Math's Fundamental Flaw

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Veritasium

Veritasium

2 жыл бұрын

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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Executive Producer: Derek Muller
Writers: Adam Becker, Jonny Hyman, Derek Muller
Animators: Fabio Albertelli, Jakub Misiek, Ivy Tello, Jonny Hyman
SFX & Music: Jonny Hyman
Camerapeople: Derek Muller, Raquel Nuno
Editors: Derek Muller
Producers: Petr Lebedev, Emily Zhang
Additional video supplied by Getty Images
Thumbnail by Geoff Barrett
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Пікірлер: 49 000
@rochestephan
@rochestephan 2 жыл бұрын
Ironic that Godel's death was the result of a self-referential paradox: he died in order to not die
@TanyaNirielle
@TanyaNirielle 2 жыл бұрын
This comment deserves more likes
@DebdyutiBiswasdebbisful
@DebdyutiBiswasdebbisful 2 жыл бұрын
Underrated
@042_a_rupamsahu9
@042_a_rupamsahu9 2 жыл бұрын
Woah...
@nDenTzMotionZztrujillo
@nDenTzMotionZztrujillo 2 жыл бұрын
You nailed this comment
@moazz5779
@moazz5779 2 жыл бұрын
This comment is just too good
@lemond1649
@lemond1649 2 жыл бұрын
I don't know why but I love the idea of mathematicians gathered in a room yelling and hurling insults at one another
@viacheslav7870
@viacheslav7870 2 жыл бұрын
"You are proof that one can actuality have a value of zero!"
@sleepybraincells
@sleepybraincells 2 жыл бұрын
@@viacheslav7870 lmao
@siinxx7656
@siinxx7656 2 жыл бұрын
@@viacheslav7870 I'd rather listen to the first 10,000 digits of Pi than some irrational numble like you *crowd commotion intensifies*
@emaanahsansarfraz1940
@emaanahsansarfraz1940 2 жыл бұрын
Hello! How are you all? If anyone needs someone to listen, someone to talk to, or a friend. I am here to talk, listen, and be a friend. I hope you all are safe and well. Know that you are amazing and have rights as a human. I am very sorry for anything that seems bad that may have happened in your life. I want you to know that you are incredible and are capable of wonders. What matters is your inside, not your exterior. Love yourself and cherish yourself. Words cannot explain how astonishing you are. You deserve care, love, and happiness, don't let anything make you feel otherwise. Please have appropriate action for anything that you know is wrong. Anything that seems bad or wrong in your life right now will get better. Please don't do what is wrong, fighting back and harming others will not solve the problem. Please understand that and do the good thing. It will one day come back to you. The people in the world are so much more than what we know about them, not everyone opens up about the beautiful things and acts they have witnessed, not all those amazing doings are acknowledged. Please understand that and know that. If you feel like no one cares about you, know that I care about you. Keep your head up high and never give up! Together, we can be a better community! Stay safe, healthy, happy, kind, understanding, positive and strong!
@rashidabegum9206
@rashidabegum9206 2 жыл бұрын
"You are more irrational than any number I've ever seen!"
@yhwh9778
@yhwh9778 8 ай бұрын
I love how the set theorists answer to self reference was "I changed the definition so that doesnt count."
@dominicbonogofski
@dominicbonogofski 6 ай бұрын
It's like a kid on a playground saying they weren't playing when someone else tags them.
@EonsEternity
@EonsEternity 6 ай бұрын
​@dominicbonogofski i dont feel like thats a valid analogy, theres nothing wrong with going youre right this is a flaw and trying to adjust the rules to fix it. Maybe its just the problem with analogies is that they can also be unproveable though so its also a contradiction based on perspective 😯
@dominicbonogofski
@dominicbonogofski 6 ай бұрын
@@EonsEternity I was just implying that it had the same energy behind it.
@smarchar
@smarchar 6 ай бұрын
this brings up a question: what if the turing machine's answer to haltability was to simply make a new rule: the turing machine cannot accept itself as an input. that would remove the proof against haltability. so does that mean mathematics could be decidable as long as it doesn't self-reference? or does this prove that set theorists were in denial? if neither, then what makes set theory different from mathematics in that in can exclude self-reference and still be useful, while mathematics/turing machines cannot?
@randompersson
@randompersson 6 ай бұрын
​​@@smarchar@dragonsaige I had that thought as well, but then that would eliminate self-reference, which is very useful in answering a lot of questions correctly. At least, that's what my logic led to. I'm just a software engineer with a passion for maths. I could be entirely wrong.
@vgamedude12
@vgamedude12 2 ай бұрын
Everytime people get into the weeds with math like this i feel like im just listening to philosophy with a different label.
@mattiamazzanti8418
@mattiamazzanti8418 Ай бұрын
Philosopher ask a question,Phisicists Turn questions into math
@chetsenior7253
@chetsenior7253 8 күн бұрын
Indeed. Just remember that numbers aren’t real. I mean that in the sense that they are always tied to an object or idea. You can’t go out and find a 7 in nature, you especially can’t find a negative seven.
@shrekeyes2410
@shrekeyes2410 8 күн бұрын
thats because they are philosophers, They are natural philosophers.
