Haha, this is just P versus NP for $970,000 less in prizes.
Wolfram Rule 30 Prizes
41–50 of 52 posts
Re: Wolfram Rule 30 Prizes
#42Has anyone seen a version of Rule 30 for a 2D array, instead of 1D? I'm doing some searching but can't find one. Somewhat tangential to my angle of attack, but would be helpful to me.
There are 2D rules that are aesthetically similar to Rule 30 (in how reactive and "fluffy" they are, and how they tend to perpetuate instead of die down), but a 2D and a 3D rule are fundamentally different. But you can apply simple transformations on rules, like reflecting them (1D and 2D) and rotating them (2D only), or layering them (having a bunch of lower dimension rules running in parallel). Or you can perform a…
> There are 2D rules that are aesthetically similar to Rule 30
This is exactly the sort of thing I was looking for (analogous rules), thanks!
> https://donhopkins.com/home/CAM6/
Directions worked perfectly, thanks!
As I mentioned, this is orthogonal to my approach, but helps me reduce my search space.
Re: Wolfram Rule 30 Prizes
#43Has anyone seen a version of Rule 30 for a 2D array, instead of 1D? I'm doing some searching but can't find one. Somewhat tangential to my angle of attack, but would be helpful to me.
What would this mean? You could have a rule that just implemented rule 30 for one adjacent row or column of the plane, but that would just give you stripes of 1d rule 30. Is there some obvious way of generalizing the 1d rules to 2d that I'm missing? What properties would you expect to be conserved?
> Is there some obvious way of generalizing the 1d rules to 2d that I'm missing?
No you are correct. I was looking for analogies, to help me flush out my thinking of the space more by looking at it from a few angles.
I wanted to think about systems of limited size or machines of different dimensions but turns out periodicity is known for those (https://www.wolframscience.com/nks/p255--systems-of-limited-...).
My main attack vector is to build up a simple new math starting with just 1 and 0 to define both the problem and solution in and see where it goes, hopefully creating useful side effects along the way. If I were to solve a problem my hunch is it will be related to impossibilities in formally defining "infinite sequence" in the problem definition in such a language.
Re: Wolfram Rule 30 Prizes
#44It is pretty hard in general to prove that calculating things takes at least O(n) time, so I wouldn't expect that one to be solved any time soon. Personally, I am curious if there is any cellular automaton that has something like 3-dimensional rotational symmetry. If our universe can be described by a cellular automaton, it isn't obvious to me how such a symmetry could arise, but I wouldn't be surprised if someone fi…
For what it's worth, Stephen decided that network was a better model for the universe than a cellular automaton, and thought that space might emerge as a property of that network rather than be "defined in", as in a cellular automaton. https://www.wolframscience.com/nks/p475--space-as-a-network/ (In the preceding section he discussed some constraints that a cellular automaton would put on the universe model, but didn…
I can't open this link for some reason (uBO?), but the title reminds me one very clever Wolfram's article where he brags about (as usual) about how he derived GTR equations from his graph model. That article had a bunch of comments with and one of them stating that in such a graph model there is always a reference frame. Wolfram didn't respond to that comment.
Re: Wolfram Rule 30 Prizes
#45Computing the nth cell clearly takes at least 1 time unit, and by the definition of O(), we have 1 = O(n). I’ll be claiming my $10,000 now.
(More seriously, don’t confuse O() with Ω() and Θ(), folks: https://en.wikipedia.org/wiki/Big_O_notation.)
Re: Wolfram Rule 30 Prizes
#46It is pretty hard in general to prove that calculating things takes at least O(n) time, so I wouldn't expect that one to be solved any time soon. Personally, I am curious if there is any cellular automaton that has something like 3-dimensional rotational symmetry. If our universe can be described by a cellular automaton, it isn't obvious to me how such a symmetry could arise, but I wouldn't be surprised if someone fi…
I think the challenge is more of a quest to find a way to compute it in less than O(n). The proof for that would just be a working algorithm.
IIRC cellular automaton are Turing-complete? We have proven we can implement simulations of 3d rotational symmetry using regular computers, so that one is straightforward, isn't it?
