Chaos provides value both by telling certain engineers where not to look for solutions to their problems, and by getting their bosses off their back about it. That’s a significant value add, but short of what I was hoping for when I started looking into Chaos.
I don't think it's a value-add, because this sort of proof-by-intimidation abuse is how chaos theory gets used in many places, such as here on Lesswrong as well, not just engineers fighting their managers. Remember the proof that humans can't get high scores playing pinball because 'chaos theory'? It's just an indiscriminate rhetorical weapon. It is not true in the case of playing pinball, it is probably not true of trebuchets in general (as opposed to cheap simple trebuchets constructed for contests or the Third World), and I would be surprised if all of those 6 successful manipulations were the valid exceptions. It is similar to the pervasive abuse of Godel or the Halting theorem; you doubtless could successfully convince some managers to not bother with things like typechecking or unit-tests or formal proofs because "Turing proved it is impossible to prove things about arbitrary programs" etc, but that is not a good thing, it is a bad thing.
1I do want to note that a lot of the claimed unpredictability from chaos only works if you can measure stuff to a finite precision only, and while this is basically always true in practice, it is worth noticing, because if you did have the ability to have an infinite memory and infinite FLOP/s computer with infinitely precise measurement, like in Newtonian physics, chaos theory doesn't matter, because in a deterministic system, if you get the exact same input, it will always have the same output, so chaos doesn't matter.
To be clear, this isn't a practical way to beat chaos, but it is an exception to the rule that chaos makes a system unpredictable.
Previously Alex Altair and I published a post on the applications of chaos theory, which found a few successes but mostly overhyped dead ends. Luckily the comments came through, providing me with an entirely different type of application: knowing you can’t, and explaining to your boss that you can’t.
Knowing you can’t
Calling a system chaotic rules out many solutions and tools, which can save you time and money in dead ends not traveled. I knew this, but also knew that you could never be 100% certain a physical system was chaotic, as opposed to misunderstood.
However, you can know the equations behind proposed solutions, and trust that reality is unlikely to be simpler[1] than the idealized math. This means that if the equations necessary for your proposed solution could be used to solve the 3-body problem, you don’t have a solution.
[[1] I’m hedging a little because sometimes reality’s complications make the math harder but the ultimate solution easier. E.g. friction makes movement harder to predict but gives you terminal velocity.]
I had a great conversation with trebuchet and math enthusiast Hastings Greer about how this dynamic plays out with trebuchets.
Transcript
Note that this was recorded in Skype with standard headphones, so the recording leaves something to be desired. I think it’s worth it for the trebuchet software visuals starting at 07:00
My favorite parts:
Explaining you can’t
One reason to doubt chaos theory’s usefulness is that we don’t need fancy theories to tell us something is impossible. Impossibility tends to make itself obvious.
But some people refuse to accept an impossibility, and some of those people are managers. Might those people accept “it’s impossible because of chaos theory” where they wouldn’t accept “it’s impossible because look at it”?
As a test of this hypothesis, I made a Twitter poll asking engineers-as-in-builds-things if they had tried to explain a project’s impossibility to chaos, and if it had worked. The final results were:
5/36 is by no means common, but it’s not zero either, and it seems like it usually works. My guess is that usage is concentrated in a few subfields, making chaos even more useful than it looks. My sample size isn’t high enough to trust the specific percentages, but as an existence proof I’m quite satisfied.
Conclusion
Chaos provides value both by telling certain engineers where not to look for solutions to their problems, and by getting their bosses off their back about it. That’s a significant value add, but short of what I was hoping for when I started looking into Chaos.