I haven't read Searle/Penrose
Or are you specifically talking about perfectly simulating human brains? Human brain emulations are only one very specific and narrow form a strong AI might take. But even in that specific subset of possible AIs, we have no real idea how precise the simulation might have to be. It might be perfectly acievable without even simulating individual molecules.
That aside, even if human cognition is a computable function, there are no guarantees that the physical process giving rise to human cognition is computable, nor that any process giving rise to cognition is computable.
Unless something in physics changes drastically, human cognition is a finite state automaton. See my other reply on the Bekenstein Bound.
The growth has an upper bound which means it's ultimately computable:
As this relates to the human brain, and even omitting any quantum weirdness (of which there is probably a lot), all we can say is the total state of the brain at time t requires at most N bits, where N is the bound over volume of the brain. It says nothing about the (information theoretic) entropy of the _dynamics_ of the brain, which is where the process of cognition actually occurs. In fact many (if not most) physical processes have infinite entropy.
For an example of a deterministic system that exhibits such behavior, Consider the logistic map at r~5.7. There exist some coarse partitions [0] of the state space such that the trajectory that can be expressed in a finite number of bits, but this is not in general the case, even though any _given_ state of the system can be expressed in a finite number of bits. Other examples include the double pendulum, three-body orbits, and in fact most real physical systems.
In fact it is not in general true that a system with N bits of state can be always simulated with <= N bits. We can obey the Bekenstein bound without necessarily being able to simulate the process, even a complete description of the state at time t.
For the time evolution of the state space of a system, the Lyapunov Time [1] and the Lyapunov Exponent [2] are much more informative. If the time required to reach another bit of precision grows faster than polynomial time, no Turing machine can hope to simulate that physical system in a practical amount of time. In fact we also have physical bounds on how much memory we have to work with, and how fast we can flip bits for a given volume of space - simply enumerating all possible state transitions of the brain using a Turing machine will require a volume of space much larger than the brain itself if the time evolution of the system produces large Lyapynov exponents (which it absolutely does). This should come as no surprise - known NP-hard problems have the same behavior.
I would also add, even if the brain turns out to have a representation in N bits, and the state transition is (somehow) computable in polynomial time, it may still be physically infeasible to do so without just building and 'running' an actual brain.
[0]http://tcode.tcs.auckland.ac.nz/~corpus/logistic.html [1]https://en.wikipedia.org/wiki/Lyapunov_exponent [2]https://en.wikipedia.org/wiki/Lyapunov_time
PS: To me all of the above suggests that whatever the universe is doing when it's doing physics, it certainly isn't computing in the Church-Turing sense.
I'm not sure how you reached this conclusion, assuming you're not just making a trivial observation that our formalisms employ the reals, which in itself entails nothing meaningful given the reals are merely a convenience, not a necessity.
If we accept that any bounded volume contains finite information I, and the laws of physics themselves have a finite description, then such laws are isomorphic to a state transition function I(t) -> I(t+1), which is readily simulable on a Turing machine. Of course, the devil's in the details of "finite" above.
> If the time required to reach another bit of precision grows faster than polynomial time, no Turing machine can hope to simulate that physical system in a practical amount of time.
I assume you're discussing the feasibility that cognition is simulable on standard computers here. I dispute your position that there's likely to be any quantum weirdness beyond ordinary chemistry, but even setting that aside, you're ascribing far too much power to the human brain.
Fact 1: natural selection would weed out any species with an organ that consumes more energy than any benefits it yields.
Fact 2: the growing evidence of many animals using tools, and our growing acceptance of a spectrum of consciousness among the animal kingdom, entails that human brains aren't too special, just special enough.
Fact 3: the detailed documentation of sensory defects, like optical and other sensory illusions indicates that whatever information processing algorithms we utilize, they are imperfect at best. This is exactly what we'd expect from evolutionary pressure, ie. we'd expect the most efficient information process that yields reproductive success, which is a flawed set of efficient heuristics that cover the majority of cases with the fewest resources needed, and not an energy-intensive, complicated, subtle but foolproof system.
Fact 4: many of the feats that were the exclusive domain of humans, like visual recognition and imagination, natural language translation, novel musical and written composition and more can be performed by computers. They're at roughly a 3 or 4 year old's level granted, but given we take 20 odd years to reach mastery levels in these disciplines, I'd wager that the computers will reach parity in that time frame too.
There's frankly little reason to believe the brain is special in any particular way, simply complex and layered, which will take some time to disentangle. It's like asking to describe the exact path of
> PS: To me all of the above suggests that whatever the universe is doing when it's doing physics, it certainly isn't computing in the Church-Turing sense.
Coincidentally, 't Hooft just released his book on the cellular automaton theory of quantum mechanics [1]. I certainly hope it will change your mind, because I think people these days far too readily dismiss determinism, and even the strong Church-Turing thesis, often for specious reasons.
[1] https://www.reddit.com/r/Physics/comments/6ntbvy/the_cellula...
Which is precisely the point I'm making. I deliberately avoided any woo about non-determinism, biology, or consciousness by providing examples of the time evolution of purely deterministic dynamical processes, very simple ones, which produce behaviors that are provably not computable in any reasonable time and have infinite (informational, not thermodynamic) entropy.
The complexity classes of generating additional bits of precision are much worse than exponential in many cases, and these are just ordinary everyday systems - nothing so complex as a brain. You provide examples of flaws in human cognition, which I acknowledge, but pointing them out does nothing to advance the idea that the brain is a computer.
But time evolution isn't relevant. Even supposing such systems exist naturally, you're conflating simulation time with real time.
> You provide examples of flaws in human cognition, which I acknowledge, but pointing them out does nothing to advance the idea that the brain is a computer.
"The brain is a computer" is a very different claim to "the brain can be simulated by a computer". I've only claimed the latter.
They do, I gave examples.
> Conflating simulation with real time
I am not talking about real time, only about finite time for any Turing machine. No matter how fast you make your machine, I can ask for another digit of precision. As I mentioned earlier, you are also bounded on how fast your machine gets to be much earlier than I'm bounded on digits. You'll be running my double pendulum until the heat death of the universe, and using all the mass energy available to do it.
> The brain is a computer" is a very different claim to "the brain can be simulated by a computer"
These are equivalent by the universality of Turing machines. You are in fact making this claim, even if you don't realize it.