Harry Veeder
Mon, 09 Jun 2008 12:52:56 -0700
On 4/6/2008 10:53 PM, Stephen A. Lawrence wrote: > > > Harry Veeder wrote: >> I am calling your bluff. ;-) > > Not a bluff, though it involves some fuzzy reasoning. The difference > between a "proof" and an "explanation" has bugged me since junior high, > when I found out that most mathematical facts are "proven" without ever > being "explained". > > As I said before, a "model" may predict what's going to happen but will > never tell you why. Using a model is a tacit admission that we don't > know what the "reasons behind" things are, or even if there are any such > reasons. I would think the _construction_ of a model depends on some a-priori explanations (or stories?) of the world. > >> What is the difference between an explanation and a model? >> You have said something substantive about models, but nothing substantive >> about explanations, except to say that explanation is not a model. >> Or is it just an issue of semantics? > > Maybe it's just semantics, but I actually think it's more a matter of > gut feel, and "satisfaction level". If you look at the link Terry gave, > the author's objection is that physics doesn't say "why" magnets > attract. Well, what would it mean to say why they attract? > > This is the heart of the issue -- just exactly what is an explanation? > In physics it's hard to say, for me, at least, because I don't know of > any explanations. As far as I know modern physics has none. It does and it is called "mechanics", and to ensure mechanical explanations remain dominant and universally applicable they have been revamped by the quantum hypothesis. > In math it's easier to see the difference. For example, we can find pi > by integrating the arctan function, or by integrating sqrt(1-x^2), both > of which are stunningly opaque approaches. We can prove that the area > of a circle is pi*r^2 using calculus, which is, again, an amazingly > opaque approach. Alternatively, we can find the circumference and area > of a circle using Pythagoras's theorem and some simple drawings, and we > can extract a value for pi that way. I would call the latter approach > an "explanation", because, to me, it "explains why" the circumference > and area of the circle are what they are. > > But something this is pointing up is that the word "explanation" is > rather slippery. I could struggle with it a bit more, and perhaps say > that an explanation works from simple things which we "know" to be true > to show that other more complex things follow inevitably from those > simple things -- but the phrase "know to be true" is already flirting > with vagueness. So I'll just let it go at saying that an explanation > leaves one feeling satisfied; a model may not... I guess the question becomes how do we learn a particular sense of satisfaction, and are there other senses of satisfaction that should be allowed in physics other than those rooted in mechanics and probability theory. > By the way, the derivation of pi from Pythagoras's theorem to which I > referred, and the derivation of the area of a circle and volume of a > sphere using geometric arguments, are here: > > http://physicsinsights.org/pi_from_pythagoras-1.html > > http://physicsinsights.org/sphere-volume-1.html > > You may not feel these pages actually "explain" anything, of course! > :-) That was, however, part of the reason for putting them together, > and perhaps these pages will give you an idea of what I think an > explanation is. Or maybe not... Aristotle's explanation of why some things fall (gravity) and why other things rise is that each element seeks its natural place of rest. Bodies made of the element "earth" tend to fall, while bodies made of the element "air" tend to rise. This may not be satisfying from a modern sensibility, but it was satisfying to many people in the past. Likewise, the sensibilities of future generations might regard today's physics as unsatisfying. In fact many people do right now. ;-) Harry