# How To Count Past Infinity

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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: https://www.youtube.com/user/numberphile

BOOKS related to these topics that I used:

“The Outer Limits of Reason” by Noson S. Yanofsky: http://amzn.com/0262019353

“Infinity and The Mind” by Rudy Rucker: http://amzn.com/0691121273

“Roads to Infinity” by John C. Stilwell: http://amzn.com/1568814666

“More Precisely: The Math You Need to Do Philosophy” by Eric Steinhart: http://amzn.com/1551119099

“Satan, Cantor and Infinity: Mind-Boggling Puzzles” by Raymond M. Smullyan: http://amzn.com/0486470369

classic book that helps introduce concept of axioms: “Introduction to the Foundations of Mathematics” by Raymond L. Wilder: http://amzn.com/0486488209

Hugh Woodin speaking about infinity at the World Science Festival: https://youtu.be/KDCJZ81PwVM?t=29m45s

Names of large (finite) numbers: https://en.wikipedia.org/wiki/Names_of_large_numbers

Geoglyphs:

The biggest number: https://goo.gl/maps/7GWcpnzo7iG2

Fovant badges: https://en.wikipedia.org/wiki/Fovant_Badges

Battalion Park: https://en.wikipedia.org/wiki/Battalion_Park

A mile of pi [VIDEO]: https://www.youtube.com/watch?v=0r3cEKZiLmg

Wikipedia’s great visualization of ordinals out to omega^omega: https://en.wikipedia.org/wiki/File:Omega-exp-omega-labeled.svg

as seen on: https://en.wikipedia.org/wiki/Ordinal_number

this is also a good page about ordinals: http://math.wikia.com/wiki/Ordinal_Number

also: http://www.cut-the-knot.org/WhatIs/Infinity/Ordinals.shtml

and: https://en.wikipedia.org/wiki/Order_type and https://en.wikipedia.org/wiki/Well-order

Axioms:

https://en.wikipedia.org/wiki/Axiom

https://www.reddit.com/r/askscience/comments/30xokb/have_there_been_axioms_that_later_have_been/

http://philosophy.stackexchange.com/questions/5922/what-is-the-difference-between-dogma-and-an-axiom

http://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf

http://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms2.pdf

THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES

[PDF]: http://www.maths.ed.ac.uk/~aar/papers/wigner.pdf

https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences

Large Cardinal game based on 2048: http://cantorontheshore.blogspot.it/2014/10/one-reinhardt-and-counting.html

Other good resources:

http://quibb.blogspot.com/2012/01/infinity-first-transfinite-cardinal.html

http://plato.stanford.edu/entries/set-theory/

http://cantorsattic.info/Cantor%27s_Attic

http://cantorontheshore.blogspot.co.at/2014/09/artemis-fowl-and-large-cardinals_22.html

http://isomorphism.es/post/10782081422/what-comes-after-infinity-transfinite-arithmetic-and-ord

MUSIC BY:

http://www.youtube.com/JakeChudnow

http://www.audionetwork.com

what about infinite^2

that feeling after u finish this kind of videos ????

People are creating or chasing an end that never ends, and we don’t accept

it until we see proof or an end, but for infinity there is none, its just a

flaw in the number system, think you found the end? Just add 1 to it.

You pronounce alef wrong

on 1 and 2 you mist 21

Not sure if his videos make me smarter or if each video makes my brain

closer to exploding.

i didnt understand this one even more than i usually dont understand these

videos

This is one of your best videos yet. You explain everything perfectly

without dumbing anything down and just make it so fascinating. And as

always, thanks for filming.

At 2:58 — 0 isn’t a Natural Number :)

This is great because I’ll finally have a comeback next time my girlfriend

says she loves me times infinity

This video triggers me.

For those who havent watched the video yet and is looking at comments…..

infinity one…

infinity two…

infinity three…

I think you should have θ amount of subscribers

My brain is smoking.

Now, I believe that mathematicians are mad with boredom

The Continuum Hypothesis (CH) was shown by Gödel to be consistent with set

theory (with or without axiom of choice (AC)). Later, Paul Cohen showed

the negation of the CH to be consistent with set theory (with or without

AC). So CH can be taken as an axiom. Or not. Your choice. You get then

to develop the consequences and see if like them. Or not.

what about the Grahams Number?

omega + infinity?

Graham’s number remains the largest number used constructively in a proof.

Can he be my math teacher please.