“Consciousness is the phenomenon whereby the universe’s very existence is known”
Roger Penrose
“Either mathematics is too big for human mind or the human mind is more than a machine.”
Kurt Gödel
Roger Penrose has a theory about human consciousness, which is claimed by him to be strictly larger than Artificial Intelligence, where he makes use of Kurt Gödel’s incompleteness theorem along with certain theorized extensions of Quantum Mechanics. The incompleteness theorem, which is related to Alan Turing’s undecidability results in theory of computation, asserts that if a mathematical system with its axioms and rules of inference has to be consistent then it has to be also incomplete. There will be mathematical statements which can not be proven or disproven. Gödel meticulously constructed the following self-referential statement in such a formal system:
“This statement is not provable”
The statement is not provable or disprovable, because if it were, then we have contradiction. Is it true? Yes, it is obvious to us, but an AI system can’t infer it based on an algorithm which works with axioms and computation steps. One has to step out of the proof machinery to see its truth, which we can do.
Penrose also speculates that Quantum Mechanics, which is currently incomplete (not in Gödel’s sense, but in the sense that it doesn’t unify with gravity and it has inexplicable measurement problem), can be extended in which some non-computational aspects will appear, at the very microscopic fabric of universe, where consciousness resides. There we “see” the truths, which AI will never be able to.
When you are reading something or working out math, what does it mean to understand? Many mathematicians state that lot of their thinking is visual. What is vision? What exactly does it mean to see?
One can refer to literature and mythology for some pointers, as this is a fundamental question, which all of us are interested in.
I was reading a book Unseeing Idol of Light written by K. R. Meera.
It is a novel in which there is love and and there is loss. There are themes of light and darkness, of vision and blindness, in a metaphorical sense, and which really relate to the same topic which Penrose is interested in. What does it mean to feel, to know, and to see? The story moves you. Literature tells us that we “see” somewhere deep inside us, but we can also lose the capacity to do so. To see is to feel.