- published: 09 Apr 2016
- views: 7076863
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Vote for Vsauce in the WEBBYS! https://pv.webbyawards.com/2016/online-film-video/video-channels-and-networks/science-education
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
Sometimes infinity is even bigger than you think... Dr James Grime explains with a little help from Georg Cantor.
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
James Grime: http://singingbanana.com/
Videos by Brady Haran
Minute Physics video on this topic http://www.youtube.com/watch?v=A-QoutHCu4o (somewhat more fast-paced... but we did film ours BEFORE his was uploaded, so similarities are coincidental... well actually, no they are not... we are all building upon Cantor's work!!)
- published: 06 Jul 2012
- views: 4743541
In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality of infinite sets. They are named after the symbol used to denote them, the Hebrew letter aleph.
The cardinality of the natural numbers is , the next larger cardinality is aleph-one , then and so on. Continuing in this manner, it is possible to define a cardinal number for every ordinal number α, as described below.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video
- published: 30 Nov 2015
- views: 437
Aleph number
In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets.They are named after the symbol used to denote them, the Hebrew letter aleph () (though in older mathematics books the letter aleph is often printed upside down by accident, partly because a Monotype matrix for aleph was mistakenly constructed the wrong way up ).
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=_wFxi22PF9w
- published: 22 Jan 2016
- views: 43
This video presents Cantor's argument that there exist different infinities by demonstrating a set that is uncountable. It will only make sense if you have watched the previous video, Part 5, which defines countable sets.
In essence, the size, or cardinality, of the rational numbers (fractions) is the smallest infinity: aleph null (or aleph zero). The cardinality of the real numbers, aleph one, is probably the next largest infinity, but that fact (the continuum hypothesis) has been shown to be impossible to prove under the current axioms of set theory.
- published: 14 Sep 2008
- views: 12360
The guys from Corvus Belli, creators of Infinity, give us the run down on one of the most mysterious factions in the Infinity game. The techno-organic ALEPH.
- published: 13 Dec 2011
- views: 6415
Infinity is one of the most interesting concepts in mathematics, and while most people have some idea of what it is as a concept, many only know of an extremely simplified version of this idea - the simple concept of "the biggest number". With so many ideas at the forefront of science relying heavily on this supposedly useless number (the study of black holes and quantum mechanics being just a few), it seems a shame to reduce this incredibly important and complex topic down to just a single sentence.
Concepts discussed:
Aleph Null: https://en.wikipedia.org/wiki/Aleph_number
Hilbert's Paradox of the Grand Hotel: https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
Uncountable sets: https://en.wikipedia.org/wiki/Uncountable_set
Cantor's Diagonal Argument: https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument
This video was produced for the Breakthrough Junior Challenge. For more information, please see: https://www.breakthroughjuniorchallenge.org
- published: 04 Oct 2015
- views: 1352
Aleph number
In mathematics, and in particular set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets. They are named after the symbol used to denote them, the Hebrew letter aleph (
) (though in older mathematics books the letter aleph is often printed upside down by accident, partly because a Monotype matrix for aleph was mistakenly constructed the wrong way up ).
The cardinality of the natural numbers is 
(read aleph-naught or aleph-zero; the German term aleph-null is also sometimes used), the next larger cardinality is aleph-one 
, then 
and so on. Continuing in this manner, it is possible to define a cardinal number 
for every ordinal number α, as described below.
The concept goes back to Georg Cantor, who defined the notion of cardinality and realized that infinite sets can have different cardinalities.
The aleph numbers differ from the infinity (∞) commonly found in algebra and calculus. Alephs measure the sizes of sets; infinity, on the other hand, is commonly defined as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or "increases without bound"), or an extreme point of the extended real number line.
