On Mon, Aug 15, 2022 at 5:51 AM Telmo Menezes <[email protected]> wrote:
> > > Am Fr, 12. Aug 2022, um 19:56, schrieb Jason Resch: > > > > On Fri, Aug 12, 2022 at 2:04 AM Telmo Menezes <[email protected]> > 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 [email protected]. 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