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I think your summary is accurate. For reference, I'm willing to cut Wolfram more slack than some people are, I think his quest to discover the ultimate laws of

I think your summary is accurate. For reference, I'm willing to cut Wolfram more slack than some people are, I think his quest to discover the ultimate laws of physics from the other end is potentially interesting, but I don't think this particular article really has even any interesting conjectures.

schoen 6y ago
I was thinking something like "Turing machines themselves can form various kinds of adjacency graphs", but I would also doubt how much we can learn from this: the behavior of adjacent Turing machines is often radically different and it's rapidly going to become undecidable to say how different, or even to confirm whether it's different or not. If you think about software running on a CPU, you can get different behavior with a very small change. I gave a talk a couple of times about how real-world fencepost errors (like writing <= in a loop when you meant <) will compile to just a single-bit difference in the binary, yet in one case you have a correct program [at least in that regard!] and in the other you have a buggy and potentially exploitable one. Or software crackers from different eras would sometimes try to remove copying restriction routines just by injecting NOPs over random conditional branches or function calls, in the hope of overwriting the relevant instruction and causing the program to entirely skip that logic. These programs are adjacent in terms of their code, or are separated by a very short distance in the CPU version of Wolfram's rulial space, but their behavior completely diverges. And I think that's a common case. Or maybe some chaos theory ideas are apposite and we could say that there are a lot of attractors and so it's never unlikely that a small change to the code will produce a big change in its behavior. Like you, I also don't mind that Wolfram is excited by this, and also am not sure that he's discovered anything here. :-)

schoen 6y ago

I was thinking something like "Turing machines themselves can form various kinds of adjacency graphs", but I would also doubt how much we can learn from this: the behavior of adjacent Turing machines is often radically different and it's rapidly going to become undecidable to say how different, or even to confirm whether it's different or not. If you think about software running on a CPU, you can get different behavior with a very small change. I gave a talk a couple of times about how real-world fencepost errors (like writing <= in a loop when you meant <) will compile to just a single-bit difference in the binary, yet in one case you have a correct program [at least in that regard!] and in the other you have a buggy and potentially exploitable one. Or software crackers from different eras would sometimes try to remove copying restriction routines just by injecting NOPs over random conditional branches or function calls, in the hope of overwriting the relevant instruction and causing the program to entirely skip that logic. These programs are adjacent in terms of their code, or are separated by a very short distance in the CPU version of Wolfram's rulial space, but their behavior completely diverges. And I think that's a common case. Or maybe some chaos theory ideas are apposite and we could say that there are a lot of attractors and so it's never unlikely that a small change to the code will produce a big change in its behavior. Like you, I also don't mind that Wolfram is excited by this, and also am not sure that he's discovered anything here. :-)