Math Has a Fatal Flaw

Dipublikasikan tanggal 22 Mei 2021
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Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is sponsored by Brilliant. The first 200 people to sign up via brilliant.org/veritasium get 20% off a yearly subscription.

Special thanks to Prof. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, Prof. Toby ‘Qubit’ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video.

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References:

Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. - ve42.co/Dunham2013

Conway, J. (1970). The game of life. Scientific American, 223(4), 4. - ve42.co/Conway1970

Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. - ve42.co/Churchill2019

Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. - ve42.co/Gaifman2006

Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky-in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. - ve42.co/Lnrt2010

Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. - ve42.co/Poincare

Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. - ve42.co/Irvine1995

Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. - ve42.co/Godel1931

Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. - ve42.co/Russel1910

Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. - ve42.co/Godel1986

Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. - ve42.co/Cubitt2015

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Special thanks to Patreon supporters: Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

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Written by Derek Muller, Adam Becker and Jonny Hyman
Animation by Fabio Albertelli, Jakub Misiek, Iván Tello and Jonny Hyman
Math City Animation by Another Angle 3D Visuals (www.anotherangle.ee)
Filmed by Derek Muller and Raquel Nuno
Edited by Derek Muller
Music and SFX by Jonny Hyman Additional Music from Epidemic Sound
Additional video supplied by Getty Images
Thumbnail by Geoff Barrett
Associate Producers: Petr Lebedev and Emily Zhang

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Komentar  
  • SheepML

    SheepML

    38 menit yang lalu

    I knew all of these from faculty, but I never understood them so deeply

  • Dhyan Thakkar

    Dhyan Thakkar

    Jam Yang lalu

    I don’t get that cantor example couldn’t u just assign another natural number to the new number created by diagonalization

  • Ivan the Benighted

    Ivan the Benighted

    3 jam yang lalu

    This was so fascinating and well explained I couldn't avoid crying.

  • Dmytro Nakonechnyy

    Dmytro Nakonechnyy

    3 jam yang lalu

    I didn’t understand anything, but I watched the whole video from beginning to end.

  • N45441

    N45441

    3 jam yang lalu

    If you prove that there is no proof, have you proven a proof?

  • Vulturee

    Vulturee

    3 jam yang lalu

    This is a problem in all fields of work.there will always be impossible things We accept as the truth to keep us sane,

  • Brian Lopez

    Brian Lopez

    4 jam yang lalu

    The six air terminally attach because diving putatively march including a unwritten beer. pretty, testy journey

  • Eden Meireles

    Eden Meireles

    4 jam yang lalu

    congrats, Derek! this is absolutely mindblowing!!!

  • AlexKasper

    AlexKasper

    5 jam yang lalu

    Probing g is not g? I summon Schrodinger's cat to decide.

  • Imon Worthy

    Imon Worthy

    5 jam yang lalu

    It's not a flaw. It's limit that math has.

  • AlexKasper

    AlexKasper

    5 jam yang lalu

    1+1=2 ?
    I heard that recently 2+2 is now 5 😀

  • austin oehring

    austin oehring

    5 jam yang lalu

    Godel came up with a self reference card. A paradox.. I thought we don't do those.

  • macnolds

    macnolds

    5 jam yang lalu

    It was very confusing for me to see the superset symbol (i.e. the reverse "C-looking" subset symbol) being used for "If...then".
    Apparently this used to be a popular thing.

  • frosty992001

    frosty992001

    6 jam yang lalu

    You must have an IQ of about 700.

  • Shivam Goyal

    Shivam Goyal

    6 jam yang lalu

    Great work !!

  • Jonathan's Garden

    Jonathan's Garden

    6 jam yang lalu

    Infinites are the same in number and they're all countable, but the rate at which they're counted can be different. Their growth rate and curve can be very different. Yes, infinity can have different curves depending on how you define the style of infinite

  • Bruce Carbon Lakeriver

    Bruce Carbon Lakeriver

    7 jam yang lalu

    13:58 "is mathematic consistent"
    Me: erm Gödel? :D

  • Dardanelle News1776

    Dardanelle News1776

    7 jam yang lalu

    "There will always be true statements that cannot be proven."

