. The deep structural properties of a quantum information theoretic approach to formal languages and universal computation, as well as those of the topology problem of defining the presentation of the Mapping Class Group of a smooth, compact manifold are shown to be grounded in the common categorical features of the two problems.

There is a vast class of things that science has so far almost entirely neglected. They are central to the understanding of physical reality both at an everyday level and at the level of the most fundamental phenomena in physics, yet have traditionally been assumed to be impossible to incorporate into fundamental scientific explanations. They are facts not about what is--the actual--but about what could be: counterfactuals. According to physicist Chiara Marletto, laws about things being possible or impossible may generate (...) an alternative way of providing explanations. This fascinating, far-reaching approach holds promise for revolutionizing the way fundamental physics is formulated, but also for providing essential tools to face existing technological challenges, from delivering the next generation of information-processing devices, beyond the universal quantum computer, to designing AIs. Each chapter in the book delineates how an existing vexed open problem in science can be solved by this radically different approach; and it is augmented by short fictional stories that explicate the main point of the chapter. As Marletto demonstrates, contemplating what is possible can give us a more complete and hopeful picture of the physical world. (shrink)