51–60 of 122 posts
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.
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.
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 w…
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…
Then it is a hint that possibly it might be the underlying mechanism of the universe. It's not exactly evidence.
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 w…
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.
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.)
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That is exactly the reason I stopped reading halfway through. I couldn't take any more of his narcissism.
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.
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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.
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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 leve…
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…
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.
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…
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Dijkstra's ideas (not just his contributions to math) survived despite his arrogance. The difference is that Wolfram's ideas are not testable.
Dijkstra's ideas survive, but are (mostly) not used...
Earlier quoted context omitted.
Dijkstra's ideas (not just his contributions to math) survived despite his arrogance. The difference is that Wolfram's ideas are not testable.
Dijkstra's ideas survive, but are (mostly) not used...