Professor of mathematics Norman Wildberger expounds on the nature of the infinite and the real numbers.<br /><br />Sponsors: <a href="https://brilliant.org/TOE" target="_blank" rel="nofollow">https://brilliant.org/TOE</a> for 20% off. For Algo's podcast <a href="https://www.youtube.com/channel/UC9IfRw1QaTglRoX0sN11AQQ" target="_blank" rel="nofollow">https://www.youtube.com/channel/UC9IfRw1QaTglRoX0sN11AQQ</a> and website <a href="https://www.algo.com/" target="_blank" rel="nofollow">https://www.algo.com/</a>. <br /><br />Patreon: <a href="https://patreon.com/curtjaimungal" target="_blank" rel="nofollow">https://patreon.com/curtjaimungal</a><br />Crypto: <a href="https://tinyurl.com/cryptoTOE" target="_blank" rel="nofollow">https://tinyurl.com/cryptoTOE</a><br />PayPal: <a href="https://tinyurl.com/paypalTOE" target="_blank" rel="nofollow">https://tinyurl.com/paypalTOE</a><br />Twitter: <a href="https://twitter.com/TOEwithCurt" target="_blank" rel="nofollow">https://twitter.com/TOEwithCurt</a><br />Discord Invite: <a href="https://discord.com/invite/kBcnfNVwqs" target="_blank" rel="nofollow">https://discord.com/invite/kBcnfNVwqs</a><br />iTunes: <a href="https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802" target="_blank" rel="nofollow">https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802</a><br />Pandora: <a href="https://pdora.co/33b9lfP" target="_blank" rel="nofollow">https://pdora.co/33b9lfP</a><br />Spotify: <a href="https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e" target="_blank" rel="nofollow">https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e</a><br />Subreddit r/TheoriesOfEverything: <a href="https://reddit.com/r/theoriesofeverything" target="_blank" rel="nofollow">https://reddit.com/r/theoriesofeverything</a><br />Merch: <a href="https://tinyurl.com/TOEmerch" target="_blank" rel="nofollow">https://tinyurl.com/TOEmerch</a><br /><br />LINKS MENTIONED:<br />-Prof. Norman Wildberger's YouTube channel: <a href="https://www.youtube.com/njwildberger" target="_blank" rel="nofollow">https://www.youtube.com/njwildberger</a><br />-Rational Trigonometry (YouTube series): <a href="https://www.youtube.com/playlist?list=PL3C58498718451C47" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PL3C58498718451C47</a><br />-Rational Trigonometry (book): <a href="https://amzn.to/3rEygVW" target="_blank" rel="nofollow">https://amzn.to/3rEygVW</a><br /><br />TIMESTAMPS:<br />00:00:00 Introduction<br />00:03:29 Behind the scenes banter<br />00:08:08 Overview of Norman's philosophy of mathematics<br />00:09:35 The problem with the concept of "infinity" in mathematics<br />00:14:46 Algorithmic reality and Wolfram's model<br />00:16:03 Physics and infinity (Riemann sphere and Spinors)<br />00:19:14 Infinity cannot be "done"<br />00:42:26 Physics doesn't actually use infinities<br />00:45:03 What about the wave function of half spin up / spin down?<br />00:47:25 Learning Tip for Math / Physics: Constantly ask "what is REALLY going on here?"<br />00:48:32 What is Rational Trigonometry and what led to it?<br />00:53:23 What compels Norman to rethink the foundations?<br />01:01:49 Is beauty (like in complex analysis) removed or added in the construcitivist approach <br />01:04:52 The simplicity of Norman's courses (links in the description)<br />01:08:31 On non-standard analysis<br />01:10:42 Why set theory has problems (even without the Axiom of Choice)<br />01:13:57 Roger Penrose's and Ed Witten's view on real numbers<br />01:16:09 Pure mathematicians vs physicists<br />01:17:17 [062985593] How would Wildberger rephrase the intermediate value theorem?<br />01:19:31 If math is currently vitally flawed, then why no inconsistencies<br />01:21:21 How do constructionists base their foundations in physics, when physics is couched in mathematics?<br />01:27:21 [Sam Thompson] Do you see problems with having infinite index sets?<br />01:32:13 [DivergentCauchy] Cranks and Platonism<br />01:34:30 Dealing with calumny as a creator<br />01:36:33 Norman is extremely interested in UFOs as well<br /><br />* * *<br /><br />Just wrapped (April 2021) a documentary called Better Left Unsaid <a href="http://betterleftunsaidfilm.com" target="_blank" rel="nofollow">http://betterleftunsaidfilm.com</a> on the topic of "when does the left go too far?" Visit that site if you'd like to watch it.<br />...<br /><a href="https://www.youtube.com/watch?v=l7LvgvunVCM" target="_blank" rel="nofollow">https://www.youtube.com/watch?v=l7LvgvunVCM</a>