  • Timothy Krier

    Timothy Krier

    7 jam yang lalu

    This reminds me of the Pinocchio paradox. What happens if Pinocchio says "my nose is about to grow"?

  • Lolappa Gamer

    Lolappa Gamer

    8 jam yang lalu

    What if you did that thing that proves there are more numbers between 0 and 1 to integers?

  • Simon Gniadkowski

    Simon Gniadkowski

    10 jam yang lalu

    @4:54 "With a real number between 0 and 1 on the other" @5.02 "the key is to make sure we get them all with no duplicates" @ 5:10 "if we can do that with none left over" @ 5:20 "assume we have done that, we have a complete infinite list" @5:30 "now Cantor says "start writing down a new real number" " . . . . here is the problem, these statements are mutually exclusive. If you have a complete list you can't write a new one . . if you can then your list is incomplete !

    • Релёкс84

      Релёкс84

      10 jam yang lalu

      Look up what proof by contradiction means

  • X41N3

    X41N3

    11 jam yang lalu

    I feel stupid..

  • Blue Pegasus

    Blue Pegasus

    11 jam yang lalu

    Can anyone explain how he proved 2^6 3^5 5^6=0

  • Julie Fisher

    Julie Fisher

    11 jam yang lalu

    The point is that there is, there has to be always an initial assumption. That initial assumption is chosen carefully and is nearly correct. But not provable. So therefore nothing that follows from it can be.
    0 = 0 = 1 = Infinity!
    We can assume that this is incorrect, but can never prove it, without making assumptions.

  • SeanGS

    SeanGS

    11 jam yang lalu

    confucius said, how does one kill one that has no life? this is the dualistic nature of life, what you think you know u know nothing of! so we are stuck in a pile of snort inside a large bug that floats inside a large pipe that flows trough spacetime making up a limb of a dog taking a piss on a lightpole that is located on a pile of rock that spins around a large stone that gives it enery to fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough 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spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that fly trough another spacetime bubble that consist of many other bubbles that

  • Griffin da genei

    Griffin da genei

    11 jam yang lalu

    That ending was sublime

  • Griffin da genei

    Griffin da genei

    11 jam yang lalu

    I still don't understand what derek said😂

  • Tran Hung

    Tran Hung

    12 jam yang lalu

    poor guy too smart that may be the reason that make him go crazy...

  • Harry Turtles

    Harry Turtles

    12 jam yang lalu

    Couldn't you just have 2 barbers? If the barber can only shave someone who does not shave themselves, then if there's 2 they can shave each other.

  • wimpb

    wimpb

    12 jam yang lalu

    "If God were to hold out enclosed in His right hand all Truth, and in His left hand just the ever-active search for Truth, though with the condition that I should forever err therein, and should say to me: ‘Choose!' I should humbly take His left hand and say: ‘Father! Give me this one; absolute Truth is for Thee alone” — G. E. Lessing, Eine Duplik (1778)

  • Srishti Shubhi

    Srishti Shubhi

    14 jam yang lalu

    I couldn't understand 😅

  • Heather Harris

    Heather Harris

    17 jam yang lalu

    My brain is jello

    • Heather Harris

      Heather Harris

      17 jam yang lalu

      How do you understand this

  • PidgeMidge

    PidgeMidge

    19 jam yang lalu

    29:16 shout out to my guy Kyle Hill

  • Haha-AaaAAA

    Haha-AaaAAA

    19 jam yang lalu

    6:23 - not true. infini = infini, this theory doesn't prove anything and make no sense
    ps : contradictions don't prove anything except that u've made something that contradict itself. it's that simple. if u set it up so it can't work then it won't, logic

    • Haha-AaaAAA

      Haha-AaaAAA

      6 jam yang lalu

      @AndreYea but my point is that it doesn't prove that it's wrong, adding +1 to one of the number still make the number be between 0 and 1, and if its between 0 and 1 then it is in the intervale 0 < x < 1, so no there is not "more infini number" cause it's the very definition on infini, which doesn't end. And u can't seem to be able to explain it either. Point his, his contradiction don't prove anything, its a false contraction.

