Gheorghe Curelet-Balan Blog

Friday, October 06, 2006

A fundamental limit yields to new discovery.

This is the main idea that I learned from Janna Levin's yesterday PI lecture. It can be rephrased as: Truth is limited but humanity's mind is limitless.

Before you jump on me I have to mention that we are talking about mathematical truth (expressed in theorems) and not the real life truth revealed by a witness or not tampered picture, video clip or audio recording.

Both Godel and Turing proved that there are limits to mathematical knowledge. In other words there are mathematical statements whose truth cannot be established if they make references to themselves. Janna started her "hard to get" explanation with the liar paradox (I used a version of it as voting for the Random Party during the political elections). Then she explained in lame terms Godel's incompleteness theorem, ending this part of the lecture with "that's OK if you don't quite get it since there are people that study this things for a year and still don't get it" (my paraphrase).

Turing's approach to use an abstract machine to decide if a proposition is true or false reached a similar result with Godel's: there are propositions whose truth cannot be proved doesn't matter how long the machine computes. His systematic approach yielded to the computer invention.

Having all these been said about the mathematical truth Janna easily introduced her main idea, in my humble opinion: A fundamental limit yields to new discovery. She explained how light's speed limit yielded to the theory of relativity and the Heinsenberg uncertainty principle yielded to the quantum mechanics. In the same way the limit of mathematical truth proved by Godel and Turing yielded to the computer discovery.

Janna found intriguing to oppose the greatness of Godel and Turing achievements with the true limit of their minds, that she characterized with a quote from a review of her book as genius obsessive disorder.


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