On 7/14/2024 8:36 AM, PGC 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 <[email protected]> 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.
Difficult is not the same as impossible. The part of quantum mechanics
that is not Turing emulable is true randomness. But Jason probably
thinks it's deterministic but non-local, which could be emulated by
pseudo-random number generators.
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.
Challenging is not impossible either.
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.
Classical chaos is deterministic by definition. It's just limitation in
practice, not in theory.
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.
You wrote, "...parts of physics being not Turing emulable." Being
Turing emulable is a provable mathematical property of a problem. It
isn't changed because the problem is hard and our hardware in not
adequate in practice.
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.
Challenging and complex but Turing emulable.
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.
Challenging and complex but Turing emulable.
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?
You can say, "I misunderstood Turing emulable."
Bren
There's unknown stuff too. And LLMs by themselves are zombies. ;-)
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