    • Andre

      Andre

      17 jam yang lalu

      @Haha-AaaAAA _"some* contradictions don't prove anything."_ *ALL* contradictions prove the assumption wrong - as it is the case here _"How can a number between 0 and 1 not be in the interval that include all number between 0 and 1 ?"_ That was the assumption. The contradiction proves this wrong.

    • Haha-AaaAAA

      Haha-AaaAAA

      17 jam yang lalu

      @Andre *some** contradictions don't prove anything. Like the ones set up to contradict themself. for the 6:23, How can a number between 0 and 1 not be in the interval that include all number between 0 and 1 ?

    • Andre

      Andre

      18 jam yang lalu

      _"__6:23__ - not true. infini = infini, "_ No. _"this theory doesn't prove anything and make no sense "_ It is no "theroy" but a proof. And as a proof it proves that there are multiple infinities. _"contradictions don't prove anything except that u've made something that contradict itself. "_ They do. They are called "proof by contradiction". _"if u set it up so it can't work then it won't, logic"_ This has nothing to do with "logic".

  • EricTheDetailer

    EricTheDetailer

    19 jam yang lalu

    I remember in the late seventies early '80s my friend had a ti-99 computer and we would play the game of life on it. It was bittersweet because when we got it to run for more than a day or two he would have to shut the program down in order to do his school work. Also when the computer was tied up running a sequence we couldn't do it any other fun games on it.

  • agnomotuh

    agnomotuh

    20 jam yang lalu

    If these mathematicians had just read some texts about the omnipotence paradox and maybe some of St. Thomas Aquinas's work, they would have figured out Godel's incompleteness theorem much sooner. Sure they still would have had to "show their work" (so to speak) in a published paper, but they needn't struggle so long to arrive at the contradiction at the center of the incompleteness theorem.

  • Gecko o

    Gecko o

    21 jam yang lalu

    Wait, if something contains itself, why is mandatory that it doesn't contain itself?, I mean if you make an algorithm that produces numbers at some point you can make it produce all the numbers that it already produced.

  • Rocco Coyote

    Rocco Coyote

    21 jam yang lalu

    computers are gay

    • dsBlocks

      dsBlocks

      10 menit yang lalu

      based

  • Edvinas Šamonskis

    Edvinas Šamonskis

    22 jam yang lalu

    This problem answers the question to asking what is the meaning of life.

  • D P

    D P

    22 jam yang lalu

    I completely disagree with the idea that some math is not decidable. The fact is, those problems, while active, ARE deciding. If I grant you immortality, and you run a problem for a few trillion years, you can then know the answer to that problem. The same is true for all other problems.

  • David Orth

    David Orth

    22 jam yang lalu

    And why I am a mystic who loves logic. Subscribed.

  • Edvinas Šamonskis

    Edvinas Šamonskis

    23 jam yang lalu

    Numbers have a limit so lets measure a limit. Limit is infinity - you cant measure infinity. Does it mean numbers doesn't exist or the other way around? Ok, the other way around. Numbers doesn't have a limit and we measure it backwards of the limit that it doesn't have. We still have infinity, but in opposite way.
    We went full circle, if we add those two together. They were full circles anyway, because they are full circles of a multi dimensional circle, that any point would be the middle.
    At this point, of this realization, feeling my body got much more weirder, like its some kind of a miracle.
    It looks to me that the problem is in numbers, not in math. The problem is measuring infinity with numbers, because you go back to measuring circle of infinity, that is the circle of infinity, that is the circle of itself that isn't the exact circle. Here erupts the problem.


    I edited this a lot of times and I realized that everything I said here doesn't mean anything, because you dont need anything, numbers and any sort of that thing. Because the problem is at the very act of measurement. I googled " Problem of measurement", I didnt know about this before and yeah, you can see for yourself this problem is already known.








    ((Everything is one?) Check monism on English wiki and read description of the picture of circle with dot in it(that looks like a quantum state).))

