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Comment by js8 | Hacker News Reader

It is hard. There are cellular automata, which are result of discrete local functions evolving in fixed space.

But what if we had something like "foam automata", discrete local functions that could alter the space they operate on? For example, if we represented the underlying space as graph, could we have functions that evolve as to change (reconnect) the edges and add/remove vertices of said graph?

Aside from 1D case, I was unable to figure out a set of rules that wouldn't quickly devolve into something that's either locally too dense or too sparse or disconnected. And making it follow some laws of conservation seems even harder.

Maybe some smarter readers of HN will figure it out, I would certainly be delighted.

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So, a lot of people are annoyed by Wolfram, but this is relevant as I think that's something that Wolfram does in his free time: http://blog.wolfram.com/2007/09/11/my-hobby-hunting-for-our-...

Not sure why you're being downvoted.

What you're describing isn't too far from Causal Dynamical Triangulation.

https://en.wikipedia.org/wiki/Causal_dynamical_triangulation

The downvotes may be from people wanting to help the uninformed/hobbyists avoid wasting time trying to do something that's unrealistic - http://advances.sciencemag.org/content/3/9/e1701758.

(I upvoted because the unrigorous idea of some sort of "foam automata" is cool, even if a formal, universal version of it is impossible.)

> Not sure why you're being downvoted.

Thanks, I was also confused, but according to some weird social customs enforced on HN, I cannot sincerely ask that question. On the other hand, I am not sure about the upvotes either.

I actually didn't mean to develop some new physics theory, I just wanted to play a mathematical game (like Game of Life, for example), which would alter its own space/geometry. And this seemed as a good place to mention it, and get some feedback if somebody was aware of something similar. Because I found it quite nontrivial (to make it work "decently", in a vague sense), despite my lack of ambitions to explain physics.

CDT looks interesting, but it's not quite what I had in mind.

There is also https://en.wikipedia.org/wiki/Shape_dynamics, which takes Mach's principle as a philosophical base and tries to rebuild (continuous) spacetime on top of it, basically by observing that any triangle with the same angles but different lengths is actually equivalent -- you can only measure distance between two things if there's a third thing that can see both of them.

It's been proven to be locally equivalent to General Relativity, but might differ globally (e.g. solving the bucket in an empty universe issue).

Here's something similar: https://arxiv.org/abs/gr-qc/0011076

I found that article from here: https://en.wikipedia.org/wiki/Pregeometry_(physics)

I may be wrong, but it sounds like you just described a mathematical model of a brain. A neuron is a discrete function, and every time it fires its connections to neighbouring neurons are subtly altered.

Maybe the trick to stability is making less radical changes per generation, like changing edge weights, rather than wholesale creation and deletion?

I'm currently reading the novel "Schild's Ladder" by Greg Egan. It opens with a similar hypothesis.

Chapter 1 In the beginning was a graph, more like diamond than graphite. Every node in this graph was tetravalent: connected by four edges to four other nodes. By a count of edges, the shortest path from any node back to itself was a loop six edges long. Every node belonged to twenty-four such loops, as well as forty-eight loops eight edges long, and four hundred and eighty that were ten edges long. The edges had no length or shape, the nodes no position; the graph consisted only of the fact that some nodes were connected to others. This pattern of connections, repeated endlessly, was all there was.

could we have functions that evolve as to change (reconnect) the edges and add/remove vertices of said graph?

Sounds familiar with someone else's post, specifically, this part: https://youtu.be/qTx98PUW6lE?t=4592

Sounds like you need some regularization that optimizes for whatever you call not 'too sparse' or 'too dense'.

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