This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Aleph_number
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
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23:46How To Count Past Infinity
How To Count Past InfinityHow To Count Past Infinity
Vote for Vsauce in the WEBBYS! https://pv.webbyawards.com/2016/online-film-video/video-channels-and-networks/science-education 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 -
8:00Infinity is bigger than you think - Numberphile
Infinity is bigger than you think - NumberphileInfinity is bigger than you think - Numberphile
Sometimes infinity is even bigger than you think... Dr James Grime explains with a little help from Georg Cantor. Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile James Grime: http://singingbanana.com/ Videos by Brady Haran Minute Physics video on this topic http://www.youtube.com/watch?v=A-QoutHCu4o (somewhat more fast-paced... but we did film ours BEFORE his was uploaded, so similarities are coincidental... well actually, no they are not... we are all building upon Cantor's work!!) -
9:35Aleph number
Aleph numberAleph number
In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality of infinite sets. They are named after the symbol used to denote them, the Hebrew letter aleph. The cardinality of the natural numbers is , the next larger cardinality is aleph-one , then and so on. Continuing in this manner, it is possible to define a cardinal number for every ordinal number α, as described below. This video is targeted to blind users. Attribution: Article text available under CC-BY-SA Creative Commons image source in video -
9:07Aleph number
Aleph numberAleph number
Aleph number In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets.They are named after the symbol used to denote them, the Hebrew letter aleph () (though in older mathematics books the letter aleph is often printed upside down by accident, partly because a Monotype matrix for aleph was mistakenly constructed the wrong way up ). -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=_wFxi22PF9w -
14:56How many kinds of infinity are there?
How many kinds of infinity are there? -
1:19ALEPH NUMBER 1 THE OX
ALEPH NUMBER 1 THE OX -
8:54Different Infinities-Series on Infinity Part 6
Different Infinities-Series on Infinity Part 6Different Infinities-Series on Infinity Part 6
This video presents Cantor's argument that there exist different infinities by demonstrating a set that is uncountable. It will only make sense if you have watched the previous video, Part 5, which defines countable sets. In essence, the size, or cardinality, of the rational numbers (fractions) is the smallest infinity: aleph null (or aleph zero). The cardinality of the real numbers, aleph one, is probably the next largest infinity, but that fact (the continuum hypothesis) has been shown to be impossible to prove under the current axioms of set theory. -
6:24Aleph number or I dont know
Aleph number or I dont know -
11:50Who are the ALEPH? | Infinity Week Discussion
Who are the ALEPH? | Infinity Week DiscussionWho are the ALEPH? | Infinity Week Discussion
The guys from Corvus Belli, creators of Infinity, give us the run down on one of the most mysterious factions in the Infinity game. The techno-organic ALEPH. -
5:23Some Infinities are bigger than other Infinities
Some Infinities are bigger than other InfinitiesSome Infinities are bigger than other Infinities
Infinity is one of the most interesting concepts in mathematics, and while most people have some idea of what it is as a concept, many only know of an extremely simplified version of this idea - the simple concept of "the biggest number". With so many ideas at the forefront of science relying heavily on this supposedly useless number (the study of black holes and quantum mechanics being just a few), it seems a shame to reduce this incredibly important and complex topic down to just a single sentence. Concepts discussed: Aleph Null: https://en.wikipedia.org/wiki/Aleph_number Hilbert's Paradox of the Grand Hotel: https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel Uncountable sets: https://en.wikipedia.org/wiki/Uncountable_set Cantor's Diagonal Argument: https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument This video was produced for the Breakthrough Junior Challenge. For more information, please see: https://www.breakthroughjuniorchallenge.org
-
How To Count Past Infinity
Vote for Vsauce in the WEBBYS! https://pv.webbyawards.com/2016/online-film-video/video-channels-and-networks/science-education 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, i...
published: 09 Apr 2016 -
Infinity is bigger than you think - Numberphile
Sometimes infinity is even bigger than you think... Dr James Grime explains with a little help from Georg Cantor. Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile James Grime: http://singingbanana.com/ Videos by Brady Haran Minute Physics video on this topic http://www.youtube.com/watch?v=A-QoutHCu4o (somewhat more fast-paced... but we did film ours BEFORE his was uploaded, so similarities are coincidental... well actually, no they are not... we are all building upon Cantor's work!!)
