Norman Wildberger on the Problem with Infinity, The Foundations of Mathematics, Finitism, and the Real Numbers

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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