How To Count Past Infinity

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  • Published: 09 April 2016
  • my twitter: @tweetsauce
    my instagram: electricpants

    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: http://stms.pro/user/numberphile

    BOOKS related to these topics that I used:

    “The Outer Limits of Reason” by Noson S. Yanofsky: amzn.com/0262019353
    “Infinity and The Mind” by Rudy Rucker: amzn.com/0691121273
    “Roads to Infinity” by John C. Stilwell: amzn.com/1568814666
    “More Precisely: The Math You Need to Do Philosophy” by Eric Steinhart: amzn.com/1551119099
    “Satan, Cantor and Infinity: Mind-Boggling Puzzles” by Raymond M. Smullyan: amzn.com/0486470369

    classic book that helps introduce concept of axioms: “Introduction to the Foundations of Mathematics” by Raymond L. Wilder: amzn.com/0486488209

    Hugh Woodin speaking about infinity at the World Science Festival: stms.pro/video/KDCJZ81PwVM/video.html?t=29m45s

    Names of large (finite) numbers: en.wikipedia.org/wiki/Names_of_large_numbers

    Geoglyphs:

    The biggest number: goo.gl/maps/7GWcpnzo7iG2

    Fovant badges: en.wikipedia.org/wiki/Fovant_Badges

    Battalion Park: en.wikipedia.org/wiki/Battalion_Park

    A mile of pi [VIDEO]: stms.pro/user/watch?v=0r3cEKZiLmg

    Wikipedia’s great visualization of ordinals out to omega^omega: en.wikipedia.org/wiki/File:Omega-exp-omega-labeled.svg

    as seen on: en.wikipedia.org/wiki/Ordinal_number

    this is also a good page about ordinals: math.wikia.com/wiki/Ordinal_Number

    also: cut-the-knot.org/WhatIs/Infinity/Ordinals.shtml

    and: en.wikipedia.org/wiki/Order_type and en.wikipedia.org/wiki/Well-order

    Axioms:
    en.wikipedia.org/wiki/Axiom
    reddit.com/r/askscience/comments/30xokb/have_there_been_axioms_that_later_have_been/
    philosophy.stackexchange.com/questions/5922/what-is-the-difference-between-dogma-and-an-axiom
    cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf
    cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms2.pdf

    THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES
    [PDF]: maths.ed.ac.uk/~aar/papers/wigner.pdf
    en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences

    Large Cardinal game based on 2048: cantorontheshore.blogspot.it/2014/10/one-reinhardt-and-counting.html

    Other good resources:

    quibb.blogspot.com/2012/01/infinity-first-transfinite-cardinal.html
    plato.stanford.edu/entries/set-theory/
    cantorsattic.info/Cantor%27s_Attic
    cantorontheshore.blogspot.co.at/2014/09/artemis-fowl-and-large-cardinals_22.html
    isomorphism.es/post/10782081422/what-comes-after-infinity-transfinite-arithmetic-and-ord
    lukepalmer.wordpress.com/2007/06/14/the-lesser-of-infinitely-many-evils/

    MUSIC BY:
    stms.pro/user/JakeChudnow
    audionetwork.com
  • Science and Technology Science and Technology

Comments • 63 505

  • small Kirb
    small Kirb  8 minutes back

    *VSauce* the game theory of reality

    • Louis Le
      Louis Le  13 minutes back

      but......








      ωhy

      • Miles Gutierrez
        Miles Gutierrez  59 minutes back

        So, why are you counting 0? I'm very confused about that one.

        • Grunglar Tigglyboo
          Grunglar Tigglyboo  2 hours back

          What about infinity + 1...

          • Sleeping Kid
            Sleeping Kid  3 hours back

            40

            • GIAN MERCK
              GIAN MERCK  6 hours back

              Are you how to basic?

              • The Phaneron
                The Phaneron  7 hours back

                *Humanity:* _Strives for meaning and purpose in a finite realm. Simultaneously seeks to annihilate any notion of precious tangible value by conceptualizing infinity._ Lol makes perfects logical sense!

                • Josephi Krakowski
                  Josephi Krakowski  8 hours back

                  Instructions Unclear.
                  Divided by Zero and created a Tear in Space and Time.

                  • Mr,Casino
                    Mr,Casino  13 hours back

                    W+999,AluMillion Power

                    • Mr,Casino
                      Mr,Casino  13 hours back

                      999,AluMillion

                      • Jason L0L
                        Jason L0L  14 hours back

                        Infinity plus 1

                        • HashBrown
                          HashBrown  15 hours back

                          Mom: From a Scale of 1 - 10 how much do you love me?
                          Vsauce : Inaccessible cardinal.

                          • HashBrown
                            HashBrown  15 hours back

                            A guy talking about numbers more exciting than my teacher.