published: 06 Jul 2012 -
Aleph number
In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality of infinite sets. They are named after the symbol used to denote them, the Hebrew letter aleph. The cardinality of the natural numbers is , the next larger cardinality is aleph-one , then and so on. Continuing in this manner, it is possible to define a cardinal number for every ordinal number α, as described below. This video is targeted to blind users. Attribution: Article text available under CC-BY-SA Creative Commons image source in video
published: 30 Nov 2015 -
Aleph number
Aleph number In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets.They are named after the symbol used to denote them, the Hebrew letter aleph () (though in older mathematics books the letter aleph is often printed upside down by accident, partly because a Monotype matrix for aleph was mistakenly constructed the wrong way up ). -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=_wFxi22PF9w
published: 22 Jan 2016 -
-
-
Different Infinities-Series on Infinity Part 6
This video presents Cantor's argument that there exist different infinities by demonstrating a set that is uncountable. It will only make sense if you have watched the previous video, Part 5, which defines countable sets. In essence, the size, or cardinality, of the rational numbers (fractions) is the smallest infinity: aleph null (or aleph zero). The cardinality of the real numbers, aleph one, is probably the next largest infinity, but that fact (the continuum hypothesis) has been shown to be impossible to prove under the current axioms of set theory.
published: 14 Sep 2008 -
-
Who are the ALEPH? | Infinity Week Discussion
The guys from Corvus Belli, creators of Infinity, give us the run down on one of the most mysterious factions in the Infinity game. The techno-organic ALEPH.
published: 13 Dec 2011 -
Some Infinities are bigger than other Infinities
Infinity is one of the most interesting concepts in mathematics, and while most people have some idea of what it is as a concept, many only know of an extremely simplified version of this idea - the simple concept of "the biggest number". With so many ideas at the forefront of science relying heavily on this supposedly useless number (the study of black holes and quantum mechanics being just a few), it seems a shame to reduce this incredibly important and complex topic down to just a single sentence. Concepts discussed: Aleph Null: https://en.wikipedia.org/wiki/Aleph_number Hilbert's Paradox of the Grand Hotel: https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel Uncountable sets: https://en.wikipedia.org/wiki/Uncountable_set Cantor's Diagonal Argument: https://en.wikipedi...
published: 04 Oct 2015
How To Count Past Infinity
- Order: Reorder
- Duration: 23:46
- Updated: 09 Apr 2016
- views: 7076863
Vote for Vsauce in the WEBBYS! https://pv.webbyawards.com/2016/online-film-video/video-channels-and-networks/science-education
Sources and links to learn more ...
Vote for Vsauce in the WEBBYS! https://pv.webbyawards.com/2016/online-film-video/video-channels-and-networks/science-education
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
https://wn.com/How_To_Count_Past_Infinity
Vote for Vsauce in the WEBBYS! https://pv.webbyawards.com/2016/online-film-video/video-channels-and-networks/science-education
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
- published: 09 Apr 2016
- views: 7076863
Infinity is bigger than you think - Numberphile
- Order: Reorder
- Duration: 8:00
- Updated: 06 Jul 2012
- views: 4743541
Sometimes infinity is even bigger than you think... Dr James Grime explains with a little help from Georg Cantor.
Website: http://www.numberphile.com/
Numberph...
Sometimes infinity is even bigger than you think... Dr James Grime explains with a little help from Georg Cantor.
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
James Grime: http://singingbanana.com/
Videos by Brady Haran
Minute Physics video on this topic http://www.youtube.com/watch?v=A-QoutHCu4o (somewhat more fast-paced... but we did film ours BEFORE his was uploaded, so similarities are coincidental... well actually, no they are not... we are all building upon Cantor's work!!)
https://wn.com/Infinity_Is_Bigger_Than_You_Think_Numberphile
Sometimes infinity is even bigger than you think... Dr James Grime explains with a little help from Georg Cantor.
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
James Grime: http://singingbanana.com/
Videos by Brady Haran
Minute Physics video on this topic http://www.youtube.com/watch?v=A-QoutHCu4o (somewhat more fast-paced... but we did film ours BEFORE his was uploaded, so similarities are coincidental... well actually, no they are not... we are all building upon Cantor's work!!)
- published: 06 Jul 2012
- views: 4743541
Aleph number
- Order: Reorder
- Duration: 9:35
- Updated: 30 Nov 2015
- views: 437
In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality of infinite sets. They are named a...
In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality of infinite sets. They are named after the symbol used to denote them, the Hebrew letter aleph.
The cardinality of the natural numbers is , the next larger cardinality is aleph-one , then and so on. Continuing in this manner, it is possible to define a cardinal number for every ordinal number α, as described below.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video
https://wn.com/Aleph_Number
In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality of infinite sets. They are named after the symbol used to denote them, the Hebrew letter aleph.
