May

23

 I am not familiar with Kurt Godel, but I think his ideas are similar to the ideas of cosmologist Max Tegmark. Here is an excerpt from the BBC documentary Horizon interviewing Max Tegmark.

He states that our Universe/Reality is math. So math is not only a language to understand the world, but it is the world itself.

My knowledge of the topic ends here-– it is fascinating though.

Quoting T. Mcclellan:

Plato was probably the last person to at least be on a level with the then leading thinkers of functionally all branches of human thought (Aristotle conventionally thought to be even more so).

There is an interesting refutation of the ideas in the Republic in the Parmenides. In this second dialogue Parmenides delivers a devastating criticism of Plato's skepticism about empirical reality. Plato has him argue strictly on Platonic lines that in fact if we grant that the Forms (for example numbers) truly exist, even then we could not know them–and worse, if we exist then pure beings such as the gods could not know us! Thus not only are ideas as unreliable as appearances they are no surer a foundation for knowledge. Obviously not a great conclusion for a Platonist!

Believe it or not, the real existence of forms–or the Pythagorean equivalent that all the universe is number (perhaps numbers) is still hotly contested today. Supposedly Kurt Godel could not understand people who did not believe in the literal existence of numbers outside the human brain. Although of what substance he thought them to be composed, I know not.

Russ Sears writes: 

The following is what I wrote to the spec-list in 2010, concerning Godel and Singularity. Kurt Godel was a close friend of Einstein, they often walked to and from the University together. He is most known for his "Incompleteness Theorem".

It has been suggested before that Godel's proof gives us insights into human intelligence. John Lucas was one of the first to suggest it. "Godel's Theorem seems to me to prove…that minds cannot be explained as a machine".

Roger Pemrose has 2 books, "The Emperors New Mind" and "Shadows of the Mind" that supposedly show Godel disproving "mechanism" and "artificial intelligence".

Pemrose suggests that while we're not a machine, we are a physical system and should consider quantum mechanics.

Godel was much too timid about conjecturing on the record. He was very fearful about confrontation. As suggested, the Third Reich probably never did give him or his kind a second thought. To his paranoid mind the world would conspire against him to keep all mankind stupid. So what we have from him on this subject is from his private conversation with Hao Wang and a lecture.

Wang on Godel: "Either the human mind surpasses all machines (to be more precise it can decide more number theoretical question than any machine) or else there exist number theoretical questions undecidable for the human mind." or as Ms Goldstein suggests: "The incompleteness theorem, by showing the limits of formalization, both suggest that our minds transcend machines and makes it impossible to prove that our minds transcend machines. Again, an almost paradox."

Or in my words we could simply be deluding ourselves that we have access to "truth" through intuition. This is of course is tragic and ironic in that while we can't know the pure case, Godel himself succumbed to some major delusions and was paranoid later in life.

And we as speculators certainly can't cast the first stone. While I would suggest that we may "transcend machines" through quantum mechanics, our minds may also transcend time through quantum mechanics, leaving a rendering of our "physical system" difficult if not impossible to interpret and to reproduce. 


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2 Comments so far

  1. Arch on May 24, 2017 12:25 pm

    “Einstein once remarked to Oskar Morgenstern, one of the cofounders of game theory, that he went to the Institute [for Advanced Study in Princeton, NJ] chiefly to walk home with Gödel.”
    http://discovermagazine.com/2002/mar/featgodel

  2. bo keely on May 25, 2017 2:06 pm

    The topic is explored in the English schoolmaster Edwin Abbott Abbott’s classic but nearly forgotten ‘Flatland’

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