@timomen1
@timomen1 2 күн бұрын
people try to take math and turn that crap into philosophy and theory all the time bunch of jerks. Facts are facts life is life. dont even start yourself down the rabbit hole of what people are doing with entropy these days it is very frustrating.
@mafuchin
@mafuchin 2 күн бұрын
PhD student here. Math is applied philosophy. You cannot have one without the other.
@amecha5368
@amecha5368 2 жыл бұрын
So basically... Can math prove itself? No. But math can prove that math can't prove itself.
@Logan-zf1ft
@Logan-zf1ft 2 жыл бұрын
hahahahha good one
@rob_olmstead
@rob_olmstead 2 жыл бұрын
well... you can't prove the rule using a rule because the rule is universal and immutable
@kathanshah8305
@kathanshah8305 2 жыл бұрын
Yesn’t
@Pineapple-hx9ty
@Pineapple-hx9ty 2 жыл бұрын
"math can't prove itself" to the power of -1
@MsHellokitty666
@MsHellokitty666 2 жыл бұрын
I was asking myself the exact same question
@chorian5424
@chorian5424 2 жыл бұрын
mom: why did you get a B in math! me: math has a fatal flaw
@cohensmith6100
@cohensmith6100 2 жыл бұрын
B is good
@ALBINO1D
@ALBINO1D 2 жыл бұрын
@@cohensmith6100 and A is excellent.
@cohensmith6100
@cohensmith6100 2 жыл бұрын
@@ALBINO1D ya but like why get mad abt a b when most mfs fail math
@ALBINO1D
@ALBINO1D 2 жыл бұрын
@@cohensmith6100 is your benchmark just to be better than worst, or to be the best? Learn a lesson from Ash Ketchum.
@cohensmith6100
@cohensmith6100 2 жыл бұрын
@@ALBINO1D Hes like over 20 and hangs with 12 yrs old girls ill pass man
@zedx4749
@zedx4749 5 ай бұрын
So this is how these things are connected to each other. In my CS degree we had to study about almost every one of these topics (at least a very little of every topic) and they seemed very disconnected and apart of each other. Discrete mathematics, Automata, Set theory, proofs... etc. This video connects dots. An actual tear fell from my eye at the end of video. Thanks for making these amazing videos.
@bladr-the-goat
@bladr-the-goat 2 ай бұрын
Me too brother, me too....
@anon1963
@anon1963 Ай бұрын
Proofs are horrible, man
@crismamuerta
@crismamuerta Ай бұрын
😢
@5001Fergies
@5001Fergies Ай бұрын
Fr its so awesome seeing everything ive learned over the years recontextualized into a cohesive story of cause and effect, i wish my professors told me about this connection before 😂
@NVIK5
@NVIK5 Ай бұрын
Weil fell off not tear
@charlesfletcher42
@charlesfletcher42 6 ай бұрын
Why didn't they just have three people stand beside John Conway after he died?
@AndresFirte
@AndresFirte 6 ай бұрын
This is the best math joke I’ve heard in a month
@prabhakarsingh6821
@prabhakarsingh6821 16 күн бұрын
Oohhhhhhhhhh
@1stlullaby484
@1stlullaby484 7 күн бұрын
Give me the reference please 😂
@charlesfletcher42
@charlesfletcher42 7 күн бұрын
@@1stlullaby484 In Conway's Game of Life, 3 living cells around a dead cell make the dead cell alive again so, the joke is that they could have resurrected Conway by having the people (cells) surround him (the dead cell).
@Mike_droptv
@Mike_droptv 12 сағат бұрын
Wouldn't work. They'd have to stand there for a whole generation and everyone's bound to use the restroom at some point 😅
@mikejohnstonbob935
@mikejohnstonbob935 2 жыл бұрын
Godel's friends: "No one's trying to kill you Godel" Godel: "You can't prove that!"
@nbjornestol
@nbjornestol 2 жыл бұрын
He actually refused to eat any food not prepared by his wife. Unfortunately she was hospitalized, and couldn't prepare food for him, causing him to starve to death.
@lavabeard5939
@lavabeard5939 2 жыл бұрын
@@nbjornestol he couldn't prepare his own food?
@segmentsAndCurves
@segmentsAndCurves 2 жыл бұрын
@@lavabeard5939 He was a mathematician (logician) after all.
@kindlin
@kindlin 2 жыл бұрын
@@segmentsAndCurves Does that excuse a man from being able to provide for... himself?
@kimochi5009
@kimochi5009 2 жыл бұрын
@@kindlin It doesn’t excuse, but it explains why he didn’t prepare his own food.
@michaelh4227
@michaelh4227 2 жыл бұрын
Teacher: Your math is flawed. Student: No, math itself is flawed.
@moncorp1
@moncorp1 2 жыл бұрын
dank meme
@inthebackwiththerabbish
@inthebackwiththerabbish 2 жыл бұрын
lmfao
@Scipio_Africanuss
@Scipio_Africanuss 2 жыл бұрын
I’m gonna go to my math teacher and be like “math is incomplete and inconsistent,” and she’s gonna say no it is and then I will now more about math than her and I will be so happy
@inthebackwiththerabbish
@inthebackwiththerabbish 2 жыл бұрын
@@Scipio_Africanuss ahahaha bro let me know what she says 😂
@Rob-cm9jr
@Rob-cm9jr 2 жыл бұрын
@@getonthecrossanddontlookba5004 I assure you math and time are constructs of man, not God.
