On Sun, Jul 14, 2024, 11:36 AM PGC <multiplecit...@gmail.com> wrote: > > > On Sunday, July 14, 2024 at 5:42:23 AM UTC+2 Jason Resch wrote: > > > > On Sat, Jul 13, 2024, 9:54 PM PGC <multipl...@gmail.com> wrote: > > > > On Sunday, July 14, 2024 at 3:51:27 AM UTC+2 John Clark wrote: > > Yes it's possible to have a universal Turing machine in the sense that you > can run any program by just changing the tape, however ONLY if that tape > has instructions for changing the set of states that the machine can be > in. > > > > It still boggles my mind that matter is Turing-complete. > > > Turing completeness, as incredible as it is, is (remarkably) easy to come > by. You can achieve it with addition and multiplication, with billiard > balls, with finite automata (rule 110, or game of life), with artificial > neurons, etc. That something as sophisticated as matter could achieve it is > to me less surprising than the fact that these far simpler things can. > > > In hindsight, every result is easy to come by. You assume sophistication > to beat simplicity. That's just weird, given how little we actually know. > Without that simplicity for example, we wouldn't have discovered computers. >
When I say that matter is more sophisticated than say, the cells in game of life, I mean matter is more flexible. So if something as limited as GoL is flexible enough to create a Turing machine in it, then to me, it is less surprising our (even more flexible) physics allows Turing machines to be constructed. > > > > And this despite parts of physics being not Turing emulable. > > Finite physical system's can be simulated to any desired degree of > accuracy, and moreover all known laws of physics are computable. Which > parts of physics do you refer to when you say there are parts that aren't > Turing emulable? > > > ? You write so much about these topics, I cannot understand how you make > that statement. Many of the known laws are > I am not aware of any exceptions (except the hypothesized objective wave function collapse) but objective wave function collapse is a rather ridiculous theory for which we have no evidence. but there is so much more to physics than known laws and their solutions. > And to any desired degree of accuracy? > When I say this, I quote the Church-Turing-Wolfram-Deutsch principle: https://en.wikipedia.org/wiki/Church%E2%80%93Turing%E2%80%93Deutsch_principle "One expects in fact that universal computers are as powerful in their computational capabilities as any physically realizable system can be, so that they can simulate any physical system. This is the case if in all physical systems there is a finite density of information, which can be transmitted only at a finite rate in a finite-dimensional space." — Stephen Wolfram in “Undecidability and Intractability in Theoretical Physics” (1985) To my knowledge, this principle remains an open conjecture in physics. I'll write fast and clumsily as I am by no means an expert and gotta go: > > Some finite-state physical phenomena present significant challenges to > computational simulation due to their inherent complexity and the > limitations of current computational models. > This is due to the time and space limits of our computer hardware, not due to any assumed inherent non-computable processes in physics. One example is quantum entanglement and superposition. In quantum > mechanics, particles can exist in multiple states simultaneously, which you > know, and influence each other instantaneously at a distance, a phenomenon > known as entanglement. > There are no non-local influence unless one believes there is objective wave function collapse. Entanglement is no more mysterious than consistency of measurements. Both are the same phenomenon. Simulating these quantum behaviors on classical Turing machines is > inherently difficult because it requires representing exponentially growing > state spaces. > Again this is a practical limitation of our hardware. > Turbulence in fluid dynamics is another challenging phenomenon. Turbulent > flow in fluids features chaotic and unpredictable patterns, including > vortices and eddies. > Chaotic behavior means a system's future state cannot be predicted by analytic means (there's not an equation we can plug a time variable into to get a result arbitrarily far into the future). Rather, chaotic systems must be simulated. Systems can be simulated to any desired degree of accuracy, and measurement limitations will impose limits on how much we can know about a system we intend on simulating. Again, the existence of chaotic systems is not an example of uncomputable physical laws. Although Navier-Stokes equations describe fluid flow, solving these > equations accurately (really accurately, beyond engineering application) > for turbulent systems is computationally intensive and doesn't look > feasible for all conditions, particularly at high Reynolds numbers where > the flow becomes highly chaotic. This makes precise simulation of turbulent > behavior quite the biscuit. Tao had the paper about when we can expect blow > out and the results are sobering