I just finished reading
A Madman Dreams of Turing Machines
by
Janna Levin.
What a wonderful book! She writes about the private life, love, desperation and achievements of these two giants of the mind, Turing and Gödel:
The human mind can also be reduced to a machine. This idea drives all the others as he runs on grass, past trees, over bridges, through cattle. States of mind can be replaced by states of the machine. Human thought can be broken down into simple rules, instructions a machine can follow. Thought can be mechanized. The connection isn't perfectly clear, but it is there, the catalyst of a great crystal. It is not just that thought can be mechanized. It is mechanized. The brain is a machine. A biological machine. The idea cools him from head to toe, a wave of understanding washing clean his confusion, his muddled notions, and his breath. Shock feels like this: There is no sky or earth. No time, no meaning. It's a throb—a hard silence, a pulse. It is colorless, tasteless, senseless. A white-hot explosion[…]
At the age of twenty-three and for the rest of his life he embraces, without reservation, a mathematics that exists independently of us—although we, by contrast, do not live independently of it. We are biological machines. Nothing more. We have no souls, no spirit. But we are bound to mathematics and mathematics is flawless. This has to be true.
Another book by Janna Levin I can recommend is
How the Universe Got Its Spots: Diary of a Finite Time in a Finite Space. It's about about the nature of our universe as we understand it today. A collection of letters Janna Levin wrote to her mother explaining her work.