If detecting the suboptimal answer takes better than exponential time, and blowing takes linear time, the total time is still better then exponential and doesn't disprove the argument. It depends how many times you have to repeat this to guarantee a optimal solution.
But I agree that the argument is badly flawed(1). The soap bubble STP machine and and similar machines are probabilistic solvers. They are doing stochastic gradient descent from initial conditions, with the usual lack of global optimal convergence guarantee.
(1) It may be satire. Does anyone know if this is so?
The video isn't supposed to be a proof that no technique can do it; the video just demonstrates that soap bubbles can get stuck in a local minimum.
(Also, blowing is not guaranteed to move the answer towards the global solution. Even if you can quickly determine that an answer is not optimal and blow it around, you could just spend forever going in circles.)
But I agree that the argument is badly flawed(1). The soap bubble STP machine and and similar machines are probabilistic solvers. They are doing stochastic gradient descent from initial conditions, with the usual lack of global optimal convergence guarantee.
(1) It may be satire. Does anyone know if this is so?