The author mentions that having an equation that describes a system accomplishes little if the solutions to that equation are unavailable. He kind of downplays quantum mechanics, but I would argue the situation is just as severe as that with turbulence. The Schrödinger equation
iħ(∂Ψ/∂t) = HΨ
is a very simple equation. Yet the solution to this equation is nearly impossible to solve for all but the simplest systems. A lot of approximations to it have been developed, but to numerically converge on the exact solution is an NP-hard problem in most cases (using QMC). And we all know what that means.
There's a famous quote attributed to Max Born: "It would indeed be remarkable if Nature fortified herself against further advances in knowledge behind the analytical difficulties of the many-body problem."
In other words, what if we discover all the equations that govern nature, but they are simply infeasible to solve (and worse, we even mathematically prove that they're intractable)? It's an interesting, yet somewhat depressing idea.
iħ(∂Ψ/∂t) = HΨ
is a very simple equation. Yet the solution to this equation is nearly impossible to solve for all but the simplest systems. A lot of approximations to it have been developed, but to numerically converge on the exact solution is an NP-hard problem in most cases (using QMC). And we all know what that means.
There's a famous quote attributed to Max Born: "It would indeed be remarkable if Nature fortified herself against further advances in knowledge behind the analytical difficulties of the many-body problem."
In other words, what if we discover all the equations that govern nature, but they are simply infeasible to solve (and worse, we even mathematically prove that they're intractable)? It's an interesting, yet somewhat depressing idea.