Penrose's Three Mysteries

Penrose’s Three Great Mysteries

In Penrose’s metaphysical framework, there are three forms of existence or “worlds”: the physical, the mental, and the Platonic mathematical, as illustrated in the figure below (extracted from p.18 of the book):

three worlds Roger Penrose

Going clockwise, the figure reads (the three mysteries):

  • A small part of the Platonic mathematical is relevant to the physical.
  • A small part of the physical induces the mental.
  • A small part of the mental is concerned with the Platonic.

Going counterclockwise, the figure reads (Penrose’s three prejudices):

  • The entire Platonic mathematical is within the scope of reason (in principle).
  • The entire mental is dependent on the physical.
  • The entire physical is governed by the Platonic.

However, since this view reflects some of Penrose’s prejudices, he has drawn another figure to accommodate different viewpoints:

three worlds modified Roger Penrose

Going clockwise, this figure reads the same as before (the mysteries remain).

Going counterclockwise, however, this figure now allows:

  • The possibility of mathematical truths inaccessible to reason (in principle)
  • The possibility of mentality not rooted in physical structures
  • The possibility of physical action beyond the scope of mathematical control

As indicated above, either view contains the same mysteries though; namely:

  • Why do mathematical laws apply to the physical world with such precision? Why are mathematical laws so beautiful?
  • How can some physical materials like human brains conjure up consciousness ?
  • How is it that we can perceive mathematical truth? How could we grasp the actual meanings of “zero”, “one”, “two”, “three”, etc.?