The cardinality of the natural numbers is , the next larger cardinality is aleph-one , then and so on. Continuing in this manner, it is possible to define a cardinal number for every ordinal number α, as described below.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video
- published: 30 Nov 2015
- views: 437
Aleph number
- Order: Reorder
- Duration: 9:07
- Updated: 22 Jan 2016
- views: 43
Aleph number
In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infin...
Aleph number
In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets.They are named after the symbol used to denote them, the Hebrew letter aleph () (though in older mathematics books the letter aleph is often printed upside down by accident, partly because a Monotype matrix for aleph was mistakenly constructed the wrong way up ).
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=_wFxi22PF9w
https://wn.com/Aleph_Number
Aleph number
In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets.They are named after the symbol used to denote them, the Hebrew letter aleph () (though in older mathematics books the letter aleph is often printed upside down by accident, partly because a Monotype matrix for aleph was mistakenly constructed the wrong way up ).
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=_wFxi22PF9w
- published: 22 Jan 2016
- views: 43
How many kinds of infinity are there?
- Order: Reorder
- Duration: 14:56
- Updated: 06 Jun 2014
- views: 387169
ALEPH NUMBER 1 THE OX
- Order: Reorder
- Duration: 1:19
- Updated: 13 Jan 2017
- views: 73
Different Infinities-Series on Infinity Part 6
- Order: Reorder
- Duration: 8:54
- Updated: 14 Sep 2008
- views: 12360
This video presents Cantor's argument that there exist different infinities by demonstrating a set that is uncountable. It will only make sense if you have wat...
This video presents Cantor's argument that there exist different infinities by demonstrating a set that is uncountable. It will only make sense if you have watched the previous video, Part 5, which defines countable sets.
In essence, the size, or cardinality, of the rational numbers (fractions) is the smallest infinity: aleph null (or aleph zero). The cardinality of the real numbers, aleph one, is probably the next largest infinity, but that fact (the continuum hypothesis) has been shown to be impossible to prove under the current axioms of set theory.
https://wn.com/Different_Infinities_Series_On_Infinity_Part_6
This video presents Cantor's argument that there exist different infinities by demonstrating a set that is uncountable. It will only make sense if you have watched the previous video, Part 5, which defines countable sets.
In essence, the size, or cardinality, of the rational numbers (fractions) is the smallest infinity: aleph null (or aleph zero). The cardinality of the real numbers, aleph one, is probably the next largest infinity, but that fact (the continuum hypothesis) has been shown to be impossible to prove under the current axioms of set theory.
- published: 14 Sep 2008
- views: 12360
Aleph number or I dont know
- Order: Reorder
- Duration: 6:24
- Updated: 04 Jun 2016
- views: 159
Miko borrowed my phone and this is what I found!
I did not understand what he's talking about.! Funny though! :-🤔😂😂😂😀
Miko borrowed my phone and this is what I found!
I did not understand what he's talking about.! Funny though! :-🤔😂😂😂😀
https://wn.com/Aleph_Number_Or_I_Dont_Know
Who are the ALEPH? | Infinity Week Discussion
- Order: Reorder
- Duration: 11:50
- Updated: 13 Dec 2011
- views: 6415
The guys from Corvus Belli, creators of Infinity, give us the run down on one of the most mysterious factions in the Infinity game. The techno-organic ALEPH.
The guys from Corvus Belli, creators of Infinity, give us the run down on one of the most mysterious factions in the Infinity game. The techno-organic ALEPH.
https://wn.com/Who_Are_The_Aleph_|_Infinity_Week_Discussion
The guys from Corvus Belli, creators of Infinity, give us the run down on one of the most mysterious factions in the Infinity game. The techno-organic ALEPH.
- published: 13 Dec 2011
- views: 6415
Some Infinities are bigger than other Infinities
- Order: Reorder
- Duration: 5:23
- Updated: 04 Oct 2015
- views: 1352
Infinity is one of the most interesting concepts in mathematics, and while most people have some idea of what it is as a concept, many only know of an extremely...
Infinity is one of the most interesting concepts in mathematics, and while most people have some idea of what it is as a concept, many only know of an extremely simplified version of this idea - the simple concept of "the biggest number". With so many ideas at the forefront of science relying heavily on this supposedly useless number (the study of black holes and quantum mechanics being just a few), it seems a shame to reduce this incredibly important and complex topic down to just a single sentence.
