This is exactly the point I was driving at (groping for) when I wrote that AI boosters' hopes depend entirely upon endless hardware improvement, chimerical innovations in software methodology and, not least of all, a deep comprehension of human cognition which appears to be beyond any forseeable improvement in our capacities.
His identification of the unspoken dependence upon *infinite time* is truly elegant.
This marries the philosophical concerns with a consideration of the architecture of actual machines very neatlt. DRM
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Not to push my luck, but... Consider that there are bio-chemical serial machines. They are molecular. The formation of micro-tubules is a serial process of adding molecules in a specific order and orientation in a cylindrical coiled helix.
It is in this realm that mathematical models really shine because they can bring together a collection of mechanical and electrical forces and orchestrate them to show the relations at work in physical pattern formation. And these of course inform nano-technology. Then in the more macro view, modelling the internal structural extensions and contractions of these tubules, in conjunction with their actin filament connectors and the stretching of the plasma membrane would be a fascinating model---something like a plastic bag of sticks that creeps along on a tread, like a tank.
These internal structural `machines' have all sorts of uses while the underlying dynamics of how they self-assemble and dissemble remains more or less the same. In plants the assembly and disassembly of the tubules react to mechanical forces. During growth in a tissue environment they seem to react to both chemical and electrical stimulus. During neuron growth, these micro-tubules are part of the neuron extensions that form axons and these seem to follow electrical pathways, something like navigation, via ion channel reactions along the membrane. In this respect they seem to have evolved a different utility with the same underlying process. Gould calls this kind of evolutionary change something, but I've forgotten what.
I've tried to follow some of the mathematical modelling of micro-tubule growth. They are composed of complex analytical functions working in an ensemble. The computed calculation requirements are huge for these simulations. And it is here that the computing problems of simulation validity show up.
On the other hand, all this a long way down the ladder from consciousness.
Chuck Grimes