What Is Spacetime, Really?
blog.stephenwolfram.com
blog.stephenwolfram.com
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!
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.
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.
Simulate the first step of the first machine, then the first step of the second machine, then the second step of the first machine, then the first step of the third machine, then the second of the second, then the third of the first, then the first of the fourth, and so on. Every step of every program/machine is eventually reached.
For the same reason that the pairs of integers can be put into bijection with the integers.
2) that is not a problem. The first step of that is not to run a step of a program it simulates. The "simulating a single step of a given machine" is not a single step. It is many steps. As such, there is no such recursive problem like you describe. Simulating a single step of a machine always finishes, regardless of what that step "represents". Even if the step being simulated is part of some simulator machine, simulating it is still done in the same way, and doesn't take longer.
3) Any programs for any computer we have can be simulated by a Turing machine. They are quite general.
You might claim that some physical process is not computable, but that has not been demonstrated for any physical process (well, except for maybe consciousness, but that is contentious), and most ideas of how physics works are computable, so there would be a significant burden of proof.
So, it seems like any program we can run can be simulated by a Turing machine.
What about for, uh...
It occurs to me that I'm not exactly sure what a chaotic function of continuous real variables is.
Is it like, one where iterating it gives chaotic results, or?
What if, instead of variables over the reals, using variables over the computable reals?
Computability makes no assumption on the geometry, only on the rules the system follows.
Also in Computer Science 201, you should encounter the Church-Turing thesis. https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis
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.
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.
So assuming a discreet space may be fruitful, but by itself is not a step forward.
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.
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)
"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?
I like this quote:
"Alice wants to synchronize her clock with Bob's, so this is how it might go:
At 12:00:00 pm Alice time, Alice sends out a beam of light to Bob, as a signal for Bob to tell Alice what time he has.
Once Bob receives the beam of light, Bob immediately sends Alice a beam of light telling her the time he has.
At 12:00:02 pm Alice time, Alice receives Bob's time, say 11:41:23 am.
At this point, how should Alice synchronize clocks? Clearly, 12:00:01 pm Alice time is 11:41:23 Bob time. We're done.
But we've unknowingly introduced an assumption here, namely that the speed of light travelling from Alice to Bob is identical to the speed of light travelling from Bob to Alice."
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.
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.
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.
So if Wolfram is correct, then there exists at the lowest level of nature a network, upon which everything else follows. Wolfram is trying to describe reality, something that exists, analogous to the existence of the atom? Do we agree this far?
If these Wolfram-nodes of our networked-reality do indeed exist, how are they connected in unique patterns if there is no "space" between them?
If his theory is not meant to predict something that actually exists, as in the prediction of the atom, well then, i'll bow out of this conversation because it's well and truly beyond my conception of what science is about.
Yes, but "model" is the key word. If it provides a set of rules which predict the way thing that exist in the world behave, then it models something (or set of things) that exits in the real world.
The existence of the atom, however, is not what is being predicted. A theory should predict the sensor readings of particular instruments during particular experiments. Those sensor readings are what is real; "The Atom" is the abstraction.
The very idea that "things exist" is an abstraction. A thing exists if we can model it, and that model corresponds with reality.
It isn't as if there is an actual line connecting two dots across space.
It's just, there's a set of "points" (there doesn't need to be any things about these "points" other than that they are distinct. You could think of them as urelements I guess.), and another set of "edges", which are each a set of two elements from the first set.
A pair of "points" are "connected" by an "edge" iff the set comprised of those two "points" is in the second set.
This doesn't need a notion of space to work, unless you need like, an idea of space to have collections of things. So unless "the collection of odd numbers" needs an idea of space, then graphs don't need space.
My mistake was thinking that he was proposing something about the nature of physical reality. Ie. that physical reality was literally a network of interconnected nodes at its fundamental level. Something along the lines of macroscopic -> atomic -> sub atomic -> wolfram-nodal. A la, string theory, et. al.
From the replies here, I gather this has nothing to do with physical reality.. he's not describing how this nodal network might be implemented in reality... just that it must be, because the predictions come out correctly.
It's "nothing" as far as we're concerned but despite being intangible, despite being nothing, it has rules and laws that govern matter that traverses it just like every other part of our universe. So what is space itself? What is it composed of? You can't take a quick step outside of the universe to get a look under the hood because you are part of the universe. You can only talk about it in terms of it's rules and behavior–in the abstract.
If we get fundamental enough, we can go below geometry, into algebra.
For a less abstract example, what's the radius of an electron in modern physics?
No, no, no! These graphs are meant to be more fundamental than spacetime. They can change in the sense that there are algebraic rules for stepping them from one state to another, but this step isn't in our time. Our space and time should be generated by operating on these graphs (let's say "stepping" them, as long as we remember that it's not a time-step in our spacetime, but just an algebraic operation).
