[thought experiments involving networks of nodes] - A New Kind of Science: The NKS Forum

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thought experiments involving networks of nodes

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Posted by: Jesse Nochella

In the past on this forum there have been a few extended thought experiments involving networks of nodes. NKS discusses physical models involving them at length.

If there is a true superior robustness in thinking about the universe in this way, then with appropriate images in mind discussion about simple features of our universe should be easier.

One thread, on a mechanical theory of gravity involving networks can be found here.

Jason Cawley started a thread a while ago including some network related ideas, which can be found here.

Any one else can post a link on other discussions I've missed, of course.

I want to help develop some new visuals/ideas that can be used to think about evolving networks, physics based on network models, other network things by dishing them out, then thinking about them and other ones that have been dished out, mix them, come up with new ones, compare.


Posted by: Jesse Nochella

Ok, what about speed?

I remember hearing/reading a comment form Wolfram about physics and the notion of speed. He said that in if somethings going fast, it might have more connections or something. How would this work? I don't know.

For me it helps to think of the effects implied by special and general relativity. Some of these things are already pretty thought provoking.

Gravity?

According to discussion in Mark Suppes' thread, gravity can be viewed as the reduction of network distance between stuff. There are a few flavors of this idea. One is that some of the nodes just dissapear. I imagine particles here as these gnarly, gritty structures that have these little stations physically placed all over them. The stations don't even necessarily need to look the same. I imagine these stations processing nearby parts of space in a very systematic, machanical fashion so that those parts of space become less locally relevant.

Particles that we measure as heavier would have more of these stations placed on them.

What about the confinement in QCD (strong force)?

Confinement is typically illustrated with rubber bands or springs. Could there be a network analog that does the same thing?

One possibility that enters my mind is that quarks essentially get heavier in a very specific way, towards eachother, as they move apart. Do they? Would this easily show up in physics experiments?

I'm thinking of a kind of thing in the middle of these two quarks, possibly some wound up wound up structure or folded up structure, that unfolds when it is pulled apart. And on this wound up bundle thing inside are those little stations I mentioned earlier. This structure might be pictured as a strip of paper folded up like an accordian, or a DNA-like strand, perhaps. When the quarks are pulled apart they suck up more and more space in between them, and when they are close together they suck up almost no space.

Another idea is to have the the quarks continually growing these stations on them maybe even growing as buds on some kind of tree/anemone like thing so that the number of them is exponential, and for the particular stations they grow to annihilate eachother upon contact and further annihilate those connected to them. Quarks would then suck up increasingly huge ammounts of space when alone and quickly find a match quark to mediate their pull.


Posted by: Tony Smith

Jesse, I'm still trying to stay focused on simple graph theoretic models, typified by Tick Tock which I announced here early in 2004, in which individual nodes and links do not persist but emergent local configurations do.

I don't expect that we are going to get within orders of magnitude of the computing power that would be needed for persuasive simulations of a sufficient variety of rules in this lifetime, if ever, so am instead concentrating on theoretical analysis of the likely behaviour of such systems. Right now an idea I find aesthetically unappealing but which other theoreticians have come to from other directions is starting to look quite credible.

The basic idea is that our cosmos arose from a bubble, the likes of which naturally appear within a hyperinflating chaotic background, and even something as simple as Tick Tock shows that getting such a background will be significantly easier than getting a more conservative universe. One key consequence of it all being a network is that the chaos outside the bubble is not able to influence the region inside which has excluded and thus cannot regain hyperinflating nuclei. Within a long lived bubble universe only polynomial expansion is possible, as well as local contraction, so long as the contraction is minor relative to the expansion. Any badly behaved sinks inside the bubble would also be quickly eliminated, maybe even seeding black holes in the process.

At its simplest, this idea explains why we find ourselves in a cosmos dominated by conservation “laws”—nothing else can persist long enough to do anything interesting.

I expect that conservation is achieved not by nodes or links which persist but by locally cyclic persistence of various network topologies, many of which will marginally increase (sources) or decrease (sinks) the local node count and some of which will produce additional sources each cycle. Hopefully commitments will soon allow me to finish writing this all up in greater detail.


Posted by: Matthew Finnigan

I like the idea that mass is related to destroyers of nodes and empty space is related to creation of nodes. However, how about having no mass / empty space dichotomy? Simply there are some orientations which destroy nodes and some orientations which create nodes.

How about this:
1. Start with a set of nodes, with N being the number of nodes.
2. Produce links between each node randomly, with L being the number of links.
3. For each node that has less than S links to other nodes, delete the node.
4. For each node that has S to T links, keep the node as it is.
5. For each node that has more than T links, create a node and link the nodes neighboring that node to it.
6. For two nodes, if they are linked, randomly delete the link with a probability of D.
7. For three nodes, if one node is linked to two nodes, randomly create a link between both its neighbors with a probability of C.
8. Finally, if there is any subsystem of nodes for which the links are M-linked, replicate the connective properties of the subsystem to the rest of the system, so that there are M copies, and in all copies reduce M-links to single links. Do NOT link ANY of the replicates to each other in this process.

The rules can be changed and altered so that the results produced are the ones desired, but these 8 rules should give some pretty interesting results. I haven't tried it myself, but if anybody wants to show me how to program such a thing, or even program it themself, they can.

Edit: If you'd like me to explain any of these rules further, you can. I basically created them on the spot, so I didn't have time to think about how to word them.




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