[FRIAM] The Unreasonable Reverence of The Unreasonable Effectiveness of Mathematics in theNatural Sciences

[Steve Smith]

Nicholas Thompson wrote: Owen, et al,   Well, isn't this part of the broader mystery of why logic should get you anywhere in the study of nature? Ah yes... *this* would be the larger and more interesting question.  But then, why would we have ever "invented" and "developed" Logic (very far) if it had no real-world use?   I suppose that is a good question for Theoretical Mathematicians and Logicians.   Isn't logic just a language trick? And Mathematics a "mere" extension of logic.   Why should nature give a fig for the tricks we play with our words? The Anthropic Principle might have  a play in this.  Any Universe that Linguistic Consciousness would evolve in would "naturally" have some patterns (follow some laws) that are tractable via such tools.    This is all reminding me, for some reason, of the "discovery" of the fact that the differential of the integral is just the original function.  There seem to be two sorts of "discovery" in our discourse:  One is the discovery of something in nature that we did not already know.  The other is the discovery of a new implication in what we have already said that we did not anticipate when we said it.  I can see why mathematics can help with the latter sort of "discovery", but have no idea why it should help with the former. I *do* believe that there have been significant examples of the former... where a bit of heretofore esoteric Mathematics is suddenly found to be *useful* in predicting/understanding a bit of heretofore unknown (or intractable) phenomenology. For Owen's *Identity* "The Universe *is* Mathematics" (or rather, his defense against *my* derisive statement to that effect), we would have to prove that not only is *all* Phenomenology describable by Mathematics, but that *all* Mathematics ultimately describes some Phenomenology. This seems to open the door nicely for the mystics.  Enter stage left, Rupert Sheldrake and the Intelligent Designers. In the emergence literature appears the endearing phrase "natural reverence".  The early philosophical emergentists believed that one had to accept emergent properties with "natural reverence," since such properties could not be reduced to the properties of their parts.  Yes, it is a sticky wicket isn't it?   I look forward to more elaboration on this topic (given the title/identity of this mail list/group). I am deeply ambivalent about natural reverence:  one the one hand, I believe that there is no point in being a scientist if you are not prepared to experience some natural reverence. Or perhaps one would not bother to be a Scientist w/o enjoying the brain chemistry induced by said "natural reverence".   It is also surprising/not that we have such brain chemistry... the love of an interesting problem well-solved! On the other hand, I also believe that natural reverence is the enemy of discovery.  Perhaps "natural reverence" is a fleeting pleasure one gets before one gets down to the dirty business of figuring out how things work: too little of it and one would never be inspired; too much of it, and one would never be curious. I think your first impulse was the most applicable... that somehow "natural reverence" is the reward for understanding the science (and mathematics) well enough to actually *feel* the reverence.  Like our Greek and Norse forebearers were wont to go up against their gods, *we* are inclined to go up against our own "natural reverence".   I don't know if the accounts of Kurt Godel's run up to kicking the stool out from under Russell and Whitehead included some of his own "natural reverence" of the *completeness* of Principia Mathematica, but I suspect it might have.   We create our god(desse)s in our own image so that we can go up against them (or make demi-gods and  through unholy unions with them?) Perhaps this is the point of of this thread in the first place, that we *do* find Mathematics amazingly (if not unreasonably) effective at predicting/describing/understanding phenomenology in the Natural Sciences.   This "natural reverence" seems to be a good point of departure, suggesting that we are compelled to question it and seek to debunk it. - Steve

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