Concepts discussed:
Aleph Null: https://en.wikipedia.org/wiki/Aleph_number
Hilbert's Paradox of the Grand Hotel: https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
Uncountable sets: https://en.wikipedia.org/wiki/Uncountable_set
Cantor's Diagonal Argument: https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument
This video was produced for the Breakthrough Junior Challenge. For more information, please see: https://www.breakthroughjuniorchallenge.org
https://wn.com/Some_Infinities_Are_Bigger_Than_Other_Infinities
Infinity is one of the most interesting concepts in mathematics, and while most people have some idea of what it is as a concept, many only know of an extremely simplified version of this idea - the simple concept of "the biggest number". With so many ideas at the forefront of science relying heavily on this supposedly useless number (the study of black holes and quantum mechanics being just a few), it seems a shame to reduce this incredibly important and complex topic down to just a single sentence.
Concepts discussed:
Aleph Null: https://en.wikipedia.org/wiki/Aleph_number
Hilbert's Paradox of the Grand Hotel: https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
Uncountable sets: https://en.wikipedia.org/wiki/Uncountable_set
Cantor's Diagonal Argument: https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument
This video was produced for the Breakthrough Junior Challenge. For more information, please see: https://www.breakthroughjuniorchallenge.org
- published: 04 Oct 2015
- views: 1352
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23:46
How To Count Past Infinity
Vote for Vsauce in the WEBBYS! https://pv.webbyawards.com/2016/online-film-video/video-cha...
published: 09 Apr 2016
How To Count Past Infinity
How To Count Past Infinity
- Report rights infringement
- published: 09 Apr 2016
- views: 7076863
8:00
Infinity is bigger than you think - Numberphile
Sometimes infinity is even bigger than you think... Dr James Grime explains with a little ...
published: 06 Jul 2012
Infinity is bigger than you think - Numberphile
Infinity is bigger than you think - Numberphile
- Report rights infringement
- published: 06 Jul 2012
- views: 4743541
9:35
Aleph number
In set theory, a discipline within mathematics, the aleph numbers are a sequence of number...
published: 30 Nov 2015
Aleph number
Aleph number
- Report rights infringement
- published: 30 Nov 2015
- views: 437
9:07
Aleph number
Aleph number
In set theory, a discipline within mathematics, the aleph numbers are a se...
published: 22 Jan 2016
Aleph number
Aleph number
- Report rights infringement
- published: 22 Jan 2016
- views: 43
14:56
How many kinds of infinity are there?
A lot.
List with links: http://vihart.com/how-many-kinds-of-infinity-are-there/
published: 06 Jun 2014
How many kinds of infinity are there?
How many kinds of infinity are there?
- Report rights infringement
- published: 06 Jun 2014
- views: 387169
1:19
ALEPH NUMBER 1 THE OX
Number 1 the ALPHA on greek
published: 13 Jan 2017
ALEPH NUMBER 1 THE OX
ALEPH NUMBER 1 THE OX
- Report rights infringement
- published: 13 Jan 2017
- views: 73
8:54
Different Infinities-Series on Infinity Part 6
This video presents Cantor's argument that there exist different infinities by demonstrati...
published: 14 Sep 2008
Different Infinities-Series on Infinity Part 6
Different Infinities-Series on Infinity Part 6
- Report rights infringement
- published: 14 Sep 2008
- views: 12360
6:24
Aleph number or I dont know
Miko borrowed my phone and this is what I found!
I did not understand what he's talking ...
published: 04 Jun 2016
Aleph number or I dont know
Aleph number or I dont know
- Report rights infringement
- published: 04 Jun 2016
- views: 159
11:50
Who are the ALEPH? | Infinity Week Discussion
The guys from Corvus Belli, creators of Infinity, give us the run down on one of the most ...
published: 13 Dec 2011
Who are the ALEPH? | Infinity Week Discussion
Who are the ALEPH? | Infinity Week Discussion
- Report rights infringement
- published: 13 Dec 2011
- views: 6415
5:23
Some Infinities are bigger than other Infinities
Infinity is one of the most interesting concepts in mathematics, and while most people hav...
published: 04 Oct 2015
Some Infinities are bigger than other Infinities
Some Infinities are bigger than other Infinities
- Report rights infringement
- published: 04 Oct 2015
- views: 1352
How To Count Past Infinity...
Infinity is bigger than you think - Numberphile...
Aleph number...
Aleph number...
