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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
Have there been axioms that later have been proven false? from askscience
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
The Lesser of Infinitely Many Evils
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