Book: The primacy of doubt

Author

Tim Palmer

Summary

An introduction to the geometry of chaos and the important role it plays in understanding scientific phenomena.

Takeaways

The climate and the economy are examples of highly complex non-linear systems. The evolution of these systems follows a fractal geometric pattern along an attractor, i.e. a set of allowed states in a high dimensional state space. Despite the fact that an exact future state is often uncomputable, mathematical models have been successfully developed to characterize possible future behavior in the form of ensembles along the attractor. These models allow to make probabilitic forecasts and statements about the likelihood that a future state will be vastly different from the present.

Invariant set theory applies the concept of the “geometry of chaos” to quantum mechanics and concludes that the laws of physics are deterministic and that its laws describe the geometry of the attractor/invariant set of the highest-order system imaginable-the universe as a whole.

Quotes

“The whole universe is a nonlinear dynamical system evolving on some fractal attractor in cosmological state space."

“Using the geometry of chaos, Einstein’s picture of an ensemble of deterministic worlds may be right after all. If this is so, we conclude that we do live in a world in which elementary particles, and indeed the notion of reality, are certain and definite."

“In short, I am suggesting that to be conscious of an object is to be aware that the object has an existence independent of the rest of the world. I am speculating that this awareness is itself a consequence of two claims: that for reasons of energy efficiency quantum physics does play a role in cognition, and that the laws of quantum physics at their most fundamental describe the geometry of the cosmological invariant set."