I'm trying to grasp the essence of what the Wolfram Physics Project is saying about the universe.
In Jonathan's paper, "Some Relativistic and Gravitational Properties of the Wolfram Model" he states in paragraph 2.1, "The essential idea here is to model space as a large collection of discrete points..."
To help me grasp this I need to compare it to my understanding of what other theories say are fundamental about the universe:
Quantum Field theory says that "fields" are fundamental to the universe and particles are "excited states" of those fields. These fields permeate all of "space" (for whatever that is and for how ever many "dimensions" it has).
String theory says that what we originally thought of as "point-like particles" are actually one-dimensional strings that propagate through "space" (for whatever that is and for how ever many "dimensions" it has). How these strings vibrate is what determines their properties and how they interact with other strings.
M-Theory extends the one-dimensional strings to include larger dimensional objects.
So, what I take away from Jonathan's statement about how to model space is: "Space" "is" a collection of points. These points are fundamental. I'll call them "Space Points" (that's a terrible term). Space Points aren't in space. They are space. If Space Points are in anything, it's not space; it would be something else entirely different. There is some underlying rule which governs how Space Points interact with each other. On scales larger than the scale of the interactions between space points emerge behaviors that look like dimensions, times, distances, speeds, fields, forces, particles, probabilities... everything.
Is this what the Wolfram Physics project is trying to say?
First, a little (personal) note on the value of the Physics Project. Science is a way to approach reality, it’s a well-defined method. It consists of theory, predictions, falsifiable experiments and observations. The reduction to ‘theory’ is what also happened to supersymmetry. It’s not because you believe in something that it automatically predicts, explains or unifies the universe. Strictly speaking, the Wolfram Physics project isn’t science and is merely a collection of ideas (with a lot of marketing). Also, by bypassing the peer-review system you automatically put yourself outside the scientific community. Through this I am not saying that the Physics project is not interesting, but let’s not confuse science with an interesting idea. The history of physics (and science as a whole) is full of smart but false (ie. experimentally unproven) ideas.
Regarding your (many) questions. I think you should not take the concept of 'point' too literal and too geometric. For example, in topology open sets consist of 'points' but it's just a name for something. In non-commutative geometric points are inferred from the algebra (of functions). Functions, just like points, are a name for an abstract entity and should also not be taken too literally. In string theory, string leads to some sort of unification but it does not mean that our universe is full of little vibrating strings. In loop quantum gravity you also have a spin network but there as well; the model produces (via deep mathematics) in the end things we can use to make predictions but it does not mean that you literally and geometrically have on the Planck scale a spin foam.
The idea that graphs can lead to fundamental physics is not new. Discrete differential structures, gauge theory and quantum gravity can be defined on graphs (without the Wolfram language). There are many exotic variations on this (topological dynamics, phase transitions on graphs leading to smooth manifolds etc.). Again, it does not mean that on a Planck scale you have points and edges flying around but that as a mathematical model you can reproduce (part of) reality and make predictions. If the predictions clash with reality your model is non-sense. If your model cannot make predictions, it's not physics.
So, I don't think you should see fields, points, manifolds, graphs as something that at the lowest level exist, but abstract entities. Same for many other concepts in physics and mathematics. Wolfram's view of fundamental physics is (presumably) an abstract model of reality, not reality itself.
your comments contain several misstatements that indicate a lack of understanding of the way science works.
(1) " Strictly speaking, the Wolfram Physics project isn’t science." This is wrong. The project does employ a different (but by no means unique) way of doing science (one might call it 'group science' or 'collaborative science' or some such terminology), but it is most definitely science. It is not necessary that any one publication to contain theory, predictions, falsifiable experiments and observations. In factThere is no one universally accepted definition of what science is but Scotus Justice Potter Stewart view on pornography "I know it when I see [read] it" works fine.
(2) "by bypassing the peer-review system you automatically put yourself outside the scientific community.". this is, and has been for some time, not true. The use of arXiv does bypass peer-review but it is a well-accepted means of scientific publication (it is not simply aa format for pre-publication). it was designed specifically to allow material to become available to the scientific community without undue (and often unhelpful) delay that peer review entails (you might look at Einstein's comment on peer review (see https://theconversation.com/hate-the-peer-review-process-einstein-did-too-27405). In fact, peer review (more specifically, anonymous review) is more commonly used to censure, rather than improve, scientific publications (and the reviewers are more commonly not one's colleagues, but ones competitors). In the modern era of 'social media' there is absolutely no reason to hold up or prevent publication (at meetings of the APS, presentations are not reviewed or chosen. all are accepted) of anything (other than the laws of libel, slander and defamation).
Well arXiv is full of pseudo-science as far as I am concerned and is not in any way a good argument. Unless you believe that the multiverse hypothesis makes any predictions or is a proven fact. Unless you have seen LHC evidence for super-symmetry and the landscape. Publishing ideas do not turn them into a scientific framework.
Again, ideas and theoretical constructs are not facts unless proven by evidence. If a set of ideas do not make any testable predictions it falls in the category of 'not even wrong'. A lot of fun, but not science.
I don't mean to be rude or pedantic about all this, you know. Just that there is a lot of fluff these days. Misinformation and too many claims starting with 'Science says...' or 'Scientists have discovered...'.
Feel free to believe in the anthropic principle, the holographic universe, graph-based quantum gravity. If a believe claims to be a scientific fact, that's where I feel obliged to make a note. In any case, this forum is not the place to discuss this I guess and I'm the last person who wishes a mud-fight.
The problem is not that arXiv is full of pseudo-science; it's that most of so-called foundational physics research (including cosmological history, interpretations of quantum mechanics, and quantum gravity) is pseudo-science. I think it's very unfortunate that Stephen refers to there being the 'fundamental' theory of physics.i don't believe there is 'a' (let alone 'the') fundamental theory of physics (read the theoretical pluralism view of Boltzmann - see the Sci. Am. blog by John Horgan https://blogs.scientificamerican.com/cross-check/pluralism-beyond-the-one-and-only-truth/) and even if it exists then as P.W. Anderson, a doyen of 'emergent physics' noted that "the ability to reduce everything to fundamental laws does not imply the ability to start from those laws and reconstruct the universe." Personally, I read physics articles based on the authors rather than on the subjects, taking the view that good people do good research.