” Here x, y and z stand for any elements. (The elements they stand for need not be distinct; for example, x and y could both stand for the element 1.”
As I read this, x and y would both be true of element 1 defined as such. If so, is this to suggest that, at any given time of defining, operating on or ”considering” element 1, it is to be known as of both x and y?
I ask this because I find a potential problem with this in the case any of x,y is actually the element of ”time” as such. Assuming 1 is a node of x= time and y=space, and with function of complete transformation, then I image x is taken for the given y.
If so, the 1 node is of two elements that are (a) mutually exclusive and (b) equally true at once.
(a) because when x is true, y is not and vice versa.
(b) because the unitary transformation is completed within exactly 1 instance of (scalar) time as such.
Conceptually, the paradox being that when 1=y, its identity is effected by retro-causation. That can lead us to assume ”time” is what caused ”space”, which is a misconception as far as I can see.
As I am just trying to grasp the abstract properties of nodes/cells and relating them to concrete physics, I search through the material here to see if the above scenario is adressed, by can’t find anything related. Can someone help me with a reference?
Please let me know if my Q is too vague or doesn’t make sense, and I will try to clarify.
Perhaps a solitary node has no physical meaning on its own. Instead, physical structures (physical phenomena, including space) arise from the relationships between multiple nodes (or even a single node relating/linking to itself).
A solitary node with no links seems to be pure abstraction. Likewise, the "situation" with no nodes or links (vertices or edges) would also be pure abstraction, lacking even time and space.
Metaphysically minded people might say the situation with no links nor nodes is the "formless consciousness" of which physical phenomena are an emergent property (instead the usual assumption that consciousness evolves from physical phenomena). This approach has been nicely developed into a scientific model of physics in the work of Steven Kaufman -- see his book "Unified Reality Theory" (his free article PDFs are also available on the interwebs) . In Kaufman's model, all phenomena result from featureless abstract "absolute reality" dynamically forming relationships (links) to itself, interactively on all scales. Using cellular automata as the basis of the model, he argues that EMR and gravity naturally arise in the model. Kaufman's model may have overlap with Wolfram's model, in that both models are based on CA/networks, both posit structure and space to arise from linking between abstract nodes, both see time as network updates, and both seem to give insight into physics.
Thanks for input.
May I challange the notion of ”meaning” in physics? I find it very problematic if assumed fundamental to a physical body. On the other hand, the notion of ”structured” as opposed to ”unstructured” is somewhat to my point.
I put a lot of effort into avoiding variables in my toy-element, and to keep it as binary as possible. It is the fluctuation or switch of identity that intrigues me. What are the polarized values of, from a physical standpoint, and what cause the switch?
My current image is of time/space and self-circulation. It is all very simplistic and trivial to be honest. My guess is that variables emerge from interaction among the binary discretes, and that this is made possible, or rather inevitable, by division and multiplication of a discrete intra-action.
I suspect this from accepting the theoretical relevance of a ”dimensionless scalar”.
But I approach this auto-verse from a Zen perspective where ”Formless” and ”Form” are of one and the same while also being radically different. I assume nothing but everything as an undefined ”Something”. Esotherical as it may seem, I find it a good ground for growing complexity, and indeed relevant for the image of the most extreme in terms of elementary ”being as such”. I do not expect it to mean anything at that level/node, but I find that ”meaning” is an aspect/pattern of its evolution as self-referring.
I am just contemplating a purely technical point of Wolframs model. The point of ”action” as essential of the ”elementary actor”. It is just a complementary idea to a very beautiful model. Or so it seems from my subjective perspective anyway.
Niklas, your explanation make sense to me, although what you point at is something (or more appropriately a "no-thing") that precedes "meaning", and thus can never really be captured in concepts, no matter how subtle. The "state" prior to the presence of the first node on the hypergraph has no properties (other than the lack of nodes), and is as abstract as one can get. A system's properties, polarities, characteristics, structures, history can only manifest as a patterns of nodes and their connections. I like to think as that formless "empty" state as being synonymous with the universal impersonal consciousness within which (and as which) everything arises.
Regarding the fundamental or original "polarization" event/process that you call the "switch", the "big bang" that got everything going, this reminds me of the number 1 ultimate question: why does anything else exist a at all? I hear that ontological mathematics has something to say about this, and I'm looking into it.
The explanation is extremely simple:
"Assuming 1 is a node of x= time and y=space"
is not correct in the Wolfram Model, since the vertices of the spatial hypergraph are atoms of space. The atoms of time are the steps in the computation. The atoms of spacetime (events) are the vertices of the causal graph, which is not the same as the spatial hypergraph. The rule is applied to the spatial hypergraph, not to the causal graph. I recommend reading Causal Graph.