Re: The Unreasonable Effectiveness of Mathematics in theNatural Sciences
Posted by
Nick Thompson on
Apr 26, 2009; 5:40pm
URL: http://friam.383.s1.nabble.com/The-Unreasonable-Effectiveness-of-Mathematics-in-the-Natural-Sciences-tp2714601p2718641.html
Owen, et al,
Well, isn't this part of the broader mystery of why logic should get you anywhere in the study of nature?
Isn't logic just a language trick?
Why should nature give a fig for the tricks we play with our words?
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.
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. 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. 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.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
----- Original Message -----
Sent: 4/26/2009 10:17:16 AM
Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences
Well said/observed David, I too am a Lakoff/Johnson/Nunez fan in this matter.
While I am quite enamored of mathematics and it's fortuitous application to all sorts of phenomenology, Physics being somehow the most "pure" in an ideological sense, I've always been suspicious of the conclusion that "the Universe *is* Mathematics".
This discussion also begs the age-old question of whether we are "inventing" or "discovering" mathematics. Similarly, it revisits the question of whether discoveries in mathematics portend discoveries in Physics (or other, "messier" phenomenological observations).
- Steve
Prof David West wrote:
I'm completely of Tegmark's ilk:
I assume that means you would also adhere to the sentiment attributed to
Einstein:
"How can it be that mathematics, being after all a product of human
thought which is independent of experience, is so admirably
appropriate to the objects of reality?" Which contains the
fallacy, "independent of experience."
Thought - and mathematics! - is but a refined metaphor of experience.
(following Lakoff)
davew
A different response, advocated by Physicist Max Tegmark (2007), is
that physics is so successfully described by mathematics because the
physical world is completely mathematical, isomorphic to a
mathematical structure, and that we are simply uncovering this bit by
bit. In this interpretation, the various approximations that
constitute our current physics theories are successful because simple
mathematical structures can provide good approximations of certain
aspects of more complex mathematical structures. In other words, our
successful theories are not mathematics approximating physics, but
mathematics approximating mathematics.
-- Owen
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Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at
http://www.friam.org