Navigating the Infinity of Mathematics

Professor of mathematics Norman Wildberger expounds on the nature of the infinite and the real numbers.

YouTube link: https://youtu.be/l7LvgvunVCM

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LINKS MENTIONED:

-Prof. Norman Wildberger's YouTube channel: https://www.youtube.com/njwildberger

-Rational Trigonometry (YouTube series): https://www.youtube.com/playlist?list=PL3C58498718451C47

-Rational Trigonometry (book): https://amzn.to/3rEygVW

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 http://betterleftunsaidfilm.com on the topic of "when does the left go too far?" Visit that site if you'd like to watch it.

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