The Fabric of Reality: Towards a Theory of Everything (Penguin Science)

by David Deutsch

The fabric of reality, then, does have a more unified structure than would have been possible if mathematical knowledge had been verifiable with certainty, and hence hierarchical, as has traditionally been assumed. Mathematical entities are part of the fabric of reality because they are complex and autonomous. The sort of reality they form is in some ways like the realm of abstractions envisaged by Plato or Penrose: although they are by definition intangible, they exist objectively and have properties that are independent of the laws of physics. However, it is physics that allows us to gain knowledge of this realm. And it imposes stringent constraints. Whereas everything in physical reality is comprehensible, the comprehensible mathematical truths are precisely the infinitesimal minority which happen to correspond exactly to some physical truth – like the fact that if certain symbols made of ink on paper are manipulated in certain ways, certain other symbols appear. That is, they are the truths that can be rendered in virtual reality. We have no choice but to assume that the incomprehensible mathematical entities are real too, because they appear inextricably in our explanations of the comprehensible ones.