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There was a discussion about dimensionality, but I couldn't decipher -- is there something intrinsic that pushes this model to look like three dimensions? It l

There was a discussion about dimensionality, but I couldn't decipher -- is there something intrinsic that pushes this model to look like three dimensions? It looked like any dimensionality is equally at home in this model, and generally a random infinite hypergraph would require infinite dimensions to represent as a manifold (or at least I'd think so after a quick think about it). So that we ended up in a universe with three seems quite arbitrary. If Wolfram can find a simple non-arbitrary explanation of why three dimensions, that would be a big step.

leumassuehtam 6y ago
The concept of updating rules underlies this model. Each rule determine the evolution of the hypergraph which is space itself, much like a cellular automata. It seems that some rules have the property that as "times goes by" the hypergraph converges to a manifold with dimension d. One can estimate the dimension of such hypergraph using, for example, the growth of the volume of balls[0]. It also seems that this concept is very generic, and many properties of the model do not depend on the dimensionality neither on the manifold or the rule itself. Because this concept is so generic, one hopes that there is a rule that the hypergraph converges to d=3 as in our world. This would also raise questions on why in the very early universe there was a "inflationary" phase. [0] https://www.wolframphysics.org/technical-introduction/limiting-behavior-and-emergent-geometry/the-notion-of-dimension/ https://www.wolframphysics.org/technical-introduction/limiti...
piannucci 6y ago
You might get an answer by reading about Hausdorff dimension.
nuncanada 6y ago
He hasn't derived 3 dimensions from this framework yet... The whole program is very interesting, it might find general laws not only for Physics but for many phenomena, but I feel like Wolfram has jumped the gun on connecting Physics to it... Particularly, I think that quantum non-locality might be evidence that fundamentally 3 dimensions is just an emergent property, but that has yet to be derived from this hypergraph framework...
- daxfohl 6y ago
  I think it's pretty good. These questions have been keeping me awake at night for the last 30 years or so, and after one big false start that I sadly realized was just a complicated method that was identical to QM, I have come to something pretty similar to this as the next approach to check out. It's pretty cool to see that others are looking in this direction too. I'm nowhere as smart as Wolfram, nor is my new approach anywhere near as developed, but the dimensionality is the thing that has been bugging me since the beginning for my own thing as well. Why three dimensions? Seems like if we can show a reason for that without too much hackery then we may be on the path to enlightenment.

leumassuehtam 6y ago

The concept of updating rules underlies this model. Each rule determine the evolution of the hypergraph which is space itself, much like a cellular automata. It seems that some rules have the property that as "times goes by" the hypergraph converges to a manifold with dimension d. One can estimate the dimension of such hypergraph using, for example, the growth of the volume of balls[0]. It also seems that this concept is very generic, and many properties of the model do not depend on the dimensionality neither on the manifold or the rule itself. Because this concept is so generic, one hopes that there is a rule that the hypergraph converges to d=3 as in our world. This would also raise questions on why in the very early universe there was a "inflationary" phase. [0] https://www.wolframphysics.org/technical-introduction/limiting-behavior-and-emergent-geometry/the-notion-of-dimension/ https://www.wolframphysics.org/technical-introduction/limiti...

piannucci 6y ago

You might get an answer by reading about Hausdorff dimension.

nuncanada 6y ago

He hasn't derived 3 dimensions from this framework yet... The whole program is very interesting, it might find general laws not only for Physics but for many phenomena, but I feel like Wolfram has jumped the gun on connecting Physics to it... Particularly, I think that quantum non-locality might be evidence that fundamentally 3 dimensions is just an emergent property, but that has yet to be derived from this hypergraph framework...

daxfohl 6y ago
I think it's pretty good. These questions have been keeping me awake at night for the last 30 years or so, and after one big false start that I sadly realized was just a complicated method that was identical to QM, I have come to something pretty similar to this as the next approach to check out. It's pretty cool to see that others are looking in this direction too. I'm nowhere as smart as Wolfram, nor is my new approach anywhere near as developed, but the dimensionality is the thing that has been bugging me since the beginning for my own thing as well. Why three dimensions? Seems like if we can show a reason for that without too much hackery then we may be on the path to enlightenment.