex effects on computing. – CuriousWebDeveloper Dec 28 '14 at 18:04
  • when you play computer game, like Battlefield or Quake - its already 4D simulation - XYZt. What's you question ? – c69 Dec 28 '14 at 18:04
  • @CuriousWebDeveloper well, too bad. Guy called Einstein (and bunch of his friends, like Lorentz) would have disagreed with you, but they died long ago. Anyway, have a look at en.wikipedia.org/wiki/Spacetime#Mathematics_of_spacetimes – c69 Dec 28 '14 at 18:13
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    I propose to put this question on hold as the philosophical problem here is ill-defined and probably too broad and reopen it when these problems are resolved. – user2953 Dec 28 '14 at 18:25

Interestingly enough we have an answer: The Blue Gene/Q has a 5D torus interconnect, meaning any software or logic developed for it would STRONGLY resemble the structure you are looking for. Developers are encouraged to think in terms which leverage this 5D structure.

This is efficient in 3D space because much of the propagation time between nodes is in the computer, not the fiber optic cables. If the latencies were simply from the fiber optics, it would be more effective to think of it as a 3D network, but the reality of hardware means they found it more optimal to have a 5D interconnect and treat all dimensions the same (even though some dimensions may have longer length fiberoptic cables)

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    I just read the entire document. I understood about 15% of it, and now have a higher respect for IBM supercomputer engineers, and those poor software engineers tasked with developing instructions optimized for a 4D torus "processing cycle". – CuriousWebDeveloper Dec 28 '14 at 19:34

I guess it depends on what you mean by power, but by the standards of what computation theory generally considers power, this is a somewhat bizarre question, for how commonly it seems to arise.

In a Turing machine model, all computing is reducible to something 1-dimensional with no loss of generality. (2 if you are counting time, and reducing the Turing machine to a tiling of something.) So dimension disappears from consideration.

And relative to "Big O's" it also lacks some sense. Computer connections are not propagated in any particularly direct spatial manner, two signals can take equally long to reach the same place even if one follows natural space and the other uses a slightly better conduit. From a direct efficiency point of view, therefore, it is graph-theoretic dimension that matters, and any graph-theoretic dimension can be modeled in 3D space. Spatial dimensions can decrease the multiplier in a speed calculation, but not the order of growth.

From the points of view where dimensionality does bear on the question, is not really an aspect of computing, but of mechanical engineering as applied to it.

From another direction, 4 spatial dimensions would make for a lovely universe, but it is not ours. Folks become strongly attached to the notion of 4D space before they realize that basic Newtonian physics indicates we cannot have four macroscopic dimensions. If we did, we would encounter some basic field effects that decrease as the cube of the distance from their origin. These should be numerous. But we never see them.

And we would have to make really serious reasons for why radiant energy itself would not be an inverse-cube field effect. Energy should not obey an inverse-square law in 4D space. Given that, if we have any additional dimensions, they are all either microscopic (curved far too tightly to have any use for computer engineering) or temporal.

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