Suppose, for instance, that we had very accurate rules for fundamental particles, rules that really do govern everything about them. Despite that, it's pretty clear that those rules would not greatly help our understanding of something like economics. We want to understand someone who goes into a supermarket, buys some bananas, and pays over some money. How do we approach that from the particle rules? We have to write down an equation for every particle in the customer's body, in the bananas, in the note that passes from customer to cashier. Our description of the transaction, money for bananas, and our explanation of it is in terms of an incredibly complicated equation about fundamental particles.
Solving that equation is even harder. And it might not even be the only fruit they buy.
We're not saying that the universe hasn't done it that way. We're saying that even if it has, that won't help us understand anything. So there's a big, emergent gap between the Theory of Everything and its consequences.
A lot of philosophers seem to have got the idea that in an emergent phenomenon the chain of causality is broken. If our thoughts are emergent properties of our brain, then to many philosophers they are not physically caused by the nerve cells, the electrical currents, and the chemicals in the brain. We don't mean that. We think it's confused nonsense. We're perfectly happy that our thoughts are caused by those physical entities, but you can't describe someone's perceptions or memory in terms of electrical currents and chemicals.
Human beings never understand things that way. They understand things by keeping them simple, in Archchancellor Ridcully's case, the simpler the better. A little narrativium goes a long way: the simpler the story, the better you understand it. Storytelling is the opposite of reductionism; 26 letters and some rules of grammar are no story at all.
One set of modern physical rules poses more philosophical questions than all the others combined: Quantum Mechanics. Newton's rules explained the universe in terms of force, position, speed, and the like, things that make intuitive sense to human beings and let us tell good stories. A century or so ago, however, it became clear that the universe's hidden wiring has other, less intuitive layers. Concepts such as position and speed not only ceased to be fundamental, they ceased to have a well defined meaning at all.
This new layer of explanation, quantum theory, tells us that on small scales the rules are random. Instead of something happening or not, it may do a bit of both. Empty space is a seething mass of potentialities, and time is something you can borrow and pay back again if you do it quickly enough for the universe not to notice. And the Heisenberg Uncertainty Principle says that if you know where something is then you can't also know how fast it's going. Ponder Stibbons would consider himself lucky if he did not have to explain this to his Archchancellor.
A thorough discussion of the quantum world would need a book all to itself, but there's one topic that benefits from some Discworld insights. This is the notorious case of the cat in the box. Quantum objects obey Schrodinger's Equation, a rule named after Erwin Schrodinger which describes how 'wave functions', waves of quantum existence, propagate through space and time. Atoms and their sub-atomic components aren't really particles: they're quantum wave functions.
The early pioneers of quantum mechanics had enough problems solving Schrodinger's equation: they didn't want to worry about what it meant. So they spatchcocked together a cop-out clause, the 'Copenhagen interpretation' of quantum observations. This says that whenever you try to observe a quantum wave function it immediately 'collapses' to give a single particle-like answer. This seems to promote the human mind to a special status, it has even been suggested that our purpose in the universe is to observe it, thereby ensuring its existence, an idea that the wizards of UU consider to be simple common sense.
Schrodinger, however, thought this was silly, and in support he introduced a thought experiment now called Schrodinger's Cat. Imagine a box, with a lid that can be sealed so tightly that nothing, not even the barest hint of a quantum wavelet, can leak out. The box contains a radioactive atom, which at some random moment will decay and emit a particle, and a particle detector that releases poison gas when it detects the atom decaying. Put the cat in the box and close the lid. Wait a bit.
Is the cat alive or dead?
If the atom has decayed, then the cat's dead. If not, it's alive. However, the box is sealed, so you can't observe what's inside. Since unobserved quantum systems are waves, the quantum rules tell us that the atom must be in a 'mixed' state, half decayed and half not. Therefore the cat, which is a collection of atoms and so can be considered as a gigantic quantum system, is also in a mixed state: half alive, half dead. In 1935 Schrodinger pointed out that cats aren't like that. Cats are macroscopic systems with classical yes/no physics. His point was that the Copenhagen interpretation does not explain, or even address, the link from microscopic quantum physics to macroscopic classical physics. The Copenhagen interpretation replaces a complex physical process (which we don't understand) by a piece of magic: the wave collapses as soon as you try to observe it.
Most of the time this problem is discussed, physicists manage to turn Schrodinger's point on its head. 'No, quantum waves really are like that!' And they've done lots of experiments to prove they're right. Except... those experiments have no box, no poison gas, no alive, no dead, and no cat. What they have is quantum-scale analogues, an electron for a cat, positive spin for alive and negative for dead, and a box with Chinese walls, through which anything can be observed, but you take great care not to notice.
These discussions and experiments are lies-to-children: their aim is to convince the next generation of physicists that quantum-level systems do actually behave in the bizarre way that they do. Fine ... but it's got nothing to do with cats. The wizards of Unseen University, who know nothing about electrons but have an intimate familiarity with cats, wouldn't be fooled for an instant. Neither would the witch Gytha Ogg, whose cat Greebo is shut in a box in Lords and Ladies. Greebo is the sort of cat that would take on a ferocious wolf and eat it. In Witches Abroad he eats a vampire by accident, and the witches can't understand why the local villagers are so ecstatic.
Greebo has his own way of handling quantum paradoxes: 'Greebo had spent an irritating two minutes in that box. Technically, a cat locked in a box may be alive or it may be dead. You never know until you look. In fact, the mere act of opening the box will determine the state of the cat, although in this case there were three determinate states the cat could be in: these being Alive, Dead, and Bloody Furious.'
Schrodinger would have applauded. He wasn't talking about quantum states: he wanted to know how they led to ordinary, classical physics in the large, and he could see that the Copenhagen interpretation didn't have anything to say about that. So how do classical yes/no answers emerge from quantum Ant Country? The closest we have to an answer is something called 'decoherence', which has been studied by a number of physicists, among them Anthony Leggett, Roland Omnes, Serge Haroche and Luis Davidovich. If you have a big collection of quantum waves and you leave it to its own devices, then the component waves get out of step and fuzz out. This is what a classical object is 'really' like from the quantum standpoint, and it means that cats do, in fact, behave like cats. Experiments show that the same is true even when the role of the detector is played by a microscopic quantum object: a photon's wave function can collapse without any observers being aware, at the time, that it has done so. Even with a quantum cat, death occurs at the instant that the detector notices that the atom has decayed. It doesn't require a mind.