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Math Has a Fatal Flaw

Veritasium
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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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2021/05/22

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コメント数 40 791
Nightangale
Nightangale 2 分 前
Mathematics, we have a paradox. Engineer; does it solve an issue? no? then it doesn't exist
JsonFt
JsonFt 12 分 前
1. thanks! i've finally understood the halting problem
Samuel Eddy
Samuel Eddy 38 分 前
I am going to divide by 0. That is the joke.
Swinison Hudson
Swinison Hudson 時間 前
I have a couple of questions. If one infinity is larger than another then the smaller can no longer be infinite or you have converted a concept into a number? If you can do the diagonal on one side then why can't you do the diagonal on the other side? I am also not entirely certain the universe gives a stuff about sets but they are a helpful crutch for us.
Alan Tew
Alan Tew 時間 前
A doubt on Cantor's diagonalization proof: Since 0.999999.... and 1 are different representations of the same number, how sure are we that the number gotten from the diagonalization process is not actually the same number as one of the numbers in the list but just a different representation of the same number?
Alexander Shamov
Alexander Shamov 31 分 前
Cantor's argument isn't really about numbers, it's about sequences of symbols.
Double Dragon
Double Dragon 2 時間 前
Goedel's proof is stupid. He didn't have to come up with such a complex mathematical house of cards to then postulate one axiom that is self-contradictory. He could have started with the self-contradictory statement and ended there. But of course, that wouldn't seem nearly so impressive! They did it on Star Trek when they caused the robot to self-destruct with the statement, "I am lying."
IsaacIsOk
IsaacIsOk 3 時間 前
this is like the fourth time ive watched this video and i still dont understand it at all but its still really cool.
Srividhya1 Raman
Srividhya1 Raman 5 時間 前
I'm kind of interested in the different infinities explained.
Mahbub Rahman
Mahbub Rahman 5 時間 前
Thank you for the video. Love your content always! will you please add the title of the video in description if you didn't use the clickbait ?
Raphael Zwander
Raphael Zwander 5 時間 前
If you abandon a book, later it will die. xD (13:26)
Surreal
Surreal 6 時間 前
and so this is also sort of why discrete mathematics and propositional Calculus/Logic exists, ands how it sort of ties into everything. interesting
Paulo Jose Castro
Paulo Jose Castro 6 時間 前
everything is a hack, everything is unstable, we just make it work somehow and hope it doesn't break
infosphere
infosphere 7 時間 前
Bro we are living in simulation :p
Bobster Clause
Bobster Clause 7 時間 前
9:25 I just can't help but laugh when the must starts. After the paradox, that classical music is so fitting. "rf r is a set that doesn't contain istelf, and it contains itself, it must contain itself but if it contains itself, it must not contain itself' du du du du dudu du du dududud dudududud dududuudududududududud
F F
F F 7 時間 前
It is not a “fatal flaw”. You just don’t understand enough about mathematics to know what’s going on. Too gay of an explanation.
Griffin Grinnell
Griffin Grinnell 7 時間 前
There is no spoon
Jacob Opstad
Jacob Opstad 8 時間 前
"There will always be statements which are true but cannot be proven" sounds like one of those statements.
Jesse
Jesse 8 時間 前
So math is only consistent for a specific frame of reference, and each bit in Turing's machine is an independent frame of reference?
Dlogs
Dlogs 8 時間 前
I didn’t understand a bit it was amazing video
Alex Tuduran
Alex Tuduran 8 時間 前
This has to be one of your best productions. It was like I didn't watch a math youtube video, but went on a historical ride that tied together things I knew, but never thought they're so deeply interconnected. I learned about Gödel in a course about logic, I came to know the Turing Machine in a compilers course, I learned about von Newman in a "computers architectures" course and found out Hilbert because I read weird Wiki pages I don't understand, like the Hilbert Spaces or the Z Transform, but nobody managed to depict a connection between these geniuses for me until now. Your work is amazing. Keep it going!
