Quotes About Dynamical

the pattern appears so ethereally, that it is hard to remember that the shape is an attractor. It is not just any trajectory of a dynamical system. It is the trajectory toward which all other trajectories converge.

Ruelle had heard talks by Steve Smale about the horseshoe map and the chaotic possibilities of dynamical systems. He had also thought about fluid turbulence and the classic Landau picture. He suspected that these ideas were related—and contradictory.

The mathematics applied to fluid systems and to electrical systems. But almost no one in the classical era suspected the chaos that could lurk in dynamical systems if nonlinearity was given its due.

The key question for a quantum theory of gravity is then the following: Can we extend to quantum theory the principle that space has no fixed geometry? That is, can we make quantum theory background-independent, at least with regard to the geometry of space? If we can do this, we will automatically merge gravity and quantum theory, because gravity is already understood to be an aspect of dynamical spacetime geometry.