GS Chandy says: >I believe it is entirely counterproductive to try to 'compare' humans (directly or indirectly) to machines because it is entirely clear by now that no such comparison is 'meaningful' at all
Doctors routinely view us as machines, and mechanical implants and parts are turning more of us into cyborgs everyday. Its only when we approach the "I" (somewhere in the brain today -- not many believe it involves the heart anymore) that objections begin to mount. Some gurus teach that the "I" isn't the true self, oh well!
But I really only brought up this bit about natural computing ala Denning because (1) I think its an interesting view that is not entirely common today, and (2) though I wouldn't know how to define "all of math" myself, it seems it never gets too far from something related to computation, be it numerical or logical or algebraic.
If computation itself is viewed as an entirely natural phenomenon (preceding the arrival of man), then math itself appears more natural, even if man did/does not recognize immediately as such. Rather than trying to reduce math to nearly nothing (just + and x), this view places it in a much grander context, in my estimation.
The question that the natural computing view raises is, what are the best concepts and language that should be employed to understand the complex information processing systems found in nature? I'll try an analogy - we know music hits our ears as sound waves. But to understand music we don't begin at the physical level and analyze the physical phenomenon of sound in all generality. Sound in general is noise - only certain sounds are music. To understand that we have concepts of rhythm, scale and harmony, and proceeding from there to larger structures (phrases, forms, etc.) Its about finding the right concepts and relations and way of talking about the phenomenon. To understand computing in all its natural glory, starting at the level of physics may be a dead end.