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What Is Spacetime, Really?
- Artistry121 11y agoThis is a very well done piece. I love how many links and additional paths it leads to in thinking. It's a constant challenge for scientists to realize that nearly _everything_ we know is an approximation or only true in certain circumstances. It also takes an amazing amount of humility to work knowing that you may be proving yourself, your heroes and all many people have worked for wrong. Thank you Mr Wolfram for your thoughts.
- javajosh 11y agoAll of our theories are single-threaded in the sense that the reader begins at the beginning of the paper and reads it through to the end. Theoretical physics at this level has always seemed to me a kind of weird mirror of this fundamental constraint on the 1-D nature of theories themselves.
- hyperion2010 11y agoThat is not necessarily true. Just because you can serialize a set of ideas does not mean that they can be interpreted or understood in their serialized form alone. You almost always require a parser that has some structure which will convert the serialized ideas into something with significantly higher dimensionality where it can actually be understood and operated on. Just because I can write down a function (using only a single dimension) that operates on 10 dimensional data doesn't somehow imply that the data is suddenly one dimensional.
- javajosh 11y agoYour understanding of the non-serialized form is itself serialized, in the sense that something in your mind is stepping the simulation. You might not perceive it, but intellectually I'm sure you know that's what's happening (unless you subscribe to some non-physical description of the mind).
- hyperion2010 11y agoI would say that the physical processes that underlie our mental representations of concepts are fundamentally not serialized (part of why it is often so hard to put thoughts into words). They are non local in the sense that many different actors can operate on the data at the same time to create or modify some higher dimensional state and are not necessarily contingent on prior state in the way parsing is. You can't really parse a paper by reading every paragraph at the same time. Even if you could do it physically, some ordering would have to be applied to interpret subsequent parts based on statements in earlier parts. Representations in the brain have no such inherent limitation on ordering.
- javajosh 11y agoWhether or not the brain is "really" parallel, with a fast enough computer you can simulate parallelism. So our "understanding" is either one-dimensional, or isomorphic to a one-dimensional process.
- nitrogen 11y agoHow many variables are part of this simulation? Are those not dimensions?
- javajosh 11y agoYou can impose a one-dimensional ordering on a finite state of any size. Drawing a parabola, for instance, yields a 2-D figure. But the process that draws it (on a computer) is 1-D: Start at the origin Move right X Move up X*X Make a dot If X = Screen.Width Stop X=X+1 Repeat There you go: a 2-D thing from a discrete sequence of 1-D steps. I hope you can see that it generalizes to N-D things.
- hyperion2010 11y agoI think the question here, which has been raised in other parts of the comments here, is what the complexity of the operation to serialize/deserialize is and how one might think about translating between computational complexity and dimensionality.
- iandanforth 11y agoAt the risk of humor, this cartoon exactly summarizes my reaction to this post: http://www.smbc-comics.com/index.php?id=3805 http://www.smbc-comics.com/index.php?id=3805
- Xcelerate 11y agoI mean... I think deep down most (scientific) people think that's probably the fundamental truth. The challenge is in reifying the notion. Let there be math, and then the laws of physics fall out as trivial tautologies.
- amelius 11y agoWhat I wonder is: how does the fact that we live in a 3D (spatial) world come out of this model? Or is that also part of the a-priori model?
- openasocket 11y agoMaybe a physicist could help me out: the idea here of treating space as a simple discrete network, and particles just being emergent behavior sounds very interesting. But doesn't this violate Bell's Theorem, that no local hidden variables could completely explain quantum mechanics?
- oofabz 11y agoIANAP, but if the values of the cells are real-world values like charge, momentum, or higgs field strength, then I don't think they are hidden variables. They are the same variables described by the standard model, but calculated discretely instead of continuously.
- philipov 11y agoI am not a physicist, but Wolfram covers this. "Because there’s a theorem (Bell’s Theorem) that says that unless there’s instantaneous non-local propagation of information, no such “hidden variables” model can reproduce the quantum mechanical results that are observed experimentally." Wolfram's continues by saying he is allowing instantaneous non-local propogation because network nodes have no coordinates; coordinates (and dimensions themselves) arise as a result of how nodes are connected. "And even though the network may mostly correspond on a large scale to 3D space, it’s perfectly possible for there to be 'threads' that join what would otherwise be quite separated regions." He has changed the definition of locality.
