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#infinity#cantor#transfinitenumbers

How To Count Past Infinity

Vsauce

25M subscribers • 3 videos on Hallway

YouTube
  • Recommended by 6 people: 6 on Hacker News.
  • Presented by Michael Stevens, creator of Vsauce

Beginner. No background in the topic needed.

29M views10 years ago6 recommendations

Computer scienceComputation and complexityMath for programmers

Michael Stevens explains transfinite numbers, ordinals, and cardinals, exploring different sizes of infinity.

Support Vsauce, your brain, Alzheimer's research, and other YouTube educators by joining THE CURIOSITY BOX: a seasonal delivery of viral science toys made by Vsauce! A portion of all proceeds goes to Alzheimer's research and our Inquisitive Fellowship, a program that gives money and resources directly to growing science channels here on YouTube! curiositybox.com my twitter: @tweetsauce my instagram: electricpants Sources and links to learn more below! I’m very grateful to mathematician Hugh Woodin, Professor of Philosophy and Mathematics at Harvard, for taking the time on multiple occasions to discuss this topic with me and help me wrap my (finite) head around it. I’m also grateful to David Eisenbud, the Director of the Mathematical Sciences Research Institute (MSRI) and professor of mathematics at the University of California, Berkeley, for his help and for connecting me with Hugh Woodin. And of course, big thanks to Brady Haran who created the “mile of pi” seen in this video and connected me with all these mathematicians in the first place. His channel, Numberphile, is superb: youtube.com/user/numberphile BOOKS related to these topics that I used: “The Outer Limits of Reason” by Noson S. Yanofsky: amzn.com/0262019353 “Infinity and The Mind” by Rudy Rucker: amzn.com/0691121273 “Roads to Infinity” by John C. Stilwell: amzn.com/1568814666 “More Precisely: The Math You Need to Do Philosophy” by Eric Steinhart: amzn.com/1551119099 “Satan, Cantor and Infinity: Mind-Boggling Puzzles” by Raymond M. Smullyan: amzn.com/0486470369 classic book that helps introduce concept of axioms: “Introduction to the Foundations of Mathematics” by Raymond L. Wilder: amzn.com/0486488209 Hugh Woodin speaking about infinity at the World Science Festival: youtu.be/KDCJZ81PwVM?t=29m45s Names of large (finite) numbers: en.wikipedia.org/wiki/Names_of_large_numbers Geoglyphs: The biggest number: goo.gl/maps/7GWcpnzo7iG2 Fovant badges: en.wikipedia.org/wiki/Fovant_Badges Battalion Park: en.wikipedia.org/wiki/Battalion_Park A mile of pi [VIDEO]: youtube.com/watch?v=0r3cEKZiLmg Wikipedia’s great visualization of ordinals out to omega^omega: en.wikipedia.org/wiki/File:Omega-exp-omega-labeled.svg as seen on: en.wikipedia.org/wiki/Ordinal_number this is also a good page about ordinals: math.wikia.com/wiki/Ordinal_Number also: cut-the-knot.org/WhatIs/Infinity/Ordinals.shtml and: en.wikipedia.org/wiki/Order_type and en.wikipedia.org/wiki/Well-order Axioms: en.wikipedia.org/wiki/Axiom reddit.com/r/askscience/comments/30xokb/have_there_been_axio… philosophy.stackexchange.com/questions/5922/what-is-the-diff… cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms2.pdf

Why it's here

6 people recommend this

What people say. Highly recommended as an approachable and mind-bending explanation of mathematical infinity.

okketon Hacker News • Recommends

On “Life on the Infinite Farm [pdf]”

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: link to this video "This is math, not science." (~12:30)

okketon Hacker News • Recommends

On “The Man Who Knew Infinity”

Completely offtopic, except for math and title, but highly recommended while waiting for the movie: "How To Count Past Infinity" link to this video

lasfteron Hacker News • Recommends

On “What I learned as a hired consultant to autodidact physicists”

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 link to this video

cjslepon Hacker News • Recommends

On “Mathematicians Measure Infinities, Find They’re Equal”

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: link to this video

hawktheslayeron Hacker News • Recommends

On “Ask HN: What are fun entertaining YouTube channels/videos you watch in free time?”

VSauce is a science channel which I find both entertaining and educational. Fun and fast paced and often mind-bending. link to this video

swfsqlon Hacker News • Recommends

On “How to explain infinity to kids”

(related - and I enjoyed the vibe he put into it): link to this video - Vsauce's "How to Count Past Infinity"

teh_klevon Hacker News • Recommends

On “Absolute Hot”

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 :) link to this video

okketon Hacker News • Mentions

On “Mathematicians Bridge Finite-Infinite Divide”

Related (a bit of Cantor and Hilbert, no direct relation to Ramsey’s theorem): "How To Count Past Infinity" link to this video

x3n0ph3n3on Hacker News • Mentions

On “TREE vs. Graham’s Number [video]”

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. link to this video 2. link 3. link

yamrzouon Hacker News • Mentions

On “The Axiom of Infinity”

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 - link to this video How real are real numbers? - link - Discussion: link / link Are Real Numbers Real? - link - Discussion: link