Joined: Sep. 2007
|Penrose is pretty cool but it still belongs in the what if department. It hinges completely on a neurological model requiring that the basic process of thinking is algorithmic.|
Seems to me he's challenging the algorithmic model, at least for higher functions (most automatic and subconscious processing/response probably is algorithmic or primarily so). Sure, quantum computation is still computation, but he makes a big enough issue of "non-computability" to highlight a different approach.
|Anyway, the issue he raises goes something like this (please correct me if I am wrong): In order to have confidence in any system (of algorithmic first order logic), the system needs to be viewed from outside to see its truth or falsehood. He claims that the existence of math is evidence that we do this. Since that violates Godel's second theorem, (a system can not prove it's own consistency) he deduces the existence of a different, non algorithmic system which functions using some kind of superposition to explore all options at once and settle into one state.|
Not quite sure how to parse that in terms of what (little, given my shortcomings) I learned. The way I grok the gist...
The only 'outside' system that might be said to 'observe' the workings of the cosmos and the mind would have to be something fundamental to the nature of cosmos and mind - a quality or parameter of the universe itself. Hameroff suggests this is consciousness (he's a bit of a panentheist or something) that seeks ever greater and more orderly expression of itself. Penrose doesn't go that far, though allows the suggestion to stand on the organic level - that which concentrates and experiences consciousness.
His process involves a separation of reality, not quite the same thing as a simple superpositioned reality. I analogized it to time for my own understanding, which Penrose probably wouldn't approve of but fits with my suspicion that nobody's paid enough attention to that factor in the overall scheme of things. As if there's a static universal 'reality' representing the collective *now* that is constantly slipping into to the next *now* as individual wavefunctions diverge from the previous measurement. When the separation of the THEN *now* and the COMING *now* reaches Planck distance, gravity serves as the collapse operator.
This would make time reducible to Plank scale 'ticks' of the cosmic clock, though, and that is much too swift for any consciousness we know of to ever keep track - our awareness time-lags are immensely longer than that. IOW, consciousness experiences itself and the universe in the (relatively distant) past instead of the measurement present. Which means our awareness is always of the reality that was measured some microseconds previously.
Penrose is a Platonist. Thus he believes in the existence of 'model' worlds where all the big-t True things reside, and this lesser manifestation is shaped (is there a better word?) in its event trajectory according to that superior model. Which people like him can describe with mathematics. Nobody - least of all Penrose - ever suggested mathematicians don't believe themselves god-like! §;o)
There are no "all options" in that process. Sum of histories (*past*) and actual state (*now*) represent everything that need be represented to accomplish the next state - the universe can't phase change into something entirely 'other', even if isolated weirdness can be tolerated in the system. The process is habitual, automatic, and governed by gravity - no truly chaotic degrees of freedom.
|If Hofstadter is right, there is a level beyond which we cannot model reality and that limit is determined by brainpower. Simple as that.|
Perhaps he is right. I am unfamiliar with his work, so can't say. But I'm fairly convinced that we DON'T model reality as-it-is because we don't know enough about reality to do so. Theorists make a mighty effort, then invest so much emotion into their provisional models that they convince themselves they do know it all and nobody can rightfully challenge. That seems to be a significant limitation. Sort of dueling wannabe godlings...
At any rate, I previously expressed my personal suspicion that Penrose's model is indeed insufficient. He suspects so himself. It may be a step in the right direction, at least to facilitate what may come from theorists 'someday'. But that obscure model I mentioned with the p-adic mathematics looks to account for more of the anomalies than Penrose's can. It's got 8 dimensions plus a "many-sheeted" spacetime! Plus: no pesky singularities. Minus: it's thick as a brick, unspecified extremal for collapse (looks to be a hedgehog). Penrose's extremal - the graviton - is not postulated to need more than a single step to align all vectors.
I am not so sure mathematics is some sort of miraculous manifestation of a Platonic realm of Absolute Truth as mathematicians are. But then, I'm not a mathematician.
|Also, embodied intelligence and the revolution in AI heralded by Brook's Subsumption architecture* makes it even dicier because it isn't clear that we are even integrating all the parts of our own system, let alone transcending the whole thing.|
Of course we aren't transcending "the whole thing"! BTW, I expect an "intelligent" machine isn't all that difficult, we'll see it relatively soon. What do you think of the idea that someday they'll create a "conscious" machine?