- Totient 11y agoScott Aaronson argues that, based on what we know about quantum mechanics, Wolfram's "long-range thread" cannot reproduce special relativity and Bell inequality violations: www.scottaaronson.com/papers/nks.ps
- smaddox 11y agoIt seems to me that Aaronson's argument can be easily bypassed by adding non-local hidden variables in the form of a loosely connected network that essentially injects pseudo-randomness into the approximately flat Minkowski spacetime network. Note that Bell's inequality does not rule out non-local hidden variables as a viable explanation of quantum mechanics.
- redthrowaway 11y agoI found this incredibly hard to read, due to Wolfram's constant need to self-aggrandize. The entire tone of the piece is, "I discovered this, then I discovered that". In reality, most of his "revelations" were discussed by others long before he arrived on set.
- paulpauper 11y agoIt's written in the first person, and he's describing the findings. How else should he have written it?
- api 11y agoWolfram is known for this. He's clearly a bright fellow but he is not even close to being the only or the first person to work on stuff like cellular automata, computational theories of physics, or complexity. He did not invent everything he claims to have invented and while he does footnote he's definitely not drawing attention to any of the others in the area. It's tragic really. A New Kind of Science is full of brilliant ideas but the narcissism that drips from every page ruins it and probably prevents some of these ideas from getting the reception they deserve.
- codingbinary 11y agoThat is exactly the reason I stopped reading halfway through. I couldn't take any more of his narcissism.
- api 11y agoI heard once that the book originally lacked many footnotes and they were added later after an outcry from the scientific community. I don't know if that's true but I can believe it. Like I said the subject area is fascinating and merits a much warmer reception than this book got. Tragic.
- lobster_johnson 11y ago
- peatfreak 11y ago> I mostly just assumed Einstein’s whole mathematical setup of Special and General Relativity—and got on with my work in quantum field theory, cosmology, etc. on that basis. I like the way he nonchalantly throws that "etc" in there, as though to indicate that working in these areas is no big deal, really.
- zzalpha 11y agoErr... is Wolfram now taking credit for this idea, which began circulating back in 2009? http://www.nature.com/news/the-quantum-source-of-space-time-1.18797 http://www.nature.com/news/the-quantum-source-of-space-time-... Because I don't see his name in the citations...
- zardo 11y agoI don't think that's the same idea, but he's got a chapter on the network universe idea in his book that was publshed in 2002. Original credit for a discrete nature of the universe belongs to Democritus.
- zzalpha 11y agoI don't think that's the same idea Hmm, upon a second read I think you're right. One of the key distinguishing factors is the aforementioned Nature article actually cites hints of a real scientific theory based on established physics, while Wolfram's self-aggrandizing ramblings haven't actually led to any real discoveries... :)
- codeulike 11y agoIn the beginning was a graph, more like diamond than graphite. Every node in this graph was tetravalent: connected by four edges to four other nodes. By a count of edges, the shortest path from any node back to itself was a loop six edges long. Every node belonged to twenty-four such loops, as well as forty-eight loops eight edges long, and four hundred eighty that were ten edges long. The edges had no length or shape, the nodes no position; the graph consisted only of the fact that some nodes were connected to others. This pattern of connections, repeated endlessly, was all there was. Intro to Schild's Ladder by Greg Egan. He was obviously thinking along similar lines.
- wlievens 11y agoLoved that book. Despite the cardboard characters :-) Please tell me that last act made your think of Cellular Automata too!
- sanderjd 11y agoThank you, I had forgotten how much I loved that book. Time for a new Greg Egan kick!
- hodwik 11y agoThat's a pretty neat idea. Then you could have gravity caused by structure -- the closer the nodes are to each-other, and the more nodes in an area there are, the easier the nodes fall into a lattice/crystal -- making masses attract. And conversely space could just be a limit to information density. If that's roughly what Wolfram was saying, I'm sorry, I couldn't read his jerk-session.
- hodwik2 11y agoOr the lattice is infinite in all directions, and is "pulled" against. So even as local objects want to fall into lattice, the fact that the network is infinite "pulls" the "space" away from the lattice. So close together the lattice force works, but it is weak across long distances, in comparison to the pulling force of the rest of the lattice out towards infinity. I really have no idea what I'm talking about.
