Physics Is About Rules, Not Facts

While in the library looking for something else, I noticed a book called The Trouble with Science by Robin Dunbar, whose description made it sound very much on point for my current project:

In The Trouble with Science, Robin Dunbar asks whether science really is unique to Western culture, even to humankind. He suggests that our “trouble with science”–our inability to grasp how it works, our suspiciousness of its successes–may lie in the fact that evolution has left our minds better able to cope with day-to-day social interaction than with the complexities of the external world.

Somewhat contrary to that description, the early bits (a potted history of science and the philosophy thereof, followed by some examples of research on science-y behaviors in other speices) were actually sort of in agreement with stuff that I’m saying in my book. The writing’s pretty dry, but I was basically okay with it until he starts into talking about the counterintuitive nature of modern science, and tries to illustrate this with references to physics. There’s a discussion of neutrinos that’s so awful I don’t even know how to correct it enough for it to be wrong, but even before that, he shows a deep misunderstanding of what’s going on with Newtonian physics. That part is at least based on misconceptions that are vaguely useful for the intro mechanics class I’m teaching this term, so it’s worth transcribing a bit and talking about why it’s wrong:

Strictly speaking, Newtonian physicsmust rank as the biggest confidence trick in the history of human learning: it makes all kinds of totally unrealistic assumptions about the existence of perfect vacuums, ideal gases, and frictionless processes, none of which ever occur in nature. Every experiment has to be carefully contrived to get it to work, otherwise extraneous variables are likely to produce results that bear no relationship to what the theory predicts. Try dropping a stone and a feather from the same height. Newtonian physics says that their rate of fall is governed only by the effects of gravity and is independent of their respective weights: they should hit the ground together. But, as everyone knows, they don’t: the stone will hit the ground before the feather. Aristotle concluded on the basis of everyday experiences of this kind that the rate at which objects fall depends on their weight (or mass, to use the proper physics term). Galileo had to cheat in a famous experiment to show that Aristotle was wrong: instead of dropping a feather and a stone from the Leaning Tower of Pisa, he dropped two cannon-balls of different weights. (Actually, he didn’t drop them from the Tower of Pisa at all: he rolled them down an inclined plane. But such is the mythology of science!) The effect is the same, at least in principle, since a light cannon-ball is standing in for a light feather. To show the same effect with a feather, you would have to carry out the experiment in a perfect vacuum, and that was impossible to do in the days before vacuum pumps (and even then isn’t all that easy). Instead, we assume that feathers will behave in the same way as cannon-balls and explain away the feather’s odd behavior as being due to air resistance.

Leave aside for the moment the dubious rhetorical tactic of telling the Leaning Tower story when you know it’s false. You don’t need a perfect vacuum to demonstrate the universality of free fall, just a physics textbook (the larger and heavier the better– any introductory text will do) and a dollar bill.

If you drop the book and the bill from the same height, the heavy book will, indeed, fall faster than the bill, due to air resistance. If you put the bill on top of the book, though, the book will clear a path for the bill, in a manner of speaking– the bill is in the lee of the book, and will not experience any significant force from the air. When you do that, the bill will remain right on top of the book all the way down to the ground, showing that they two fall at the same rate due to the force of gravity. No elaborate vacuum apparatus needed.

There’s a bigger problem here, though, which is the identification of Newtonian physics with a single thought experiment. Newtonian physics doesn’t consist of its most basic example; it’s a grand framework for understanding how interactions between objects affect their motion. Air resistance isn’t some extraneous force that Newtonian physics can’t hope to explain– it’s easily accommodated within the Newtonian framework. Which is why we know how to design aerodynamic cars, and efficient sailboats, and airplanes– the engineers working on those projects aren’t using quantum physics to do those designs, just Newton’s famous laws of motion.

The idea that air resistance forces somehow invalidate Newtonian mechanics is depressingly common, but it’s based on a common misconception of what physics is. Physics is not a collection of facts, it’s a set of rules for understanding the universe– in the specific case of Newtonian physics, rules governing the effect that forces have on the motion of objects. “All objects near the Earth’s surface fall at the same rate” is not a central idea of Newtonian physics, just one of the simplest predictions from it. The central ideas of Newtonian physics are the rules used to quantify the effect of interactions, chiefly the “second law of motion” which says that the rate of change of the momentum of an object is equal to the sum of all the forces acting on it.

The business with feathers and stones is a consequence of Newtonian rules, specifically the second law combined with Newton’s universal law of gravitation, which determines the strength of the gravitational force an object experiences. It’s explicitly only exactly valid in the approximation where there is no other significant force acting, but the presence of additional forces is not a problem– if you want to know the behavior of falling feathers in a room filled with air, you just add in the appropriate air resistance force, and you will get a prediction that exactly matches reality.

If Newtonian physics weren’t able to accommodate systems with more than one force acting, it wouldn’t be good for anything. You wouldn’t even need air resistance to invalidate it– I could drop one rock, and tie a string to a second rock of equal mass, and wind the string around a spool. The second rock will fall more slowly, as it also starts the spool spinning, and, hey presto, Newtonian physics is invalid. Other than, you know, the part where the falling rock tied to a rotating spool is a homework problem we assign in Newtonian physics classes.

