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://superiorjanitorial.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: superiorjanitorial.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]: superiorjanitorial.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:
    superiorjanitorial.pro/user/JakeChudnow
    audionetwork.com
  • Science and Technology Science and Technology

Comments • 63 484

  • HashBrown
    HashBrown  4 minutes back

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

    • HashBrown
      HashBrown  19 minutes back

      A guy talking about numbers more exciting than my teacher.

      • Finley Donn
        Finley Donn  2 hours back

        Do the lowest

        • Leon Van Heerden
          Leon Van Heerden  5 hours back

          17:30 well that de-escalated quickly

          • PaintedPerfect
            PaintedPerfect  5 hours back

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

            • CliffJumper gaming
              CliffJumper gaming  6 hours back

              mom come pick me up i'm scared

              • wow2 chicken nuggets
                wow2 chicken nuggets  7 hours back

                You heard it here folks 40 is the biggest

                • Teo Sega Sumić
                  Teo Sega Sumić  8 hours back

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

                  • Klapto
                    Klapto  10 hours back

                    Just say infinity and 1

                    • Kocsis Kolos Kende
                      Kocsis Kolos Kende  10 hours back

                      It hurts my brain so much

                      • Connor Clark
                        Connor Clark  12 hours back

                        Vsauce has a hot face, boi

                        • Keira Cloud
                          Keira Cloud  12 hours back

                          Infinity and 1

                          • ThunderWolf 56570
                            ThunderWolf 56570  18 hours back

                            Me: 40, 41

                            I’m smarter than vsause

                            • ToxicRolo
                              ToxicRolo  19 hours back

                              Infinity and 1

                              • No Entity
                                No Entity  21 hours 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  10 hours back

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

                                • Caladbolg
                                  Caladbolg  12 hours 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  22 hours back

                                me researching how you beat exodia

                                • What The Cinnamon toast fuk

                                  Crush: How much do you love me
                                  Me:

                                  • Jonathan Robertson
                                    Jonathan Robertson  22 hours 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  12 hours 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  1 days back

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

                                    • Troy Tran-le
                                      Troy Tran-le  1 days back

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

                                      • Troy Tran-le
                                        Troy Tran-le  1 days back

                                        40AET

                                        • HarisPlaysYT
                                          HarisPlaysYT  1 days back

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

                                          • Wrave
                                            Wrave  1 days back

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

                                            • Wrave
                                              Wrave  1 days back

                                              The way this guy hypes stuff is too much

                                              • juan garcia
                                                juan garcia  1 days back

                                                It's rayo number

                                                • Sean Robertson
                                                  Sean Robertson  1 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  12 hours 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  1 days back

                                                  ez, infinity + 1

                                                  • KING _GAMES
                                                    KING _GAMES  1 days back

                                                    ΩоΩин

                                                    • chekystar
                                                      chekystar  1 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

                                                                      • Wiktor Zakrzewski
                                                                        Wiktor Zakrzewski  2 days back

                                                                        I am no matematician but I had some study in logic. And mathematics is based on logic. And this whole omega buisines seems to me to brake the fundamental law of logic. In any moment you add or multiply to infinity, you produce a paradox, so it becomes clear why you can come to 0=1. Logic says that Dog is not cat. 0 is not 1. Only because we defined them so. So the meaning of Infinity is infinity, period. There can be nothing more, because the definition of infinity encompasses everything and more. So any omegas are simply play on language based on nonsense. Nonsense is fun, can't say it isn't. But it's non-sense. Non-logic.

                                                                        • Wiktor Zakrzewski
                                                                          Wiktor Zakrzewski  9 hours back

                                                                          I'm sorry about your headache. Well I said before I am no matematician. I would gladly admit I was wrong, but I fail to understand the omega +1. I will abandon the subject here until I understand more.

                                                                        • Caladbolg
                                                                          Caladbolg  12 hours back

                                                                          @Wiktor Zakrzewski If you knew math, you would see there's no error there. Successors in ordinals are defined thus: successor of x is xU{x}. Omega+1 is a notation used for the successor of omega. Successor of a number is bigger than that number.

                                                                          "Comes after" is the same as "bigger" in ordinals, genius. This topic is clearly way over your head so I don't understand this obstinate refusal to admit you're wrong. The only thing I'm suffering from is a headache from your apparent lack of math knowledge.

                                                                        • Wiktor Zakrzewski
                                                                          Wiktor Zakrzewski  18 hours back

                                                                          And according to Michael Stevens omega is not bigger. It comes after.

                                                                        • Wiktor Zakrzewski
                                                                          Wiktor Zakrzewski  18 hours back

                                                                          @Caladbolg I'm afraid you suffer the thing you claim others do. You define omega as a set of all integers and count past it by adding an integer to it. You clearly made an error here.

                                                                        • Caladbolg
                                                                          Caladbolg  19 hours back

                                                                          @Wiktor Zakrzewski But we don't say that that exists, do we? Besides, that is not even a claim about existence.

                                                                          Also, congratulations on avoiding the explanation. It's clear you have zero mathematical education and don't really care to learn. You don't even understand what math is nor how it works. You just care to play rhetorical gotchas, which only betray your lack of understanding on the subject.

                                                                          Fortunately, math has proofs, so unlike other fields, it's conclusions are certain within a given axiom system. Omega is bigger than any integer, and has numbers bigger than it still. Doesn't depend on intuition, real world, or even scientific authority. It follows from definitions and axiomd taken.

                                                                          Anyways, I have better stuff to do. Bye now.

                                                                      • Barleykid 12
                                                                        Barleykid 12  2 days back

                                                                        Well what could you call omega x 2 instead of omega x 2 like how you call two ones the number 2 and then so on and so on

                                                                        • Foxy - TheMemelords
                                                                          Foxy - TheMemelords  2 days back

                                                                          To the infinity and beyond

                                                                          • Isaac Asmah
                                                                            Isaac Asmah  2 days back

                                                                            Vsauce is the prince ea of science

                                                                            • Aiden Westcott
                                                                              Aiden Westcott  2 days back

                                                                              and i thought 1st grade math was hard

                                                                              • Chronical Kiefer
                                                                                Chronical Kiefer  2 days back

                                                                                The last number is...






                                                                                That’s what I found




                                                                                -siri

                                                                                • Matt25
                                                                                  Matt25  2 days back

                                                                                  You count to infinity 1 to infinity 1000000000000000000000000

                                                                                  • まだ寒い ッ
                                                                                    まだ寒い ッ  2 days back

                                                                                    Infinity and one

                                                                                    • clorans from clorox
                                                                                      clorans from clorox  2 days back

                                                                                      2:37 yeah, most people are thinking about the gd level right now..

                                                                                      • Gabe
                                                                                        Gabe  2 days back

                                                                                        Gabe Newell: *Wait what?*

                                                                                        • AReallyGudzy Guest
                                                                                          AReallyGudzy Guest  2 days back

                                                                                          If u can count past infinity...... can you count past pi?