- amelius 11y agoSame topic, different approach: [1] [1] https://www.youtube.com/watch?v=W2XdhzCORbo https://www.youtube.com/watch?v=W2XdhzCORbo
- amoruso 11y agoIf you want a second opinion, Cosma Shalizi reviews A New Kind of Science by Stephen Wolfram: http://bactra.org/reviews/wolfram/ http://bactra.org/reviews/wolfram/
- hughw 11y agoSerendipity. This morning, in another context, I learned for the first time about E.T. Jaynes' work and downloaded a copy of his unfinished tome. And now, this afternoon, in Shalizi's review, I again see it honorably mentioned. Thanks for this link.
- username223 11y agoSubtitle: "A Rare Blend of Monster Raving Egomania and Utter Batshit Insanity." This is a classic that everyone should read, utterly destroying a shameless self-promoter gifted with some intelligence and a grasp of jargon.
- MrQuincle 11y agoNot so kind, but I loved to read that!! Thanks! I'll definitely buy http://www.amazon.com/The-End-Science-Knowledge-Scientific/dp/0465065929 http://www.amazon.com/The-End-Science-Knowledge-Scientific/d... as well, the books he recommends w.r.t. Prigogine.
- joekim 11y agoThanks for the link. I found the article to be very informative. Can't say the same thing about the original Wolfram article.
- fanchao 11y agoThis more of a personal attack than a thoughtful review. No content.
- 4ad 11y ago> OK, so one can derive Special Relativity from simple models based on networks. What about General Relativity—which, after all, is what we’re celebrating today? Here the news is very good too: subject to various assumptions, I managed in the late 1990s to derive Einstein’s Equations from the dynamics of networks. What a crackpot. He links to his own book, which is a non-mathematical, non-technical book. There is no mathematics in the linked material, so it's impossible to see whether he is correct, in fact it's impossible to see what he means at all! Nobody has seen this mythical derivation he did in the 90s. Amazing how someone brilliant who used to do real science fell into crackpottery like this.
- tux1968 11y agoThings like this always leave me feeling stupid. How is one supposed to wrap their mind around the idea of space emerging from an underlying "network"? What exactly is being networked; what is the "stuff" of the network? He describes the network in terms of connections, which in my mind requires a topology, or space within which to exist; yet space does not apparently exist at this level. If there is no space, then what separates the nodes in the network? If no space separates the nodes, what defines the distinct connections between them? Yes, i'm completely lost.
- codeulike 11y agoWhat is matter made of? The answer, whatever it is, cannot be matter. From what fundamental thing does 'space' arise? The answer, whatever it is, cannot be anything that would exist in a 'space' as such. And so we creep towards the idea that at a low enough level, everything is just information.
- tux1968 11y agoMy confusion arises from his model of space emerging from something than in and of itself requires space to exist. It just seems circular. And i don't see how the term "information" has much descriptive power when discussing nature at its most fundamental level. That may be a way to model it, or describe the physics of it, but that's just an abstraction of whatever that fundamental building block is.
- philipov 11y agoIt seems to me that the fundamental thing that Wolfram is saying is that reality is non-local. Locality itself is an emergent phenomenon. This is his clever way of getting around Bell's Theorem. His networks don't require space to exist, they are space. When we think of spacetime, we think of a manifold, and he's saying that what looks like a manifold at a macro level is really just a discrete network at a micro level, and this sort of data structure is more suitable for explaining non-local phenomena, because locality is an effect, not a property, of the model. But for that to work, he has to derive all the current laws from his new model, and he is far from doing that, even though it is a quite fantastic thought experiment. I think the confusion comes from the fact that at a fundamental level, we do not have the capability to know anything but models and abstractions derived from sense data, and no one is claiming their theories are more than models.
- maurits 11y agoIt is a tragedy really, his ideas always seem to get lost in senseless narcissism.
- copperx 11y agoDijkstra's ideas (not just his contributions to math) survived despite his arrogance. The difference is that Wolfram's ideas are not testable.
- AnimalMuppet 11y agoDijkstra's ideas survive, but are (mostly) not used...
- maaku 11y agoI just coded an algorithm due to Dijkstra yesterday. His influence is very much alive...
- GFK_of_xmaspast 11y agoThere's a whole lot of structured programming going on these days.
- jerf 11y agoIndeed! I've got a blog post on deck that likens it to a fish in water; we all use it so thoroughly nowadays we don't even notice it because an unstructured programming language is almost inconceivable to us.
- AnimalMuppet 11y agoAh, yes, I had forgotten structured programming. Yes, it won and goto lost, and the world is better for it. What I was referring to, though, was what I think was Dijkstra's main idea: That programming should be done by a particular approach (the "postulational method") that allows/requires mathematical reasoning about code, and that code should be mathematically proven to be correct. That idea is used very little.