It’s absolutely true that there’s a level of abstraction away from the everyday required to come up with Newton’s Laws in the first place. That was a big part of Newton’s genius– the realization that moving objects slow down not because it is in the nature of moving objects to slow down, but because there are other forces acting on them. To develop universal laws applicable to all motion, you need to abstract away everything complicated, and get to the imaginary simple case where only a single force acts (or even no force at all). For this reason, most of the examples we deal with in the first couple of weeks of class involve things like rocks floating in interstellar space, or simple objects sliding on icy surfaces with no appreciable friction. Those simple cases let you understand the universal rules, and see their implications.

The theory isn’t limited to simple cases, though. It’s vastly richer than that, and can accommodate basically any situation you care to throw at it, provided the speeds are low compared to the speed of light, and the masses are large enough to remove quantum effects from the problem. Though it should be noted that as stupid and abstract as they may seem, the simple cases can often be an excellent approximation to reality– see pretty much everything on Rhett’s blog.

Unfortunately, the fundamental misconception in this passage about the nature of Newtonian physics is sufficiently deep and wrong that it makes me question all the other stuff that I found sort of interesting in the book. And the utter gibberish he writes about neutrinos in the following pages even more so. I may manage to get some use out of this, in the form of pointers to other authors and some research within his own field (something in the biology/ psychology/ anthropology borderlands, apparently), but I’ll have to read anything he cites really carefully, because this does not inspire confidence that they’ll turn out to say what he says they do.

12 thoughts on “Physics Is About Rules, Not Facts

  1. More than a few times, while TAing, I’ve encountered students who seem to have a deeply seated inability to recognize that there is any such thing as a general case. They can generalize, if forced to by direct questions (“What do all these things have in common?”), but they only take it as far as the immediate question demands. They have great difficulty with the notion that the same rule might apply to a broad class of situations, and actively resist the notion that they should begin by identifying which broad class they’re looking at.

    It seems to me that this is kind of the same thing as the distinction between “facts” and “rules” you are making. I don’t have all that much teaching experience; I wonder if you have had any luck with such students and if so, how.

  2. [Newtonian physics] makes all kinds of totally unrealistic assumptions about the existence of perfect vacuums, ideal gases, and frictionless processes, none of which ever occur in nature.

    I suspect Mr. (Dr.?) Dunbar never learned calculus, or he would have been familiar with the concept of approximations. They arise both in derivatives and in integrals. Approximations are an important part of how physics is done, because there are many applications where the effect of something is small compared to the effect of what you are actually trying to measure. (The old spherical cow joke takes this notion to a logical extreme.) Indeed, the specific approximations Dunbar mentions are valid in a surprising number of cases, at least within the precision available in a freshman physics lab.

    A slightly more sophisticated version of Dunbar’s argument would be that Newtonian mechanics assumes the speed of light is infinite, Planck’s constant is 0, and the metric is -g00 = g11 = g22 = g33 = 1 with off-diagonal elements equal to 0. (Violating these assumptions gives you special relativity, quantum mechanics, and general relativity, respectively). These assumptions are false, too, and IMO it is a flaw in physics pedagogy that these assumptions (unlike the assumptions Dunbar mentions) are usually not made explicit in freshman mechanics. Nonetheless, there are many situations in which you can make all three of these approximations. This is why Newtonian mechanics is useful (and a big part of why physics envy is a problem in economics is that the corresponding approximations in freshman economics are never valid beyond the trivial examples covered in those classes).

  3. It sounds like Dunbar gets tripped up a lot by the riddle: Which weighs more, a pound of feathers or a pound of lead?

    Or the eternal conundrum — how does the large amount of water in the tall skinny glass manage to fit into the tiny space of the short fat glass?

  4. It seems to me that he doesn’t even understand how to test a hypothesis. The notion to drop two cannonballs of different weights is “cheating” while dropping a cannonball and a feather is a sensible experiment. The hypothesis that heavy things fall faster can only be tested if the weight of the falling object is the only thing that changed. If you change the shape, then you have a confounding variable and can’t decide if it’s the weight that mattered or the shape! Indeed, such a confounding effect can be ameliorated by doing the experiment in a vacuum!

  5. I like your discussion, but I think it doesn’t enough place the difficulties. I suggest one difficulty is that the rules for how to construct a model given a *complex* physical situation are not easy. I think of these rules as “engineering rules”, even though they’re as much used by applied physicists as they are by engineers, because Newton’s laws don’t spell out how to model, say, a steam engine to arbitrary accuracy. Engineering rules are vastly richer than Newton’s rules, enough so that they are a work in progress insofar as they are only spelled out by example or by sets of rules that are more complex than necessary. FWIW, the difficulty is more acute when using QFT to model anything complex.