Re: Wolfram Rule 30 Prizes
#47An aside: 3D cellular automata https://www.youtube.com/watch?v=_W-n510Pca0
Very beautiful and artistically rendered! Those would make great fireworks and weapons in Minecraft! From a different engineering perspective, Dave Ackley had some interesting things to say about the difficulties of going from 2D to 3D, which I quoted in an earlier discussion about visual programming: https://news.ycombinator.com/item?id=18497585 David Ackley, who developed the two-dimensional CA-like "Moveable Feast…
> Very beautiful and artistically rendered! Those would make great fireworks and weapons in Minecraft!
Someone coded similar things in minetest, the open source clone of minecraft:
Re: Wolfram Rule 30 Prizes
#48Earlier quoted context omitted.
For what it's worth, Stephen decided that network was a better model for the universe than a cellular automaton, and thought that space might emerge as a property of that network rather than be "defined in", as in a cellular automaton. https://www.wolframscience.com/nks/p475--space-as-a-network/ (In the preceding section he discussed some constraints that a cellular automaton would put on the universe model, but didn…
I can't open this link for some reason (uBO?), but the title reminds me one very clever Wolfram's article where he brags about (as usual) about how he derived GTR equations from his graph model. That article had a bunch of comments with and one of them stating that in such a graph model there is always a reference frame. Wolfram didn't respond to that comment.
I haven't followed this closely, but did SW provide a paper showing how he derived GTR from the graph?
Re: Wolfram Rule 30 Prizes
#49Earlier quoted context omitted.
I can't open this link for some reason (uBO?), but the title reminds me one very clever Wolfram's article where he brags about (as usual) about how he derived GTR equations from his graph model. That article had a bunch of comments with and one of them stating that in such a graph model there is always a reference frame. Wolfram didn't respond to that comment.
I haven't followed this closely, but did SW provide a paper showing how he derived GTR from the graph?
He made the claims but not sure if that paper ever appeared.
Re: Wolfram Rule 30 Prizes
#50Earlier quoted context omitted.
For what it's worth, Stephen decided that network was a better model for the universe than a cellular automaton, and thought that space might emerge as a property of that network rather than be "defined in", as in a cellular automaton. https://www.wolframscience.com/nks/p475--space-as-a-network/ (In the preceding section he discussed some constraints that a cellular automaton would put on the universe model, but didn…
I can't open this link for some reason (uBO?), but the title reminds me one very clever Wolfram's article where he brags about (as usual) about how he derived GTR equations from his graph model. That article had a bunch of comments with and one of them stating that in such a graph model there is always a reference frame. Wolfram didn't respond to that comment.
I think SW became too obsessed with the mathematical and computational approach to CA, while (as usual) 't Hooft pursued his physics intuitions to create a candidate CA theory:
https://arxiv.org/abs/1405.1548
I say as usual, because G'tH had already formulated the holographic principles that would allow space-time (hence GTR) to be encoded non-locally over a graph.
https://arxiv.org/abs/gr-qc/9310026
There need not be a preferred reference frame if the space-time events do not occur at individual nodes in the graph, but emerge at scales much larger than the graph, with some holographic or permutation symmetry that can reproduce the diffeomorphism invariance of GTR. It is also plausible that the position-momentum duality of space-time could emerge from such a theory.
Space-time would be created by the events that occur, not the other way around, hence the aphorism spooky distance at an action, because the events are primary, and distance is the strange phenomenon that emerges from them.
There has been much recent progress in making space emerge from entanglement, which also implies that locality emerges from non-locality:
https://arxiv.org/abs/1005.3035
https://phys.org/news/2015-05-spacetime-built-quantum-entang...
https://www.scientificamerican.com/article/tangled-up-in-spa...
Note that LQG has produced a nice discretization of space, based on graphs that have observable quanta of area and volume, but not length. Directions and lengths are defined as normals to areas, which is reminiscent of Clifford Algebra. Having derived (emergent) lengths also makes diffeomorphism easier.