- peter303 11y agoIf he finds a network that is consistent with what we have observed so far, then predicts something new, and we find it, then it will be significant.
- j2kun 11y agoIf the answer is "there is such a program that reproduces the universe," then I have already found one such program that does it. Here it is: interleave the simulation of individual steps of every Turing machine in lexicographic order. That is, if the Turing machines are enumerated T_1, T_2, T_3, ... you do the following: i = 1 while True: j = 1 while j <= i: simulate step j of Turing machine T_i j += 1 i += 1 If there is some program, it will be in the list. This is the pitfall you get into when you only care about finding extremely short programs and don't think about efficiency. Similar pitfalls are in the philosophy of artificial intelligence. You get no useful information or theory or model if you ignore computational complexity.
- Pharaoh2 11y agoDoes this set of all turing machines contain the given turing machine? If yes, then it would seem that you can never simulate even a single iteration of the inner loop. If no, then you are not actually simulating all the programs are you? This goes a little beyond NP hard complexity, I believe.
- j2kun 11y agoThis set of Turing machines is the set of all Turing machines. But you misunderstand, I am only simulating a single step (constant time) of a finite number of Turing machines in any given iteration of the inner loop. It goes arbitrarily far beyond NP hard complexity, which is my point. Wolfram ignores complexity entirely, and that means this algorithm is fair game.
- Pharaoh2 11y ago1. Why are the number of turing machines finite. 2. But to simulate a single step of the turing machine, you will have to simulate this turing machine too, so what you will end up doing is recursively simulating the first step of this machine to infinity. 3. Why do you assume all the programs in the world are turing computable.
- chengiz 11y agoIf all you have is cellular automata, everything starts looking like a network.
- iofj 11y agoSame can be said about string theory. In fact, there's an (in)famous book about exactly that statement : http://www.amazon.com/Not-Even-Wrong-Failure-Physical-ebook/dp/B00JLMMEQQ http://www.amazon.com/Not-Even-Wrong-Failure-Physical-ebook/... (Word of warning: do not indicate to your promotor that you're interested in this book's subject, or even have read it, unless you're damn sure where he stands on the subject, unless you want get a very effective demonstration that physics might be value-free, professors definitely aren't)
- yk 11y agoI think Stephen Wolfram fell in the trap, that any continuous dynamical system can be approximated by a discrete one. His position is a bit like claiming the fundamental theory of the universe is Brainfuck. Proof: I can encode general relativity and quantum field theory in Brainfuck, at least to a arbitrary good approximation. The initial conditions are then just the program to simulate GR and QFT plus the initial conditions in more conventional physics. Thus the fundamental theory of the universe is Brainfuck. ( At least if Turing machines are the most powerful model of computation that can be implemented in our universe.)
- hcarvalhoalves 11y agoWhy would it be a "trap"? The uncertainty principle hints that something discrete may lie at the bottom. It's clear it's deliberate, not something you fall into due to naiveness. Also, Wolfram isn't the only one in this line of thinking, and this is a topic that rears it's head time and time again in the history of physics.
- yk 11y agoIt is a trap in the sense, that nothing he discusses is convincing me that it is any more than a simple application of a general theorem. ( See my example above, obviously we learn nothing about physics, we just shift the missing information from 'theory' to 'initial conditions.') So assuming a discreet space may be fruitful, but by itself is not a step forward.
- euyyn 11y ago> The uncertainty principle hints that something discrete may lie at the bottom. Not necessarily. The uncertainty principle is a direct consequence of some quantities being "the Fourier transform" of each other. You can't play a pure tone unless it extends infinitely in time, and vice versa: You can't play an infinitesimally short sound unless you ring all frequencies. That's all. And actually, if something discrete lies at the bottom of spacetime, the uncertainty principle implies that there's a maximum energy and a maximum momentum. For the same reason that there's a Nyquist frequency when sampling. So, if anything, our intuition that there aren't such maxima makes the uncertainty principle hint that there's nothing discrete underneath.
