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.)
What Is Spacetime, Really?
61–70 of 122 posts
Re: What Is Spacetime, Really?
#62Earlier quoted context omitted.
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…
> 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 .
Yes perhaps evidence is too strong a word, though that's not what Wolfram would have you believe.
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.
Re: What Is Spacetime, Really?
#63Earlier quoted context omitted.
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.
1. Why are the number of turing machines finite. 2. But to simulate a single step of the turing machine, you will have to simulate this turing machine too, so what you will end up doing is recursively simulating the first step of this machine to infinity. 3. Why do you assume all the programs in the world are turing computable.
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.
Re: What Is Spacetime, Really?
#64Earlier quoted context omitted.
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, som…
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", whic…
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.
Re: What Is Spacetime, Really?
#65Earlier quoted context omitted.
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.
1. Why are the number of turing machines finite. 2. But to simulate a single step of the turing machine, you will have to simulate this turing machine too, so what you will end up doing is recursively simulating the first step of this machine to infinity. 3. Why do you assume all the programs in the world are turing computable.
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.
Also in Computer Science 201, you should encounter the Church-Turing thesis. https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis
Re: What Is Spacetime, Really?
#66Earlier quoted context omitted.
Dijkstra's ideas survive, but are (mostly) not used...
There's a whole lot of structured programming going on these days.
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.
Re: What Is Spacetime, Really?
#67Earlier quoted context omitted.
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.
1. Why are the number of turing machines finite. 2. But to simulate a single step of the turing machine, you will have to simulate this turing machine too, so what you will end up doing is recursively simulating the first step of this machine to infinity. 3. Why do you assume all the programs in the world are turing computable.
Re: What Is Spacetime, Really?
#68Earlier quoted context omitted.
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…
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.
Re: What Is Spacetime, Really?
#69Earlier quoted context omitted.
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…
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.
Re: What Is Spacetime, Really?
#70 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