In spirit I agree with “the real rules have no exceptions”. I believe this applies to physics just as well as it applies to decision-making.
But, while the foundational rules of physics are simple and legible, the physics of many particles—which are needed for managing real-world situations—includes emergent behaviours like fluid drag and turbulence. The notoriously complex behaviour of fluids can be usefully compressed into rules that are simple enough to remember and apply, such as inviscid or incompressible flow approximations, or tables of drag coefficients. But these simple rules are built on top of massively complex ones like the Navier-Stokes equation (which is itself still a simplifying assumption over quantum physics and relativity).
It is useful to remember that the equations of incompressible flow are not foundational and so will have exceptions, or else you will overconfidently predict that nobody can fly supersonic airplanes. But that doesn’t mean you should discard those simplified rules when you reach an exception and proceed to always use Navier-Stokes, because the real rules might simply be too hard to apply the rest of the time and give the same answer anyway, to three significant figures. It might just be easier in practice to remember the exceptions.
Hence, when making predictive models, even astrophysicists will think of gravity in terms of “stars move according to Newton’s inverse square law, except when dealing with black holes or gravitational lensing”. They know that it’s really relativity under the hood, but only draw on that when they know it’s necessary.
OK, that’s enough of an analogy. When might this happen in real life?
One case could be multi-agent, anti-inductive systems… like managing a company. As soon as anyone identifies a complete and compact formula for running a successful business it either goes horrifyingly wrong, or the competitive landscape adapts to nullify it, or else it was too vague of a rule to allow synthesizing concrete actions. (“Successful businesses will aim to turn a profit”).
Thanks!
I think my point is different, although I have to admit I don’t entirely grasp your objection to Nostalgebraist’s objection. I think Nostalgebraist’s point about rules being gameable does overlap with my example of multi-agent systems, because clear-but-only-approximately-correct rules are exploitable. But I don’t think my argument is about it being hard to identify legitimate exceptions. In fact, astrophysicists would have no difficulty identifying when it’s the right time to stop using Newtonian gravity.
But my point with the physics analogy is that sometimes, even if you actually know the correct rule, and even if that rule is simple (Navier-Stokes is still just one equation), you still might accomplish a lot more by using approximations and just remembering when they start to break down.
That’s because Occam’s-razor-simple rules like “to build a successful business, just turn a huge profit!” or “air is perfectly described by this one-line equation!” can be very hard to apply to synthesize into specific new business plans or airplane designs, or even to make predictions about existing business plans or airplane designs.
I guess a better example is: the various flavours of utilitarianism each convert complex moral judgements into simple, universal rules to maximize various measures of utility. But even with a firm belief in utilitarianism, you could still be stumped about the right action in any particular dilemma, just because it might be really hard to calculate the utility of each option. In this case, you don’t feel like you’ve reached an “exception” to utilitarianism at all—you still believe in the underlying principle—but you might find it easier to make decisions using an approximation like “try not to kill anybody”, until you reach edge-cases where that might break down, like in a war zone.
You might not even know if eating a cookie will increase or decrease your utility, so you stick to an approximation like “I’m on a diet” to simplify your decision-making process until you reach an exception like “this is a really delicious-looking / unusually healthy cookie”, in which you decide it’s worth dropping the approximation and reaching for the deeper rules of utilitarianism to make your choice.