• vsauce
• michael stevens
• Math
• Maths
• infinity
• transfinite
• paradox
• education
• learning
• space
• time
• spacetime
• neanderthal
• homo sapien
• humans
• curiosit...

The Vsauce Holiday Box is here! It's full of exclusive Vsauce merch, cool science toys, and ALL Vsauce proceeds are donated to Alzheimer’s research!! ORDER HERE: http://geekfuel.com/Vsauce

SOURCES AND EXTRAS:

my twitter: http://www.twitter.com/tweetsauce
my instagram: http://www.instagram.com/electricpants

Gabriel’s horn:

https://en.wikipedia.org/wiki/Gabriel%27s_Horn
http://blog.plover.com/math/gabriels-horn.html

Gabriel’s wedding cake:

https://oumathclub.wordpress.com/2015/01/25/gabriels-wedding-cake/
PDF: http://people.emich.edu/aross15/math121/misc/gabriels-horn-ma044.pdf

Supersolid PDF: http://people.emich.edu/aross15/math121/misc/love-1989-supersolids.pdf

Zeno’s supertask paradoxes:

https://en.wikipedia.org/wiki/Zeno%27s_paradoxes
https://math.dartmouth.edu/~matc/Readers/HowManyAngels/SpaceTimeMotion/STM.html
https://www.youtube.com/watch?v=u7Z9UnWOJNY

Staccato Zeno runner with no velocity/acceleration discontinuities: https://goo.gl/2mYdcT

General supertask reads:

http://personal.lse.ac.uk/robert49/ebooks/PhilSciAdventures/lecture25.html
http://plato.stanford.edu/entries/spacetime-supertasks/
http://mathpages.com/rr/s3-07/3-07.htm
https://math.dartmouth.edu/~matc/Readers/HowManyAngels/SpaceTimeMotion/STM.html
https://en.wikipedia.org/wiki/Supertask
http://www.vordenker.de/gunther_web/achill1.htm

Big book of collected supertask writing: https://books.google.co.uk/books?id=0AzP9WLLJLcC&dq=order+type+of+the+integers&source=gbs_navlinks_s

PDF’s about supertasks:

http://pitt.edu/~jearman/EarmanNorton1996a.pdf
http://www.interciencia.es/infinity/thomsonlamp.pdf
http://arxiv.org/pdf/1309.0144.pdf
http://www.pitt.edu/~jdnorton/papers/onjpl.pdf
http://personal.lse.ac.uk/ROBERT49/teaching/ph103/2013-2014/pdf/EarmanNorton_CommentsOnLauraudogoita.pdf
http://arxiv.org/pdf/1503.05847v1.pdf
http://www.phys.nthu.edu.tw/~pep/download/Drawer/187.pdf
http://arxiv.org/pdf/math/0212047.pdf

Plank scale:

https://en.wikipedia.org/wiki/Planck_scale
http://astronomy.swin.edu.au/cosmos/P/Planck+Units
https://www.reddit.com/r/explainlikeimfive/comments/1oetkk/eli5_why_is_a_planck_length_the_smallest_possible/

Hyper computation and supertasks:

http://georgschauer.com/2013/04/03/overcoming-constraints-on-reliability-in-nomologically-accessible-m-h-relativistic-hypercomputers/
http://www.hypercomputation.net/download/1996a_hogarth.pdf

Thomson’s Lamp:

https://en.wikipedia.org/wiki/Thomson%27s_lamp
http://alexanderpruss.blogspot.ro/2009/05/thomson-lamp.html

Benacerraf on supertasks: [PDF] http://joelvelasco.net/teaching/hum9/benacerraf62-supertasks.pdf

Ordinal numbers (omega and omega+1):

https://en.wikipedia.org/wiki/Ordinal_number
http://www.sjsu.edu/faculty/watkins/ordinals.htm
http://math.wikia.com/wiki/Ordinal_number

Ross-Littlewood paradox:

https://en.wikipedia.org/wiki/Ross%E2%80%93Littlewood_paradox
https://angryfaic.wordpress.com/2011/02/25/four-paradoxes-involving-infinity/

New York Times Neanderthal genome article: http://www.newyorker.com/magazine/2011/08/15/sleeping-with-the-enemy

Neanderthals:

https://en.wikipedia.org/wiki/Neanderthal
http://ngm.nationalgeographic.com/2013/01/125-restless-genes/dobbs-text
https://rogerdhansen.wordpress.com/2011/08/21/the-wandering-gene/
and boats: https://www.newscientist.com/article/mg21328544.800-neanderthals-were-ancient-mariners/

Another fun infinity paradox: http://lesswrong.com/lw/isp/on_the_importance_of_taking_limits_infinite/

SMBC Zeno comic: http://www.smbc-comics.com/?id=2759

MATH!

https://www.youtube.com/user/standupmaths
https://www.youtube.com/user/numberphile
https://www.youtube.com/user/singingbanana
https://www.youtube.com/user/Vihart

music from:

http://www.youtube.com/JakeChudnow
and
http://www.audionetwork.com