How To Count Past Infinity
Vsauce6 HN recommenders · recommended in 5 months, 2016–2022
explainer · general · evergreen · 2016–2022 on HN
Vsauce's Michael Stevens takes viewers past infinity using transfinite numbers, ordinals and cardinals, with input from mathematician Hugh Woodin. It is a fast-paced, mind-bending tour of different sizes of infinity.
HN recommends it as the most accessible introduction to what lies beyond infinity.
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10 comments from Hacker News
My personal favourite to illustrate infinity (as possible) and some math concepts around it is still the video "How To Count Past Infinity" from Vsauce: ▶ this video "This is math, not science." (~12:30)
(related - and I enjoyed the vibe he put into it): ▶ this video - Vsauce's "How to Count Past Infinity"
Thanks for that, I hadnt' bumped into that channel before. After watching this one I watched the one on how to count past infinity....mind suitably blown :) ▶ this video
VSauce is a science channel which I find both entertaining and educational. Fun and fast paced and often mind-bending. ▶ this video
There is one English definition of infinity, but when applied to ordinals ("degrees of freedoms"), you get different mathematical concepts of infinity. Vsauce's explanation is approachable: ▶ this video
The issue is that there are different infinities. The infinity the parent is talking about, the one that you generally run into in calculus class and the like, is straightforward. The research in the past century was about what happens _past_ infinity, e.g. ordinal numbers. I'm no mathematician either, so I'll stop there before I embarrass myself. The most accessible resource I found was this VSauce video [1]. [1] ▶ this video
Completely offtopic, except for math and title, but highly recommended while waiting for the movie: "How To Count Past Infinity" ▶ this video
Thanks for sharing. I'm going to add here some links that I've been curating regarding the "existence" of infinity: The physics of infinity - link - Discussion: link Is infinity Real? - link - Solution: link Do infinities exist in nature? - link Does infinity exist? - link - Discussion: link How to count past infinity - ▶ this video How real are real numbers? - link - Discussion: link / link Are Real Numbers Real? - link - Discussion: link
I really need a video on transfinite cardinals and ordinals beyond Aleph_0 and Epsilon_0. The VSauce video [1] on the topic only made me more curious with an elusive tree diagram displaying a few, and PBS Infinite Series [2] [3] just barely touched it. The mention of the Veblen hierarchies really piqued my interest, but much of what I've found on them has been a bit too dense for me. 1. ▶ this video 2. link 3. link
Related (a bit of Cantor and Hilbert, no direct relation to Ramsey’s theorem): "How To Count Past Infinity" ▶ this video