                            • Finley Donn
                              Finley Donn  16 hours back

                              Do the lowest

                              • Leon Van Heerden
                                Leon Van Heerden  19 hours back

                                17:30 well that de-escalated quickly

                                • PaintedPerfect
                                  PaintedPerfect  20 hours back

                                  How to count past infinity.
                                  Turn the infinity sideways, *9, 10, 11* ...

                                  • CliffJumper gaming
                                    CliffJumper gaming  21 hours back

                                    mom come pick me up i'm scared

                                    • wow2 chicken nuggets
                                      wow2 chicken nuggets  22 hours back

                                      You heard it here folks 40 is the biggest

                                      • Teo Sega Sumić
                                        Teo Sega Sumić  23 hours back

                                        Everytime i finish a VSauce video i fell like ive been high on something

                                        • Klapto
                                          Klapto  1 days back

                                          Just say infinity and 1

                                          • Kocsis Kolos Kende
                                            Kocsis Kolos Kende  1 days back

                                            It hurts my brain so much

                                            • Connor Clark
                                              Connor Clark  1 days back

                                              Vsauce has a hot face, boi

                                              • Keira Cloud
                                                Keira Cloud  1 days back

                                                Infinity and 1

                                                • ThunderWolf 56570
                                                  ThunderWolf 56570  1 days back

                                                  Me: 40, 41

                                                  I’m smarter than vsause

                                                  • ToxicRolo
                                                    ToxicRolo  1 days back

                                                    Infinity and 1

                                                    • No Entity
                                                      No Entity  1 days back

                                                      1 is the biggest number because 1 could have infinite 0's and zero doesn't have a value for example, 1=10000000000000000000000000000000.

                                                      • No Entity
                                                        No Entity  1 days back

                                                        @Caladbolg shhhhhhh the 9 yr olds don't know that

                                                      • Caladbolg
                                                        Caladbolg  1 days back

                                                        1 cannot have infinite zeroes. By that logic 1=10. No integer can have infinite digits.

                                                        Zero does have a value: zero.

                                                    • flyte
                                                      flyte  2 days back

                                                      me researching how you beat exodia

                                                      • What The Cinnamon toast fuk

                                                        Crush: How much do you love me
                                                        Me:

                                                        • Jonathan Robertson
                                                          Jonathan Robertson  2 days back

                                                          Micheal, I disagree with this, here's why.


                                                          (I am basing all of this off of the fact that, by definition, infinite means not finite.)


                                                          The entire field of mathematics is nothing more than a system of ideas we made up that have to consistently follow rules (which, yes, we made up). Numbers consist of a set amount of characters and a pattern which they follow (cycle through all the characters, add another power, repeat). These numbers don't actually mean anything though, they just represent a value. That value is simply which combination of characters in this set pattern of combinations it is. That's why each number in the base ten system has a corresponding number in binary, base three, base google, or any base n number system. They are all made up, yet they all represent the same values. These values are real, tangible things.
                                                          Infinity is not a real, tangible thing. It is an idea. (yes I know that space is as far as we know infinite, but that is a quality of space, not a quantity, and this video is addressing the quantity of infinity) This idea of infinity has one rule, it's definition: not finite (yes I know that's the definition of infinite, not infinity, but by definition infinity is infinite, and the only quality of infinity is that it is not finite).
                                                          Following this rule, it is impossible to have a quantity greater than infinity. That is because, by labeling a number as such, a finite value is put on infinity. This contradicts the idea of infinity and thus can not be true. But there are other ways to prove this.


                                                          Replacement is wrong because it's nothing more than a base infinity number system. In all that effort to show how replacement goes on forever and ever until it reaches... the inaccessible cardinal, all you showed was that there are an infinite number of numbers, and in reality, aleph null is the inaccessible cardinal. All those aleph and omega numbers you made up were just that, numbers. Numbers which only have a value equivalent to which one of the combination of characters in the pattern you made up they are. Each one with a corresponding number in any other number system. You can continue counting in any number system all the way up to every number you displayed using replacement.


                                                          Power sets are literally just binary. The only value that power sets have is the quantity of sets contained in them. You displayed these as combinations of y's and n's. The only way to insure that you go through every single possible set of y's and n's is if you follow a pattern. Lets start with all n's: n... Then lets replace the first one with a y: yn... there aren't any more options for that place so let's switch to the next, then we'll have that option open again: nyn... Now we can do yyn... Then nnyn... ynyn... yyyn...nnnyn... It's an exact mirror image of the binary you're familier with, just with different characters: ...0 ...01 ...010 ...011 ...0100 ...0101 ...0111 ...01000
                                                          (Sure there might be four power sets for 1 and 2, and eight power sets for 1, 2, and 3, but the four sets from 1 and 2 are all repeated in the sets for 1, 2, and 3, so they don't count for any new quantity, and two of those are in the power sets of 1 and one of those is the power set of no number and the last set is accounted for in 0. This is because the lack of a quantity and a quantity of zero are represented differently in these power sets and thus both represent a quantity equal in value to one combination of characters from any number system. Therefor every power set is accounted for)


                                                          Sure you can make up ways to count past infinity, but the only way to consistently follow those systems is to put a finite value on infinity, which contradicts the whole idea of infinity, which is unfathomably, inaccessibly, existentially..... infinite.