Georgy Tarasov
Georgy Tarasov 8 時間 前
(18:38) Здесь ошибка. Доказательство где 1 не равно 0 , имеет и обратное доказательство, где 0 = 1. Доказательство следующее... . Если вы разложите числа на числовой прямой от 0 до любого числа, допустим 9 и замкнёте её в циферблат подобно часам, а затем сотрёте цифры и вместо них просто поставите счётные палочки (единицы), то выясните, что складывая по одному каждое деление покажет, что каждая цифра будет прибавлять единицу, включая цифру " 0 " . Каждое деление это цифра, по этому цифровая шкала не может начинаться с ноля, она может начинаться только с единицы. Ноль придумали дураки. От ноля и проблемы. Не просто так в древности числа начинались с Бога 1- раз = Ра-Аз.
Md Fahim
Md Fahim 9 時間 前
🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵😵🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙄🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂🙂
Laxman Neupane
Laxman Neupane 9 時間 前
Maths is invented. Since Maths seems to underlie almost everywhere we go & it is considered a mystery as to why, intuitively I think the implications are - All of what we see is just an illusion & that's why another rational illusion explains the illusion deeply. Now, how do I start working on this!
MrBastard
MrBastard 10 時間 前
Hilbert: "So, math is Complete-" Godel: "Actually Mr.Hilbert..." Hilbert: "... At least, mathematics is consistent" Godel: "To be fair, Mr.Hilbert..." Hilbert: "OK THEN MATH IS, AT LEAST, DECIDABLE!" Turing: "... I'm so sorry Mr.Hilbert..."
jim Parr
jim Parr 12 時間 前
...airline ticketing systems... Love that TIC addition.
Zenpai
Zenpai 13 時間 前
I keep coming back to this video monthly and it just doesn't get less interesting.
Jason Wood
Jason Wood 13 時間 前
Very first example is a set of two left shoes XD
Natsco
Natsco 13 時間 前
Another great video is a video by vsauce called "how to count past infinity"
The doctor Jobabyjo
The doctor Jobabyjo 15 時間 前
conway did die from influenza. a poor made german fake test did show covid to sell a vaccination. old story...
Borislav Mitev
Borislav Mitev 15 時間 前
about the card "g" - the statement that "there is no proof for the statement with Godel number g", doesn't mean that there is no proof at all, in fact there is at least one, which roughly should be something in the line of "in a set of proofs there is at least one proof that can't be proven with any other members of the set", or in other words while that proof can't be proven by any other members of the set, being part of that set proofs that it can't be proved! So it should be the set itself that holds the proof for that unprovable by the other members of the set proof!
[AnRuBe] presents
[AnRuBe] presents 15 時間 前
14:20 But is math related to science?
WP Randall
WP Randall 11 時間 前
It's considered to be a science in itself. It's of course used in other sciences.
Danny Thunda
Danny Thunda 15 時間 前
A quantum computer could solve any of this i would assume
Nolan Reach
Nolan Reach 16 時間 前
Isn't barber can shave himself "once" and only after he did so.... he no longer can do it again? Sort of that you can find the proof to "g card" after you derived it you no longer can do it again?....
W. T.C.
W. T.C. 16 時間 前
Why am I watching this before my math exam💀
Marc Alampi
Marc Alampi 17 時間 前
Call me crazy! The answer to Math is infact art, an absence of continuous looping and a randomness. That in itself is the answer.
Julie Jane Smith
Julie Jane Smith 17 時間 前
First sentence: I’m a GENIUS! I could have told you this in 7th grade! I’m a mathematics GENIUS!
