Mathematics is the study of surprising relationships between patterns. Almost nobody outside the subject can see why anyone would want to spend grown-up time on it.
The mathematician starts with some definitions, adds a few axioms, and then spends the next twenty years discovering consequences which were logically but obscurely present from the beginning. Occasionally it turns out that two completely different branches of mathematics are covertly describing the same structure. This is regarded as tremendously exciting, and quite properly so, by the twelve people capable of understanding it.
In the future no-one will understand it.
Physics is what happens when people rummage through this enormous mathematical warehouse and discover that some of the weirder items appear to describe actual phenomena.
Physicists are much less fussy than mathematicians about whether the machinery is actually legal. If an integral diverges, a function does not really exist, or an infinite quantity has to be subtracted from another infinite quantity to obtain the measured mass of an electron, the physicist just calculates to see what number comes out. If the answer agrees with experiment to eleven decimal places, this is normally regarded as ok. The mathematicians can tidy up afterwards (if they feel like it; the physicist does not care).
Chemistry begins where physics is too hard to use.
In principle, most chemists know perfectly well that everything they are doing is quantum mechanics. In practice, doing chemistry from quantum mechanics is like deriving the rules of chess from quantum chromodynamics. There may be no philosophical objection - but life will be over before you have got anywhere.
Chemists therefore employ a magnificent collection of approximations, heuristics, semi-empirical rules, diagrams, conventions and things which generally happen if you heat something for twenty minutes in the presence of a catalyst. Electrons are represented by dots. Bonds are represented by lines. Molecules actually have 'shapes' which are not quite the shapes shown in the book. Reactions proceed through mechanisms which are not little films of what the atoms are actually doing, but which are close enough to enable somebody to manufacture aspirin.
At intervals a physicist explains why one of these rules works; nobody cares.
Biology is chemistry complicated by the fact that human beings cannot bring themselves to believe that a cat is merely a complex series of chemical reactions at scale.
This is biology's permanent intellectual embarrassment. Every biologist knows that organisms consist entirely of ordinary matter obeying ordinary physical laws. Yet almost the entire vocabulary of biology suggests otherwise. Hearts are for pumping blood. Eyes are for seeing. Cells send signals.
Evolution by natural selection makes this language legitimate without requiring God, Aristotle or an élan vital to be hiding inside the mitochondria. Everyone plays lip service to it, even the media.
But there's a robust emotional resistance to the proposition that a living creature really is an immensely complicated chemical system. Tell someone that a crystal is molecules and they nod. Tell them that what they see in the mirror is molecules and they feel that biology has omitted something important.
Economics, by contrast, is largely common sense formalised for the benefit of people whose common sense stops working when the answer becomes politically or emotionally disagreeable. Not that those folk will pay any attention.
Most of its elementary propositions are almost insultingly obvious. People respond to incentives. If a product gets cheaper, people mostly want more of it. If you make an activity more expensive, they tend to do less of it. Resources used for one purpose cannot simultaneously be used for another. Somebody always eventually pays. You can't indefinitely distribute goods which nobody has produced.
None of this sounds like much of a science, and indeed much of it would not be necessary if human beings were better at following an argument through its second and third consequences.
Which unfortunately they are not.
And sociology? Tell me, how do you feel about that?
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