                                                          Infinite as a quality of space also proves this. No matter how far out you measure, you can always go farther: it's infinite.

                                                          • Caladbolg
                                                            Caladbolg  1 days back

                                                            There is no requirement that math have anything to do with the real world. You are also conflating numbers and numerals, as well as mathematical infinity with some philosophical or intuitive infinity.

                                                            You are implicitly assuming that a value must be finite, i.e. that infinity is not a value that can be compared. That depends on what you mean by infinity.

                                                            Would you agree that {1,2,3,4...} is infinite in some sense? That set btw is omega. Omega has a successor omega+1.

                                                        • Zombiewolf 132
                                                          Zombiewolf 132  2 days back

                                                          I’m telling you
                                                          Soon he’s gonna say something that creates a black hole

                                                          • Troy Tran-le
                                                            Troy Tran-le  2 days back

                                                            Infinity is something beyond our universe.
                                                            Gbfvgn(fcsftjj,ninhb$egyj(j6rcscfnjjmffaswfgmjmfvxcaxdvgnhmfvsxqxscfnhmjmn fcscfhhmjnttgsc

                                                            • Troy Tran-le
                                                              Troy Tran-le  2 days back

                                                              40AET

                                                              • HarisPlaysYT
                                                                HarisPlaysYT  2 days back

                                                                Vsauce: how to count past infinity
                                                                Me: *iNfInItY aNd BeYoNd*

                                                                • Wrave
                                                                  Wrave  2 days back

                                                                  Nobody:
                                                                  Absolutely Nobody
                                                                  Vsauce: *hOw tO CoUNt PaSsEd InFiNiTy*

                                                                  • Wrave
                                                                    Wrave  2 days back

                                                                    The way this guy hypes stuff is too much

                                                                    • juan garcia
                                                                      juan garcia  2 days back

                                                                      It's rayo number

                                                                      • Sean Robertson
                                                                        Sean Robertson  2 days back

                                                                        Serious question: at this point, is it even mathematics? Or is this philosophy? It’s dealing with stuff that isn’t real and can never be proven, so is it really math?

                                                                        • Caladbolg
                                                                          Caladbolg  1 days back

                                                                          It is mathematics. Numbers aren't "real" in the sense objects are anyways. They are concepts, albeit useful ones.

                                                                          Everything in this video can, and has been proven. Math is the only discipline in which things can actually be proven. "Proof" means a logical deduction from a chosen set of initial assumptions. Natural sciences don't have that - even in physics, everything is just approximations, though incredibly accurate ones. The fact that much of theoretical math doesn't have a real world application (yet) has no bearing on whether or not it is legitimately math.

                                                                      • kuba tutak
                                                                        kuba tutak  2 days back

                                                                        ez, infinity + 1

                                                                        • KING _GAMES
                                                                          KING _GAMES  2 days back

                                                                          ΩоΩин

                                                                          • chekystar
                                                                            chekystar  2 days back

                                                                            izy you start counting while you drive past infinity she is slow driver :P

                                                                            • Cooxq - _ - YT
                                                                              Cooxq - _ - YT  2 days back

                                                                              Infinity and a google and one

                                                                              • [Camp] Hot Nuke
                                                                                [Camp] Hot Nuke  2 days back

                                                                                My mom saying I love you

                                                                                Me hesitating to say I love you back

                                                                                Takes 23 minutes to say I love you back to her

                                                                                • Charles JSB
                                                                                  Charles JSB  2 days back

                                                                                  Rip math teachers

                                                                                  • Clogged toilet
                                                                                    Clogged toilet  2 days back

                                                                                    Vsauce is like that one geeky kid that took Rick and Morty way too seriously

                                                                                    • Phanuroj 37
                                                                                      Phanuroj 37  2 days back

                                                                                      Is alif null odd or even

                                                                                      • DarKStaR Of Legend
                                                                                        DarKStaR Of Legend  2 days back

                                                                                        Me: watching the vid till end
                                                                                        My brain: i want to explode

                                                                                        • Julie Ann Luague
                                                                                          Julie Ann Luague  2 days back

                                                                                          Vsauce is right. 40 is the largest number because 40 in roman numerals is XL, meaning "Extra Large".

                                                                                          • CONTENT
                                                                                            CONTENT  2 days back

                                                                                            Infinity one
                                                                                            Infinity two
                                                                                            Infinity three