There’s actually an almost infinite diversity of different ways to describe and experience our universe, or in effect an almost infinite diversity of different “planes of existence” for entities in the universe—corresponding to different possible reference frames in rulial space, all ultimately connected by universal computation and rule-space relativity. This is so flawless, beautiful and ‘intuitively trustworthy’, I feel like scientists will learn how to use that theory not just to explain, but to find new discoveries, in my lifetime. For our original hypergraphs, we imagined that we’d get something like ordinary physical space (say close to three-dimensional Euclidean space). (And, yes, this would mean that for an intelligence to “quantum grok” our galaxy would take maybe six months.). We’re dividing the causal graph into leaves or slices. One of the great achievements of the mathematical sciences, starting about three centuries ago, has been delivering equations and formulas that basically tell you how a system will behave without you having to trace each step in what the system does. Bob Yirka, Phys.org And let’s try to make this the time in human history when we finally figure out how this universe of ours works! Normally in physics, Einstein’s equations are what you start from (or sometimes they arise as a consistency condition for a theory): here they’re what comes out as an emergent feature of the model. In a sense computational irreducibility implies that there will always be surprises, and that’s certainly what I constantly find in practice, not least in this project. My guess is that the precise list of what particles exist will be something that’s specific to a particular underlying rule. One reason is that in Einstein’s general relativity they’re the paths that light (or objects in “free fall”) follows in space. (And, for example, this irreducibility is what I believe is responsible for the “encrypting” of initial conditions that is associated with the law of entropy increase, and the thermodynamic arrow of time.) But imagine making a multiway graph of absolutely everything that can happen—including all events for all possible rules. 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. in the same slice of the foliation), as in this picture: OK, now let’s connect this to physics. And each node is joined by arrows to the state or states that one gets by applying a single update to it. After all, if we look at one of our causal graphs, a lot of the causal edges are really just going into “maintaining the structure of space”. It’s just that—with some particular mode of description that we choose to use—there will be some definite rule that describes our universe. But what was most important about it to me was that it was so elegant and minimal. So, OK, what might we see in the universe today that would reflect what happened extremely early in its history? Think about expanding out an algebraic expression, like (x + (1 + x)2)(x + 2)2. [12][15] Physicist Sean Carroll commented that "it would be more effective to write short papers addressing specific problems with this kind of approach rather than proclaiming a breakthrough without much vetting. One feature of our models is that there should be a “quantum of mass”—a discrete amount that all masses, for example of particles, are multiples of. And in fact we’ve already got some good hints of bizarre new things that might be out there to look for. So, for example, if we look at the picture of our string-sorting system above, we can see relativistic time dilation. And while this is what makes them easy to recognize, it also means that they’re not actually much like our universe, where there’s in a sense much more going on. And what it corresponds to physically is what’s normally called a light cone (or “forward light cone”). It’s an amazing unification that I have to say I didn’t see coming; it’s something that just emerged as an inevitable consequence of our simple models of applying rules to collections of relations, or hypergraphs. It isn’t surprising that after thousands of years, we still haven’t perfected the seer’s skill set. And it’s because branchial space is wild—and effectively very curved—that you get the uncertainty principle. If you’d asked me even a couple of months ago when we’d get anything experimentally testable from our models I would have said it was far away. You just need to toy with it and your imagination long enough! As time progresses we are in effect seeing the results of more and more steps in a computation. And—much like in the spatial hypergraph case—an excess of these causal edges will have the effect of producing what amounts to curvature in branchial space (or, more strictly, in branchtime—the analog of spacetime). As everything can be defined with a few simple rules, would It mean that all Knowledge, Past AND Future can be defined, for instance teleportation? And actually it’s based on the exact same phenomenon—causal invariance—that gives us relativity. But for now, we don’t have these. And for this to be the case we actually have to freeze time for that qubit. The form of the whole multiway system is completely determined by the rules. Very interesting! Could it in fact be that underneath all of this richness and complexity we see in physics there are just simple rules? It’s computation, but it’s computation sampled in a different way than we’ve been used to doing it. I soon realized that if that was going to be the case, we’d in effect have to go underneath space and time and basically everything we know. (Image credit: Wolfram Physics Project) Physicist Stephen Wolfram thinks he's figured out a framework that … And it’s certainly satisfying to see that the basic structure of the models we’re using can be expressed very cleanly and succinctly in the Wolfram Language. In many ways it’s the ultimate question in natural science: How does our universe work? (And, yes, this part of what we’re doing is basically following what Einstein did when he originally proposed special relativity.). (Somehow it’d be like the