  6. Actually, it is very easy to point out where misunderstand (or rather ignorance) shows in Dunbar’s presentation of Newtonian mechanics. Newton never claimed that the rate of fall is governed only by the effects of gravity and is independent of weight. That is the case when the only force acting on an object is gravity. Fnet=ma and by F it is meant a total force acting (in the case of objects falling on the Earth it is not only gravity) so what we can derive is that if Fnet = G than would fall at equal rate and if Fnet is proximately G they would fall at nearly the same rate.
    My point is that we do not need a big picture where misunderstanding lies (“Physics is not a collection of facts, it’s a set of rules for understanding the universe”) because it is easy to show how ignorant Dunbar of what Newtonian theory claims in the first place.

  7. Science is not a collection of fact and rules it is a way of looking and trying to understand the World/universe. It to often (even at university) is taught as a collection of facts and know solutions – this can lead to misconceptions.

  8. I guess I’m a little more accepting of Dunbar’s point. One issue with the apparent interpretation of it here, is the ham-handed phrasing (“confidence trick” is a little much). I’m guessing Dunbar isn’t making a point about Newtonian physics in-and-of-itself, but rather people’s ability to interpret and conceptualize it.

    As an experimentalist, I’m a bit surprised you take the position you do. Think of it from a person just being introduced to Newtonian physics. There point isn’t so much “air resistance invalidates Newtonian physics”, but more “the results that this theory predicts appear to contradict these experiments that I previously ran.” If it was a theory new to you, I doubt you’d be satisfied by someone saying “Yeah, just ignore that. Trust me, the theory works. Your experiments had some extraneous factor I’ll just hand-wave away. My theory works perfectly for conditions you’ll never actually encounter.”

    There’s a large propensity to simplify things from the messy truth when explaining and modeling them. “Imagine a spherical cow” and all that. You can say “imagine if there was no friction and no air resistance”, but the fact remains that there *is* friction and air resistance in normal experience. Telling a normal person “Well, if there wasn’t friction, then things would happen like this …” is somewhat akin to telling a physicist “Well, if the law of conservation of energy didn’t exist, then things would happen like this …”. They might be able to accept it, but they also might shoot back with “You’re talking nonsense – friction/energy conservation *does* exist!”

    The world is complex, and those simplifying assumptions don’t necessarily hold – Chad, you’ve even succumbed to the simplified-world assumption. “put the bill on top of the book” – right, and ignore Bernoulli’s principle exists and the falling book will “suck” the bill down with it. (By how much? I don’t know. But the example isn’t as simple, straightforward and conclusive as you portray.)

    I don’t think the use of the Leaning Tower story is dubious in this context – it illustrates his point. In order to explain physics, we habitually simplify things. Differently weighted balls and ramps are difficult to understand – it’s much simpler to say he dropped two balls straight down. Explaining all the complexities of the LHC, talking about energy spectra and resonances, background calculations, sigmas, etc. is complicated. Just say that physicists “observed” the Higgs Boson. I’d guess most laymen assume there’s a really big microscope attached to the LHC which printed out a photograph, which now has a post-it arrow labeled “Higgs!” stuck to it near some little spot or streak.

    Not having read the book, I think that’s his point. Not that Newtonian physics is wrong, or that it’s based on a single experiment, but in order to explain it to someone, we routinely resort to simplifications and generalizations. As Zack indicates, it can be difficult to convince people that the simplifications are valid, and that you can generalize from what you’re generalizing from. That would be “the trouble with science” Dunbar’s making the case for – humans’ difficulty with being able to ignore the extraneous complications from the messiness of reality and abstract to the rules underneath.

  9. “Newtonian physics says that their rate of fall is governed only by the effects of gravity and is independent of their respective weights”

    One doesn’t have to understand the facts/framework issue to pinpoint what’s wrong here. The first half of the sentence is plain false. Newtonian physics simply does not say the rate of fall is governed only by gravity. Newtonian physics takes no position on what forces might be active.

  10. It sounds like he is not even well read concerning Galileo, whose argument was as much philosophical as based on the experiment you mention. He pointed out the absurdity that two separate cannonballs would fall twice as fast if you merely connected them with a chain or rod into a single body. Teachable moment for the idea of free-body diagrams in Newtonian physics?

    Excellent point about rules versus facts. A common misconception of most students, fed perhaps by the proliferation of HW cheat sites, is that physics is made up of thousands of specialized equations that each solve thousands of specific problems rather than a tiny set of rules combined with a brain that can think.

    PS – The riddle does not concern lead and feathers, it concerns a pound (avoirdupois) of feathers or copper and a pound (troy) of silver, probably going back to the Manhattan Project’s request for X tons of silver to make calutrons.

  11. In Mr. Dunbar’s book, he commonly refers back to the Galileo theory of in a perfect world the feather and the stone when thrown or dropped from a height would hit the ground at the same time. Evertime he refers to this statement, he lacks to point out that Galileo’s statement was only a theory not a hard fact. In the “perfect world” there would be no air resistance, allowing the feather and stone to drop at the same rate. Once again, when he refers to Galileo’s “supposed” experiment of rolling two cannonballs of different weights down an inclined plane, Mr. Dunbar fails to think in Galileo’s sense of a perfect world, which would not only neglect air resistance would neglect the laws of friction. Neglecting friction would allow the two cannonballs to roll down the incline plane and hit the ground at the same time.

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