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. 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 but there is so much more to physics than known laws and their solutions. And to any desired degree of accuracy? 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. 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. Simulating these quantum behaviors on classical Turing machines is inherently difficult because it requires representing exponentially growing state spaces. Turbulence in fluid dynamics is another challenging phenomenon. Turbulent flow in fluids features chaotic and unpredictable patterns, including vortices and eddies. 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. 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. 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. 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. 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. And LLMs by themselves are zombies. ;-) -- 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.
