Traditional differential equations is not one of the more useful college math classes(star), but a few useful things can be extracted from it. One of the most interesting is that under certain circumstances, oscillation is inevitable, by the very nature of how the system reacts to its own changes.
A classic example is the well-known "simple harmonic oscillation", where the only solution that doesn't oscillate is to start right at 0.
The market is more complicated. If simple harmonic motion is caused by negative feedback (the further you get from the origin, the stronger the force pulling you back), market instability is caused by positive feedback and the fact that there is a cap in how far bubbles can inflate. Excitement engenders excitement, so bubbles inflate. Depression engenders depression, so contractions also tend to overshoot vs. the "true" state of the economy.
Stripping this effect out of the economy would take more than just making it "smarter", you'd have to rewrite the whole foundation of it.
Mitigating recessions (and depressions) may be possible. Trying to stop them just makes them hit harder.
((star): DiffieQs are of course themselves useful; it is the class itself that is considered a bit of a waste by professors. Closed form solutions to diffieqs are the exception, not the rule, and mathematicians in general are not very interested in further pursuing the problem.)
A classic example is the well-known "simple harmonic oscillation", where the only solution that doesn't oscillate is to start right at 0.
The market is more complicated. If simple harmonic motion is caused by negative feedback (the further you get from the origin, the stronger the force pulling you back), market instability is caused by positive feedback and the fact that there is a cap in how far bubbles can inflate. Excitement engenders excitement, so bubbles inflate. Depression engenders depression, so contractions also tend to overshoot vs. the "true" state of the economy.
Stripping this effect out of the economy would take more than just making it "smarter", you'd have to rewrite the whole foundation of it.
Mitigating recessions (and depressions) may be possible. Trying to stop them just makes them hit harder.
((star): DiffieQs are of course themselves useful; it is the class itself that is considered a bit of a waste by professors. Closed form solutions to diffieqs are the exception, not the rule, and mathematicians in general are not very interested in further pursuing the problem.)