- justifier 11y agoI’ve come to suspect it may actually have led us on a century-long detour in understanding the true nature of space and time come to suspect? knowing theories are incomplete is science, seek questions stead answers detour? hardly, science is directed by utility and the systems inherent in the theoretical coupling that formed relativity have shown to be extremely useful and any inevitable addendum, appendage, or usurper will need to prove itself more useful we need to ask the questions that will reveal those use cases untouched by the contemporary thought now we have to wonder how long it will be before we actually know the final theory i see, and foresee, an existence where every new finality conjures new questions
- justifier 11y agoi wish i knew what was so unsettling about the above opinion i'm interested in discussion
- Pyxl101 11y agoI haven't voted on your comment, but here's what stands out to me: (1) It's not written in good style. People who care about how their ideas are received by others take the time to write properly, including capitalization and punctuation. (2) It reads like a middlebrow dismissal. It's critical but doesn't add much of substance on its own through the criticism. Wolfram certainly realizes that he hasn't proven his case, that current science is indeed incredibly useful, and that the current path will only be a "detour" if network- or automata-based models are proven correct in the end. That's why he says he "suspects" it "may" have led us to a detour. He certainly understands that the theory needs to be developed further. Put simply, Wolfram would probably agree with your overall sentiment, so the remarks are not insightful, but they're presented as if they'd likely be at odds with his position. (3) Beyond style, the diction is unclear, such as the choice of the word "use-case". It's unclear to me what you're referring to. It's unusual to refer to physics as "use-cases". If that's intended as an analogy, then for me it doesn't connect or succeed. (4) The ideas themselves are not clear. "... reveal those use-cases untouched by contemporary thought"; "an existence where every new finality conjures new questions". It's not clear what you're trying to convey with those phrases. You probably could say what you're trying to say in a simpler, more direct, and less critical way way. You might benefit from this advice: http://paulgraham.com/talk.html http://paulgraham.com/talk.html > Here's a simple trick for getting more people to read what you write: write in spoken language. Something comes over most people when they start writing. They write in a different language than they'd use if they were talking to a friend. The sentence structure and even the words are different. [...] But perhaps worst of all [mistakes], complex sentences and fancy words give you, the writer, the false impression that you're saying more than you actually are. If I was to try to rephrase what you've said in simple language, then I end up with something like: "The ideas need to work to be useful. We need to think up new ideas. I think we'll always have more questions to answer", which isn't that interesting. With the current phrasing it reads like a middlebrow dismissal.
- drdeca 11y agoI'm having trouble finding any other references to a notion of a dimension of a graph which is based on howthe number of vertices which can be reached through a path of a given length increases with the length. I'm finding things like, a dimension of a graph as the minimum dimension of euclidean space where the vertices can be placed and have each edge have length 1, and another thing which seems closer which is based on a metric from the graph, but that is based on the idea of a metric basis, which I don't think is equivalent (in it, a subgraph can have a higher dimension than the graph it is a subgraph of, which I don't think is the case in the version mentioned in this blog post. And one example I'm p sure has finite dimension in the blog post version, but infinite dimension in the other thing, so, I'm p sure they are different things). Does anyone have any non wolfram references for the notion of the dimension of a graph as is explained in the post linked?
- chr1 11y agoHis definition of the dimension is quite similar to the definition of the dimension of a fractal. His definition also works better than euclidean dimension, e.g. for a grid on cylinder euclidean dimension will be 3 and his definition will give 2. I think a modification of the definition above to allow minimum dimension of non-euclidean space will be same as Wolframs definition for the cases when dimension of the graph is not fractional number.
- hguant 11y agoIt's interesting to see that, while philosophy has been sitting in the post-Hume doldrums for the last hundred years, physics has gone all the way around and started tackling metaphysics again!
- memracom 11y agoLet's see, everything is just nodes and connections. Category theory says everything is just objects and morphisms. Brown's Laws of Form starts with "drawing a distinction". Could this last be the starting point? Is it consistent with either the network or with Category Theory? Lots to think about...
- interpol_p 11y agoThe thing that bugs me about his theory is that it just assumes the existence of time. That patterns within the network are replaced according to certain rules. And it seems that this replacement rule corresponds to time at the high level. His low level model seems to require propagation / evolution without being able to model it. Whatever enacts the replacement rule is an external force that acts upon his network, and so falls outside his definition of the universe. I guess it's a limitation of the cellular automata model. You have to assume that something outside of the system "steps" the simulation forward.
- mrwilliamchang 11y agoHere's my attempt at a summary. Wolfram speculates that the universe is a network of nodes and connections. This network changes over time by simple substitution rules. Specific patterns in the network give rise to effects that on the larger scale that we experience as the physical world. He has shown that if you model the universe this way, you can neatly derive special relativity and general relativity. He is also doing a brute-force search through networks to look for one that exhibits properties like our universe. I'm curious if I got it wrong.