Tuesday, August 16, 2011

On simple explanations

Clever Connolley caught me out with a comment here on simple explanations. Mencken says that the reason for the 'inferior man' hating knowledge is because it is complex. All superstition is a short cut to make the unintelligible simple. Connolley, apparently agreeing with Mencken, chides me for wanting a simple explanation for global warming.

But is Mencken right? The appeal of true scientific explanation generally does lie in its simplicity. There are obvious exceptions - the proof of the four colour theorem for example. But consider the explanation of an eclipse. That is pretty simple. The moon goes round the earth, the earth goes round the sun. The sun lights up the earth. Occasionally the moon gets in the way and casts a shadow. How simpler could it get? The theory that the eclipse is caused by a dragon crossing the sun, by contrast, requires a theory of dragons, and no theory of dragons - at least not one that gives a comprehensive treatment of them, including their metabolism, genetic structure etc - could be simple at all.
Or consider Augustine's explanation of why evil exists:
That the whole human race has been condemned in its first origin, this life itself, if life it is to be called, bears witness by the host of cruel ills with which it is filled. Is not this proved by the profound and dreadful ignorance which produces all the errors that enfold the children of Adam, and from which no man can be delivered without toil, pain, and fear? Is it not proved by his love of so many vain and hurtful things, which produces gnawing cares, disquiet, griefs, fears, wild joys, quarrels, lawsuits, wars, treasons, angers, hatreds, deceit, flattery, fraud, theft, robbery, perfidy, pride, ambition, envy, murders, parricides, cruelty, ferocity, wickedness, luxury, insolence, impudence, shamelessness, fornications, adulteries, incests, and the numberless uncleannesses and unnatural acts of both sexes, which it is shameful so much as to mention; sacrileges, heresies, blasphemies, perjuries, oppression of the innocent, calumnies, plots, falsehoods, false witnessings, unrighteous judgments, violent deeds, plunderings, and whatever similar wickedness has found its way into the lives of men, though it cannot find its way into the conception of pure minds? (City of God, Book 22 chapter 22)
The explanation - that Adam and Eve offended God, and that these evils are a punishment - appears simple at first sight, just like the dragon explanation.  But it is not, for it requires a theory of God, and also a theory of Paradise, which is problematic.  Sociobiology could probably provide a simpler one (although I'm not sure it has, yet).

Superstition is not necessarily a simpler theory. So, what distinguishes superstition from science?


William M. Connolley said...

Picking just one thing that has a fairly simple explanation won't do. Try explaining the double-slit diffraction of electrons, for example. Or indeed, try explaining the precession of Mercury's orbit. Even why there are two tides a day baffles many intelligent people.

Edward Ockham said...

Correctly explained, the two daily tides should not be baffling (although the Wikipedia article which attempts to explain it certainly is baffling). The moon rotates, relative to the earth, once a day, as can easily be observed by watching the moon. The gravitational pull of the moon is greater on the side of the earth that faces it, and weakest on the opposite side of the earth. This is similar to pulling a circular balloon at opposite ends, creating a sausage shape. The whole sausage shape moves round the earth once a day, and because the sausage has two ends, there are two tides a day, not one.

I don't know what double-slit diffraction is, but I am sure there is a simple explanation.

Edward Ockham said...

Also, I am not saying that a scientific explanation should be simple. Merely that it should be the simplest.

A theory of dragons, by contrast, will have to be very complex.

William M. Connolley said...

Well, you fail on the tides at least, though you have part of the answer. Perhaps you need a more complex explanation?

Incidentally "The moon rotates, relative to the earth, once a day, as can easily be observed by watching the moon" is unambiguously false.

Edward Ockham said...

Can you be a little more specific. What is wrong with the explanation of the tides?

And what is wrong with
Incidentally "The moon rotates, relative to the earth, once a day, as can easily be observed by watching the moon"? I was watching the moon every day from the beach while on holiday, and it rotates (or at least appeared to rotate) with the sun. In a slightly different position, to be sure. I am aware that it is not exactly one day, and I am also aware that the rotation is apparent or 'relative'. Relative to the stars, it rotates around approximately one month, no?

William M. Connolley said...

Rotation: I've answered this at "How often does the moon rotate around the earth?": DRY, you know.

"What is wrong with the explanation of the tides?" - there is nothing wrong with *the* explanation of the tides. What is wrong is that you haven't got it all. You haven't explained why a weaker pull on the far side corresponds to material on the far side moving away. In your picture of forces, all the moon should be moving towards the earth.

Edward Ockham said...

I did explain it. I said "This is similar to pulling a circular balloon at opposite ends, creating a sausage shape. "

Exerting a force of +3 at far end and +5 at the near is equivalent to a uniform force of +4, plus a -1 at one end and +1 at the near end. The uniform +4 exerts no deforming stress, but the -1 and +1 do.

Is that not correct?

William M. Connolley said...

Err, it is correct, but as I said, incomplete, because in your model all the forces are positive, and so the moon and earth would approach. I tried to say that last time, I'm not sure how I can make it any simpler.

Edward Ockham said...

>>and so the moon and earth would approach

Incidentally, would it matter if they did approach? Assuming the moon is not orbiting, and will at some point crash into the earth. Will the bulge on the far side not still exist?

And if that is true, the rule of simple explanation is not to mention orbits or anything like that. (I may be wrong).

William M. Connolley said...

> Incidentally, would it matter if they did approach?

Not fundamentally, because the same gravitational physics applies (the wiki page covers this point). But that wouldn't be the explanation of the original question. A simple answer to a different question isn't really an acceptable answer.

Ignorance said...

Double slit diffraction occurs in optics when there are two apertures closely packed together. You get interference between the waves emanating from the two slits, resulting in some crests being reinforced while a minimum and a maximum with the same amplitude can cancel each other.