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):
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:
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.?