Samuel Clemens
Samuel Clemens 18 時間 前
It should be mentioned, the Turing machine can have more than binary numbers
Kris Osterhout
Kris Osterhout 18 時間 前
This is a truly incredible video. It is impactful in more ways than I can realize.
ifonlyurmum
ifonlyurmum 19 時間 前
Wouldn't "Diagonalization proof" be a paradox? Because in the spirit of this video, it would be a theory and there would be no way to actually prove the 'new' real number doesnt already exist in an infinite list.
jameson44k
jameson44k 10 時間 前
@ifonlyurmum I understand the video's contents very well, thank you. You, on the other hand, have taken an entirely wrong message from it. What Gödel's incompleteness theorems mean is that for any set of axioms there are consistent propositions that can't be proved by those axioms. It doesn't mean that any question in mathematics involving infinity is unprovable. Cantor's diagonal argument, infinite sets, the cardinalities of natural numbers and real numbers and so on are some of the basics of set theory, a branch of mathematics considered foundational to modern mathematics.
ifonlyurmum
ifonlyurmum 11 時間 前
@jameson44k have you watched this video? It clearly explains there is no possible way to prove something in an infinite puzzle, you can't apply logic to infinite
jameson44k
jameson44k 11 時間 前
@ifonlyurmum Yes I can, and I just showed you how. There is a logic here, follow it. The new real number is, _by construction_ , different from _every_ real number that is enumerated on the list. There is no way it can already be on the list. Furthermore, you can obtain more numbers like this from the diagonal - an infinitude of them.
ifonlyurmum
ifonlyurmum 11 時間 前
@jameson44k But you cant prove that, on an infinite list, that number doesnt already exist
jameson44k
jameson44k 12 時間 前
The new real number obtained from the diagonal provably doesn't exist on the list of real numbers enumerated by natural numbers, because it is, by construction, different from every nth number (as enumerated) at its nth digit. So if you would object that the new number is already on the list and it's enumerated by n, then we can simply show that the new number is different at the nth digit from the number actually enumerated by n. Since this holds for any n, then the new number cannot and will not be already on the list.
Thomas Murphy
Thomas Murphy 19 時間 前
Is this the proof of God !?
Billy Sharp
Billy Sharp 19 時間 前
This video is dope af
Anan Haque
Anan Haque 20 時間 前
I dont get how the diagonalization thing makes sense
Anan Haque
Anan Haque 20 時間 前
Just cuz one decimal is changed from each number on the list shouldn’t mean that number doesn’t exist on that list. The chance that that specific decimal is on a randomly generated list probably has some sort of small probability to it. Idk I’m an idiot
Nicholas Gordon
Nicholas Gordon 22 時間 前
I like the video but I got lost with the gudole numbers stuff
Sophia Schier-Hanson
I had no idea that actual legit mathematics could resemble numerology weirdness to this extent! Nor that the philosophical bedrock of Enlightenment science and rationality rests on... faith. Nor that any of this could be so... Lovecraftian. The idea of the entire postwar era and Information Age being based on attempts to study Things Man Was Not Meant to Know seems far, far too true these days. Whoa.
Sasha R.S
Sasha R.S 日 前
weird place to ask but i thought someone might be able to help me does anyone know a good place to find math papers?
Siliconius Antogramaphantism
What truly boggles my mind about the game of life within the game of life clip? It's that the display of the game of life, within the game of life, on a digital screen that uses the game of life within a game of life pixilated algorithm to create its graphical display. I am truly humbled by this.
HawkFest
HawkFest 日 前
Before both wars... It would be nice to have an episode about Charles Babbage: he was the very 1st to design the main architectural elements of a "modern" computer, although the technological limitations of his time (required precision etc.) only allowed him to put it on paper.
AuthorRoy
AuthorRoy 日 前
29:44 I'm just looking at it at a glance, but, it would seem to me that the pattern and direction it's moving in at the macro scale and micro scale is identical. Is it perchance, not just running itself...but, running iself... *running itself?*
Floyd 957
Floyd 957 日 前
I keep reading 'Meth has a fatal flaw'.
Ismam Sakib
Ismam Sakib 日 前
I found this so beautiful
Mayank Raj Singh
It's the THIRD time in one day that I have clicked on a video of yours that I have already seen. It's really sad that creators like you are also forced to follow the CLICKBAIT methods. I wish we will see a day when Varitasium - The Element of Truth will rise above this. :)
ToT
ToT 日 前
The best part is you made this understandable good job
Joe C
Joe C 日 前
I find this concept deeply unsettling. Also, if Godel really did starve himself to death because he believed someone was trying to kill him with poison in his food, that is somehow a fittingly paradoxical death.
