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Several questions, but mostly what are nodes?

Posted 4 months ago
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OK, so I feel like I have a pretty good grasp on the rules surrounding how nodes work, but this question is a little different, I want to know what a node actually represents in rule space. Are they little processors being co-opted out of an endless block of computronium? Are they deformations in some kind of computational topology? Why do they seem to be freely created and destroyed without cost? The same questions could technically be applied to edges, etc. If nodes aren't free or infinitely created, does that mean there is an infinite Turing tape out there (infinite free storage to store node states) chunking away? That feels less elegant to my flavor receptors.

Also, is there a way rules can influence other rules? Can universes rub against each other? Steal each other's computational power?

Is there some kind of conservation law at work for computation, nodes, or storage?

When connections pop up between existing nodes that had no previous connection, how does a node "know" how to form that new edge? Or is each possible unique computational state always existing somewhere and does the processing of these hypergraphs just weave patterns among these nodes?

These are the questions I've got burning in my mind right now. And others, but I'm trying not to be too overwhelming.

8 Replies
Posted 4 months ago

Michael:

I wish I had an answer for you. But when you figure this out, there might be a great sci-fi story to be told about these nodes and edges.

Posted 4 months ago

I'll get right on it. Should only take me a decade or two. No biggie.

Wouldn't it be funny if the fundamental rule was a computational expression of "Whatever makes a good story." Narrative becomes the fundamental concept at the heart of our universe? ;)

Posted 4 months ago

I won't be surprised if the new Wolfram Model has some of the secrets.

But to be fair, we already know the answer is 42. But we have to figure out the question.

Just remember to bring your towel with you.

Posted 4 months ago

No problem there, as a hoopy frood, I always have a towel with me.

And what name do we use to refer to the situation before the first node is drawn? (or after the last one is removed).

Posted 3 months ago

That's the phase transition between primordial chaos and primordial order. Rulial rain on an endless ocean of half computed universes and primordial order icebergs.

In any formal system, you need to have undefined terms, i.e., terms that cannot be analyzed in simpler terms. Otherwise, you will never end the explanations. So, the easiest answer to your question

I want to know what a node actually represents in rule space

is that the nodes and the hyperedges are undefined terms from which everything else emerges. It is like the strings in string theory: they are not made of something more fundamental, they are the most fundamental objects in their theory. Nevertheless, this status does not exclude the possibility that the nodes, if they exist in nature, may have internal structures. If this is the case, then a more precise theory could be developed in the same way that the theory of quarks was made in order to express the internal structure of protons, neutrons and other particles.

Posted 2 months ago

“I want to know what a node actually represents in rule space”. If we analogize to networks in other applications (e.g., computers connected to Internet, cells in a body, or persons in a social network) then nodes can be born, die, and connect or disconnect to other nodes. In a fundamental physics context, I would expect nodes (under whatever specified conditions) can do the same. Links between nodes can represent communication lines that allow for passage of information from one node to another node. Along the lines of what happens in cellular automata, I would also suggest that nodes process a limited amount of information and can change states as a result.

“Why do [nodes and links] seem to be freely created and destroyed without cost?” Inflationary theories of cosmology suggest that a whole universe can be generated from nothing (or almost nothing). Similarly, Wolfram suggests we can start from very slim initial conditions and create a whole universe. Hence, there would be no material cost to copying existing nodes to create new nodes, but there is a time cost. Similarly, there would be time costs to processing information within a node, transferring information between nodes, or creating new links between existing nodes. I would conjecture: (a) The time cost of processing information within a node, is less than (b) the time cost of transferring information between nodes, is less than (c) the time cost of creating new links between existing nodes, is less than (d) the time cost of creating new nodes. Wolfram’s 2020 book ignores (a) and (b) and implicitly assumes the time cost of (c) and (d) are equal. Also, the 2020 book ignores the possibility that nodes might be in different states, or exhibit different behavior, depending on their own states or the states of their neighbors.

“When connections pop up between existing nodes that had no previous connection, how does a node ‘know’ how to form that new edge?” For a node (A) to form a link with non-connected node (B), I would suggest three requirements: There must already exist an indirect link via other node(s) (C or Cs). There must be a movable link that proceeds from node A to node B via nodes C or Cs. All the in-between nodes C or Cs must cooperate in passing the link onto B and B must accept the proffered link. Naturally, the time cost for linking up to a distant node will be larger than for a nearby node.

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