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' [LW · GW]? 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.

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.

This claim seems really weird to me. Why do you think that's true? A lot of things we accomplished with technology today might seem impossible to someone from 1700. On the other hand, you could have thought that e.g. perpetuum mobile, or superluminal motion, or deciding whether a graph is 3-colorable in worst-case polynomial time, or transmitting information with a rate higher than Shannon-Hartley is possible if you didn't know the relevant theory.

• If a trebuchet requires you to solve the double pendulum problem (a classic example of a chaotic system) in order to aim, it is not a competition-winning trebuchet.

Ah, this is not quite the takeaway- and getting the subtlety here right is important for larger conclusions. If a simulating a trebuchet requires solving the double pendulum problem over many error-doublings, it is not a competition-winning trebuchet. This is an important distinction. 

If you start with a simulator and a random assortment of pieces, and then start naively optimizing for pumpkin distance, you will quickly see the sort of design shown at 5:02 in the video, where the resulting machine is unphysical because its performance depends on coincidences that will go away in the face of tiny changes in initial conditions. This behaviour shows up with a variety of simulators and optimizers.

An expensive but probably effective solution is to perturb a design several times, simulate it several times, and stop simulation once the simulations diverge. 

An ineffective solution is to limit the time of the solution, as many efficient and real-world designs take a long time to fire, because they begin with the machine slowly falling away from an unstable equilibrium. 

The chaos-theory motivated cheap solution is to limit the number of rotations of bodies in the solution before terminating it, as experience shows error doublings tend to come from rotations in trebuchet-like chaotic systems. 

The solution I currently have implemented at jstreb.hgreer.com is to only allow the direction of the projectile to rotate once before firing (specifically, it is released if it is moving upwards and to the right at a velocity above a threshold) which is not elegant, but seems mostly effective. I want to move to the "perturb and simulate several times" approach in the future.

I enjoyed doing this interview. I haven’t done too much extemporaneous public speaking, and it was a weird but wonderful experience being on the other side of the youtube camera. Thanks Elizabeth!

Why does the video show up so tiny?

It seems to me that chaos control and anti-control is another non-application.

[Handbook of Chaos Control: Schöll, Eckehard, Schuster, Heinz Georg](https://www.amazon.com/Handbook-Chaos-Control-Eckehard-Sch%C3%B6ll/dp/3527406050)

I 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.