This 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.
Maybe 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?
IANAP, 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.
"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."
Scott Aaronson argues that, based on what we know about quantum mechanics, Wolfram's "long-range thread" cannot reproduce special relativity and Bell inequality violations:
It 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.
So quantum effects like entanglement are distortions in the structure of the network. So basically quantum effects are due to distortions in space-time, i.e. there is a 'worm hole' type structure connecting entangled particles?
This is getting out of my depth, but isn't that basically what Loop Quantum Gravity proposes?
Bell's theorem assumes that spacetime is locally Euclidean so it is not relevant when there are networks and rules that allow for causal connections that appear to be an observer at a distance.
It wasn't resolved. Pilot Waves have nonlocality, which contradicts Relativity. (I don't know, it may be correct that quantum mechanics is non-local, but Relativity-minded folk are rightfully suspicious of such a model.)
There are other formulations of relativity which aren't nonlocal!! Like the Tangherlini transformations.
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."
Loop Quantum Gravity (LQG) and Causal Dynamical Triangulations (CDT) are two theories of quantum gravity that describe spacetime as arising from a network of sorts. For LQG, spacetime emerges from a spin foam quite elegantly. And for CDT things are also quite elegant. I'm not aware of either violating Bell's Theorem, but quantum gravity isn't my specialty.
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.
I 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.
Wolfram 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.
I 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.
I really appreciated his tone. I'm incredibly fascinated by ideas like quantum physics and basic building blocks of the universe, but am often left behind when I read articles about them due to a lack of understanding of the core mathematics. His tone makes this complicated subject understandable.
The article would certainly be less awkward and more interesting if he involved other people than just himself and Einstein.
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!
Agreed. Benoit Mandelbrot was the same; "When I discovered Fractals, which are a thing that I discovered, including the Mandelbrot Set, which is named after me, because I discovered it..." Wth some people it means I just stop listening to them, but I just ignore it here, since both Mandelbrot and Wolfram usually have interesting and insightful things to say as well.
> 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.
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... :)
In 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.
That'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.
Or 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 haven't read Schild's Ladder, but that section strongly reminds me of a lecture I attended by David Finkelstein (https://en.wikipedia.org/wiki/David_Finkelstein) given to a physics department composed largely of condensed matter physicists. He basically said that he was going to attempt to explain space-time as a crystal structure, and he said that structure was most analogous to diamond. Then he used condensed matter formalisms to explore the crystal structure and explain how this created the properties of space-time that we see. This was back in 1996 or so.
FYI - "The first lecture in a series given by Dr Peter Rowlands of the University of Liverpool on the Foundations of Physical Law. Further lectures will be uploaded after they have been given."
Serendipity. 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.
> 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.
Things 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?
What 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.
My 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.
It 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.
But a theory is supposed to model something that actually exists, yes? So for instance when philosophers made the conjecture for the existence of the atom, their theory was either correct or not, on the basis of whether the atom actually existed in nature.
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.
> But a theory is supposed to model something that actually exists, yes?
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.
This is a classic debate in the philosophy science. Should theories describe the world, or merely make predictions about it? Because no one these days believes that quantum mechanics really describes the world, we live firmly in the realm of theories being things that make predictions.
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.
I don't understand why you feel that there needs to be a space in order to have a collection of nodes and edges that connect the nodes.
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.
This conversation has given me lots to think about and I was ready to let it trail off. But wanted to answer you just out of respect.
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.
I'm as dumb as they come, so take this with a grain of salt: I think he is describing (a theory about) physical reality. To give you a different perspective: You position his theory of the universe as a network of nodes along with distances/measurements. But if you think for a moment about the void that you have to cross to get from one object to another (like from our star system to another) what is it? If you put it under an electron microscope it doesn't reveal itself.
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.
No, I don't think that's it. He is saying that physical reality is literally a network of interconnected nodes at its fundamental level. I think you're still assuming that these graphs have to be embedded in some space to be real.
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?
These graphs have to be embedded into a computation device to be real and changing in time. To build such a computation device, maybe you need time and space. It could even be that our Universe is of the minimum complexity required to build a computation device capable of computing the graphs that describe our Universe.
> These graphs have to be embedded into a computation device to be real and changing in time.
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.
This is a fundamental philosophical question. The same question can be asked about more traditional physical models, e.g. what is Einstein's spacetime composed of, and how did his equations of general relativity come to be? Are they real, or are they just a model that we use to describe reality?