ultimate calculus epsilon-delta proof: you challenge the universe with an epsilon, and before you can get the result, the universe has made a smaller delta.). I think this is extremely unlikely, but it’d certainly be an amazing thing if the universe were “self-documenting” that way. That’s actually happened for nearly a century in the case of deriving fluid equations from molecular dynamics. But let me make at least a few comments here. The model doesn’t tell us. Perhaps that’s implied, or you have made it explicit elsewhere, or it’s just the wrong way to think about this. And I don’t know how hard that’s going to be. But remember, the pictures we’re drawing are just visualizations; the underlying structure is a bunch of discrete relations defining a hypergraph—with no information about coordinates, or geometry, or even topology. And one way to characterize them is by their local curvature. I expected that we’d start exploring simple rules and gradually, if we were lucky, we’d get hints here or there about connections to physics. It looks it’s “trying to make” something 3D. Amazing stuff. Still, the “core feature” of the particles will presumably define things like their charge, quantum numbers, and perhaps spin—and the fact that these things are observed to occur in discrete units may reflect the fact that it’s a small piece of hypergraph that’s involved in defining them. The presence of energy effectively causes curvature in branchial space which causes the paths of geodesics through branchial space to turn. Haven’t we got physics licked? “But how will you ever get quantum mechanics?”, physicists would always ask me when I would describe earlier versions of my models. When he introduced “rulial space” that issue went away and I was sold. When the causal graph gets complicated, the whole setup with light cones gets complicated, as we’ll discuss for example in connection with black holes later. And already there are people in … Now evaluate f[10]. Distances have to be large compared to individual hypergraph connections, but small compared to the whole size of the hypergraph, etc. And in a sense what has made this project feasible now is that we’ve come so far in developing ways to express computational ideas—and that through the Wolfram Language in particular those forms of expression have become familiar, at the very least to me. And that in some other universe, with some other rule, the entities that exist there would set up their ways of describing things so that the rule for their universe is simple to them, even though it might be very complex to us? Again, there’s some math involved. I was personally struggling with “rules” as the fundamental way the universe works. I always wanted to mount a big project to take my ideas further. So as toy model let’s look at our BA→AB rule for strings. But now think about our hypergraph. Yes, it’s structurally discrete, but the scale of discreteness relative to our scale is always getting smaller and smaller. OK, so how does it all work? He is the brains behind Wolfram Alpha, a website that tries to answer questions by using algorithms to sift through a massive database of information.He is also responsible for Mathematica, a computer system used by scientists the world over.. Last week, Wolfram launched a new venture: the Wolfram Physics … So it looks like this great discovery won’t solve our day-to-day problems, but so be it. But here what’s important about it is that it’s what’s going to make our universe, and everything in it. in your approach what the graphs themselves comprising of, what is the entity actually changing and why! Note: From 1987 to 2020, Stephen Wolfram’s intellectual efforts have not primarily been reported in academic articles. But every new mathematical model pose new issues associated with itself, e.g. But as we’ve gotten further in investigating our models something amazing has happened: we’ve found that not just one, but many of the popular theoretical frameworks that have been pursued in physics in the past few decades are actually directly relevant to our models. Or, put another way, even though in the full multiway graph there’s all sorts of other “quantum mechanical” evolution of states going on, the observer has set up their quantum observation frame so that they pick out just a particular, definite, classical-like outcome. And if this happens fast enough, we’d never be able to “see the discreteness”—because every time we tried to measure it, the universe would effectively have subdivided before we got the result. And here there’s an interesting possibility that’s relevant for understanding cosmology. 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). But causal invariance has other consequences too. Categories of articles by Stephen Wolfram. Another member of our team (Jonathan Gorard) has written two 60-page technical papers. But for now let’s just recall that particles (like electrons) in our models basically correspond to locally stable structures in the hypergraph. We plan to have a centralized effort that will push forward with the project using essentially the same R&D methods that we’ve developed at Wolfram Research over the past three decades, and that have successfully brought us so much technology—not to mention what exists of this project so far. There are some other strange possibilities too. And see if we can finally deliver the answer to how our universe fundamentally works. But we plan to do everything in a completely open way. I never really thought of it as something that one could identify abstractly in the very structure of the universe. I’ve mentioned several times that the formation of an event horizon around a black hole is associated with disconnection in the causal graph. I’m not sure what its value is, but a possible estimate is that it corresponds to entangling about 10102 new quantum states per second. I’m posting all my working materials going back to the 1990s, and we’re releasing all our software tools. Enter Stephen Wolfram. Underneath, it’s a bunch of discrete, abstract relations between abstract