# How To Count Past Infinity

## Description

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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

https://lukepalmer.wordpress.com/2007/06/14/the-lesser-of-infinitely-many-evils/

MUSIC BY:

http://www.youtube.com/JakeChudnow

http://www.audionetwork.com

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

https://lukepalmer.wordpress.com/2007/06/14/the-lesser-of-infinitely-many-evils/

MUSIC BY:

http://www.youtube.com/JakeChudnow

http://www.audionetwork.com

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