James haren
James haren 20 時間 前
Yea I think he..like alot of mathematicians, scientists, and physicists through out history..spent too much of their brain power for too long dedicated to purely logical and esoteric thinking...we evolved for Malinia not realy doing much of that at all..it has realy only been post Renaissance that we have seen individuals doing this..I don't think, in extreme examples, that this is good for mental health and human psychology..there's just so many examples of brilliant people like this exhibiting obviously ubsurd and destructive behavior..espicaly once past middle age.
Muhammad Aamir
Not to mention that Georg Contor was afflicted bipolar disorder and spent his rest of life in sanatorium
Richard Oakley
I just want to know if that was snow blowing around and he was inna short sleeve shirt, or just something else blowing around?
Muhammad Aamir
Why godel was doing that all mess when there is already zero equal zero
Travis Beard
Travis Beard 日 前
Mtg ftw
Magnus Jonsson
There is no such thing as complete infinite list.
Poli Alte
Poli Alte 日 前
W wwe wa
kimber Lee
kimber Lee 日 前
Turing saved the world from the Nazis and they still couldn’t give the guy a pass for being gay… the most diabolical injustice the British could have enacted for that man.
Joshua Vander Plaats
Duality is a bitch! An age old, unsolvable, problem this side of Saturn. Knowledge is the study of division. Wholeness is the study of religion. And the two are diametrically opposite each other, but each have their place along the great circle. What is sad is that these two fight with each other and cause us all to suffer here.
N1K0
N1K0 日 前
Think my brain died
Brian Oxley
Brian Oxley 日 前
One of the best things I have ever watched on JPvid
Binary Finery
I coded Conway's game of life for Android
Jorge Sanchez
Isn’t Cantor’s proof of larger infinities a paradox of self reference? The initial assumption that the two infinite sets can be paired up is like saying that something undecidable is decidable i.e that the pairing of the two infinites sets does halt. After the initial assumption, the proof uses self reference of the initial set of real numbers to “prove” that there is a number not in the set. But how can the proof self reference a set that never halts (i.e. never finished generating in the first place)?
Arjan Groenewoud
Godel showed that deciding that something is true, is a function of the mind. And it proofs that thinking is something that will never be understood as coming out of something else then thought itself...not material, not energy, not the absolute etc...as Sartre says: selfcon is not a being, but always something evolving... Thinking is something humans do, to evolve them to be free and do more and more love in the process....how strange it would be, that something like that a computer could do... if you reduce humans to some atoms and energy you will never understand...and make moral progress. you stay in an infinite loop😃
Sean Kiely
Sean Kiely 日 前
This is a great episode thank you very much
Sean Parker
Sean Parker 日 前
I wonder what % of the people who heard that misunderstood the last concept and pooped their pants.
Jay Pierson
Jay Pierson 日 前
Amazing that you can say 0:40 and then say 1:13 with such confidence.
katzen kampf
katzen kampf 日 前
this entire video is when the teacher tells you to show your work, and you somehow do a long string of wrong math to get the correct number and get failed anyway
Sally Fontenot
Oh for Gawds sake STOP!!!! You are making my head hurt!!! I'm still trying to figure out if daylight savings time is based on Pacific Time, Central Standard time, Or Eastern Standard Time paradoxes!!
jjiacobucci
jjiacobucci 日 前
Enjoyed this presentation immensely
Texas NightOwl
Religion is good...the way they caused the death of a good person. Nothing much has changed if they are of one party.
Texas NightOwl
Amazing how JPvid auto-censures that if Christian is used instead of Religion. No freedom speach in the USA.
Luis Torres
Luis Torres 日 前
I’m very dumb but.. doesn’t it means that decimal system is wrong to start with?
