uncertain about uncertainty
I was thinking about physics again.....
Why is the relationship between mathematics and physics so strong? Remember, where Plato taught had the sign "Let no one enter who does not first know Geometry". Examine (though bad examples of philosophers) Descartes, Leibnitz, Kant (in his own way), even in modern times Edmund Husserl, - all mathematicians. Even the Pricipia is a truncated title. Maybe it is because Physics is the science of nature, and dispuisti omnia secundum numerum, (something I can't remember - probably Latin for weight) et mensuram. How the world is created is according to mathematics. To describe it in intelligible human terms we must describe it mathematically. This leads to the question of why Physicists do not call themselves philosophers - a question I have often asked. Not to cut my meandering preface short, but I stumbled across another very interesting passage from a book, I would like to painstakingly type out and comment on. Without further ado, the reason I started writing this:
Why is the relationship between mathematics and physics so strong? Remember, where Plato taught had the sign "Let no one enter who does not first know Geometry". Examine (though bad examples of philosophers) Descartes, Leibnitz, Kant (in his own way), even in modern times Edmund Husserl, - all mathematicians. Even the Pricipia is a truncated title. Maybe it is because Physics is the science of nature, and dispuisti omnia secundum numerum, (something I can't remember - probably Latin for weight) et mensuram. How the world is created is according to mathematics. To describe it in intelligible human terms we must describe it mathematically. This leads to the question of why Physicists do not call themselves philosophers - a question I have often asked. Not to cut my meandering preface short, but I stumbled across another very interesting passage from a book, I would like to painstakingly type out and comment on. Without further ado, the reason I started writing this:
At the quantum level, the electromagnetic forces between charged particles A and B are understood in terms of the exchange or transfer of photons. . . . . In this way, forces between particles are transmitted by other particles (photons in this case). Actually, this description is rather simplified. The transmission involves a complex web of short-lived (or "virtual") particles travelling in both directions and also buzzing around each of A and B individually. A similar sort of description may be given for nature's other fundamental forces. The diagrams are a symbolic representation of abstract mathematical terms that can be used to compute subatomic processes correctly to a very high accuracy.
Paul Davies, God and the New Physics, pg. 148
All the boldface is mine, but it highlights what concerns me. First, there is the "understood". What is to prevent me from giving another physical explanation for this force without resolving to particles that yeilds the same mathematical results? See my last post for thoughts on the sentences from "Actually," to "individually" - I would hate to try to type out another exposition on Feynman diagrams. Finally, there is the troubling phrase - also in bold - in the last sentence. I thought when I was force-fed a highschool Chemistry (or Physics) text that these diagrams were supposed to in some way reflect the reality of nature. But here we have a PhD telling us that that is not the case - that the particles are abstract mathematical entities. Where do mathematical entities reside? Certainly not in my beer bottle in front of me. The only math there is ounces (sadly down to about two). Abstract mathematical entities are notional, more to the realm of philosophy than to the study of nature. But that's okay, Davies reassures us, even if they don't exist they still calculate (numbers?) to a "high degree of accuracy" - but what are we calculating? Is this like a non-Euclidean Geometry, whose axioms are not self-contradictory, but distasteful, and can still give demonstrations? Does this reside only in the mind? I have to cut this short (I doubt anyone's made it this far anyway) but I have a few more thoughts about the card tower itself. But, that will have to wait until another day...........
