roger:
To clarify a couple of points.
When I've been talking about a "brain" and "thoughts" on this thread, I've been meaning a conscious brain and conscious thoughts.
I don't doubt that a TM can be called a kind of brain, if you like.
You say that your pencil brain can do anything a human brain can do, because both are computable.
But that assumes that speed must be irrelevant. In other words, that nothing the human brain does is dependent on speed.
And that's what I've been trying to focus on.
I think we're butting heads because you're focused pretty much exclusively on information theory, and I'm focused on how the brain appears to create the phenomenon of consciousness.
Well, to my point of view speed is an implementation detail, and thus pretty uninteresting.
To expand on that, no, a pencil brain, actually and really implemented by a person sitting at a desk with a pencil, or by a TM, will not be conscious, or even work for no other reason that in a person's lifetime they won't even be able to compute one state of the brain, let alone have it do any processing. It'd take more than your life just to write the starting condition on paper.
So, yes, on a practical level a real pencil brain wouldn't work, especially if you were trying to process data in our world, real-time.
But, this whole thread is about thought experiments. I'm free to assume that I have an infinite life, essentially infinite paper (you'd need a very large, but finite amount of paper to simulate the brain) and the speed of inputs would have to be very, very slow compared to you. So, accelerate to relativistic speeds, tunnel to a multiverse, whatever it takes to get that time dilation.
What we are trying to get to here is whether the brain and consciousness is nothing more than a consequence of matter - a completely non dualistic position. Sure, in this world a pencil brain is ridiculous - it'd never process data fast enough, but we are interested in principles. So, the chain of reasoning goes like this:
1) the universe at a macro level is computable
2) everything in the brain that we have observed - neurons, chemical soup, the networks, are computable, and not susceptible to noise that would make them non-computable
3) consciousness comes from the brain ad it's coordinated activities
4) So, consciousness is computable, or there is something 'extra' in the brain we have never observed
5) hence, it's a very strong position(meaning likely) to state that a computer could be conscious, so long as it was structured the same as a brain
Note there is no dualism in 5. We don't require a person to interpret the symbols in the brain, or the computer. The organizational structures in the brain, their self-referential way of computing, is the consciousness (I have trouble talking about 'creating' consciousness, as I don't think of it as a 'thing', to me consciousness is just the brain's machinery doing its thing).
Now, information theory tells us a TM - a pencil, a paper tape, a motor, and just a tiny handful of operation, can do anything computable. So, a person with a pencil can do the same, following rules blindly, neither understanding what they are doing, why they are doing it, or the meaning of all the 1s and 0s they are writing down.
When we talk of a pencil brain, we mean formalizing
all of the systems, components, and data in the brain as a set of computable functions, and then implementing it as a TM and associated program. Realistically, TMs are really slow, and we'd really write a program on a supercomputer, but there is nothing stopping you from doing a TM or a person and a pencil.
And this sort of tests your convictions here, because it is very counterintuitive. Because my claim is that form of a pencil brain, a human with a pencil, would indeed be conscious, though that consciousness would stretch out over eons. Certainly as the person sat there and wrote 1s and 0s, there would be nothing you'd call consciousness, but then are you 'conscious' during a single planck time interval (~10^-44 secs)? I'd say no more than a pencil brain would be conscious over a year period. But that doesn't mean you are not conscious over a second, and that a pencil brain is not conscious over many eons. Consciousness is nothing more or less than the processes running.
So, going back to the OP, you can see I hope that Paul was asking questions about the pencil brain. Remember, computationally, the pencil brain is exactly the same as the biggest baddest supercomputer you can imagine, just a heck of a lot slower. So, if a pencil driven by a TM, or a human blindly following a program, is doing exactly the same thing as 1) a supercomputer, and 2) your brain, does the fact that the pencil goes a lot slower mean no consciousness will form? Again, this is a thought experiment, no bringing up the speed of impulses, or the indubitable fact that when trying to simulate 100billion neurons by hand the pencil marks for neuron one will fade long before you reach the 100 billionth neuron.
I say yes, the pencil brain will be conscious, measured in appropriate timescales (millions of eons, not seconds). Our year will be it's planck time. But that is just a scaling issue.
If you say no, and not for some practical concern like who has enough paper to write the state of 100 billions neurons, or pencil fade over several hundred years, then you must be introducing something extra - something noncomputable - in the brain that creates consciousness.
Is this clearer?
edit: since we've strayed so far, I'm going to quote the OP, and give my answer, with all of the above informing it. perhaps that'll add nothing, but perhaps it'll make it clear why pencil brains have been such a topic for us