> but emperically it has held true to the limits of our knowledge of physics

Considering that our entire knowledge of physics is encoded as computational rules, because that's all we really know how to do, this statement is basically a tautology.

We do physics this way exactly because it works so well - it is "unreasonably effective", as the saying goes.

No, we do physics this way because we don't know any other way. When this way fails (e.g. quantum gravity, turbulence), we assume that the problem is that we haven't tried hard enough yet. Which may be true, but it's also possible that the computational approach simply doesn't work for those phenomena.

This sounds an awful lot like "God of the gaps" argumentation with "non-Turing hypercomputation" substituting for "God". If the computational approach doesn't work — that's all of human reason, to emphasize: any symbols you can scribble on paper and reason about over coffee, that's a finite algorithmic process — then there's no humanly-achievable endeavor that can solve the problem. It's forever hiding in the gaps, the shadows; it's definitionally unknowable.

So what field of science are we discussing right now? One of the more frivolous branches of philosophy: talking about something that we can't define, can't reason about, won't ever be able to reason about; something which marks no experimental evidence in our human sciences. Therefore: it doesn't exist. Apply your favorite razor. Something we can't possibly talk about, let's not talk about. Something whose existence or non-existence are indistinguishable, which leaves no shadow in the observable universe: it does not exist.

It's not a "God of the gaps" argument because I'm not claiming that "God" (that is, incomputable physics) exists. I'm simply pointing out that the fact that our entire understanding of physics is built on a computational framework doesn't actually say anything about the Universe, merely about the way we do physics. There is a priori no reason to expect that the Universe would be in any way amenable to human understanding. We have just found that in some cases, it is.

And non-computability doesn't make something philosophical or mystical. We have encountered phenomena beyond the reach of any computation in mathematics and computer science many times. They exist, no matter which "razor" you apply.

- "We have encountered phenomena beyond the reach of any computation in mathematics and computer science many times. They exist, no matter which "razor" you apply."

The razor applies as to whether the physical universe runs on laws that don't fit in Turing machines. It applies because it's an unfalsifiable proposition. You can't embed a Turing machine in a super-Turing universe, ask it "what is the nature of your cosmos?", and have it determine (within finite computation) there are more things in heaven and earth than it can compute.

(This is the ordinary Church-Turing thesis: if some finite interaction between Turing observer and super-Turing universe convinces the Turing observer of the super-Turingness of its universe, within finite time... then an ordinary Turing machine can also do exactly the same thing, by simulating the first Turing machine, and brute-force enumerating every possible interaction within that finite bound. The nature of super-Turing machines is incomprehensible to Turing machines; there's nothing a super-Turing machine can do to prove it exists to a mere Turing machine).

You're conflating computability with computational complexity; that seems to the source of most of your confusion.

I don't remember the name of the complexity-theory analog of the Church-Turing thesis; but it's an open problem what types of computers physics can support the existence of, how they relate to classical Turing machines in complexity theory. See for example: quantum complexity theory.

About halting: there is provably no way to verify an oracle for the Halting Problem, even if you had one. You can't even ask a hypercomputer to write a proof for you: in general there exist no finite-length proofs.

As someone who works in a custom fabrication shop and who has been research job shop scheduling for over a decade as an attempt to get better at it, it's a computationally impossible task. There are huge numbers of "optimal" ways to schedule the shop and all of them require enormous amounts of computation. Genetic algorithms are offering the most promise right now, but the schedule has to be constantly updated because things never take as long as you think they will.

This is primarily because, unlike manufacturing, the basic unit of our system is a person, with all of their chaotic outputs. You start stacking those up and you end up with "long, fat tails" in every analysis you do. Your probabilities are spread almost flat over a broad range of outcomes.

It's fascinating and definitely falls into the category of uncomputable.

I'm not clear what you mean about turbulence? Quantum gravity involves as-yet unknown physics but turbulence is surely just a case of "the number of calculations we need to simulate it grows quicker than we can reasonably keep up with"? i.e. simple toy simulations work fine but we don't have a planet-sized computer to do something more extensive.

(Just to clarify - this isn't a "classical vs quantum" thing - it's a "we know the equations vs we don't" thing. I'm sure QED simulations are fairly similar within a known domain)

Presumably the GP refers to turbulence being infamously difficult to model analytically. But we have a great model for turbulent flow, the Navier–Stokes differential equations, it’s just that we can only solve them numerically in all but the simplest of cases. But when we do we get good results, so it’s not like turbulence is some mystical phenomenon beyond the reach of our standard mathematical tools!

My knowledge is a bit weak but aren't there non-analytic ways to model turbulence? "Analytical" isn't the whole of maths.

(I might not have a clear understanding of what "analytic" means so please correct me if I'm talking hogwash)

The alternative is numerical approximation, as I mentioned. Like always in physics, any analytic (ie. "closed form") solutions would also necessarily have to be special-cases, approximations, and simplifications. The problem with turbulence is that it's so chaotic and complex that it doesn't seem to be reducible to simpler models while still retaining some predictive power. But that's not very surprising; we're talking about the chaotic motion of molecules at the Avogadro scale! After all, we can't even write closed-form solutions (or even approximations) to the motion of merely three bodies under gravity, never mind ten to the power of twenty-three.

But what is fascinating about turbulence, though, is the "edge of chaos" – the boundary conditions at which laminar (non-turbulent) flow suddenly turns turbulent. On one side of the boundary analytic treatment is possible, on the other it is not.

But physics isn't a full description of reality. It certainly hasn't conquered consciousness and qualia and subjective experience.