EDIT> I should say that this whole idea is a model. The question of whether a model is real or not independent of the system being modeled is a philosophical one that we can't really do justice to in an HN comment thread.
Over time, physicists have come to take models very seriously (thanks in part to Einstein's 1905 papers). That is, when our model says that electrons act like particles and waves, we assume that electrons really are these odd things that are somewhere in between a particle and a wave.
So, if it turns out that Wolfram's ideas have merit, and there really is an underlying spacetime network which can be used to model and derive all of the known equations of physics (and likely some unknown equations), then at that point we would have to take very seriously the existence of such a network. We would be forced to think of a seemingly continuous spacetime as a special facet or feature of this underlying network, in the same way that we now think of space as a special feature of the more general spacetime.
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.)
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.
Although to be fair, it's going to be quite cumbersome to discount every other statement in a book almost a thousand pages in length.
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.
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.
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.
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.
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.
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.
Start at the origin
Move right X
Move up X*X
Make a dot
If X = Screen.Width Stop
X=X+1
Repeat
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.
1) sorry, it's the way i write
2) solid response:
It's critical but doesn't add much of
substance on its own through the criticism.
So then the question arises: could one of these simple
programs in the computational universe actually be the
program for our physical universe?
if the universe is programmable, then surely within the bounds of every possible permutation of computation therein must lie a representation of the universe..?
3) 'use case' and 'science as directed utility' seemed explicitly to go hand in hand
4) "... reveal those use-cases untouched by contemporary thought"
one such important use case that showed the inherent utility of relativity was understanding retrograde motion(o), this was the sort of use case i was referring to one where the contemporary thought was unable to reach insight
"an existence where every new finality conjures new questions"
here i'd agree i erred on poetics to allow for some self discovery, what i hoped to express was that every 'final theory', as wolfram puts it or finality as i put it, i think will introduce more questions mocking the title of final
relativity is sussed out and people, as wolfram attested, assume it to be true, but then later find it only reveals, seemingly by conjuring, questions they were unaware of
even einstein, the one person who stood to gain the most by espousing that his theory was 'the final theory', knew relativity to be wanting
it is my impression that i do write 'in spoken language'
when was the last time you heard a capital letter? or 'proper' punctuation?
these are the words i would use to talk to you about this topic
the diction may seem off because i avoid negative constructions:no, not, never, none,etc; with hopes that the a subsequent generation will have the patience to write out even negating prefixes: un-,i-,a-,etc;
i find removing negative constructions is a means of making discussion more inviting and less authoritative
next time someone asks if you've seen some new media, instead of saying 'no' see what reaction something like 'i've yet to have seen it' will afford
if a sentence comes easily as "which isn't that interesting" i will take whatever time necessary to rewrite in order to write out the negative
reading your rewrite:
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
i'll express it as your rewrite on one side of a colon and applicable sections from wolframs piece on the other, ctrl-f confirmation encouraged
ideas need to be useful: "provides the only successful way
we have of describing spacetime"
we need to think up new ideas: "started on my long journey
to go beyond traditional mathematical equations and instead
use computation and programs as basic models in science"
I think we'll always have more questions to answer:
"But what would such a program be like?..what’s the basic
“data structure” on which this program operates?.." and on and on
(o) http://theory.uwinnipeg.ca/mod_tech/node60.html
.. an aside, can we talk to the fact that middlebrow seems the only brow held in contempt, i feel low brow and high brow each have their accepted merits(i) but i've yet to have seen something quantified as being middlebrow used in promotion
i wonder what the says about adjudged middles
what's the alternative to detours? waiting, still, until one is shown the direct route? how will it reveal itself? what defines direct? are there direct and detour routes between wolfram's network nodes?
bones had a hard time appreciating the efforts of his predecessors(o), but does the potential of a future technology rendering a current technology obsolete, barbaric even, mean we should avoid it's utility because it's merely a 'detour'
i think the probabilistic nature of quantum bodies is an incorrect model but i wholly endorse its use in those scenarios in which results are found where they were previously elusive
i think monte carlo descision tree traversal is a misguided method but i wholly endorse its use in those scenarios in which results are found where they were previously elusive
utilise and iterate on best fit 'detours' while still seeking direct routes
my response to wolfram was asking: why call something a detour when everything is a detour, even his unfinished attempt at finalising all detours
i want to make it clear that i encourage wolfram to continue his work on his theory, but careful judging lest ye be judged
hey einstein, “Don’t waste your time working on that!” and, “Please don’t work on that.” it's merely a detour
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.
Like I said the subject area is fascinating and merits a much warmer reception than this book got. Tragic.
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!
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.
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.
Let there be math, and then the laws of physics fall out as trivial tautologies.
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... :)