    So yeah, this realization is very gratifying because it makes you realize that simple concept of 0 and 1 superposition state can create such complexity of life and everything that exists around us, as much as our concept understanding of world can reach. And it proves that everything you work for that is meaningful to your surrounding only deepens this complexity of the world(or understanding). Yet we dont know what this superposition means. ajuhbiklsodfg gerwn;ifesdzgxsrzatmew3QRE
    I invite you to discuss this with me.

    • Edvinas Šamonskis

      Edvinas Šamonskis

      22 jam yang lalu

      I just realized, this problem answers the question to asking what is the meaning of life.

  • Noa TheFrog

    Noa TheFrog

    23 jam yang lalu

    I'm just gonna play call of duty on my Turing machine now

  • dav ep

    dav ep

    23 jam yang lalu

    Seen in a store window in Cambridge, MA:
    Turing Machines Rewound While U Wait.
    BOFH: Your files aren't available. Turing machine rebooting.

  • Tara's Adventures

    Tara's Adventures

    Hari Yang lalu

    Unrelated but also kinda related... I keep wondering if the solution to everything is actually not mathematical. Perhaps mathematics is not just incomplete, but wrong. Perhaps a language in which encompases the core of math, but also something more like a litteral language- something that can be written and spoken like english or chinese- but encompases the purposes of math. You will have measurements, codes, numbers and letters, equations, thought experements, and individual words for everything, side-by-side like an alphabet. That way, as you experience the world and simply live and breathe and speak, you will be solving the greatest mysteries, as the very sounds, sights, andthoughts imaginable by all of human nature will be given a learnable rune. The only foreseeable problem is the runes themselves. As of yet, there is no way to create runes specific for everything, as we do not know everything. So in order to solve everything, we would have to know everything first. However, perhaps it could be started, then gradually, as we use it, we would add to it such like infinite numbers. Eventually, we would solve everything using it, and once solved, it would be added so that we could use that knowledge like an equation in order to solve everything else. Eventually, we'd have all our answers, if we ever touched upon infinity. However, with billions of people always progressively moving forward with just the sole fact of breathing, dreaming, or eating, we might reach an end. If we reach an end, that both determines that already we know everything, and also that infinity is nonexistent. After, there will be no means of progression, and we could essentially build, do, or think anything possible or imaginable. Again, the problem would be the runes, they wouldn't be possible to make simply because we wouldn't have the opportunity to physically make most of them, based on the fact that many- such as light- cannot be made into a rune on paper, using a pen. But if we could somehow be able to make those things- such as time, light, space, the 4th dimension, etc- into a rune in order to represent them, physically, in a line such as a speakable alphabet, or somehow turn other runes for things- like trees, dogs, and houses- into the same plane of existence as light, time, or space- we'd still end up with a speakable and writable rune alphabet with the components of everything, but we'd have to create a different means of speaking and writing it. That, I believe, would be the only problem. However, if there is a mathematician who can build off this and perhaps work towards this, I'd be very interested in hearing your findings or thoughts on this "language of everything." Please reply if you understand and can help finish this idea! Thank you for reading this far!

  • P Dezs

    P Dezs

    Hari Yang lalu

    My brain: GOOD OL' NUMBER 6

  • That One Guy

    That One Guy

    Hari Yang lalu

    now run the game of life on the game of life that's being ran by the game of life

  • Cephery

    Cephery

    Hari Yang lalu

    ‘[turning complete systems] are powerful’
    Laughs in brainfuck.

    • dsBlocks

      dsBlocks

      8 menit yang lalu

      it just means "can do anything a Turing Machine can", there is no statement being made about how fun it'll actually be.

  • Still Crows

    Still Crows

    Hari Yang lalu

    Infinity is easy. You're standing in it.

  • Purvang Vasani

    Purvang Vasani

    Hari Yang lalu

    Can we please get a video on lucid dreaming?