@axmedazeez
@axmedazeez 6 ай бұрын
Truly one of the greatest mathematics-related video out there on KZbin. I often find myself returning back to this video, and thanks to you, I was inspired to major in engineering. I started loving math; it's such a great language!
@tpbenze5032
@tpbenze5032 3 ай бұрын
It really is and highlights how amazing math is and how useful it is despite its limitations. I think most people would be surprised that our whole modern system of science is built on these grounds, but it works amazingly
@TheAlmightyFather
@TheAlmightyFather 2 ай бұрын
Not to disway you, but if you love math, go to math! Not engineering. As much as math is involved in engineering in a lot of ways, in practice it does not.
@P-39_Airacobra
@P-39_Airacobra 4 ай бұрын
This is actually the MOST interesting video I have EVER seen. Every minute was amazingly clear and intriguing.
@Mackinstyle
@Mackinstyle 2 жыл бұрын
If you're a mathematician and you are labelled a "corrupter of the youth", you are doing something very right.
@TheOOOOOOOOOOOOOOO
@TheOOOOOOOOOOOOOOO 2 жыл бұрын
nerd burns
@Aereto
@Aereto 2 жыл бұрын
@Linus Fu Yet neither can prove nor unprove logical paradoxes. The same way no one figured out why we can pin point an electron's vector and position separately at the expense of the other, and never both.
@deepankurnayantara
@deepankurnayantara 2 жыл бұрын
I watched this video when its title was still "There's a Hole at the Bottom of Math".
@tannerwitt3030
@tannerwitt3030 2 жыл бұрын
@@Aereto wait whaaaaaat
@theycallmealex454
@theycallmealex454 2 жыл бұрын
Exactly. If one proposes a theory or statement that pushes all of our minds to think hard enough, regardless if it's wrong or not, overall it's something right.
@OddNumber1524
@OddNumber1524 2 жыл бұрын
"How about you just hire another barber?" Said the engineer
@Smitology
@Smitology 2 жыл бұрын
And you only need two barbers to break the paradox. They can shave each other; the rules never said that wasn't allowed.
@jamesflanagan6977
@jamesflanagan6977 2 жыл бұрын
Engineering student here, my first thought as well
@jeffirwin7862
@jeffirwin7862 2 жыл бұрын
2 barbers 1 town
@kelpf0rest
@kelpf0rest 2 жыл бұрын
@@jeffirwin7862 IYKYK
@majiachen101
@majiachen101 2 жыл бұрын
@@theknightwhosayn1 only the barber can shave anyone, that was one of the rules
@FeichengLuo
@FeichengLuo 6 ай бұрын
I learn about the Veritasium by watching this video about 2 years ago, and it turned out to be the most valuable 30 minutes that I spent on the internet. Maths became almost religious to me after watching it, for it is capable of proving its own limitations within its limited system, although my father kinda disagrees with me on the religious part as a professional in maths. But there's a reason for me. It actually reminds me of the philosophical question of "what we are" and "what we are made for" since they are also related to the self-reference paradox. I have been suffering from depression and anxiety at the time when I first saw this video. I was about to graduate but had no idea of what I am going to do nor what is the meaning of my life. But this video somehow saved me. For no reason, I suddenly feel relaxed after learning about Godel number and the answer and proof to the three questions. I realized that, just like maths, life is not about meaningful or desidablility either, but we may find what we have done meaningful years later. And this is a proven truth. Just like one of the most famous Chinese poems said, "everyone was made with some talent that must be useful". Anyway. I finally found my own belief after watching this video. And now, after 2 years, I am back to the college for postgraduate degree and for working out my own value of life. Many thanks to Veritasium for the great work. Wish everyone a great life.
@bryantaylor993
@bryantaylor993 2 ай бұрын
Wow! I’m sincerely happy to see that you’ve found your path! Keep it up! …And don’t worry; no religion makes any sense.. if you found something to believe in, charge on!
@captainzork6109
@captainzork6109 Ай бұрын
I've been wondering how numbers relate to life. I'm approaching it from the perspective of psychology, where we often use null hypothesis significance testing and the law of big numbers. We take a group of people, do an experiment, and we check the average. But our phenomenon of interest is the (average) individual, which is different from the group average! Group-to-individual generalizability cannot be taken for granted. The difficulty lies with multiple realizability: -2 and +2 are the same as 0+0. Except for the standard deviation of course, I guess. But clearly, taking averages obfuscates things. Why? Because counting things reduces information. When you say a pair of shoes, or even two shoes, you equivocate two non-identical things. And it is the same for people with depression, who may not even have a single symptom in common with each other. One study which checked "depression profiles" of ~3,000 people found that the most commonly occurring profile occurred 1.4% of the time amongst the ~1,000 different depression profiles identified. Yet, if a study is done on depression, imagine how difficult it would be to test a psychotherapy or psychoactive drugs without being able to refer to depression as a single concept The question is whether mathematics applies to the real world. The answer is obviously still: yes, extremely applicable. Numbers allow us to see patterns in the world, which is an utmost necessary condition for intelligence to work. The way the universe and its objects worked in the past is, at the very least, a really great analogy for the future But might it be possible to describe accurate and precise truths about the world with numbers? The capacity to abstract is fundamental for us to make to be capable to think and talk about the world -- to talk about "depression", without having to mention all the specific cases in mind which represent that concept. Yet, if the utmost of specificity is desired, would that be possible? It would be interesting to see if quantification, or counting, is valid in its strictest sense. Is there any phenomenon in the world which is identical with another (as opposed to merely equivalent), and of which we would therefore not lose any information if counted? Or might every single thing, in its strictest sense, be different from one another?