> It certainly hasn't conquered consciousness and qualia and subjective experience.

I'm not sure how you're so certain of this. It is entirely possible that all we need to do to create a conscious mind is run a full molecular dynamics simulation of a detailed enough human brain scan. We know the equations to do this, we just don't have nearly enough computational power.

That would only be possible if qualia has no causation. In the case where our experiences have real effects they cannot be fully described by a Turing architecture.

How are you certain? Has someone published a paper that I'm not aware of that settles this?

You are missing a dimension here by the way. Even if we could find a physical location of the brain that lights up when the color red is experienced, that doesn't have any explanatory power for the nature of subjective experience. How can it be possible to experience being a brain, being a brain itself? Not just observing another brain and correlating brain activity with reported experiences.

Experience and consciousness are axiomatic and precede theory about the physical world. You started with sensory experience and perception, and built models of how your brain works on top of that, not the other way around.

> How are you certain? Has someone published a paper that I'm not aware of that settles this?

That's kinda the point. I'm not certain at all, but given the available information, it is the simplest explanation.

> How can it be possible to experience being a brain, being a brain itself?

I'm not really sure what you're asking here. A clock can tell time, but if it was _like something_ to be a clock, it would feel like knowing what time it is, it would not (and pretty much couldn't) involve awareness of all that goes into producing that feeling (because then you'd need a mechanism for awareness of that, and then a mechanism for awareness of that mechanism, and etc). The difference with the brain is that we're pretty sure it is _like something_ to be a brain in a body, and we also know it doesn't include perfect awareness of what goes into producing that feeling. So when you ask 'how can it be possible to experience being a brain, being a brain itself' I would say that it isn't? because your awareness is limited to the qualia that bubbles up out of the mechanics in the brain, and your experience of being a brain is similar in fidelity to the clock's experience of being able to tell the time.

> Experience and consciousness are axiomatic and precede theory about the physical world. You started with sensory experience and perception, and built models of how your brain works on top of that, not the other way around.

This is just solipsism. Sure, it is entirely possible all of the experiences and perceptions I've experienced have misled me into thinking that the brain is all there is, but that seems kind of contrived? I'm just as confused as you about why we aren't all p-zombies, but, well... the history of all knowledge has basically been "yeah it turns out to just be physics", so my guess is that qualia is also just physics.

It's not solipsism. The idea that "you" exist is just as conceptual as physics - there is no solipsism without "you". And the idea that it "turns out to just be physics" is a concept rather than reality. It's a thought of yours, not ground truth. And labeling this "solipsism" is just falling into that trap once again. It's really a miasma of perception in the form light and shadow and color and sound and pressure and heat (which are crude conceptual labels themselves for actual experience), and thoughts emerge in this cloud of sensation, also as independent phenomena in themselves. This subjective experience is first and primary. Any structure you build on top of it is conceptual and not ground truth.

It's not solipsism or contrived, quite the opposite. It's profound. Whether we like the fact or not, or that it's not convenient to your desire to have a mathematical formulation of the world, doesn't make it any less true. To downgrade the most direct experience of reality and give primacy to the conceptual is to confuse the map with the territory.

> Experience and consciousness are axiomatic and precede theory about the physical world.

Actually, they seem unnecessary to any theory about the physical world. They likely don't exist, but if they do, it's just bad psychology that wasn't quite debilitating enough for evolutionary pressure to weed them out.

I don't even think I'm conscious myself in the way you imagine yourself to be. "Consciousness" probably belongs in poetry, it definitely doesn't belong in philosophy and that goes double for real science.

So just ignore first hand experience as a phenomenon at all? That seems like a huge thing to pull the wool over.

It absolutely belongs in philosophy, and is one of the core topics in any philosophy program, and I'm not talking about "real science", which is precisely why I said that physics doesn't explain it.

There's nothing to ignore. Some evolved monkeys have vivid imagination, which they mistake for reality. Phenomenon noted, time to move on to important things.

Are you speaking as the representative of "reality"? Are you somehow the embodiment of "science"? Is it possible to experience and reason about reality without going through the eyes of an "evolved monkey"? You are speaking as if you are disembodied and floating around in the ether experiencing reality directly. It's so close to you that you don't even notice that you exist, and you are the only window you have to reality. There isn't any reality that you can be aware of outside of your own subjective perception, despite you "vivid imagination". You are confused if you think "reality" and "your model of reality" are two different things.

> Already you've sneaked in the presupposition that consciousness is only a result of your brain activity.

What else could it be? The interesting question is how and why.

> Have you ever not eaten for two days? Or not slept for more than 24 hours? Have you ever had an itch under a cast that you couldn't itch, and been constantly distracted by it?

Sure, I've done all of those things, but they all cause physical changes in the brain. These physical changes then directly affect your qualia-type experience of reality.

Have you read "What is it like to be a bat?" by Thomas Nagel? It's readily available online as a pdf. It discusses the hard problem of consciousness and the mind-body problem that I only briefly and poorly hinted at with my earlier questions. Reductionism doesn't work for consciousness. At all.

It hasn’t conquered beauty and comedy and love either. The things you mention will turn out to be folk human notions without satisfying scientific descriptions. They are no less real for it, but we simply don’t ask physics to describe love. I suspect consciousness will turn out to be an idea that is not amenable to physics or computational explanation as a coherent single phenomenon.

Right, so to get back to the original point of the thread, the universe is not necessarily confined by the Physical Church-Turing Thesis

As a joke, evolution adapted humans to have malfunctioning brains.