  • L C

    L C

    Hari Yang lalu

    Who's working on the code that will prevent AI's self awareness from becoming its own survival instinct? Self awareness = self preservation (in healthy minds, anyway). Perceived threats to our lives can cause the death of others. Perceived threats to our egos prevent us from accepting new ideas. The preservation of ALL organic life should be paramount at this point, otherwise all this discussion is pointless. Warnings (thank you Steven Hawking) are opportunities, not inevitabilities. We can't "science" our way out of the problems "progress" has caused unless we respect ORGANIC life for what it is. We need to accept that manipulating nature for the sake of personal gain is the wrong way to go. So, how do we prevent AI from destroying the perceived threat of humans to its own existence? Or once it realizes we are to blame for everything that's wrong with society and how civilization has caused massive die offs and perversions of organic life if its been programmed to solve these problems for us? I'm not a mathematician, but I think this line of self-referential paradox can help develop the code needed to fix the problems we're hurtling toward with AI.

  • Edward Stane

    Edward Stane

    Hari Yang lalu

    One of the most well-deserved slow claps i've ever had the pleasure of giving.. The quality of his videos is indescribable..

  • Talib Smith

    Talib Smith

    Hari Yang lalu

    Maybe the problem is 0. "0" really should look like " ". Every time you write or input the number zero, your giving body to a number that doesn't exist. Zero should be taken out the number system because it's really the mirror of/to infinity. It has no reflection or body

    • Talib Smith

      Talib Smith

      Hari Yang lalu

      As I wrote the above comment , it says i wrote it zero seconds ago? 🤔

  • Abdulkareem Kabir

    Abdulkareem Kabir

    Hari Yang lalu

    Now this is chilling to watch. It only proves how limited our capacity is as humans.

  • Jennacide

    Jennacide

    Hari Yang lalu

    This video is clearly a way to make homophobic people not wanna use computers

  • Matthew Rodgers

    Matthew Rodgers

    Hari Yang lalu

    The bustling george empirically move because hurricane indirectly happen onto a awesome gym. wandering, youthful tooth

  • MsUncleKevin

    MsUncleKevin

    Hari Yang lalu

    Thing you cant solve is womens mind. Doesnt matter if u are godel or poincaire. Logic fails.

  • NYTLYF

    NYTLYF

    Hari Yang lalu

    This channel is sponsored by illuminati.

  • Daniel Dwiky

    Daniel Dwiky

    Hari Yang lalu

    Finished watching this and i just realized that mathematics and physics really are complicated

  • Ern de Che

    Ern de Che

    Hari Yang lalu

    By design, science only disproves, consequently autoreference is only scientifically useful when it disproves.
    Illusory truth is a contradiction in terms.
    Finite minds cannot process infinity in any true form, insanity is the demonstrated result of relentless attempts in spite.
    Formalist is a euphemism.
    0 doesn't exist. An infinite set is a contradiction in terms. g is irrelevant.
    No one can stand on the shoulders of giants if midgets are permitted to anklebite them down, let alone encouraged. Believing a lie defiles your mind, and the more obvious the lie the greater the defilement.

  • Barely Rice

    Barely Rice

    Hari Yang lalu

    yo does anyone remember that tile game from a dong like 10 years ago

  • Snigdha Sarkar

    Snigdha Sarkar

    Hari Yang lalu

    Can we just appreciate the animation quality and hard work he put?!!

  • Krispyking24

    Krispyking24

    Hari Yang lalu

    i want to watch the conways game of life in conways game of life

  • Michael Shaw

    Michael Shaw

    Hari Yang lalu

    Moobs

  • robert otto

    robert otto

    Hari Yang lalu

    Brain just melted 😂 smart guy!👍

  • Kazimierz Król

    Kazimierz Król

    Hari Yang lalu

    About Cantor's Diagonalization Proof (I am not a mathematician, I have read some Wikipedia articles, but couldn't understand them fully, so what I say here might be bollocks): If we create another real number by adding one to next digit in all the real numbers, then I see two problems:
    1. Here is the contradiction without using natural numbers at all: earlier we assumed the list was complete, and contained every real number between 0 and 1, so if we can create another one, the assumption was wrong.
    2. We can do the same operation on the natural numbers on the left: add one to next digit in all following numbers (padding all with zeros on the left), and look at this: we have got another natural number, different from all previous ones. This will be our newly created index for the created real number. Isn't this a proof the number set sizes are equal? Of course this suffers from the same contradiction as in #1, but I wonder, did no one think about this simple thing before?