@LukeRadick
@LukeRadick 4 ай бұрын
I love how tightly intertwined mathematics and philosophy are
@matthewyoung6263
@matthewyoung6263 2 жыл бұрын
"1+1=2" "The above proposition is occasionally useful."
@Jayess-c
@Jayess-c 2 жыл бұрын
What's 3x+1?
@Jayess-c
@Jayess-c 2 жыл бұрын
Or y3X+1 it is impossible to get an answer it's like pi
@kam9910
@kam9910 2 жыл бұрын
@@Jayess-c lol dude they literally made a vid about that, it’s that where you got it from
@Jayess-c
@Jayess-c 2 жыл бұрын
@@kam9910 what are you referring to?
@kam9910
@kam9910 2 жыл бұрын
@@Jayess-c if you were trying to pose it as your own equation you made up, I’m not sure rlly, I’m just 11 lol
@cipherxen2
@cipherxen2 2 жыл бұрын
Mathematicians: we must prove this equation Engineers: Eh, it's good enough, we'll just use it
@mattstokes3881
@mattstokes3881 2 жыл бұрын
bridge collapses
@cipherxen2
@cipherxen2 2 жыл бұрын
@@mattstokes3881 and they learn from their mistakes, and makes better bridges
@MarkAvo
@MarkAvo 2 жыл бұрын
I feel seen
@aloysiusvo318
@aloysiusvo318 2 жыл бұрын
@@cipherxen2 No no no as a civil engineer student u have to prove some math equations to make sure the measurements are right. So idk what tf are u talking about
@deusexaethera
@deusexaethera 2 жыл бұрын
Mathematicians: "We must prove this equation is true in all possible scenarios across all possible universes." Engineers: "Bro, do you even constraints? I only need the equation to be true _on Earth for the next 50 years."_
@xintongbian
@xintongbian 7 ай бұрын
I've known these topics for years and also watched many videos, I have to say this one is so beautifully done, all those thoughtful illustrations
@daimaryjohn
@daimaryjohn 7 ай бұрын
I love you
@emotional.support.goblin
@emotional.support.goblin 8 ай бұрын
Sorry, I'm a little late! 😂 The part near the end, where the game of life was running in the game of life? Wow. That was beautiful. It gave me chills. I'm severely deficient in math, at about a 6th grade level (6th grade in the 80s, not the madness they teach now, I'm so lost 😂) but the abstract concepts, the beauty and art has always fascinated me. Thank you for this video, and all the others on this channel. The way you explain it makes it understandable even to a math dummy like me. ❤
@Tynach
@Tynach 6 ай бұрын
There's a program called 'Golly' that includes a bunch of pre-built simulations like that. Worth checking out, and it runs very fast on even slow hardware!
@benjaminparker5044
@benjaminparker5044 2 жыл бұрын
Ah yes, the iconic half way point of the video where I stop comprehending a single thing said
@chronicles1192
@chronicles1192 2 жыл бұрын
that feeling
@Smo1k
@Smo1k 2 жыл бұрын
Read Douglas Hoffstadter and comprehend even less. In an entertaining way ;)
@SoloPilot6
@SoloPilot6 2 жыл бұрын
If we had had videos like this in high school, I wouldn't have come out of math class convinced that 2 + 2 = CAT . . .
@yash5879
@yash5879 2 жыл бұрын
It is a proof which proves that not everything that is true can be proven after all ¯\_(ツ)_/¯
@akhilaryappatt7209
@akhilaryappatt7209 2 жыл бұрын
it's zone out time
@krissisk4163
@krissisk4163 2 жыл бұрын
"There will always be true statements that cannot be proven." Oh yeah? Prove it. ....He proved it.
@poorvisingh232
@poorvisingh232 2 жыл бұрын
Brains!
@levibyler1132
@levibyler1132 2 жыл бұрын
Plp are to smart
@charlesballiet7074
@charlesballiet7074 2 жыл бұрын
you mean like Epstein not killing himself
@jenidu9642
@jenidu9642 2 жыл бұрын
Proving something is impossible is also a proof
@HerrCookienator
@HerrCookienator 2 жыл бұрын
Dis gave my brain a new wrinkle
@daniela.fagundes1448
@daniela.fagundes1448 4 ай бұрын
I truly believe that this was the most spectular video I've ever seen on this channel! Congratulations to you and your team, Derek!
@blackdwarfrecords
@blackdwarfrecords Ай бұрын
Oh, well done sir. Your closing line here very nearly sent a chill up my spine. Thank you for another well-spent half hour.
@DanielG03
@DanielG03 2 жыл бұрын
Me: *failing my math class* Veritasium: “they could be something like the twin prime conjecture” Me: go on...
