Editing The Road to Reality Study Notes (section)

=== 1.4 Three worlds and three deep mysteries ===
[[File:Three worlds penrose.png|thumb|Figure 1.3: Penrose three worlds]]
Penrose outlines his conception of three worlds:
* The Platonic Mathematical
* The Physical
* The Mental
as shown in figure 1.3. Connections between these worlds present a great number of mysteries. The main focus of the book is to explore the connection between mathematics and its use in describing the physical world. Note that only a small subset of the mathematical world is utilized in describing the physical world. The reason why mathematics can describe the physical world so accurately is unknown. Moving in the counter clockwise direction there is a mysterious connection between the physical world and that of the mind. He believes that there must be some basis of consciousness in physical reality, but it is still unknown. Finally there is the connection between the mental world and mathematics. Penrose believes that there is no mathematical notion beyond our mental construction. He highlights that this figure represents many of his prejudices and might upset some people. Maybe the connections from one world do not fully describe the other, or are incomplete.  Penrose believes that not much progress can be made with respect to the mental world until we know much more about the physical world.