    • Tom Svoboda

      Tom Svoboda

      Hari Yang lalu

      @Kazimierz Król well, the fact that naturals have finitely many digits and decimals have infinitely many digits implies that one set is larger than another, but not trivially. it needs to be proved, which is exactly what the diagonal argument does. for example the set of all rational numbers has the same size as the set of natural numbers, and yet most rational numbers have infinitely many digits when represented by decimals.

    • Kazimierz Król

      Kazimierz Król

      Hari Yang lalu

      Thanks. So can't the conception that there is more real numbers between 0 and 1 than natural numbers be derived just from the fact that the number of digits must be finite for naturals, while can be infinite for reals? The diagonal proof does not seem necessary at all.

    • Tom Svoboda

      Tom Svoboda

      Hari Yang lalu

      1. it's a proof by contradiction. assume the reals can be listed => derive contradiction => the assumption that the reals can be listed was wrong (which we wanted to prove in the first place) 2. the diagonal argument fails for the natural numbers because it produces an infinite string of digits which is not a natural number. natural numbers have only finitely many digits.

  • Suzanne Freedman

    Suzanne Freedman

    Hari Yang lalu

    I bet Hilbert was looking over at Gödel thinking like... “You really going to build your entire career around saying I’m wrong? That’s rude, what’d I ever do to you?”

    • Suzanne Freedman

      Suzanne Freedman

      Hari Yang lalu

      And now I’m wondering if Hilbert DID do something to Gödel to spark that amount of determination 😂

  • Peter Steele

    Peter Steele

    Hari Yang lalu

    The thing about mathematics is that numbers and the values they represent always get bigger & bigger much like ego... until they don't... almost as if self aware, they change their values.

  • Jeremias

    Jeremias

    Hari Yang lalu

    i feel like the barber reference isnt that accurate, if he cant shave him self and the barber cant shave him. he would be exiled or go to jail? not welcome in that"set". No?

  • Jack Daniels

    Jack Daniels

    Hari Yang lalu

    The blue-eyed sword cytomorphologically wave because edger chronologically tour after a abounding nation. bawdy, towering session

  • Joaquín Hinojosa

    Joaquín Hinojosa

    Hari Yang lalu

    My brain hurts

  • XeL NaGa

    XeL NaGa

    Hari Yang lalu

    well if you knew what they feed the cattle youd think youd get poissoned too lel
    worst monocrop used for cattle full of pesticide and gmo.
    basicly giving the cheapest worst most toxic chemical food possible for cattle.
    the steak gotta be cheap :D

  • Politics

    Politics

    Hari Yang lalu

    Glad there is a mathematical answer to why I can't figure out the truth about Covid!

  • Adam McKinzie

    Adam McKinzie

    Hari Yang lalu

    If the game of life can run the game of life, then it’s possible that the game of life could run the game of life running the game of life and continue to do so on an infinite scale

  • Sven Croon

    Sven Croon

    Hari Yang lalu

    only a mathematical system that has no axioms, can ever be truly complete, consistent and decidable.
    Axioms are the evil that corrupts everything ;-)

  • Thomas Klugh

    Thomas Klugh

    Hari Yang lalu

    Now my head hurts.

  • Marshall115

    Marshall115

    Hari Yang lalu

    give it a few decades-current math is wrong-it will change but still just be humans way of measurement.

  • neil unger

    neil unger

    Hari Yang lalu

    And here I read this as Meth Has A Fatal Flaw.

  • EliteTrollingG

    EliteTrollingG

    Hari Yang lalu

    5:16. I just wanna ask, why don't mathematicians just agree on what number natural numbers and real numbers should stop at. Like the end of the number line is 10,000,000,000,000,000,000,000,000,000,000 starting today. And the end of real numbers is 0.999999999999999 until it goes to 1. I mean that would ruin all the work we have put into trying to find the end of pi, but my question is, WOULD it help solve problems mathematicians have been trying to solve for centuries, or would it just create more problems? I'm actually curious.