@tejasdeepsingh456
@tejasdeepsingh456 2 жыл бұрын
Lmfao
@SoumilSahu
@SoumilSahu 2 жыл бұрын
tbh the conjecture itself is pretty elementary to understand.
@wildanimus2559
@wildanimus2559 2 жыл бұрын
@@tejasdeepsingh456 ditto
@angryyoungman4389
@angryyoungman4389 2 жыл бұрын
@@wildanimus2559 Charizard
@crystalgiddens7276
@crystalgiddens7276 2 жыл бұрын
@@SoumilSahu what is gobbledygook? - In particle physics, a lepton is an elementary particle of half-integer spin (spin 1⁄2) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutral leptons (better known as neutrinos). (fûr′mē-ŏn′, fĕr′-) Any of a class of particles having a spin that is half an odd integer and obeying the exclusion principle, by which no more than one identical particle may occupy the same quantum state.
@mit5oner
@mit5oner 7 ай бұрын
This is top 10 videos of all time. Literally the best explanation ever of one of the most interesting scientific (and existential) concepts.
@user-cw5ob3nd4v
@user-cw5ob3nd4v 8 ай бұрын
As a mathematician I am deeply disturbed but also inspired by this.. This video is actually a masterpiece..
@thepunisherxxx6804
@thepunisherxxx6804 8 ай бұрын
Math is just a tool humans created to understand, predict, and do things reliably in our reality. Math itself isn't a natural concept in and of itself, it simply accurately describes things, but even that accuracy isn't 100% to reality. Why is this video disturbing and surprising? We made this system up entirely. Of course its going to have limits and other constraints around it. People like to think Math is some secret to the universe, but if that's the case its a very very incomplete inaccurate tool if it needs to do that.
@kazikmajster5650
@kazikmajster5650 7 ай бұрын
As a mathematician, you should have already known all this.
@admazzola3569
@admazzola3569 4 ай бұрын
gotta start somewhere ha@@kazikmajster5650
@Alex-02
@Alex-02 4 ай бұрын
@@thepunisherxxx6804The only reason it’s obvious is because the answer has just been handed to you and you’ve come up with a justification after the fact. Try coming up with the proof yourself and see just how obvious it is. It took until the 1930s and a genius to discover this, and at one point, a large amount of mathematicians even thought it was bollocks. This is not obvious stuff.
@thepunisherxxx6804
@thepunisherxxx6804 4 ай бұрын
@@Alex-02 You're putting words in my mouth dude, I'm not saying I could solve th is or discover it, or that its easy. Where did you get that from??? I'm commenting on how math is just a tool and system we invented, and that its "laws" or "constraints" are malleable because of that fact. Even the best equations have wide tolerances and gaps in their accuracy depending on what's being modeled (because its a tool we made up to bring order to our reality).
@temiolu3049
@temiolu3049 2 жыл бұрын
OVER HALF AN HOUR OF CONTENT, youtube> TV any day
@Medan1993
@Medan1993 2 жыл бұрын
and here I am, watching this on TV ;)
@AxxLAfriku
@AxxLAfriku 2 жыл бұрын
WOAH WOAH WOAH!!! Let me get this perfectly straight: You comment something that is completely unrelated to the fact that I have two HAZARDOUSLY HOT girlfriends? Considering that I am the unprettiest KZbinr worldwide, it is really incredible. Yet you did not mention it at all. I am VERY disappointed, dear te
@LeventK
@LeventK 2 жыл бұрын
@@AxxLAfriku Are you OK?
@nothuman5335
@nothuman5335 2 жыл бұрын
@@AxxLAfriku what
@halfblood7
@halfblood7 2 жыл бұрын
@AxxL Some types of madness are beyond the limit of infinity
@emilyrln
@emilyrln 2 жыл бұрын
"19th century mathematicians HATE this one weird trick!"
@gmarais1986
@gmarais1986 2 жыл бұрын
Haha when will those ads stop being a thing? Gödel would have known
@splifstar85
@splifstar85 2 жыл бұрын
Funny thing is Henry Pointcare seems to be a formalist at heart, as he claimed “later generations would have recovered from the disease” - meaning maths is Complete, Consistent and Decidable.. since he was sure that there would be a system that could with certainty disprove Canter 😏🤷‍♂️
@billrich9722
@billrich9722 2 жыл бұрын
Oh, look. A meme.
@FlyoviaUSA
@FlyoviaUSA 2 жыл бұрын
You won't believe what Kurt Gödel looks like at age 115!
@Jnglfvr
@Jnglfvr 2 жыл бұрын
Comment of the year.
@ZZ-sn7li
@ZZ-sn7li 6 ай бұрын
This is the only KZbin subscription channel you need... Can't get enough. Thank you so much.
@ogieomorose3628
@ogieomorose3628 Ай бұрын
This channel teaches the basics so easily. When explaining something such as complex numbers, they go into the most basic foundations, akin to explaining an organism from the level of quarks and gluons as opposed to the conventional educational system which just tells properties outright. Brilliant chose an awesome channel to sponsor
@tlewis84able
@tlewis84able 2 жыл бұрын
I can’t decide if I’m smarter or dumber after watching this.
@cjc722
@cjc722 2 жыл бұрын
The smarter you are, the less you know
@YavNe
@YavNe 2 жыл бұрын
@@cjc722 The smarter you are, the more you know. But the smarter you are, you know that you know less.
