Am Mo, 15. Aug 2022, um 17:27, schrieb Jason Resch: > > > 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)
Thanks Jason! > >> >> >>>> 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]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CA%2BBCJUiggZ6ZC3RjQ5XaRMiV%3DXLMLrF4Swk1xU_7UKs-aP665Q%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CA%2BBCJUiggZ6ZC3RjQ5XaRMiV%3DXLMLrF4Swk1xU_7UKs-aP665Q%40mail.gmail.com?utm_medium=email&utm_source=footer>. -- 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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/5fda9b6d-fd51-4b20-8694-e6f20b03d4e1%40www.fastmail.com.