points. But the big recent surprise for me is that we seem to be lucking out. It has to be a language that can express computational ideas. Thanks to my classmate who showed me this. Imagine what happens if we change our foliation, say tipping it to correspond to motion at some velocity, as we did in the previous section. ... How We Got Here: The Backstory of the Wolfram Physics Project April 14, 2020. So each “step” that we showed before actually consists of several individual “updating events” (where here newly added connections are highlighted, and ones that are about to be removed are dashed): But now, here is the crucial point: this is not the only sequence of updating events consistent with the rule. events), either in time (i.e. It was in some ways simple and obvious, if very abstract. We just apply a simple rule to them, over and over again. Here’s roughly how this works. But then—as the rule gets applied—it progressively expands. In other words, to successfully make a qubit, you effectively have to isolate it in quantum space like things get isolated in physical space by the presence of the event horizon of a black hole. Stephen Wolfram is a British-American computer scientist, physicist, and businessman. But what kinds of reference frames might observers set up in rulial space? 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. We didn’t put in anything about this shape. Yes, the underlying structure of our models is different. So what does all this mean for our original goal—of finding a rule to describe our universe? In standard current physics, there’s space—described mathematically as a manifold—and serving as a kind of backdrop, and then there’s everything that’s in space, all the matter and particles and planets and so on. But let’s imagine that we’ve drawn a circle on the surface of a sphere, and now we’re measuring the area on the sphere that’s inside the circle: This area is no longer πr2. It’s unexpected, surprising—and for me incredibly exciting. Then for each of the results of these, there are four additional possibilities. We think we’re “going forward in time”. Stephen Wolfram is a computer scientist, mathematician, and theoretical physicist who is the founder and CEO of Wolfram Research, a company behind But now there’s a crucial question. Try using sophisticated methods from mathematics; they will almost always fail. Of course, perhaps not surprisingly, it’s still technically difficult. In the end our goal must be to build a bridge that connects our models to existing knowledge about physics. And typically it won’t even be finite-dimensional. A book, A Project to Find the Fundamental Theory of Physics, was published about the project in June 20… But the very fact that we’ve been able to find definite scientific laws—and that systematic physics has even been possible—suggests that the rule at least doesn’t have that level of complexity. It’s a strange but rather appealing picture. Stephen Wolfram, a controversial physicist and computer scientist, has united relativity, quantum mechanics and computational complexity in a single theory of everything. This is very interesting. Is it trivalent graphs? In physical space we talk about light cones as being the regions that can be causally affected by some event at a particular location in space. The basic structure of our models seems alien and bizarrely different from almost everything that’s been done in physics for at least the past century or so. [10][13], While Stephen Wolfram claims the project has been a success with scientists and others engaging with the project through the livestreamed content,[14] other prominent physicists have leveled criticism at the project. I’m exhilarated that I can understand any of it! At least relative to the particles we currently know, such particles would have few hypergraph elements in them—so I’m referring to them as “oligons” (after the Greek word ὀλιγος for “few”). Well, something similar happens if you pass the entanglement horizon—except now you’ll get elongated in branchial space rather than physical space. But what does moving in rulial space correspond to? {{x, x, y}, {z, u, x}} → {{u, u, z}, {v, u, v}, {v, y, x}}. So this gives us a way to measure the effective dimension of our hypergraphs. There’s something else I didn’t expect, but that’s very important. [11], The Wolfram Physics Project is being presented to the public as an open project, where all the technical documentation as well as software tools and live recordings of working sessions on the project are freely accessible to the public. Here’s one more example. This rule says that any time there’s a B followed by an A in a string, swap these characters around. But what should the description language for the rule itself be? In our models what this means is that the “mind of the observer”, just like everything else in the universe, has to get updated through a series of updating events. The rule just says to find two adjacent connections, and if there are several possible choices, it says nothing about which one. We’ve built a paradigm and a framework (and, yes, we’ve built lots of good, practical, computational tools too). 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. So they’ll construct their own version, where the slices are horizontal: But now there’s a purely geometrical fact: to make this rearrangement, while preserving the basic structure (and here, angles) of the causal graph, each moment of time has to sample fewer events in the causal graph, by a factor of where β is the angle that represents the velocity of the observer. And here there’s potentially a fundamental problem: the phenomenon of computational irreducibility. This is again somewhat complicated. So how does an observer deal with that? But the basic point is that both theories are consequences of causal invariance—just applied in different situations. And a pretty natural thing for observers like us to do is just to say “one set of things happens all across the universe, then another, and so on”. 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