Norman Wildberger: The Problem with Infinity in Math
Professor of mathematics Norman Wildberger expounds on the nature of the infinite and the real numbers. Sponsors: for 20% off. For Algo's podcast and website
LINKS MENTIONED:
-Rational Trigonometry (book by Prof. Wildberger):
TIMESTAMPS:
00:00:00 Introduction
00:03:29 Behind the scenes banter
00:08:08 Overview of Norman's philosophy of mathematics
00:09:35 The problem with the concept of "infinity" in mathematics
00:14:46 Algorithmic reality and Wolfram's model
00:16:03 Physics and infinity (Riemann sphere and Spinors)
00:19:14 Infinity cannot be "done"
00:42:26 Physics doesn't actually use infinities
00:45:03 What about the wave function of half spin up / spin down?
00:47:25 Learning Tip for Math / Physics: Constantly ask "what is REALLY going on here?"
00:48:32 What is Rational Trigonometry and what led to it?
00:53:23 What compels Norman to rethink the foundations?
01:01:49 Is beauty (like in complex analysis) removed or added in the construcitivist approach
01:04:52 The simplicity of Norman's courses (links in the description)
01:08:31 On non-standard analysis
01:10:42 Why set theory has problems (even without the Axiom of Choice)
01:13:57 Roger Penrose's and Ed Witten's view on real numbers
01:16:09 Pure mathematicians vs physicists
01:17:17 [062985593] How would Wildberger rephrase the intermediate value theorem?
01:19:31 If math is currently vitally flawed, then why no inconsistencies
01:21:21 How do constructionists base their foundations in physics, when physics is couched in mathematics?
01:27:21 [Sam Thompson] Do you see problems with having infinite index sets?
01:32:13 [DivergentCauchy] Cranks and Platonism
01:34:30 Dealing with calumny as a creator
01:36:33 Norman is extremely interested in UFOs as well
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Just wrapped (April 2021) a documentary called Better Left Unsaid on the topic of "when does the left go too far?" Visit that site if you'd like to watch it.