(This is a comment that has been turned into a post.)
From Chris_Leong’s post, “Making Exceptions to General Rules”:
Suppose you make a general rule, ie. “I won’t eat any cookies”. Then you encounter a situation that legitimately feels exceptional , “These are generally considered the best cookies in the entire state”. This tends to make people torn between two threads of reasoning:
Clearly the optimal strategy is to make an exception this one time and then follow the rule the rest of the time.
If you break the rule this one time, then you risk dismantling the rule and ending up not following it at all.
How can we resolve this? …
This is my answer:
Consider even a single exception to totally undermine any rule. Consequently, only follow rules with no exceptions.[1]. When you do encounter a legitimate exception to a heretofore-exceptionless rule, immediately discard the rule and replace it with a new rule—one which accounts for situations like this one, which, to the old rule, had to be exceptions.
This, of course, requires a meta-rule (or, if you like, a meta-habit):
Prefer simplicity in your rules. Be vigilant that your rules do not grow too complex; make sure you are not relaxing the legitimacy criteria of your exceptions. Periodically audit your rules, inspecting them for complexity; try to formulate simpler versions of complex rules.
So, when you encounter an exception, you neither break the rule once but keep following it thereafter, nor break it once and risk breaking it again. If this is really an exception, then that rule is immediately and automatically nullified, because good rules ought not have exceptions. Time for a new rule.
And if you’re not prepared to discard the rule and formulate a new one, well, then the exception must not be all that compelling; in which case, of course, keep following the existing rule, now and henceforth.
But why do I say that good rules ought not have exceptions? Because rules already don’t have exceptions.
Exceptions are a fiction. They’re a way for us to avoid admitting (sometimes to ourselves, sometimes to others) that the rule as stated, together with the criteria for deciding whether something is a “legitimate” exception, is the actual rule.
The approach I describe above merely consists of making this fact explicit.
By which I mean “only follow rules to which no legitimate exception will ever be encountered”, not “continue following a rule even if you encounter what seems like a legitimate exception”. ↩︎
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").
Oh, I don’t object to what nostalgebraist says! I think it’s entirely right. (Also, to be clear, his post was written some time before my comment, so it’s not in any way a response to the latter.)
I say only that despite what he says seemingly being a serious challenge to (or even contradiction of) my post, nonetheless the post’s thesis survives the challenge intact, if not unscathed—mostly because no alternative approach to mine de
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