How many kinds of infinity are there?...
ALEPH NUMBER 1 THE OX...
Different Infinities-Series on Infinity Part 6...
Aleph number or I dont know...
Who are the ALEPH? | Infinity Week Discussion...
Some Infinities are bigger than other Infinities...
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Donald Trump inauguration live: Billionaire reality TV star to become US President amid massive protests
Edit The Independent 20 Jan 2017
Here are the latest updates ... ....
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Was Fort Lauderdale Shooter Another Case of Deep State’s MKUltra-Mind Control?
Edit WorldNews.com 20 Jan 2017
Article by WN.com Correspondent Dallas DarlingWith regards to Esteban Santiago, the 26-year-old U.S.-Iraq War veteran accused of systematically killing five people in a shooting rampage at a Fort Lauderdale, Fla ... With 80 institutions, including 44 colleges and universities, as well as hospitals, prisons and pharmaceutical companies,1 technocratic psy-ops programming (tpp) has indeed become normalized ... 1. 2 www.groundzeromedia.org ... ....
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Spain Arrests Russian Programmer Over Hacking On US Request
Edit WorldNews.com 20 Jan 2017
Spanish officials announced on Thursday that they arrested a Russian computer programmer on orders from the United States while waiting on a decision to extradite him, according to Al Jazeera ... The hacking by Russian officials has been a number one topic in the US after a leaked dossier describes techniques used by Russian president Vladimir Putin to influence the 2016 US presidential election. -WN.com, Maureen Foody....
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Osama Bin Laden Documents: Worry Over ISIS Tactics, 'Aging' Al-Qaeda
Edit NDTV 20 Jan 2017
Months before his death, Osama bin Laden fretted about the ISIS group's impatient, violent tactics and the fading of Al-Qaeda, documents released by the CIA Thursday showed. The latest release from... ....
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BREAKING: Report Say Eight Survivors Found Inside Italian Hotel Buried By Avalanche
Edit WorldNews.com 20 Jan 2017
“We always hoped to find someone alive. The fact we found people alive after so many hours give us even more hope.” –Titti Postiglione, Civil Protection Agency Rescuers believe up to 30 people, including an unspecified number of children, were reported missing after an avalanche buried the four-star hotel on Wednesday, the report said.....
Natalie Portman: ‘JFK was a great proponent of civil rights. Trump is taking us backwards’
Edit The Guardian 19 Jan 2017
The Oscar-tipped star of Jackie talks about playing the widowed first lady of the progressive president and why the new inauguration is an ‘upsetting moment’. @rorycarroll72 ... The effect is stylish, if sombre. She could be in mourning ... She looks great ... She has moved back to Los Angeles from Paris, is about to have a second child (her son, Aleph, was born in 2011) and is receiving rapturous reviews for her performance in Jackie ... Twitter ... “No....
Much hype, few sales
Edit DNA India 15 Jan 2017
In the run-up to Zee-Jaipur Literature Festival, literary agent Kanishka Gupta looks back at what’s happened in the world of fiction in the past year. And he’s not too happy with what he sees. Since its inception, JLF has been featuring heavyweight literary fiction authors, both from the subcontinent and elsewhere ... Publishers like Aleph and Speaking Tiger still focus on literary fiction ... Kanishka Gupta. ....
Interview: Natalie Portman on making her new film, Jackie
Edit Scotsman 14 Jan 2017
Natalie Portman gives the performance of her life in biopic Jackie, which focuses on the immediate aftermath of the assassination of JFK. Jackie emerges as a powerful champion for her late husband’s legacy, while struck down by her own grief. Janet Christie hears more ... Then she tells him he won't be writing any of this ... She adds ... They already have one son together, five year old Aleph, with the baby due in the spring ... “Yes.” ... “Yes.” ... ....
Case of 'fattened' Jorge Luis Borges story headed to court in Argentina
Edit The Guardian 10 Jan 2017
Writer Pablo Katchadjian says The Fattened Aleph, a lengthened version of Borges’s story The Aleph, is not plagiarism because it is ‘open about its source’ ... It doesn’t say ‘The Aleph by Borges, altered by Katchadjian’ ... Katchadjian’s many supporters argue that El Aleph is so well-known that its reworking did not require a Borges attribution and that, in any case, only a few hundreds copies of the reworked story were published....
