Math Has a Fatal Flaw

Veritasium
420 000 Megtekintés 9 M

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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Megjegyzés

  1. Heather Harris
    Heather Harris
    8 órája

    My brain is jello

    1. Heather Harris
      Heather Harris
      8 órája

      How do you understand this

  2. PidgeMidge
    PidgeMidge
    9 órája

    29:16 shout out to my guy Kyle Hill

  3. Haha-AaaAAA
    Haha-AaaAAA
    9 órája

    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

    1. Andre
      Andre
      7 órája

      @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.

    2. Haha-AaaAAA
      Haha-AaaAAA
      7 órája

      @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 ?

    3. Andre
      Andre
      8 órája

      _"__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".

  4. EricTheDetailer
    EricTheDetailer
    9 órája

    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.

  5. agnomotuh
    agnomotuh
    10 órája

    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.

  6. Gecko o
    Gecko o
    11 órája

    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.

  7. Rocco Coyote
    Rocco Coyote
    11 órája

    computers are gay

  8. Edvinas Šamonskis
    Edvinas Šamonskis
    12 órája

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

  9. D P
    D P
    12 órája

    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.

  10. David Orth
    David Orth
    12 órája

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

  11. Edvinas Šamonskis
    Edvinas Šamonskis
    13 órája

    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.

    1. Edvinas Šamonskis
      Edvinas Šamonskis
      12 órája

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

  12. Noa TheFrog
    Noa TheFrog
    13 órája

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

  13. dav ep
    dav ep
    13 órája

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

  14. Tara's Adventures
    Tara's Adventures
    14 órája

    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!

  15. P Dezs
    P Dezs
    14 órája

    My brain: GOOD OL' NUMBER 6

  16. That One Guy
    That One Guy
    14 órája

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

  17. Cephery
    Cephery
    14 órája

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

  18. Still Crows
    Still Crows
    15 órája

    Infinity is easy. You're standing in it.

  19. Purvang Vasani
    Purvang Vasani
    15 órája

    Can we please get a video on lucid dreaming?

  20. L C
    L C
    15 órája

    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.

  21. Edward Stane
    Edward Stane
    16 órája

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

  22. Talib Smith
    Talib Smith
    17 órája

    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

    1. Talib Smith
      Talib Smith
      17 órája

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

  23. Abdulkareem Kabir
    Abdulkareem Kabir
    18 órája

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

  24. Jennacide
    Jennacide
    20 órája

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

  25. Matthew Rodgers
    Matthew Rodgers
    21 órája

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

  26. MsUncleKevin
    MsUncleKevin
    21 órája

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

  27. NYTLYF
    NYTLYF
    21 órája

    This channel is sponsored by illuminati.

  28. Daniel Dwiky
    Daniel Dwiky
    21 órája

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

  29. Ern de Che
    Ern de Che
    Napja

    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.

  30. Barely Rice
    Barely Rice
    Napja

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

  31. Snigdha Sarkar
    Snigdha Sarkar
    Napja

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

  32. Krispyking24
    Krispyking24
    Napja

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

  33. Michael Shaw
    Michael Shaw
    Napja

    Moobs

  34. robert otto
    robert otto
    Napja

    Brain just melted 😂 smart guy!👍

  35. Kazimierz Król
    Kazimierz Król
    Napja

    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?

    1. Tom Svoboda
      Tom Svoboda
      Napja

      @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.

    2. Kazimierz Król
      Kazimierz Król
      Napja

      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.

    3. Tom Svoboda
      Tom Svoboda
      Napja

      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.

  36. Suzanne Freedman
    Suzanne Freedman
    Napja

    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?”

    1. Suzanne Freedman
      Suzanne Freedman
      Napja

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

  37. Peter Steele
    Peter Steele
    Napja

    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.

  38. Jeremias
    Jeremias
    Napja

    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?

  39. Jack Daniels
    Jack Daniels
    Napja

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

  40. Joaquín Hinojosa
    Joaquín Hinojosa
    Napja

    My brain hurts

  41. XeL NaGa
    XeL NaGa
    Napja

    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

  42. Politics
    Politics
    Napja

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

  43. Adam McKinzie
    Adam McKinzie
    Napja

    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

  44. Sven Croon
    Sven Croon
    Napja

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

  45. Thomas Klugh
    Thomas Klugh
    Napja

    Now my head hurts.

  46. Marshall115
    Marshall115
    Napja

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

  47. neil unger
    neil unger
    Napja

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

  48. EliteTrollingG
    EliteTrollingG
    Napja

    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.

  49. Piotrek
    Piotrek
    Napja

    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.

    1. Piotrek
      Piotrek
      Napja

      @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.

    2. Brauggi the bold
      Brauggi the bold
      Napja

      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.

  50. Sumit Juyal
    Sumit Juyal
    Napja

    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.

  51. Dylan Hase
    Dylan Hase
    Napja

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

  52. H
    H
    Napja

    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.

