On Mon, Aug 15, 2022 at 5:51 AM Telmo Menezes <te...@telmomenezes.net> wrote:
> > > Am Fr, 12. Aug 2022, um 19:56, schrieb Jason Resch: > > > > On Fri, Aug 12, 2022 at 2:04 AM Telmo Menezes <te...@telmomenezes.net> > wrote: > > > Hi Jason, > > This is really interesting, thanks for sharing. Since Wolfram started > going in this direction, something that occurs to me is this: hypergraphs > are perhaps one of the most general mathematical constructs that can be > conceived of. Almost everything else can be seen as a special case of > hypergraphs. Like you say, with the update rules, we shouldn't be surprised > if they are equivalent to the UD. My scepticism is this: is anything being > gained in terms of explanatory power? Should we be surprised that such a > powerful representation can contain the rules of our reality? I do admit > that I have to study these ideas in more detail, and there is something > really compelling about hypergraphs + update rules. > > > That is a good question. I am not familiar with them myself, but my > understanding is they do not provide for any form of computation beyond > what is turing computable, so in that sense, I don't know that they provide > any additional explanatory power beyond the simple statement that all > computations exist. > > A commenter on my site recently asked, what can we say about the > "computer" that computes all these computations. My reply was: > > > "There is no single one. There are infinite varieties of different TMs, > and all can exist Platonically/Arithmetically. Gregory Chaitin discovered > an equation whose structure models LISP computers. There are likewise other > equations corresponding to the Java Virtual Machine, and the Commodore 64. > > > This is really interesting, I didn't know about that! Can you provide some > references? > Sure. In his 1987 book Algorithmic Information Theory <https://archive.org/details/algorithmicinfor00chai>, Gregory Chaitin <https://en.wikipedia.org/wiki/Gregory_Chaitin> describes one such equation: the “*Exponential Diophantine Equation Computer*.” It has 20,000 variables and is two hundred pages long. This equation perfectly replicates the behavior of the LISP programming language <https://en.wikipedia.org/wiki/Lisp_(programming_language)>. He describes the equation as follows: If the LISP expression <https://en.wikipedia.org/wiki/Expression_(computer_science)> k has no value, then this equation will have no solution. If the LISP expression k has a value, then this equation will have exactly one solution. In this unique solution, n = the value of the expression k. Gregory Chaitin <https://en.wikipedia.org/wiki/Gregory_Chaitin> in “*META MATH! The Quest for Omega <https://arxiv.org/pdf/math/0404335.pdf>*” (2004) > > All these Turing machines, and their execution traces of every computer > program they can run, exist in math in the same sense that the Mandelbrot > set or the decimal expansion of Pi exist in math. Despite the infinite > variety of architectures for different Turing machines, their equivalence > (in the Turing computability sense) makes the question of “Which Turing > machine is running this universe?” impossible to answer, beyond saying, > “all of them are.”" > > > I agree. > Nice. > > I think hypergraphs, then, would be just one more mathematical object we > could add to the heap of Turing universal mathematical objects which could > (and would, if Platonism is correct) underlie the computations of our > universe/experiences. > > > > > "As soon as one starts talking about “running programs” some people will > immediately ask “On what computer?” But a key intellectual point is that > computational processes can ultimately be defined completely abstractly, > without reference to anything like a physical computer. " > > > My same reply also provided an explanation/argument, which is applicable > to anyone who accepts simple truths concerning abstract objects have > definite and objective true/false values, paired with a rejection of > philosophical zombies. I think John rejects zombies, so he would have to > reject objective truth to believe a physical computer is necessary to > produce observers. Below is what I wrote: > > The way I like to think about it is this: If one is willing to believe > that truth values for mathematical relations like “2 + 2 = 4” can exist and > be true independently of the universe or someone writing it down, or a > mathematician thinking about it, that is all you need. > > > For if the truth values of certain simple relations have an independent > existence, then so to do the truth values of far more complex equations. > Let’s call the Diophantine equation that computes the Wave Function of the > Hubble Volume of our universe “Equation X”. Now then, it becomes a question > of pure arithmetic, whether it is true or false that: > > > “In Equation X, does the universal state variable U, at time step T > contain a pattern of electrons that encode to the string: > ‘why does the existence of Universal Equations imply the existence of > iterative search processes for solutions?'” > > > If that question has a definitive objective truth, then it is the case > that in the universe U, at time step T, in equation X, there is some person > in that universe who had a conscious thought, and wrote it down and it got > organized into a pattern of electrons which anyone who inspects this vast > equation with its huge variables could see. > > > Once you get to this point, the last and final step is to reject the > possibility that the patterns found in these equations, which behave and > act like they are conscious, and claim to be conscious, are philosophical > zombies. In other words, to accept that they are conscious beings, just > like those who exist in “physical” universes (assuming there is any > possible distinction between a physical universe, and a physical universe > computed by a Platonic or Arithmetic Turing Machine). > > > I tend to agree with you, because this is the most parsimonious > explanation of reality than assuming some mysterious > process/mechanism/entity that makes it so that this particular Universe and > this particular state of affairs and this particular moment in time is real > and others are not. > Thank you for that. I have yet to find an idea that can explain more while assuming less (in this case only assuming that 2+2=4, and the rest can be shown constructively). Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. 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