Quantum mechanics and general relativity, the last two foundational breakthroughs in science, are a century old each. Since then we have made tons of progress in more applied science, such as learning to decode and manipulate DNA and RNA, but we have been in a rut when it comes to developing a deeper understanding of such fundamental phenomena as information and heat. I believe that this lack of a new fundamental breakthrough is contributor to an overall slowing down of scientific progress that has been widely noted.

In her wonderful book “The Science of Can and Can’t” Chiara Marletto takes us on a fascinating journey into the foundations of scientific theories. Newtonian (classical) mechanics, quantum mechanics and general relativity all share the same structure: a description of states of the world combined with laws of motion which govern how states evolve. This approach has proven incredibly powerful but also has important limits.

Chiara introduces an alternative approach called Constructor Theory, which she has been developing together with David Deutsch and a small team at Oxford. Instead of states and laws of motion. Constructor Theory builds upon the distinction between possible and impossible transformations (hence the title of the book). In doing so, Constructor Theory makes counterfactuals first class elements of science, i.e. statements about what could be or could have been, but maybe has not (yet) occurred.

The book does a terrific job explaining why this matters and what Constructor Theory is seeking to accomplish. Let me provide just a few hints. First, a precise theory of such phenomena as heat, which current theories approach statistically. Second, a unification of our understanding of classical and quantum information theories. Third, a theory of quantum computing that is abstracted from quantum mechanics (our theory of classical computation after all isn’t tied to classical mechanics or electric fields).

One of the many lovely illustrations from the book:

There is also an important philosophical aspect to this new approach. In our existing theories there is exceedingly little room for freedom. In the strictest application of the laws of motion approach the fact that I am writing these words right now was already determined eons ago. In fact everything that’s happening is just the deterministic consequence of prior states via the laws of motion (this is even true for the fundamental equations of quantum mechanics). Constructor Theory, on the other hand, by allowing for counterfactuals, cracks space wide open for meaningful constructs of human freedom and agency.

What is highly unusual about this book is that it provides an introduction accessible to lay readers to a theory that is currently under active development. This is a bit akin to being able to look over the shoulder of someone like Bohr or Einstein while they were working on their breakthroughs. This serves as an invitation to follow along on a journey that will be ongoing for many years. There is no way to read the book and not marvel simultaneously at how far we have come and how much still lies ahead.

Full disclosure: Susan and I have been supporting Chiara’s research for several years and thus aren’t exactly unbiased observers of the importance of her work.