at this time. > A gram of matter has 10^23 particles in it. Today's best computer's have perhaps 10^18 bits of memory. > Weather systems also exemplify the difficulties in simulating complex > physical phenomena. Despite significant advancements in weather modeling, > predicting weather with high precision over long periods remains a > challenge due to the chaotic elements and the large number of interacting > factors involved. The inherent unpredictability of weather systems > underscores the limitations of current computational approaches. > We can only sample a miniscule fraction of the data that is relevant to long term accurate computational simulation. > Magnetohydrodynamics (MHD) adds another layer of complexity, particularly > when modeling fusion processes and fluid behavior in stars, which also > boggles my mind. MHD describes the dynamics of electrically conducting > fluids like plasmas, liquid metals, and saltwater, combining principles > from both magnetism and fluid dynamics. The equations governing MHD are > highly nonlinear and coupled, making them difficult to solve to understate > things. Simulating fusion reactions, such as those occurring in stars, > involves not only MHD but also nuclear physics, thermodynamics, radiation > transport, and things I can't probably name. These interactions take place > under extreme conditions of temperature and pressure, further complicating > the modeling efforts. This is some fancy shit, but do show me any > simulation you know of with high or infinite accuracy. > > In the context of astrophysics, modeling the behavior of fluids in stars, > such as the convective and radiative zones, requires simulating the > intricate interplay between gravity, fluid dynamics, magnetic fields, and > nuclear fusion. The immense scales involved, both in terms of size and > time, along with the chaotic nature of the processes, make it a challenging > task to say the least. Accurate simulations of these phenomena are crucial > for understanding stellar evolution, but they remain computationally > intensive and challenging due to the complex, multi-physics nature of the > problem. > > Biological systems, such as protein folding, further illustrate the > challenges of finite-state simulations. Protein folding involves a protein > chain finding its energetically favorable three-dimensional structure, > which is critical for its biological function. The number of possible > configurations for a protein is astronomical, making it a computationally > hard problem. Although molecular dynamics simulations and AI have advanced > our understanding here and there, achieving precise predictions for protein > folding remains difficult due to the immense complexity of the process. > Things can be computationally intractable, (like brute forcing an encryption key or solving chess), without being uncomputable. I think these examples above are examples of computation intractability. > These examples are just what springs to mind immediately but there are so > many other things like gravity, solving the field equations in GR etc. etc. > etc. which highlight the significant challenges posed by complex physical > systems to computational simulation. > If actual infinities are involved (and perhaps there are in gravity or some other deeper theory) then they would be examples of uncomputability in nature. But I don't know whether such infinities have been demonstrated. "We have never measured anything in physics to more than about 15 significant digits, and no experiment has been carried out whose outcome depends on the hypothesis that a true continuum exists, or hinges on Nature computing something uncomputable." — Max Tegmark in “The Mathematical Universe” (2007) While ongoing advancements in computational methods and technologies > continue to improve our ability to simulate these phenomena, certain > aspects of their behavior remain unclear to say the least, emphasizing the > need for further research and development in both computational theory and > physical sciences. > > Again, I would have thought that you reading this list for years, just > like most regular members/poster, are aware of these difficulties. What can > I say Jason? There's unknown stuff too. > I'm aware of difficult problems, but I'm not aware of any uncomputable laws. I'm not sure that it even makes sense for there to be a law that's not computable, as we could never test its predictions (as we couldn't compute them). And LLMs by themselves are zombies. ;-) > LLMs are based on the decoder model, which I believe has been shown to be Turing complete. If we are machines there is some LLM which is the same as us. 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. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/ddb49d07-a6dd-4f71-97a7-f75ee956d5f4n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/ddb49d07-a6dd-4f71-97a7-f75ee956d5f4n%40googlegroups.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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CA%2BBCJUjrwKtwP5Z%3DtiXdateo%2BV7pjFuSBEGTbqqqxjE9WewdGA%40mail.gmail.com.
