Harry Veeder
Thu, 12 Jun 2008 11:03:21 -0700
On 9/6/2008 3:51 PM, Stephen A. Lawrence wrote: > > > Harry Veeder wrote: >> 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. > > > Not necessarily, though some certainly seem to be. > > Aether theory is predicated on the notion that there is some kind of > aether which carries some kind of vibrations; as such that's a sort of > fuzzy explanation (though the details are pretty wild if you stop and > think about what sort of material aether must be, keeping in mind the > obvious fact that planets and stars plow through the aether with no > impediment to their motion, along with the fact that vibrations > traveling in any known medium go faster as the medium becomes stiffer > and slower as the medium becomes floppier -- and vibrations in the > aether travel really wicked fast, so it must be really wicked stiff, > which makes those planets cruising through the middle of it all the > harder to understand). An aether is untenable if one begins with the assumption that the aether is some sort of medium which obeys Newton's three of laws motions. One could argue that the medium offers no resistance (i.e. has no inertia), but instead is limited by how fast it can "part" or "give way" to the motion of a body through it. This "parting" occurs at the speed of light. An an illustration consider this non-mechanical analogy: A queen is walking through a crowd of loyal subjects. The crowd offers no drag, but the speed of the queen is limited by the ability of the crowd to part. > But to take a contrary example, special relativity postulates no > mechanism at all for anything; it's just a proposal that the geometry of > space is just like what you get if you assume the distance between any > two events is fixed for all observers *if* you measure distance as x^2 - > t^2. The justification for it is that it works, with no reference to > whether or not it "makes sense" or "explains" anything. > > Another contrary example is Ptolemaic cosmology, which as far as I can > see explains nothing, and is really just a mathematical construct. You have to situate it within the cosmology from which it emerged to find the explanation. In that cosmology a distinction exists between the celestial relm and the earthly relm. Heavenly bodies had to move in circles because circular motion expressed the perfection of the heavens. > >> >>>> 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", > > > I can't really agree. We tend to think "mechanics" explains something > because it so neatly matches our experience with stuff, but really it is > nothing more than a *description* of what Newton thought things did. > > A centerpiece of Newtonian mechanics is the law of gravity, which is > simply a bald statement that two bodies attract with a force equal to > > G m_1 m_2 / r^2 Although it was formally consistent with his laws of motion Newton's notion of gravity as universal attraction was very unmechanical, as it violated another aspect of the mechanical paradigm which only permits one body to influence another body by collision or through the action of an intervening material (inertial) medium. > with no hint of an explanation -- and what's more, that's a description > of action at a distance, with information as to where each body is > located being transmitted to the other body in *zero* time, with, again, > no proposed mechanism for this information transfer. Newton, as I > recall, had misgivings about that (and he was right, of course). He was not the first to suggest gravity was a kind of attraction. At the time this would have been called an "occult" theory. I believe he distanced himself from his own "occult" theory because the mechanical paradigm had become the dominant paradigm among his peer group. > More basically, Newton's second law (I think it's the second law -- it's > hot has heck here today and my head's full of fuzz as a result) says that > > sum (dx_i/dt * m_i) > > must be constant. No reason is given; no mechanism is provided; it is > merely a mathematical statement, chosen to match Newton's observation. I really don't think Newton came up with the expression by simply playing around with equations. BTW, he did not exclude occult explanations from the domain of (his) physics: "But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered. And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea." > Of course it turns out that there can be no simple (and correct) > mechanism given for either Newtonian gravitation nor the conservation of > Newtonian momentum, because both laws turn out to be untrue at the > "edges" -- over very large distances, at very high velocities, they > don't work perfectly. So their "mechanism", if it were stated, would > necessarily be something which doesn't quite apply in all situations. > That would tend to make it less than satisfactory as an "explanation", I > would think. > > >> and to ensure mechanical >> explanations remain dominant and universally applicable they have been >> revamped by the quantum hypothesis. > > > But again, they're not "explanations", at least not as I understand the > term. If _explanation_ means the same thing as _mechanism_. > Tell me *why* momentum is conserved -- that would be an "explanation". > But Newton didn't tell us *why*, he merely told us that it *is* > conserved. It's like the following little convsersation: > > "Go to bed NOW!" > > "Why?" > > "Because I told you to!" You need to go back to the early 1600's. While Descartes did not posses the precise formulation for the law conservation of momentum, he did have a law of inertia and the rough idea that a quantity of motion is conserved. He provided a theological explanation for conservation, which when I think about it, is also a theological justification. >> >> >>> 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. > > > Yes, I agree; that sounds right. > > >> >>> 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. ;-) > > > Yes indeed -- and learning more of it doesn't necessarily make one feel > more "satisfied" with it... > Harry