But a set of abstract entities with relations between them is a mathematical structure.

He then points out that a completely human-baggage-free description is precisely a mathematical structure: by the mathematical definition of equivalence, two descriptions are equivalent if there is a correspondence between them that preserves all relations. He points out that if reality exists independently of humans, then a complete description must be well-defined according to nonhuman entities (aliens or supercomputers) that lack human concepts. (Mathematical universe hypothesis): Our external physical reality is a mathematical structure.(External reality hypothesis): There exists an external physical reality completely independent of us humans.Tegmark then proposes his own theory to explain Wigner’s paradox. Galileo wrote that the book of the universe “is written in the language of mathematics.” Wigner, writing in 1960, remarked that “the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and … there is no rational expiation for it.” Tegmark starts out by noting that scientists for centuries have noted how the universe is governed by mathematical laws. Of particular interest to readers of this column is the last portion of the book, chapters 10-13. Next, Tegmark introduces the emerging “multiverse” theories: Level I (the universe external to ours, as a result of the inflation at the big bang), Level II (the ensemble of pocket universes, the result of “eternal inflation”), Level III (the bifurcating universe, as a consequence of the “many worlds” formulation of quantum mechanics) and Level IV (Tegmark’s own notion of all mathematical structures, which he proposes actually exist and constitute the ultimate “stuff” of existence). Tegmark starts out by exploring a list of questions, such as “How big is space?,” “Where did our solar system come from?” and “Where did our big bang come from?.” He then examines some of the difficulties with current theories, including both the successes and failures of the “inflation” cosmology of the very early universe. In this very lucidly written book, Tegmark takes the reader on a tour of modern physics and then introduces his theory of the ultimate nature of the universe. Physicist Max Tegmark has just published an interesting new book entitled Our Mathematical Universe: My Quest for the Ultimate Nature of Reality.

Mathematical universe book