@janmango4692
@janmango4692 2 жыл бұрын
@@YavNe This is at the core of the Dunning-Krugereffect.
@joaogabriellucas1865
@joaogabriellucas1865 2 жыл бұрын
You are both, that's the lesson 😉
@Ou8y2k2
@Ou8y2k2 2 жыл бұрын
Both; it's a paradox.
@anthead7405
@anthead7405 2 жыл бұрын
Gödel was also first to ask P vs NP question and he asked it in the letter to John von Neuman. Those dudes had some world changing conversations.
@batfan1939
@batfan1939 2 жыл бұрын
Was waiting for P = NP after The Halting Problem. Maybe next time.
@enemdisk6628
@enemdisk6628 2 жыл бұрын
Nice
@DavidLiMusic
@DavidLiMusic 2 жыл бұрын
Veritasium needs a video on P vs NP! Would be amazing.
@pvic6959
@pvic6959 2 жыл бұрын
meanwhile me to my friend: Do you think dogs know theyre adorable?
@codycast
@codycast 2 жыл бұрын
@@DavidLiMusic yeah because there isn’t enough n/np out there
@MidNightStudiosFilms
@MidNightStudiosFilms 7 ай бұрын
Wow, this is great content, Veritasium! Sometimes your videos just transcend the brilliant educational films they always are, and become pure art.
@lexslort1437
@lexslort1437 5 ай бұрын
I honestly and wholeheartedly believe this is the best video this platform had ever seen. I share it often with my students. Derek, Amazing work and Thanks.
@tuomasronnberg5244
@tuomasronnberg5244 2 жыл бұрын
"Later generations will regard set theory a disease", "No one shall expel us from the paradise that Cantor has created" Those dudes felt *really* strong about abstract maths back then.
@Kabup2
@Kabup2 2 жыл бұрын
It did remember 'God don't play dices' from Einstein.
@JonathanHuertayMunive
@JonathanHuertayMunive 2 жыл бұрын
you might want to read mathematicians debates nowadays... nothing has changed
@abhisheksoni2980
@abhisheksoni2980 2 жыл бұрын
Later generations are just making tiktok videos.
@DevinDTV
@DevinDTV 2 жыл бұрын
it's not at all surprising that they had strong feelings. they were literally debating how reality works. not just physical reality, but abstract reality too.
@RandomFilmmaker
@RandomFilmmaker 2 жыл бұрын
Pythagoras beat them at their game though
@ArthurBCamara
@ArthurBCamara 2 жыл бұрын
I'm a PhD in computer science. This is a full-on Discrete Mathematics intro course. This is amazing.
@Kirmeins
@Kirmeins 2 жыл бұрын
I never saw much of this in DiMa... most of this I picked up somewhere along the line and often in the actual CS introductory courses or while trying to understand more basic concepts using YT. Only to be distracted by that one video on the side called "The halting problem" or some such and getting curious. :D
@ltu42
@ltu42 2 жыл бұрын
Right on! A semester of DM in one video.
@camrouxbg
@camrouxbg 2 жыл бұрын
@@Kirmeins Yeah, thing is that DM is so vast that it is really easy to set up a course that doesn't touch on any of this material. The DM course I took was like this... introduction to game theory, a little combinatorics and cryptography, coin weighing problems, stuff like that. But I think the important thing is the ability to get students interested in the material, and then they go looking for other courses that cover it.
@sanjarcode
@sanjarcode 2 жыл бұрын
I agree, this is also the key for appreciating the role of AI/ML theory. And randomised algorithms.
@iamtheusualguy2611
@iamtheusualguy2611 2 жыл бұрын
I had this in my theoretical CS module more than the discrete maths one and while I hated the exams and the assignments, I thoroughly enjoyed getting my mind blown by such a profound topic. I've never thought that we actually would go into deeply philosophical questions about the fundamentals of logical systems, truths and math itself while studying computer science. And how it all connects to computers in the end. Brilliant video, it creates this amazing feeling of profound enlightenment I had when I first encountered this topic and I hope it reaches as many people and blow people's minds just like it had mine.
@baronblair5811
@baronblair5811 7 ай бұрын
To me this is one of the most influential videos I've ever seen on KZbin. I think this video should be a prerequisite for children to watch in education. Why does this discovery not disturb more people?!
@voidentity4295
@voidentity4295 Ай бұрын
This is so beautiful! Thanks for being one of the people that helped me truly discover mathematics. I grew up hating math, but thanks to mathematicians, physicist, computer scientists and programmers here on youtube i have grown to really love and appreciate the subject.
@TylerJaneBronson
@TylerJaneBronson 2 жыл бұрын
Seeing the game of life running inside the game of life gave me goosebumps. Had to pause for a minute to digest that. Just beautiful!
@sherlockmaverick
@sherlockmaverick 2 жыл бұрын
Where?
@RAMBO14001
@RAMBO14001 2 жыл бұрын
Just like the human dimension...
@Touay.
@Touay. 2 жыл бұрын
@@RAMBO14001 It's simulations all the way down ....
@Alex_Hetherington
@Alex_Hetherington 2 жыл бұрын
So wait... if the camera kept zooming out on the game, it would continuously be simulating itself?