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.
> What is matter made of? The answer, whatever it is, cannot be matter.
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.)
Wolfram is proposing a radically different way of interpreting the universe. His main argument is that if his cellular automatons can achieve emergent behaviour similar to real physics, then it is evidence for it being the underlying mechanism in the universe.
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.
> His main argument is that if his cellular automatons can achieve emergent behaviour similar to real physics, then it is evidence for it being the underlying mechanism in the universe.
Then it is a hint that possibly it might be the underlying mechanism of the universe. It's not exactly evidence.
More precisely, simple rules can have emergence. Wolfram's most common example is simple cellular automata. Cellular automata do not need to be simple. Other rules like Turing machines can have emergence.
Tell me about it. I still remember asking my dad what came before the universe when I was a kid and he said, "No, there was no before." When I inquired again he said "Time is a property of our universe. You can't have a before without it. There wasn't nothing, there wasn't a before. You are part of this universe and cannot exist without it. There's no curtain to look behind, this is it."
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.
Indeed! 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.
Ah, 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.
If 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.
Does 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.
This 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.
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.
1: they aren't. They don't need to be, and they cannot be.
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.
Chaotic functions of continuous real variables are not computable. Computable physics assumes a discrete lattice, which the universe is not proven to be.
Can't find any proof of that claim. So far it seems more likely that all physical systems are computable. Although you may need infinite time to achieve perfect accuracy when computing them in a simulation, but matematically that's still computable.
Computability makes no assumption on the geometry, only on the rules the system follows.
This is computer science 201. You enumerate all possible Turing Machines (possible because they are countably infinite), then diagonalize their execution. For any execution state that any Turing Machine reaches in any finite period of time, this simulation will also reach it in a finite period of time. A very large "amount" of time, sure, but "time" in a Turing Machine is an abstraction anyhow.
(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)
All 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.
That 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.
Your 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).
I 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.
Whether 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.
You 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.
I 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.
My contention is that all things are understood one step at a time, and I believe this is influencing theoretical physics in a way that the theoreticians themselves are not fully aware of. Especially Wolfram's theory.
I 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.)
Why 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.
It 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.
> 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.
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
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
I 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
> 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.
i appreciate the thought out response.. i'll try to address your points
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.
what you said there mirrors my immediate reaction to the linked piece by wolfram, and in all fairness i felt it myself of my comment and intended to reply with a more directed response to the piece but found it difficult to find anything to riff off of
So then the question arises: could one of these simple
programs in the computational universe actually be the
program for our physical universe?
this seems to be the base line on which his potential final theory is predicated, but this just reads as a rewrite of the infinite monkey theorem
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
could placehold as a rewrite of wolfram's piece
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
I don't find it unsettling but it's not particularly interesting. You can view epicycles as detour before Copernicus, I think that's more of the sense of what Wolfram is referring to as a detour.
wolfram's use of detour seemed like a dismissal of the utility of relativity, i read it as 'a waste of time'.. taking an indirect route when a direct route would have been preferred.. was something else meant by the word? people mock an earth centered universe today but was the idea a waste of time?
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
I'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?
His 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.
It'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!
The 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.
Here'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.
121 comments
[ 3.3 ms ] story [ 221 ms ] threadIt'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.
"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.
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!
https://www.youtube.com/watch?v=cAYDiPizDIs
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.
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... :)
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!
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.
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.
[1] https://www.youtube.com/watch?v=W2XdhzCORbo
http://bactra.org/reviews/wolfram/
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 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.
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.
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.
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
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)
Let there be math, and then the laws of physics fall out as trivial tautologies.
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.
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.
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
i see, and foresee, an existence where every new finality conjures new questionsi'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:
what you said there mirrors my immediate reaction to the linked piece by wolfram, and in all fairness i felt it myself of my comment and intended to reply with a more directed response to the piece but found it difficult to find anything to riff off of this seems to be the base line on which his potential final theory is predicated, but this just reads as a rewrite of the infinite monkey theoremif 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:
could placehold as a rewrite of wolfram's piecei'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
so yes, i agree, markedly uninteresting(o) http://theory.uwinnipeg.ca/mod_tech&#...
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
(o) https://www.youtube.com/watch?v=MMaGnpVaSGQ
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.