Of course, 2.7 is not 3, and presumably this particular rule isn’t the one for our particular universe (though it’s not clear what effective dimension it’d have if we ran it 10100 steps). So, for example, if we look at the picture of our string-sorting system above, we can see relativistic time dilation. Until, suddenly, in the fall of 2018, I had a little idea. Our Mission and the Opportunity of Artifacts from the Future, Faster than Light in Our Model of Physics: Some Preliminary Thoughts, Launching Version 12.2 of Wolfram Language & Mathematica: 228 New Functions and Much More…, Where Did Combinators Come From? So can our rules reproduce that? In our models, space is defined by the large-scale structure of the hypergraph that represents our collection of abstract relations. In typical cosmology, it’s been quite mysterious how different parts of the early universe managed to “communicate” with each other, for example, to smooth out perturbations. Of course if you’re thinking about modeling the whole universe and everything in it, this isn’t ultimately a reasonable way to think about things. But let’s just imagine all the possibilities. through timelike hypersurfaces). May it be only the beginning! Or could it be that this is a kind of question that’s just outside the realm of science? It’d be as if the speed of light is infinite. And each node is joined by arrows to the state or states that one gets by applying a single update to it. Slice one way and you’ll see relationships in physical space; slice another way and you’ll see relationships in branchial space, between quantum states. And in the context of our models they’re just different facets of the same idea. There’s more to say about the structure of rulial space. And it turns out that we can think of them as being laid out in an abstract kind of space that we’re calling “branchial space”. And while we think our universe is three-dimensional, it’s quite possible according to our models that there are at least local deviations—and most likely there were actually large deviations in the early universe. Love from Germany. I tried to start around 2004. But branchial space is something more abstract—and much wilder. In the end, if we’re going to have a complete fundamental theory of physics, we’re going to have to find the specific rule for our universe. But now we actually have a structural reason for this to be the case. Stephen Wolfram publicly kicks off an ambitious new project to find the Fundamental Theory of Physics. But one example of an extreme situation where they can mix is black holes. And a crucial idea in our model is in a sense just to do all of them. Or, said another way, what events must have happened in order to create the input that’s needed for some other event? Could it for example be that the rule is only simple because of the way that we, as entities existing in our particular universe, choose to set up our ways of describing things? Measurement in quantum mechanics has always involved a slightly uncomfortable mathematical idealization—and this now gives us a sense of what’s really going on. One way to get out of this is to introduce a so-called cosmological term, that’s just an extra term in the Einstein equations, and then posit that this term is sized so as to exactly cancel (yes, to perhaps one part in 1060 or more) the energy density from virtual particles. Well, for our models of the universe this is potentially a big problem. And at least in some approximation we can then say that energy is associated with activity in the hypergraph that propagates information through time, while momentum is associated with activity that propagates information in space. In what we’ve discussed so far we’re imagining that there’s a particular, single rule for our universe, that gets applied over and over again, effectively in all possible ways. There’s something else I didn’t expect, but that’s very important. I love the explanation of the uncertainty principal using geodesic routes through ‘branchial space’ Very intuitive ideas with lots of traction it feels. It’s always a test for scientific models to compare how much you put in with how much you get out. Everything could be represented as 1 or infinity nothing could be represented by 0 or 1 because it is something or infinity. So as toy model let’s look at our BA→AB rule for strings. In special relativity, the key idea is that the “laws of physics” work the same in all inertial reference frames. Things rapidly get complicated. Is casual invariance just associativity? And maybe the limit from which it appears is not a clearly defined one …. But the main thing is to think about the limit when we’re looking at a very large causal graph. (It isn’t terribly surprising that a fundamental theory of physics—inevitably built on very abstract ideas—is somewhat complicated to explain, but so it goes. While we view our universe—and reality—through our particular type of description language, there are endless other possible description languages which can lead to descriptions of reality that will seem coherent (and even in some appropriate definition “meaningful”) within themselves, but which will seem to us to correspond to utterly incoherent and meaningless aspects of our universe. Looking at your graphs also reminds me of neural networks and your work may also be able to address the enigma of the ‘unreasonable effectiveness of mathematics’ and why our very parochial brains, evolved on the savannahs of Africa, can discover mathematics and contemplate the Universe. 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