@GaganpreetSinghKapula
@GaganpreetSinghKapula 2 жыл бұрын
Same feeling 🤩
@J_Stronsky
@J_Stronsky 2 жыл бұрын
7:49 - 'corrupter of the youth' haha "Hey kids come here, you want to learn about some illicit infinities"
@igorswies5913
@igorswies5913 2 жыл бұрын
wanna learn how to divide by zero?
@tilakmehrotra
@tilakmehrotra 2 жыл бұрын
Noooooooo
@mischief9499
@mischief9499 2 жыл бұрын
lmaoo
@bujfvjg7222
@bujfvjg7222 2 жыл бұрын
illicit infinities are creations of the universe, just like ourselves.
@TheJanitorIsIn
@TheJanitorIsIn 2 жыл бұрын
Socrates back from the dead
@tetraphobie
@tetraphobie 4 ай бұрын
This is a fantastic video and the best explanation of Godel's incompleteness theorem. 👍 👍 for showing how it relates to the halting problem, too. I wish I had access to your videos back when I was in college trying to study engineering. I find them truly inspirational.
@Chasedoessolaratx
@Chasedoessolaratx 8 ай бұрын
Thank you so much for you video. The soft and friendly presentation helped me to hang in there until the end. You articulated a lot of what I suspected-that at the heart of the way math is practiced is the flawed belief that if we just work it out until the end, we'll have a pretty, perfect answer. I think it's why I feel so hostile overall to Newton and his systems, despite him being undeniably brilliant. I never thought I'd say this EVER, but your video makes me want to learn more and maybe even DO and practice some math myself! Thanks again!
@shubashuba3978
@shubashuba3978 2 жыл бұрын
Godel really woke up and said "i'm gonna ruin this man's whole career".
@Kirmeins
@Kirmeins 2 жыл бұрын
He failed... I mean... I've heard Hilbert's name propably a thousand times but this video felt like the first time I heard about Gödel. And I'm from Germany... :D
@guifdcanalli
@guifdcanalli 2 жыл бұрын
@@Kirmeins its a joke my dude
@bibi1338
@bibi1338 2 жыл бұрын
That's probably because you're from Germany and Hillbert was german. I'm from Austria and I heared about Gödel way earlier and lot more than Hillbert.
@DonVigaDeFierro
@DonVigaDeFierro 2 жыл бұрын
Gödel could have nuked the basis of formal logic, for all I understand.
@camrouxbg
@camrouxbg 2 жыл бұрын
@@Kirmeins even if you're only studying mathematics, you won't really hear Gödel's name until final year of undergraduate study at the earliest, unless you do an awful lot of advanced reading. Hilbert, on the other hand, has his name scattered throughout undergraduate and graduate topics in mathematics and physics. Gödel's work is considered fairly esoteric and difficult, while Hilbert is more spread out. So it's not surprising that you wouldn't have heard of Gödel if you haven't touched on foundations of maths.
@elchingon12346
@elchingon12346 2 жыл бұрын
“1+1=2 The above proposition is occasionally useful “ I need this on a poster for my classroom 😂😂😂
@PiotrKaszuba8403
@PiotrKaszuba8403 2 жыл бұрын
😂
@sdgathman
@sdgathman 2 жыл бұрын
“1+1=2 The above proposition is occasionally useful “ It's also racist. smh
@LIGHTISBURNING
@LIGHTISBURNING 2 жыл бұрын
So trueee
@ccgarciab
@ccgarciab 2 жыл бұрын
@@sdgathman "I proudly and loudly misunderstand things"
@DevinDTV
@DevinDTV 2 жыл бұрын
@@ccgarciab sounds like you weren't aware that math and logic are constructs of whiteness which inherently oppress people of color
@jasonevans4970
@jasonevans4970 4 ай бұрын
When you put it like incompleteness it sounds negative, but I think that the fact that mathematics is essentially endless is incredibly hopeful, when viewed as a human activity.
@Zenovarse
@Zenovarse Ай бұрын
I mean when you view it that way then a theorem can absolutely be complete and consistent and decidable. A system that assigns true to every statement in inherently complete and consistent and decidable. Even a system that assigns the value to be an oracle that is possibly obtained tomorrow is consistent and complete and decidable - all undecidable problems are simply deferred.
@Zenovarse
@Zenovarse Ай бұрын
All Gödel proves is the symbols not, and, or, sets and whatever logic used to manipulate those are incomplete.
@MindForgedManacle
@MindForgedManacle 20 күн бұрын
@@Zenovarse Well, not quite. Basic logical systems of propositions are complete. But once it's got the machinery to encode number theory then yeah.
@Zenovarse
@Zenovarse 20 күн бұрын
@@MindForgedManacle WDYM? If you write your logical system as propositions in your logical system, Gödel shows either it will not be complete or not consistent?
@Zenovarse
@Zenovarse 20 күн бұрын
@@MindForgedManacle a kind of a trivial system that works is a system that has 1 statement, corresponding to the system validity is true. But in a non trivial system like the ones we use it is not the case?
@johaanvinaysingh7898
@johaanvinaysingh7898 Ай бұрын
I admire the fact that you take concepts and bring it to life. Taking us on an adventurous journey making it more fun. You really brought my intrust in science back I had took a break but coming back here after a year feels great. Great work! Nice explanation on how math is incomplete and inconsistent and how a turing machine program with binary code makes it different.