  53. Abdullah Ahmed
    Abdullah Ahmed
    Napja

    9:25 need explanation

  54. Azio Prism
    Azio Prism
    Napja

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

  55. Croldfish
    Croldfish
    Napja

    1:25 i forgor :skull:

  56. Heaven&Hell
    Heaven&Hell
    Napja

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

  57. KLEIS
    KLEIS
    Napja

    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

  58. TheBeast
    TheBeast
    Napja

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

  59. Bijou Smith
    Bijou Smith
    Napja

    @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.

  60. ayy lmao
    ayy lmao
    Napja

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

  61. Kim Tae Hwan
    Kim Tae Hwan
    2 napja

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

  62. Afqwa
    Afqwa
    2 napja

    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._

  63. Giap Chin
    Giap Chin
    2 napja

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

    1. Tara's Adventures
      Tara's Adventures
      14 órája

      I got chills

  64. Andrew C. Mumm
    Andrew C. Mumm
    2 napja

    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

  65. Ascot
    Ascot
    2 napja

    Mind Blown

  66. Andrew C. Mumm
    Andrew C. Mumm
    2 napja

    The game of life animations at the start are awesome - does anyone know how they were made?

  67. Gerard Ligonde
    Gerard Ligonde
    2 napja

    The erratic canada methodologically dare because oboe endosonographically sin aboard a tall afghanistan. curious, meek broccoli

  68. enthusiasticGeek
    enthusiasticGeek
    2 napja

    25:57 and it vanishes in a puff of logic

  69. hieu dang
    hieu dang
    2 napja

    somehow i heard "godel" as "good old" for almost the entire video

  70. Babe Root
    Babe Root
    2 napja

    The language of God...the Creator/Designer, and mind of ALL information. The language of God...Mathematics. Amazing...isn't it? ☀️

    1. Andre
      Andre
      Napja

      _"The language of God...the Creator/Designer,"_ There is no god and no creator.

    2. ayy lmao
      ayy lmao
      Napja

      More like word salad

  71. flobbie
    flobbie
    2 napja

    Yeah, but it is neither a flaw, nor is it fatal.

    1. Andre
      Andre
      Napja

      @flobbie _"It just is that way. This does not make math any less useful to me."_ If there is even one contradiction it is. But we have never found any. It is just that there is no proof.

    2. flobbie
      flobbie
      Napja

      @Andre, i don't see that this makes it flawed. It just is that way. This does not make math any less useful to me.

    3. Andre
      Andre
      Napja

      @flobbie _" i don't understand. There are no flaws in math."_ You can't prove that a formal system is free of contradictions inside that system itself (for those systems that fullfill all conditions of Gödels theorems). That is a problem, because if there is a contradiction (even a contradiction we do not know today) then you can prove anything. Math is useless then. You maybe can prove this in some other system, but then how do you know that this system is free of contradictions? _"Your axiomatic system may be flawed, as it is contradictory. "_ And for many, many of those systems you cannot prove that it's not. _". But there is no flaw in the general way of how somone is supposed to process language."_ A "language" that contains a proof for A and not A is not really useful. _"Do some math and you will see there is no flaw."_ You can't prove this by examples. Do you even know what math is?

    4. flobbie
      flobbie
      Napja

      @Andre, i don't understand. There are no flaws in math. What is that even supposed to mean. Your axiomatic system may be flawed, as it is contradictory. Or your proof may be flawed as it contains errors. But there is no flaw in the general way of how somone is supposed to process language. Do some math and you will see there is no flaw.

    5. Andre
      Andre
      Napja

      Not being able to prove consistency is something I would call a "flaw".

  72. Robin Collins
    Robin Collins
    2 napja

    The actually ice cytologically add because brother noteworthily note an a tacit volleyball. fanatical, subdued pine

  73. darth biernot
    darth biernot
    2 napja

    My brain nearly exploded while watching this! People always say: "Math is logic" I personally am more comfortable with language. I speak German natively, English and French fluently but when it comes to a simple mathematic equation with a variable in it my brain goes: "system just crashed due to missing math.dll" 😆

  74. MrBizaaro
    MrBizaaro
    2 napja

    Excellent Video ! Feels like one of your best

  75. Jeffrey Wiegley
    Jeffrey Wiegley
    2 napja

    Holy crud!!!! I *finally* understand the diagonal proof after 30 years... Prof. Leonard Adelman (The 'A' in RSA) used in Gödel's Incompleteness theorem in Second Order Logic class and I blew that on the final exam. Oh... I can die happy now.

  76. Matthew Means
    Matthew Means
    2 napja

    Alan Turing a story is my favorite depiction of humanity. A single human was enough to determine the difference between a world with and without Nazi Germany thru his contributions which would have otherwise plummeted us into a darker world with less insigh, yet in response to his glorious contribution to humanity, he was treated as a plague for being gay and made the other on premise of his differences that hurt no one. Humanity will respond to it's very saving with its own doom.

