I cannot overstate the importance of the recent discovery that artificial neural networks can predict the behavior of chaotic systems out to eight ‘Lyapunov times’. Imagine, instead of forecasting a week of the world’s weather, you could predict eight weeks in advance. For planning around hurricanes, drought, frost, such weather prediction will be worth tens of billions of dollars each year.
That won’t be the only benefit of a neural network that understands chaos. Even NASA would have an easier time of things, aided in the discovery of viable flight paths around various planets. The plasma in fusion reactors behaves chaotically, too — and the difficulty in predicting that plasma’s behavior is exactly why fusion has remained outside our grasp. Most of the world is chaotic, and a machine that can comprehend and predict such chaos is invaluable.
Yet, there is a deeper insight to this discovery: we are also neural networks. We, like the researchers’ machine, can observe chaotic systems and predict their behavior far beyond what is possible with standard algorithms. We have, in our own skulls, a shortcut for chaos.
This upends a tradition stretching back to Norbert Wiener — the belief that chaotic systems will remain inscrutable, unpredictable. If we, and machines we create, can easily unravel unpredictability, then it is no longer a cacophony. Chaos is tame. By comprehending chaos, the whole world is known like clockwork.
I predict that, when we use these machines to plan possible futures, there will be divergences and convergences. Consider: a system is chaotic if any small change in the system cascades into a large change. Two states which begin close to each other will diverge, resulting in vastly different final states. Yet, there are only so many possible states — if two states diverge from each other, they each must have grown close to other states. Those others began greatly different from their new neighbors; chaos separates similar states, and it brings disparate states together.
We could model the paths of many similar states — beginning with slight variations on a weather model, for example. Those related states would rapidly diverge due to chaotic mixing. However, the weather forms as a result of an arrangement of water and land, each acting as an attractor for certain kinds of behavior. Even though our weather models split along various paths, those paths will tend to reunite in certain places. The paths weave past each other, and overlap at events which are likely in almost all futures. Chaotic systems have a kind of destiny, at times.
Together, prediction of chaotic systems and the overlap of neighboring paths point to a strange conclusion: we have the power to perceive and predict likely futures, despite their chaotic nature. We see where many paths overlap as destiny, through the fog of chaos that forfeits algorithms.