Week 7 - Neurosci + Art

In this week's material the idea that interests me the most is Roger Penrose's claim that the human consciousness must contain some non-computable ingredients.
The Emperor's New Mind, first edition.jpg


The idea of the world not being real can be traced back in the ancient times, from Zhuangzi's Dream of Butterflies in the eastern culture to Descartes' external world skepticism. Due to the advancement in modern technology, especially in the invention and rapid progression of computers, a lot of people have hypothesized further that our own consciousness may well not be true but is oply part of a computer simulation. Roger Penrose refutes the idea by pointing out that due to Gödel's Incompleteness Theorem our consciousness cannot be part of a computer simulation.
Roger Penrose at Festival della Scienza Oct 29 2011.jpg

Roger Penrose
Gödel's Incompleteness Theorem merely states that in any logic system of the first or higher order that permits the representation of Peano Axioms (which defines natural numbers), there must be some statement compatible with the system not provable in the system. For a more straightforward example, imagine a book with infinitely many pages. On each page of the book reads the same sentence: at least one of the statement on the succeeding pages is false. The book then becomes a logical paradox.
A Computer Simulation on the Molecular Level
Penrose’s point lies in that, any computer program must first of all be computable, thus provable in the logic system that guides the computer that runs the program. Our ability of understanding Gödel's Incompleteness Theorem proves that our own consciousness is not provable within the logic systems that constitutes our world, thus the world and our own thoughts cannot be part of a computer simulation.

Sources:

"Roger Penrose." Wikipedia. Wikimedia Foundation, 21 May 2017. Web. 21 May 2017. <https://en.wikipedia.org/wiki/Roger_Penrose>.

The Third Culture - Chapter 14. N.p., n.d. Web. 21 May 2017. <https://www.edge.org/documents/ThirdCulture/v-Ch.14.html>.

"Gödel's incompleteness theorems." Wikipedia. Wikimedia Foundation, 09 June 2017. Web. 21 May 2017. <https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems>.

"Simulation hypothesis." Wikipedia. Wikimedia Foundation, 17 May 2017. Web. 21 May 2017. <https://en.wikipedia.org/wiki/Simulation_hypothesis>.
"The Emperor's New Mind." Wikipedia. Wikimedia Foundation, 12 May 2017. Web. 21 May 2017. <https://en.wikipedia.org/wiki/The_Emperor%27s_New_Mind>.

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