"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.
www.scottaaronson.com/papers/nks.ps
This is getting out of my depth, but isn't that basically what Loop Quantum Gravity proposes?
Also, physicists don't generally take Wolfram's claims about how cellular automata are related to quantum or classical gravity or anything else in fundamental physics very seriously. A New Kind of Science cites very few sources and makes it seem like everything in there is new, which isn't the case. There was loads of criticism about that when the book was released. Nonetheless, it's an interesting idea and if something useful came from the work it would be good.
I don't think Bell's theorem raises a problem in either LQG and CDT because they have the traditional quantum theory built into them. They are not deterministic theories like Wolfram's. Bell's theorem discounts the possibility of quantum (as it is observed) if there were no long range connections defying locality.
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.
Sure it could (in principle) be; its matter all the way down, and there is no lower-level thing of which matter is made. (Though, actually, I think the standard answer to "what is matter made of" under current way of interpreting things would be "energy", but then you could repeat the exercise with "energy" in place of "matter" and its the same issue, mutatis mutandis.)
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.
That realization made me feel pretty stupid and caused a minor existential crisis.
1) Decompose into smaller components and put back together 2) Look at it's structure
It's the diference between describing a cardboard box and a cube (platonic solid).
To describe the first, I have to describe what is cardboard, what is cellulose, what is a cell, what is matter, ... all the way down, and then I hit a wall.
To describe the second, I just need topology.
This definition of space is that space "just is", resembles a network, and that the "stuff" in it is just how we perceive particular local structures.
The network is only a geometrical analogy, there's no "space" between the nodes because the nodes don't represent anything concrete. You can describe the same network algebraically, but then you're left with no pictures to illustrate the article.
For a (really long) discussion on how this simulation parallels physics, check his book, A New Kind of Science, out.
Then maybe you would want to read Aaronson's review of it, just for a balanced perspective.
Then it is a hint that possibly it might be the underlying mechanism of the universe. It's not exactly evidence.
Even if he's exclusively describing the evolution of his own thought and linking to his own articles, each discovery and theoretical advancement would better be presented in terms of upstream research that brought it along and predated it, crediting others whenever possible. Science is a network, too!
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.
This is a classic that everyone should read, utterly destroying a shameless self-promoter gifted with some intelligence and a grasp of jargon.
I'll definitely buy http://www.amazon.com/The-End-Science-Knowledge-Scientific/d... as well, the books he recommends w.r.t. Prigogine.
i = 1
while True:
j = 1
while j <= i:
simulate step j of Turing machine T_i
j += 1
i += 1
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.
This goes a little beyond NP hard complexity, I believe.
It goes arbitrarily far beyond NP hard complexity, which is my point. Wolfram ignores complexity entirely, and that means this algorithm is fair game.
Intro to Schild's Ladder by Greg Egan. He was obviously thinking along similar lines.
Please tell me that last act made your think of Cellular Automata too!
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.
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.
So assuming a discreet space may be fruitful, but by itself is not a step forward.
I’ve come to suspect it may actually have led us on a
century-long detour in understanding the true nature
of space and time
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'm interested in discussion
(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
> 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.
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.
http://www.nature.com/news/the-quantum-source-of-space-time-...
Because I don't see his name in the citations...
Original credit for a discrete nature of the universe belongs to Democritus.
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... :)
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)
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?
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.
Let there be math, and then the laws of physics fall out as trivial tautologies.
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.
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.
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.
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...
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.
I'm curious if I got it wrong.