Gödel, Escher, Bach - Lecture 1: Part 3 of 7

During the summer of 2007, Gödel, Escher, Bach was recorded for OpenCourseWare.

Original Content Location: http://ocw.mit.edu/OcwWeb/hs/geb/VideoLectures/

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Category:

Education

Tags:

• Gödel
• Escher
• Bach
• Education
• Strange Loops

[happyman]

zeno didn't use it to prove that motion was impossible. instead, with the obvious fact of motion as premise, he sought to discredit this whole affair of breaking things apart as though they were not a continuum...

[happyman]

@jdkhanlian the paradox lies on this conflict: if you break things into parts then you cannot have motion. so something must give. he chose to deny that you can break things apart instead of denying motion. it is all part of his agenda of promoting the metaphysical "One" of parmenides against its critics by showing that the metaphysical "many" implies more ridiculous things like the impossibility of motion .

[azkeyz]

The failure here is the syntax.

[DarkwingScooter]

@Mattris Ah, but you cannot use the concept of infinity unless you are prepared to descend to irrationality.

Infinity doesn't exist as an actual thing, it is just a tool that mathematicians use to solve problems.

Since infinity doesn't exist in the real world you cannot use it to prove that math solves real world problems consistently. That is the essence of the problem as far as I understand it.

Infinity is a mathematician's version of "then verily god spake and yeah, it was so!"

[DarkwingScooter]

The real answer to Zeno's paradox that is in keeping with modern physics is that there is no such thing as a continuum of space or time. You cannot infinitely divide a length because below the Planck distance the concept of length ceases to have any meaning.

[jacquesgambl36]

This video went viral on Nicosia

[DraskyVanderhoff]

AGH, FORMAL SYSTEMS ARE BORING?! Puff, that's a great attitude to make any progress in life -.-

[mrfatmann]

GROAN. 7:50. I am enjoying the lecture. I felt compelled to comment on this aside on infinity. The example here dropping Cantor's diagonalization seems out-of-kind with the rest of the lecture's naive mathematics. If you're going to explain the "surprising dimensionalization of fractals" you should certainly take a little more time to explain any "surprising notion of the magnitude of infinity" by Cantor--do it well or don't mention it.

[fakpuppet]

@veedoubleyou So your proposition is that if there was such a thing as a continuum motion in fact in such a continuum would not be possible? :)

[Mattris]

Even if we did not no about the Planck length, Zeno's paradox isn't that hard to disprove using infinite geometric series. I did it back in Calc 2, & yes it did involve taking a limit as n --> infinity, but no derivatives, or integrals, just discrete math with a limit to show that the geometric series converges as long as |r| < 1, and you can show the exact value it converges to since it's a geometric series.

[veedoubleyou]

The reason Zeno's paradox is incorrect is not because of calculus.  The assumption of the infinite divisibility of space is wrong. You eventually hit a physical limit (planck length).

[nicoheckens1]

Barbers Paradox.... s={x/ x=/x} is s a subset of itself? S e/ s S-------S e S-----?????How can a function be its own argument... so trivial....frankly even irritating.