Scoops
Scoops 日 前
Thought it said meth
Andrew Timothy
What I hate about math so much is how 90% of these complex questions like the Barber paradox can be solved with common sense.
james hallam
james hallam 日 前
I see a error with the diagonal proof eventually it would fail, if you had the list of all numbers between 0-1, and go down it diagonally, what happens when you reach 0.14, or any number like that,
Jon Mendez
Jon Mendez 日 前
We wished the Universe was Euclidian. But it's not. It's Fractal.
Aqua Dog
Aqua Dog 2 日 前
I wonder what Poincare and Herbert would've thought of today's Crypto and NFT and DeFy protocals
эмрмр р гсррач
Amazing video, thank you, genius!
Grim Reaper
Grim Reaper 2 日 前
From very young age it bothered me why if you devide something by 0 you will get 0. But if you try to devide an apple in real life by nothing then you will still get 1 apple.
MilkJug
MilkJug 2 日 前
Now that's a good ol' number
iworkforwendys
iworkforwendys 2 日 前
it's ignorant to believe that we have completed math, our accomplishments are so underwhelming.
Alvaro Lozada
Alvaro Lozada 2 日 前
most beautiful of your videos!
bace cern
bace cern 2 日 前
Universe is expanding faster.. mybe thats why?
Yi Juan Huang
Yi Juan Huang 2 日 前
243000000
M Koushik
M Koushik 2 日 前
Mathematics has always been a mystery to me. I could not watch the full video because my brain is overloaded and I feel lost. But our mathematical system is flawed. We have so many paradoxes and there are negative numbers. How does one describe a negative number in real life? I don’t think we’re allowed to say “I have -1 apple.”
Anthony
Anthony 2 日 前
Principia Mathematica... PrinSippia... not PrinKippia.
Doppler Vocals
Doppler Vocals 2 日 前
I’d say it’s an undefinable ‘yes’
Marc Matta
Marc Matta 2 日 前
I just watched a 34 min long video and didn’t understand the last 35 minutes
Paul Miller
Paul Miller 2 日 前
There is no countable infinite list anyway. Georg Cantor spent his last 20 yrs in a mental institution.
Noel Lundström
Noel Lundström 2 日 前
Sure there is, this is math not science. The set of natural numbers is a set because we say it is.
Daniel DeFelippis
My takeaway from this video is that math is just about finding the smartest way to say "we don't really know what we're doing here"
matthew wringer
matthew wringer 2 日 前
Perhaps I'm just confused at the moment by undecidability, or is the output of H+ decided already, as it will always have the same answer?
matthew wringer
matthew wringer 2 日 前
I do believe I already corrected myself, but I would like to hear other people's opinions
jarrod mcdonald
jarrod mcdonald 2 日 前
You can’t prove anything, you can only believe. It’s not just mathematics, it’s literally everything. You can’t even prove if you’re real or not. All you can do is believe the Word. Card “G” stated there is no proof for card “G” then believe it. If Jesus is the Word as he claimed and all he ever asked any of us to do is to believe Him then we should. “In the beginning was the Word” …and it still is.
Rapid Foal
Rapid Foal 2 日 前
This entire video sounds like a big word salad.
Noel Lundström
Noel Lundström 2 日 前
@Rapid Foal Yes, he didn't explain it particularly well. But you can just think of a turing machine as an algorithm for doing something. If a computer can do it then a turing machine can do it.
Rapid Foal
Rapid Foal 2 日 前
@Noel Lundström he lost me at Gödel. Let's make words equal numbers, the numbers equal letters and then say g can't prove its proof is false or true...... Then the Turing machine. It looks for a 1 or zero, it can change it, move left or move right.... does it just run at random? What are the instructions? Either I missed something or he didn't explain it very well.
Noel Lundström
Noel Lundström 2 日 前
To someone who doesn't know anything about mathematics. Yes, it's a word salad. Derek didn't really do the best job explaining.
zhemful
zhemful 3 日 前
This is the first time in my life I've enjoyed a JPvid comments section. PS: is that an iron ring? I graduated from Queen's with a BSc in computer engineering in 2010.
