Hello again, Barnaby ,
Sorry it took me so long to respond .

(Much events offline call for attention)

Barnaby Posted : What exactly is "real" in calculus? The equations?

Response: Ontolgically real ---yes .

Barnaby Posted :It doesn't seem strange to me that two mathematicians working in the same small culture with the same problems should simultaneously come up with similar techniques around the same time.

Response: Well Germany and England weren't exactly the same culture . But calculus was also a new field of math at its onset . Was there a proto-calculus in the annals of math to act as a template for it ? And if there was what sort of inter-cultural lexicon of mathematical algorithmns and signs would have been extant to that proto-calculus in both Germany and England at that time to serve as a common shared group of symbols and proceedures as precedent for the discoveries of Newton and Leibniz about claculus ?

Barnaby Posted : Math does pose some very interesting and deep questions. I think there is a deep affinity between the pattern-generating processes that order human cognition and the pattern-generating processes that give rise to ordered dynamical aggregations of matter and energy in our physical universe.

Response : But what *sort* of ontological structure or structures is that deep affinity between the predicated on ? Is it (A) merely an affinity based on some sort of morphologies that merely arises as a result of recurring patterns of efficent causation shared by both the pattern-generating processes that order human cognition and the dynamical aggregations of matter and energy --due to the way physical processes tend to push and pull OR is it (B) bsed on some sort of trans-situtational *prescriptive* sort of patterns of causation ---something more akin to what Aristotle called formal cause . ?

(The notion of formal cause is *not* that far in terms of thmatic content from the Platonic notion of idea essences --though Aristotle elsewhere tends to have a nominalist rather than a Platonist mood to many of the thesis he supports )

Barnaby Posted : So there is a homology there, which goes a long way to explaining this kind of mimesis. But I'm not seeing the necessity for truly-existent, transcendental mathematical objects or patterns for math to work.

When you find natural systems that math does a good job of modeling, such as in classical mechanics, it can be tempting to feel there is something to this kind of neo-Pythagorean thinking.

Response : But what other sort of ontological structure can there be to act as the source of the homolgy, other than some prescriptive , trans-situational structures ?

Barnaby Posted :But then there is a vast array of natural phenomena that math can say little about. Consider the three-body problem.

Response: I'm earnestly not familiar with the three body problem,though I think I've heard of it in passing. Please elaborate on the three body problem .