Natalie Portman: bringing Jackie Onassis back to life
Edit The Guardian 08 Jan 2017
Natalie Portman is disarmingly self-effacing for an Oscar winner with a good chance to net a second golden statue next month ... “Usually I cringe through the premiere and hate everything I do ... Or, at least, no one should.” ... The two have a son together named Aleph (after the first letter of the Hebrew alphabet) ... Best of times She gave birth to her son, Aleph Portman-Millepied, on 14 June 2011, shortly after winning her Oscar for Black Swan....
10 books we’re watching out for this year
Edit Hindustan Times 07 Jan 2017
#BrunchBookChallenge. If you’re a bibliophile, 2016 didn’t give you much to complain about. There was some great non-fiction (Amitav Ghosh’s The Great Derangement), scandalous memoirs (Yaseer Usman’s Rekha. The Untold Story) and even comebacks (Aravind Adiga with Selection Day). 2017 promises to be no less ... 1 ... Shashi Tharoor (Aleph) ... Jeet Thayil (Aleph) ... Amitava Kumar (Aleph) ... Edited by MJ Akbar (Aleph)....
An anthology that takes you into the dark places of the mind
Edit Hindustan Times 06 Jan 2017
A young girl, recovering from the recent death of her father, discovers some Dean Martin records in her dusty attic and falls in love with the singer, who’s long dead ... These wonderfully dark and twisted stories are from environmental researcher and author Tejaswini Apte-Rahm’s recent debut anthology, These Circuses That Sweep The Landscape (Aleph). Excerpts from an interview. ... I love the genre ... And I try to bring that out ... ....
What to read in 2017
Edit Kashmir Observer 02 Jan 2017
Is any year a good year for books? Despite doomsday predictions, the book is alive and kicking. Here’s a list of titles to look out for in 2017, from all God’s publishers, big and small. The God of Small Things came out in my last year of college in 1997 ... Has she changed; have we changed? We shall find out soon ... From Aleph Book Company, comes Irwin Allan Sealy’s long poem Zelaldinus ... Also from Aleph. S ... From Hachette ... Also from HC ... Also....
Interview with a bookstore: DIESEL, A Bookstore in California
Edit The Guardian 02 Jan 2017
DIESEL, A Bookstore opened in 1989. Its knowledgable booksellers, possessed with ‘eerie biblio-intuitive skills’, share their formative bookstore experiences and why they love working there. Alison Reid and I opened DIESEL, A Bookstore in 1989 in Emeryville, California ... Before the transformation was complete we moved our store back to our original stomping grounds in North Oakland ... Butler Yeats, and The Aleph and Labyrinths by Borges ... ....
Distrust Forecasts
Edit Seeking Alpha 01 Jan 2017
This is the time of year where lots of stray forecasts get given. I got tired enough of it, that I had to turn off my favorite radio station, Bloomberg Radio, after hearing too many of them. I recommend that you ignore forecasts, and even the average of them. I'll give you some reasons why. Most forecasters don't have a good method for generating their forecasts ... And, from David at the Aleph Blog, have a happy 2017. Disclosure. None. ....
A collection of short stories that promises to linger on for a long time
Edit Hindustan Times 30 Dec 2016
By its very nature, a short story is instantly gratifying. A great short story, however, lingers on. It reaches into the inner recesses of your mind, tickles you and comes back to haunt you over and over again ... Lanka’s Princess. A book that attempts to humanise the demonic Surpanakha ... Title ... Author ... Aleph Book Company ... ....
The Best Reads of 2016
Edit Hindustan Times 30 Dec 2016
Like all Best-of Lists, the HT Editors’ list of the most interesting reads this year is subjective. However, unlike lists that emerge from a single literary critic’s fevered brain or from sales figures collated from book stores across the country, this one manages to be at once engaging, wide ranging and intelligent with a good mix of Indian and international titles across genres ... A wide-ranging list ... Rs 299 ... Aleph....
The Best Writing Advice of 2016
Edit The Atlantic 27 Dec 2016
2016 was not an easy year to be a writer. Not just because of the constant, concentration-wrecking pull of our devices, their glowing screens beckoning with the promise of fresh horrors ... They’re asking themselves ... In his discussion of Borges’s great short story “The Aleph,” Michael Chabon, the author of Moonglow, spoke at length about detail and description—the process by which he chooses the right words from a sea of possible choices ... ....
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