How To Count Past Infinity
25,710,790
Published 2016-04-09
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: • Infinity: The Science of Endless
Names of large (finite) numbers: en.wikipedia.org/wiki/Names_of_large_numbers
Geoglyphs:
The biggest number: goo.gl/maps/7GWcpnzo7iG2?entry=yt
Fovant badges: en.wikipedia.org/wiki/Fovant_Badges
Battalion Park: en.wikipedia.org/wiki/Battalion_Park
A mile of pi [VIDEO]: • Mile of Pi - Numberphile
Wikipedia’s great visualization of ordinals out to omega^omega: en.wikipedia.org/wiki/File:Omega-exp-omega-labeled…
as seen on: en.wikipedia.org/wiki/Ordinal_number
this is also a good page about ordinals: math.wikia.com/wiki/Ordinal_Number
also: www.cut-the-knot.org/WhatIs/Infinity/Ordinals.shtm…
and: en.wikipedia.org/wiki/Order_type and en.wikipedia.org/wiki/Well-order
Axioms:
en.wikipedia.org/wiki/Axiom
www.reddit.com/r/askscience/comments/30xokb/have_t…
philosophy.stackexchange.com/questions/5922/what-i…
www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf
www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms2.pdf
THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES
[PDF]: www.maths.ed.ac.uk/~aar/papers/wigner.pdf
en.wikipedia.org/wiki/The_Unreasonable_Effectivene…
Large Cardinal game based on 2048: cantorontheshore.blogspot.it/2014/10/one-reinhardt…
Other good resources:
quibb.blogspot.com/2012/01/infinity-first-transfin…
plato.stanford.edu/entries/set-theory/
cantorsattic.info/Cantor%27s_Attic
cantorontheshore.blogspot.co.at/2014/09/artemis-fo…
isomorphism.es/post/10782081422/what-comes-after-i…
lukepalmer.wordpress.com/2007/06/14/the-lesser-of-…
MUSIC BY:
youtube.com/JakeChudnow
www.audionetwork.com/
All Comments (21)
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listen to what I say at exactly 0:40
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-So can we count to Infinity? -ℵₒ
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The seemingly random "post credits" scene was incredible. "Omega + one" indicates a number that is in order after the "last" of the natural numbers. Having that bit play AFTER the "end" of the video was absolutely genius and wonderfully creative.
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1:00 How to count according to Michael: 40, 41, 42, 43, a billion, a trillion
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9 year old me: Infinity plus one.
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"Mom, Vsauce glitched my brain again!"
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21:00 and this is why i absolutely love and adore mathematicians they're just like me "oh this is absurd that makes no sense but yknow what let's keep going anyway let's see how far we can go"
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16:03 "we’re cooking now". I didn’t know people said this 7 years ago I thought that only came out last year?? How ahead of vsauce’s time was he?
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"0=1" Yup, I've had enough of math today.
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Important note about the continuum hypothesis (CH): It's not just that it's unsolved, it's actually unsolvable. CH has been shown to be logically independent from the ZFC axioms of set theory - that is, you can show that CH is not a theorem of ZFC and that the negation of CH is also not a theorem of ZFC. This is ultimately a consequence of incompleteness - any set of axioms and system of proofs must contain propositions which are neither provable or disprovable
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This video is 7 years old yet still feels like it was uploaded yesterday
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40: exists 41: I'm about to end this man's whole career
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Fun fact: infinity+1 is bigger than infinity. Source: 7 year old me arguing with my siblings
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“All we have to say is ‘Let there be Omega’, and it will be good.” Why does this sound like a quote from a fantasy movie lmao He would definitely be the cool wizard guy that guides the hero
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Man, for some reason no matter how hard I try, I cant bring myself to stop watching. I ask myself, "When will i ever use this knowledge?" and my answer is never. But still its so entertaining to watch numbers over numbers of complexity and pretend i comepletely understand and I believe I understand too just because of his amazing teaching. Well Vsauce, you just gained another VERY big fan and subscriber. I got notifications going.
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Nobody: Vsauce: How to taste the color 7.
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Never discuss infinity with a mathematician, they can go on about it forever.
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I'm in tears (I exaggerated. Actually, better than in tears) and with thrills (shivers? I don't know English) each time I watch this video and the Theta is reached. Really big thanks to you, Michael, for having brought me joy, having brought me sense, after I discovered that atoms are not so tiny, galaxies not so big, the universe not so old (recent history is comparable with the history of life and Earth), that anything material is not surprising but that there are things, actual logical things (don't know how much this counts), that can go even way beyond what satisfies me, my hunger for the greatness and the epicness, and Sense. Sense of life to me is merely complexity. I discovered the magnitude if Graham's number and felt shocked. I discovered these "numbers" in the video, in respect to which Graham's is totally nothing (actually infinitesimal) just in comparison with the first one, the numeral infinite, aleph_0. I will take refuge in the ideal world. Mathematics, with its total rigor, the minimal starting points and its complexity, hasn't disappointed me much, yet.
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we had dimensions in objects (e.g. 2D, 3D), and the way vsauce described infinities, i think we also found them number dimensions
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God: how many years do you want to live? Queen Elizabeth II: