Norman Wildberger: Why Infinity Is a Mathematical Mistake

Theories of Everything with Curt Jaimungal

Curt Jaimungal

Physics, Philosophy, Society & Culture, Science

4.6 • 606 Ratings

🗓️ 9 February 2022

⏱️ 106 minutes

🔗️ Recording | iTunes | RSS

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Summary

Norman Wildberger (UNSW) dismantles infinity and real numbers, defending finitism as math's true foundation He also explains his rational trigonometry approach and discusses how his views intersect with physics, set theory, and even UFOs.- 00:00:00 - Introduction- 00:03:29 - Banter- 00:08:08 - Overview of Wildberger's philosophy- 00:09:35 - Problem with infinity in mathematics- 00:14:46 - Algorithmic reality & Wolfram model- 00:16:03 - Physics and infinity (Riemann sphere, spinors)- 00:19:14 - Infinity cannot be "done"- 00:42:26 - Physics doesn't use infinities- 00:45:03 - Wave function of half spin up/down- 00:47:25 - Learning tip: ask what is really going on- 00:48:32 - What is Rational Trigonometry?- 00:53:23 - Why Wildberger rethinks foundations- 01:01:49 - Beauty in constructive approach- 01:04:52 - Simplicity of Wildberger's courses- 01:08:31 - Non‑standard analysis- 01:10:42 - Problems with set theory- 01:13:57 - Penrose and Witten on real numbers- 01:16:09 - Pure mathematicians vs physicists- 01:17:17 - How would Wildberger rephrase IVT?- 01:19:31 - Is math flawed but no inconsistencies?- 01:21:21 - Constructionists' physics foundations- 01:27:21 - Infinite index sets?- 01:32:13 - Cranks and Platonism- 01:34:30 - Dealing with calumny- 01:36:33 - Wildberger interested in UFOsSPONSORS:- Brilliant: 20% off - https://brilliant.org/TOE- Algo podcast channel - https://www.youtube.com/channel/UC9IfRw1QaTglRoX0sN11AQQ- Algo website - https://www.algo.com/- Patreon - https://patreon.com/curtjaimungal- Crypto - https://tinyurl.com/cryptoTOE- PayPal - https://tinyurl.com/paypalTOE- Twitter - https://twitter.com/TOEwithCurt- Discord - https://discord.com/invite/kBcnfNVwqs- iTunes - https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802- Pandora - https://pdora.co/33b9lfP- Spotify - https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e- Reddit - https://reddit.com/r/theoriesofeverything- Merch - https://tinyurl.com/TOEmerchRESOURCES:- 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- https://youtu.be/l7LvgvunVCM- http://betterleftunsaidfilm.com Theories of Everything with Curt Jaimungal features long-form, technically detailed interviews with leading researchers in physics, mathematics, consciousness, and philosophy, exploring topics at the level of active research. For academics, graduate students, and anyone seeking depth beyond popular science. SPONSOR: I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE FOLLOW: Substack | Spotify | YouTube | Twitter Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

Transcript

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0:00.0	It's rare that I feel such an instantaneous warmth with the guest, especially when we're meeting for the first time.
0:06.0	Hopefully you sense the comfort and mutual adoration as well.
0:08.0	As many viewers often joke, it's not a live stream, it's a love stream.
0:12.0	Norman will be back for a part two, so make sure to write your questions down in the comments.
0:17.0	Norman Wildberger is a professor of pure mathematics at the University of New South Wales
0:21.6	and is the founder of the YouTube channel Insights into Mathematics, which just passed its 100,000 subscriber mark.
0:28.6	Norman Wildberger is one of the rare examples of a mathematician examining the foundations of mathematics
0:34.6	in order to reformulate it, ridding it of the qualities considered
0:38.2	abhorrent by the intuitionists. If these phrases or concepts are unfamiliar to you, don't
0:43.1	worry, keep watching and it will be explained in detail within the podcast. Today we discuss
0:48.0	whether the concept of infinity is well founded, as well as the reality or unreality to
0:53.1	the real numbers. Click on the timestamp in the description if you'd like to skip this intro.
0:57.6	My name is Kirchai Mungle.
0:59.1	I'm a Torontoian filmmaker with a background in mathematical physics dedicated to the
1:04.3	explication of the variegated terrain of theories of everything, from a theoretical physics
1:09.4	perspective, but as well as analyzing consciousness and seeing its potential connection to
1:14.3	Fundamental Reality, whatever that is. Essentially, this channel is dedicated to exploring the underrived
1:19.5	nature of reality, the constitutional laws that govern it, provided those laws exist at all, and are even knowable to us.
1:25.5	If you enjoy witnessing and engaging with others
1:28.1	on the topics of psychology, consciousness, physics, etc., the channel's themes, then do consider
1:33.8	going to the Discord and the subreddit, which are linked in the description. There's also a link
1:38.1	to the Patreon. That is patreon.com slash Kirchai Mungal. If you'd like to support this podcast,
	...

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