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_o…
Geoglyphs:
The biggest number: https://goo.gl/maps/7GWcpnzo7iG2
Fovant badges: https://en.wikipedia.org/wiki/Fovant_…
Battalion Park: https://en.wikipedia.org/wiki/Battali…
A mile of pi [VIDEO]: https://www.youtube.com/watch?v=0r3cE…
Wikipedia’s great visualization of ordinals out to omega^omega: https://en.wikipedia.org/wiki/File:Om…
as seen on: https://en.wikipedia.org/wiki/Ordinal…
this is also a good page about ordinals: http://math.wikia.com/wiki/Ordinal_Nu…
also: http://www.cut-the-knot.org/WhatIs/In…
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/c…
http://philosophy.stackexchange.com/q…
http://www.cs.umd.edu/~gasarch/BLOGPA…
http://www.cs.umd.edu/~gasarch/BLOGPA…
THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES
[PDF]: http://www.maths.ed.ac.uk/~aar/papers…
https://en.wikipedia.org/wiki/The_Unr…
Large Cardinal game based on 2048: http://cantorontheshore.blogspot.it/2…
Other good resources:
http://quibb.blogspot.com/2012/01/inf…
http://plato.stanford.edu/entries/set…
http://cantorsattic.info/Cantor%27s_A…
http://cantorontheshore.blogspot.co.a…
http://isomorphism.es/post/1078208142…
https://lukepalmer.wordpress.com/2007…
MUSIC BY:
http://www.youtube.com/JakeChudnow
http://www.audionetwork.com
msamba 
That is where my understanding is challenged, when we calculate with infinities and curves that disappear in infinity and at a point come back from there … that is for me the point where mathmatics stop to be an “exact” science, as it is proclaimed to be.
Instead I was wondering what these “40 let” (40 years in Russian) are standing for, but could not find out yet. 🙂
LikeLike
Ithoughtofit as more akin to one of those animations of zooming out from the detail of a fractal only to see a very similar pattern; not so much a definitive pattern as simply the current level of scrutiny.
That idea of mathematics as an abstraction from our observations of the world around us (and therefore necessarily selective) is so easily forgotten whilst we’re using it to manipulate materials.
I don’t think my “let” stand for anything other than change…
LikeLiked by 1 person
That is how mathmatics was taught to us when I was young, that it was for manipulating materials and that it was an exact science. I should take a more open attitude when I hear or read mathematics, because it is not what it was then.
LikeLike
Me too Stella. Happy Christmas to you and yours!
LikeLiked by 1 person
Thank you, the same to you!
LikeLiked by 1 person