Leke Osmani
Leke Osmani 3 日 前
Wouldn't the H+ machine first realize that it never halts, as it is in a never ending loop, and then realize that it should halt because it never halts. Therefore, the H+ machine would first be in a never ending loop and then would stop realizing that it is in that loop. Therefore, the main component that is missing from whether or not the Mathematical decidability of a contradiction is decidable is consciousness. Therefore, adding another variable into the mix of mathematics, consciousness itself, would create an endgame for all these contradictions. The H+ machine in this video shows that it is undecidable, but it presumes that it either comes out with one answer or the other. It becomes a sort of Schrodinger's cat, constantly in a flux of "Halt" and "Never Halts". By adding consciousness into the equation we can realize that it can "Never Halt" therefore it should "Halt". To explain my thoughts on this matter more clearly, let's take a look at the barber contradiction. All men in the village who do not shave themselves must be shaved by the village's barber. The barber himself does not shave himself and so he must be shaved by the village's barber. But is this is a contradiction. I do not think that it is a contradiction, I shall explain my reasoning in the next paragraph. 1. Firstly, the barber barber has a beard and he has not shaved himself. 2. Therefore, he must be shaved by the village's barber which is himself. 3. So, the barber picks up the razor and is now shaving himself because a man who does not shave himself must be shaved by the village barber. 4. He is now shaved. 5. He now does not need to be shaved by the village's barber because he shaves himself. 6. Therefore, he can now shave himself because he shaves himself and does not need to be shaved by the village's barber but that does not mean that he cannot be shaved by the village's barber. 7. Therefore, no contradiction. If the Village Barber is denoted as "V", and he himself is denoted as "A", all the other men in the village that do not shave themselves are denoted as "B" and all the men in the village that do not shave themselves are in the set "1". Then, set "1" contains "A" and "B" and "V". When "V" shaves "A" then set 1 no longer contains "V" and "A" and only "B". Therefore, until the moment in time that "V" shaves "A" they are in the same set, upon completion of the action the set itself no longer contains both of them. Therefore, it can be seen that time, space and reality are not being precisely conveyed in these contradiction theories and therefore I do not agree with Goudel and these claims that Math is flawed. I think the realization that Math is directly involved in reality, in conscious thoughts and in the physical world which make up the complete reality, allows us to realize that the way we currently see Math is flawed rather than the Math itself. :D
oooBASTIooo
oooBASTIooo 日 前
No, you got it wrong. The assumption is that the machine H outputs, whether the input machine halts or not. H itself *always* halts. H+ simply goes into a loop, whenever H says, the program it read would halt. So, if you input the code for H+ into H+, the result that H produces will always be wrong..
Alive_Twice Dead_once
~in just about every example you mentioned, the common thread is the reality on a finite mind not being able to know all of the infinite. Obviously, every mathematical exercise that runs out into infinity will then cause you problems when you ask about what happens in regard to the unobservable infinity with no set visible pattern. What happens all throughout infinity??? Everything, except nothing.
Pop OP
Pop OP 3 日 前
Everything in life is : True or False ; yes or no ; 0 or 1 ; positive or negative. In this video you are basically saying that false answer exist only because you that a false answer can exist. ''B'' cannot be the Parent of ''B'' . Call that a ''set'' if you want. The only thing you can say is that ''I know that this possibility can be true, but it's just not visible yet. How can we call this math or science ?
Pop OP
Pop OP 3 日 前
I'm still totally addict to you r vids by the way :)
Geoffrey Taylor
Geoffrey Taylor 3 日 前
Fascinating to say the least, and I'm no Mathematician, but surely this Theorem or Analogy didn't need to be taken to all those lengths as we all know if you divide the number 10 by exactly the number 3, you will never arrive at the exact number, as we all know it's 3.33333333333333333333333333333333333333333333 recurring! so the exact answer can never be know or proven written down.
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