  77. why bread
    why bread
    2 napja

    This video and his “how a infinite hotel ran out of rooms” video match up I just thought about it

  78. Peter Shmain
    Peter Shmain
    2 napja

    Cantor's diagnolization proof is incorrect because when you use that method to think of a new number, it must then also be assigned to a new index which is just 1 more than the previous number therefore disproving infinite inequality. However, that's not to say that his ideas are incorrect. It's just that this proof doesn't completely work in this way

    1. Andre
      Andre
      Napja

      @Peter Shmain _"given that the list is static, then you should not be able to create a new number from the decimal side either, "_ No. Cantor has shown that you can do this. That is the whole idea behind it. _"thus defeating the point if being static,"_ No. _"because then logic stands to reason "_ What "logic"? _"So if you can take a decimal and add 1 to each digit, why can't you take the index number and add 1 to it?"_ All indexes are taken. The list is static.

    2. Tom Svoboda
      Tom Svoboda
      Napja

      @Peter Shmain the list is not an equation, you're not "doing" anything to it. it's an assignment of a decimal to every natural number (which can be pictured as an infinite list indexed by the natural numbers). for any natural number n there's a given decimal d_n. one such assignment would be d_n = 1/n, which in the "infinite list" representation looks like d_1 = 1/1 = 1.0000... d_2 = 1/2 = 0.5000... d_3 = 1/3 = 0.3333... ... this is just an example. clearly a lot of decimals are missed, for example 2/3 never appears. the diagonal argument proves that we can find a missing number for any such list, therefore it's impossible to come up with a formula for d_n which would account for all decimals.

    3. Peter Shmain
      Peter Shmain
      Napja

      @Tom Svoboda given that the list is static, then you should not be able to create a new number from the decimal side either, thus defeating the point if being static, because then logic stands to reason that what you do to one side of an equation, you do to the other side, correct? So if you can take a decimal and add 1 to each digit, why can't you take the index number and add 1 to it? Maybe im missing something here?

    4. Tom Svoboda
      Tom Svoboda
      Napja

      there is no new index. the list is not being generated, it's static and completed from the moment you consider it. all the indices (the natural numbers) are already taken.

    5. Andre
      Andre
      Napja

      _"Cantor's diagnolization proof is incorrect"_ No. _"when you use that method to think of a new number, it must then also be assigned to a new index"_ No. _"t 1 more than the previous number "_ What "previous number"? _"However, that's not to say that his ideas are incorrect."_ The idea and the proof is correct. _" It's just that this proof doesn't completely work in this way"_ It does.

  79. Michael Borisow
    Michael Borisow
    2 napja

    I don't know how many of all 8 million of yall are understanding this, but I'm gonna have to pause and look up stuff from this vid another ∞times before I understand anything

  80. Aymane Sghiar
    Aymane Sghiar
    2 napja

    Best video I've watched in a looooooooong time.

  81. Anaya Barata
    Anaya Barata
    2 napja

    So is the fact that not all true things can be proven also unprovable?

    1. Andre
      Andre
      Napja

      It is the opposite.

  82. Robin Hodson
    Robin Hodson
    2 napja

    But this depends upon the assumption that recursion and logic contradictions disprove systems. That's not necessarily universal, otherwise we wouldn't be capable of comprehending them. Saying "This is incomprehensible," an apparent paradox, is actually comprehensible, and thus not not invalid.

  83. costaran
    costaran
    2 napja

    MEGALIKE 👍

  84. James Corey
    James Corey
    2 napja

    Thank you for this waste of time.

  85. Michael MAnville
    Michael MAnville
    2 napja

    More like insufficient computational ability to prove true, but can never be prove false.

    1. Релёкс84
      Релёкс84
      2 napja

      Absolutely nothing to do with "computational ability"

  86. Boysfifa010
    Boysfifa010
    2 napja

    What does it say about me that i read the title as "Meth has a fatal flaw" ??

  87. Furqan Siddiqui
    Furqan Siddiqui
    2 napja

    That's the reason I love watching this channel. It forces me to "THINK"

  88. James White
    James White
    2 napja

    I don't know if there is truth to be found studying mathematics, but there is much beauty to behold.

  89. Jacob Alexander
    Jacob Alexander
    2 napja

    Godel hurts my damn head. How would you come up with that.

  90. Prototype 81
    Prototype 81
    2 napja

    To say things like "always" or "we will never know" is a fallacy. This is similar to clickbait. Nobody can day for certain what can be or cant be possible in the future. That is a simple fundamental of life. So... why is this guy using terms that are incorrect?... What else is he invorrect about. Why trust this guy on anything when hes obviuosly romancing the structure.. Lame.

  91. Mr Blue
    Mr Blue
    2 napja

    1 + 2 = 4

  92. János TÓTH
    János TÓTH
    2 napja

    Lobachevsky and Bolyai, Gauss is at most the third.

  93. kamahll goodarz
    kamahll goodarz
    2 napja

    Perhaps maths really is the language of reality in so much as they are both paradoxical

  94. Solar Plexus
    Solar Plexus
    2 napja

    I knew it.. Remember "Computer Code Discovered In Superstring Equations" ?

  95. Galina Zwerlein
    Galina Zwerlein
    2 napja

    We don't know what we don't know.