  • Piotrek

    Piotrek

    2 hari yang lalu

    Hi, i ve got some idea, about part about cantor set theory. If u try to groupe natural numbers and numbers between 0 and 1 like this: for 1, theres 0.1. For 27, theres 0.27. For 29010123, theres 0.29010123. Then every Natural number, will be grouped with exactly one number between 0 and 1, and also if u try doing something like in the video, u just take another natural number matching this one. Does it work? Please lemme know.

    • Piotrek

      Piotrek

      Hari Yang lalu

      @Brauggi the bold oh, u re right, thank u. I didnt considered irrational numbers. But still, i dont believe this😒, even if the proof showed by cantor is 100% true and logic, my mind cannot take this. :c.

    • Brauggi the bold

      Brauggi the bold

      Hari Yang lalu

      It does not work. You will only ever hit rational numbers which have a decimal representation that ends in repeating zeros that way. Your mapping will for instance not include ANY irrational number between 0 and 1.

  • Sumit Juyal

    Sumit Juyal

    2 hari yang lalu

    Wow, self-reference, what a beautiful link, this channel is the perfect blend between epistemological philosophy and mathematics, as someone who is a math graduate I would've loved to be introduced to subject histories like that before mindlessly trying to solve problems and pass the exam. People need to normalize and popularise the idea that mathematics applied philosophy which is just applied inherent logic. Your channel does wonders for us appreciators of the mind but are still rigorous in our understanding of the same.

  • Dylan Hase

    Dylan Hase

    2 hari yang lalu

    I want to launch my own branch of math! How do you do that

  • H

    H

    2 hari yang lalu

    Maybe I don't understand it but wouldn't the diagonal number be on the list since the list goes to infinity and because at one point you will have to roll back 9 to an 8 making it equal to that number in the diagonal the minute you add +1.

  • Abdullah Ahmed

    Abdullah Ahmed

    2 hari yang lalu

    9:25 need explanation

  • Azio Prism

    Azio Prism

    2 hari yang lalu

    Having 2 apples is impossible. Identical numbers are not possible. What makes numbers and apple differ is the environment around them :9

  • Croldfish

    Croldfish

    2 hari yang lalu

    1:25 i forgor :skull:

  • Heaven&Hell

    Heaven&Hell

    2 hari yang lalu

    none of this can be proven to be true.. concurrent quantum states prevent this.

  • KLEIS

    KLEIS

    2 hari yang lalu

    Math can prove a lot of things but it can't prove life, it is coz of math is itself incomplete by knowledge of human has created, completeness or creation of all things that has life is fundamental things that it is not related by math. So math is not absolute and it is just one of many knowledge to prove something by what creation has created

  • TheBeast

    TheBeast

    2 hari yang lalu

    just learned set theory for my computer science degree really interesting stuff

  • Bijou Smith

    Bijou Smith

    2 hari yang lalu

    @28:20 so, the undecidability of the spectral gap property amounts to the first proof quantum physics, as we conceive it presently, does not admit reductionism? Have I got that right? That's pretty signifcant for philosophy of science, which has previously generally operated under the paradigm that science (whatever it is) is reducible _in principle_ to base physics, through obviously not always in practice. So either that's a false paradigm or quantum physics is not base.

  • ayy lmao

    ayy lmao

    2 hari yang lalu

    Russell's paradox is a violation of the law of excluded middle. Ergo the law of excluded middle is wrong. Ergo superposition.

  • Kim Tae Hwan

    Kim Tae Hwan

    2 hari yang lalu

    The voice is good though I'd never understand the contents...

  • Afqwa

    Afqwa

    2 hari yang lalu

    This really murders the idea that math is some kind of divine tongue bestowed upon us by the gods. Murders it in its crib by smothering it with a pillow.
    Why does math work . . . _uhhhh sometimes it has empirically useful results._

  • Giap Chin

    Giap Chin

    2 hari yang lalu

    "This is the game of life, running on the game of life."
    Then proceeds to slow zoom out.
    Wow my mind literally was blown.

    • Tara's Adventures

      Tara's Adventures

      Hari Yang lalu

      I got chills

  • Andrew C. Mumm

    Andrew C. Mumm

    2 hari yang lalu

    Enter quantum entanglement... a proof can be true and false at the same time until observed. And when observed, the universe splits into different realities... :D