GS Chandy says: >the story Poincare tells about how he managed 'in his sleep' to resolve a particular complex problem that had been troubling him - which resolution later, I believe, led him to 'chaos theory'
I'll say more later - but why should we expect all of our "computation" to be available to introspection? I've also had the wonderful experience of waking up with fresh new insights that led to fruitful accomplishment.
GS Chandy says: >I claim that computation is definitely an 'entirely natural phenomenon' - but whether it 'precedes' the arrival of man, I do not know. It does seem to be something that humans do explicitly. However, animals, too (I believe) do 'computation': e.g. an anthill is definitely based on extremely complex calculations (probably more complex than those in the most modern and ambitious of our skyscrapers). True, those ants do not seem (in our rather limited understanding of them) to compute 'explicitly'.
You say "explicitly" - I might say "consciously," or as above, in a way available to introspection. That's a good distinction, but it may not (or it may!) make much difference in how computation proceeds in general, or tell us much about how to describe it or analyze it. Humans also do much computation without any self-awareness at all - in say, your vision system.
GS Chandy says: >In any case, I do have rather grave doubts about our current (human) ability to understand the relationship 'precedes' (in any 'systemic sense')
I merely meant in the chronological sense.
GS Chandy says (regarding music analogy): >At a 'broad' level, I agree entirely - though I do not understand the mental models you are working from in any detail.
That's too bad - rather key to my whole argument. The point is concepts, language, and rules can be formulated directly at a level appropriate to some given phenomenon, without starting from the "ground up". Chemistry, for example, made a great deal of progress even though at the time, in the 1700s and 1800s it could not really be reduced to the physics of the time. That needed to wait till quantum theory of the 20th century.
Here's a thought experiment, maybe it will work for you, maybe not. Suppose an extra-terrestrial intelligence examines one of our computers, and suppose it is a completely different technology from anything they've seen. Furthermore, let's grant them supreme knowledge and competence in measuring and analyzing electro-magnetic and quantum phenomenon. So they could see all the voltages flying around, the whole fantastic dance at quite a closeup and complete viewpoint.
Now uppose they don't have a vocabulary and mental concepts that includes the likes of, RAM, CPU, register, ALU, program, etc. etc. etc. Well then, this intricate mechanism may be a complete mystery to them, even though in principle they have complete physical knowledge of it. Those higher level concepts serve as a key to unlocking the meaning of the device, much like a Rosetta stone. Without those concepts further understanding may be completely blocked. Its not as if complete physical knowledge serves as any kind of automatic gateway to obtaining these higher level concepts.