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25,720,530 Views ā¢ Apr 9, 2016 ā¢ Click to toggle off description
my twitter: @tweetsauce
my instagram: electricpants
Sources and links to learn more below!
Iām 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.
Iām 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 āmile of piā 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:
āThe Outer Limits of Reasonā by Noson S. Yanofsky: amzn.com/0262019353
āInfinity and The Mindā by Rudy Rucker: amzn.com/0691121273
āRoads to Infinityā by John C. Stilwell: amzn.com/1568814666
āMore Precisely: The Math You Need to Do Philosophyā by Eric Steinhart: amzn.com/1551119099
āSatan, Cantor and Infinity: Mind-Boggling Puzzlesā by Raymond M. Smullyan: amzn.com/0486470369
classic book that helps introduce concept of axioms: āIntroduction to the Foundations of Mathematicsā by Raymond L. Wilder: amzn.com/0486488209
Hugh Woodin speaking about infinity at the World Science Festival: Ā Ā Ā ā¢Ā Infinity:Ā TheĀ ScienceĀ ofĀ EndlessĀ Ā
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]: Ā Ā Ā ā¢Ā MileĀ ofĀ PiĀ -Ā NumberphileĀ Ā
Wikipediaās great visualization of ordinals out to omega^omega: en.wikipedia.org/wiki/File:Omega-exp-omega-labeledā¦
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.shtmā¦
and: en.wikipedia.org/wiki/Order_type and en.wikipedia.org/wiki/Well-order
Axioms:
en.wikipedia.org/wiki/Axiom
www.redlib.matthew.science/r/askscience/comments/30xokb/have_tā¦
philosophy.stackexchange.com/questions/5922/what-iā¦
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_Effectiveneā¦
Large Cardinal game based on 2048: cantorontheshore.blogspot.it/2014/10/one-reinhardtā¦
Other good resources:
quibb.blogspot.com/2012/01/infinity-first-transfinā¦
plato.stanford.edu/entries/set-theory/
cantorsattic.info/Cantor%27s_Attic
cantorontheshore.blogspot.co.at/2014/09/artemis-foā¦
isomorphism.es/post/10782081422/what-comes-after-iā¦
lukepalmer.wordpress.com/2007/06/14/the-lesser-of-ā¦
MUSIC BY:
youtube.com/JakeChudnow
www.audionetwork.com/
Views : 25,720,530
Genre: Science & Technology
Date of upload: Apr 9, 2016 ^^
Rating : 4.91 (13,760/596,770 LTDR)
RYD date created : 2022-04-09T21:37:24.717299Z
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YouTube Comments - 82,717 Comments
Top Comments of this video!! :3
-So can we count to Infinity?
-āµā
32K |
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.
579 |
1:00 How to count according to Michael:
40, 41, 42, 43, a billion, a trillion
415 |
How to count past infinity:
Dumb people: infinity+1
Smart people: you canāt
Top mathematicians: infinity+1 lmao
6.8K |
40: exists
41: I'm about to end this man's whole career
1.9K |
16:03 "weāre cooking now". I didnāt know people said this 7 years ago I thought that only came out last year?? How ahead of vsauceās time was he?
403 |
This video is 7 years old yet still feels like it was uploaded yesterday
123 |
Nobody:
Vsauce: How to taste the color 7.
5.6K |
"There are numbers bigger than 40.. 41.. 42.. 43..
A B I L L I O N
A T R I L L I O N "
Man that escalated quickly
3.2K |
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"
105 |
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
27 |
The largest number is āerrorā you can ask the calculator
7K |
How to count past infinity:
40
1.5K |
āAll we have to say is āLet there be Omegaā, and it will be good.ā
Why does this sound like a quote from a fantasy movie lmao
He would definitely be the cool wizard guy that guides the hero
31 |
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.
36 |
āI love you infinity +1.ā
āI love you 40.ā
āDamnā
2.2K |
i remember, this was the first ever Vsauce video i watched, at my Grandmas house on a laptop. i came back here to say that. ok bye
14 |
we had dimensions in objects (e.g. 2D, 3D), and the way vsauce described infinities, i think we also found them number dimensions
7 |
short answer: No
long answer: Yes
680 |
@NoobHashtagPLS
4 years ago
9 year old me: Infinity plus one.
15K |