Jacques Pienaar’s guide to making physics (Pt.1)

PRINCIPLES AS TOOLS
(Not to be confused with using Principals as tools, which is what happens if your school Principal is a tool because he never taught you the difference between a Principal and a principle. Also not to be confused with a Princey-pal, who is a friend that happens to be a Prince).

`These principles are the boldly generalized results of experiment; but they appear to derive from their very generality a high degree of certainty. In fact, the greater the generality, the more frequent are the opportunities for verifying them, and such verifications, as they multiply, as they take the most varied and most unexpected forms, leave in the end no room for doubt.’ -Poincaré

 
One of the great things Einstein did, besides doing physics, was trying to explain to people how to do it as good as him. Ultimately he failed, because so far nobody has managed to do better than him, but he left us with some really interesting insights into how to come up with new physical theories.

One of these ideas is the concept of using `principles’. A principle is a statement about how the word works (or should work), stated in ordinary language. They are not always called principles, but might be called laws, postulates or hypotheses. I am not going to argue about semantics here. Just consider these examples to get a flavour:

The Second Law of Thermodynamics: You can’t build an engine which does useful work and ends up back in its starting position without producing any heat.

 
Landauer’s principle: you can’t erase information without producing heat.

 
The Principle of Relativity: It is impossible to tell by local experiments whether or not your laboratory is moving.

And some not strictly physics ones:

Shirky’s law: Institutions will try to preserve the problem to which they are the solution.

 
Murphy’s law: If something can go wrong, it will go wrong.

Stigler’s law: No scientific discovery is named after its original discoverer (this law was actually discovered by R.K. Merton, not Stigler).

 
Parkinson’s law: Work always expands to fill up the time allocated to doing it.
(See Wikipedia’s list of eponymous laws for more).

You’ll notice that principles are characterised by two main things: they ring true, and they are vague. Both of these properties are very important for their use in building theories.

Now I can practically hear the lice falling out as you scratch your head in confusion. “But Jacques! How can vagueness be a useful thing to have in a Principle? Shouldn’t it be made as precise as possible?”

No, doofus. A Principle is like an apple. You know what an apple is right?

hipstercat

Well, you think you do. But if I were to ask you, what colour is an apple, how sweet is an apple, how many worms are in an apple, you would have to admit that you don’t know, because the word “apple” is too vague to answer those questions. It is like asking how long is a piece of string. Nevertheless, when you want to go shopping, it suffices to say “buy me an apple” instead of “buy me a Malus domestica, reflective in the 620-750 nanometer range, ten percent sugar, one percent cydia pomonella“.

The only way to make a principle more precise is within the context of a precise theory. But then how would I build a new theory, if I am stuck using the language of the old theory? I can make the idea of an apple more precise using the various scientifically verified properties that apples are known to have, but all of that stuff had to come after we already had a basic vague understanding of what an “apple” was, e.g. a kind of round-ish thing on a tree that tastes nice when you eat it.

The vagueness of a principle means that it defines a whole family of possible theories, these being the ones that kind of fit with the principle if you take the right interpretation. On one hand, a principle that is too vague will not help you to make progress, because it will be too easy to make it fit with any future theory; on the other hand, a principle that is not vague enough will leave you stuck for choices and unable to progress.

The next aspect of a good principle is that it “rings true”. In other words, there is something about it that makes you want it to be true. We want our physical theories to be intuitive to our soft, human brains, and these brains of ours have evolved to think about the world in very specific terms. Why do you think physics seems to be all about the locations of objects in space, moving with time? There are infinitely many ways to describe physics, but we choose the ones we do because of the way our physical senses work, the way our bodies interact with the world, and the things we needed to do in order to survive up to this point. What is the principle of least action? It is a river flowing down a mountain. What is Newtonian mechanics? It is animals moving on the plains. We humans need to see the world in a special way in order to understand it, and good principles are what allow us to shoehorn abstract concepts like thermodynamics and gravitational physics into a picture that looks familiar to us, that we can work with.

That’s why a good principle has to ring true — it has to appeal to the limited imaginative abilities of us humans. Maybe if we were different animals, the laws of physics would be understood in very different terms. Like, the Newtonian mechanics of snakes would start with a simple model of objects moving along snake-paths in two dimensions (the ground), and then go from there to arbitrary motions and higher dimensions. So intelligent snakes might have discovered Fourier analysis way before humans would have, just because they would have been more used to thinking in wavy motions instead of linear motions.

Plissken

So you see, coming up with good principles is really an art form, that requires you to be deeply in touch with your own humanity. Indeed, principle-finding is part of the great art of generating hypotheses. It is a pity that many scientists don’t practice hypothesis generation enough to realise that it is an art (or maybe they don’t practice art enough?) It is also ironic that science tries so hard to eliminate the human element from the theories, when it is so apparent in the final forms of the theories themselves. It is just like an artist who trains so hard to hide her brush strokes, to make the signature of her hand invisible, even though the subject of the painting is her own face.

Ok, now that we know what principles are, how do we find them? One of the best ways is by the age-old method of Induction. How does induction work? It really deserves its own post, but here it is in a nutshell. Let’s say that you are a turkey, and you observe that whenever the farmer makes a whistle, there is some corn in your bowl. So, being a smart turkey, you might decide to elevate this empirical pattern to a general principle, called the Turkey Principle: whenever the farmer whistles, there is corn in your bowl. BOOM, induction!

Now, what is the use of this principle? It helps you to narrow down which theories are good and which are bad. Suppose one day the farmer whistles but you discover there is not corn in the bowl, but rather rice. With your limited turkey imagination, you are able to come up with three hypotheses to explain this. 1. There was corn in the bowl when the farmer whistled, but then somebody came along and replaced it with rice; 2. the Turkey Principle should be amended to the Weak Turkey Principle, which states that when the farmer whistles, food, but not necessarily corn, will be in the bowl; 3. the contents of the bowl are actually independent of the farmer’s whistling, and the apparent link between these phenomena is just a coincidence. Now, with the aid of the Principle, we can see that there is a clear preference for hypothesis 1 over 2, and for 2 over 3, according to the extent that each hypothesis fits with the Turkey Principle.

This example makes it clear that deciding which patterns to upgrade to general principles, and which to regard as anomalies, is again a question of aesthetics and artistry. A more perceptive turkey might observe that the farmer is not a simple mechanistic process, but a complex and mysterious system, and therefore may not be subject to such strong constraints with regards to his whistling and corn-giving behaviour as are implied by the Turkey Principle. Indeed, were the turkey perceptive enough to guess at the farmer’s true motives, he might start checking the tool shed to see if the axe is missing before running to the food bowl every time the farmer whistles. But this turkey would no doubt be working on hypotheses of his own, motivated by principles of his own, such as the Farmer-is-Not-to-be-Trusted Principle (in connection with the observed correlation of turkey disappearances and family dinner parties).

An example more relevant to physics is Einstein’s Equivalence Principle: that no local experiment can determine whether the laboratory is in motion, or is stationary in a gravitational field. The principle is vague, as you can see by the number of variations, interpretations, and Weak and Strong versions that exist in the literature; but undoubtedly it rings true, since it appears to be widely obeyed all but the most esoteric phenomena, and it gels nicely with the Principle of Relativity. While the Equivalence Principle was instrumental in leading to General Relativity, it is a matter of debate how it should be formulated within the theory, and whether or not it is even true. Much like hammers and saws are needed to make a table, but are not needed after the table is complete, we use principles to make theories and then we set them aside when the theory is complete. The final theory makes predictions perfectly well without needing to refer to the principles that built it, and the principles are too vague to make good predictions on their own. (Sure, with enough fiddling around, you can sit on a hammer and eat food off a saw, but it isn’t really comfortable or easy).

For more intellectual reading on principle theories, see the SEP entry on Einstein’s Philosophy of Science, and Poincare’s excellent notes.

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2 thoughts on “Jacques Pienaar’s guide to making physics (Pt.1)

  1. Shouldn’t your induction example run: The last N times the farmer made a whistle, there was some corn in your bowl. So, being a smart turkey, you might decide to elevate this empirical pattern to a general principle, called the Turkey Principle: every time the farmer whistles, there will be corn in your bowl. I realize this implies some kind of time ordering or causality, which is not really part of induction. But hey, turkeys are not that smart anyway!

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