@alexander1989x
@alexander1989x 2 жыл бұрын
When he showed "It's the Game of Life... running on the Game of Life" it literally blew my mind.
@ritwikism
@ritwikism 2 жыл бұрын
Can someone explain that better? It was cool but I think I don't fully comprehend what is happening
@amineabdz
@amineabdz 2 жыл бұрын
@@ritwikism he put an input in the game of life that it's output, instead of random patterns, was the game of life itself.
@guack1453
@guack1453 2 жыл бұрын
@@ritwikism they basically built a computer on the game of life that runs the game of life
@cookiecan10
@cookiecan10 2 жыл бұрын
@@ritwikism Since the Game of Life is Turing complete, that means you can essentially program anything with the Game of Life. At 29:50 they zoomed out to show how someone had programmed the Game of Life inside of the Game of Life. The idea is somewhat similar to simulating a computer on a computer, like a macbook running a virtual machine of that same type of macbook.
@ProfezorFirdaus
@ProfezorFirdaus 2 жыл бұрын
@@cookiecan10 hence going back to Derek's first answer: Life. If life is turing complete (which it must be), there must be a way to fully simulate itself
@judypetree2589
@judypetree2589 2 жыл бұрын
I'm 75, female; I am grateful that I have had enough education to have at least heard of the people you reference. Awed that you explained it all so well that I could not stop listening. Lastly, so proud to have lived this era from beginning to undecidable end.
@carealoo744
@carealoo744 2 жыл бұрын
I get my education from youtune videos:)
@kebekbutcher
@kebekbutcher 2 жыл бұрын
@@carealoo744 Self education is better than forced education! Have a good day!
@palashrajput428
@palashrajput428 2 жыл бұрын
@@kebekbutcher well said
@scoogsy
@scoogsy 2 жыл бұрын
So awesome to have people of all ages getting so much from these videos. I’m 38 and make, and have watched Ve videos for what feels like a decade.
@oreoicecream1829
@oreoicecream1829 2 жыл бұрын
I hope you live long and healthy 🙏❤️👍
@rafaelubal
@rafaelubal 6 ай бұрын
Amazing video. I'm very impressed about the quality of this content; through and deep, yet approachable. Congratulations.
@wojciechlawniczak645
@wojciechlawniczak645 6 күн бұрын
The quality of this documentary is astonishing. I wish I had access to such materials as a kid, actually I felt like a kid again for over 30 minutes
@steelfirebladez1081
@steelfirebladez1081 2 жыл бұрын
Mathematicians: “I used the math to destroy the math”
@hisxmark
@hisxmark 2 жыл бұрын
Math is not destroyed. It is a science. It improves itself.
@caber1487
@caber1487 2 жыл бұрын
@@hisxmark i do fear the day human is no longer able to wrap our brain around maths, that we might hit a "wall", if we have not already had.
@sajeucettefoistunevaspasme
@sajeucettefoistunevaspasme 2 жыл бұрын
@@caber1487 that is not how it works
@larrycarter1192
@larrycarter1192 2 жыл бұрын
0 is like infinity and infinity and is like 0?
@goodgoyim9459
@goodgoyim9459 2 жыл бұрын
@@hisxmark race and IQ proves many things regardless of what you want to believe lots of anti science ppl here. odd.
@kyriakosmousias9009
@kyriakosmousias9009 2 жыл бұрын
As a mathematician I haven't seen a more elegent presentation of these concepts,especially Godel's theorem. Amazing job thank you.
@WritersMoment
@WritersMoment 2 жыл бұрын
I just don't understand where equation g came from. Why would it have been a contradiction to prove g, just because it said "this can't be proven"? If one had proven it anyways, Gödel's statement would have been wrong, yes,but what of it? Why did he write "this can't be proven"? Purposefully trying to MAKE a paradox by setting contradicting rules and then saying "See? Major problem, math incomplete." doesn't make any sense to me. If things naturally contradict, isn't it the axiom's fault? Shouldn't we just rethink the basics?
@abhinavgaming2110
@abhinavgaming2110 2 жыл бұрын
@@WritersMoment well if he didnt do that contradiction then we wouldnt know the completeness of math
@henningbreede6428
@henningbreede6428 2 жыл бұрын
@@WritersMoment I didn't watch the video, so I don't know how they explained it, quite possibly very incorrect. However the point of the 2nd Gödel incompleteness theorem is if your axioms fulfill a bunch of desirable attributes (such as being able to prove all true statements about the natural numbers), then you can encode its own consistency. Those are known as Gödel sentences. As the axiom system can not prove that, it's therefore not complete if it's consistent. It's possible for an axiom system to not have arithmetic, but be complete and consistent, have arithmetic, be complete but not consistent or be consistent, have arithmetic but not be complete. So it's not possible to rethink the basics to get all desirable quantities. Math is not flawed tho, since having arithmetics and a consistent axiom system is possible and absolutely sufficient for everything that mathematicians do.
@WritersMoment
@WritersMoment 2 жыл бұрын
@@henningbreede6428 Wait, do you always comment in comment sections of videos you haven't actually seen?
@henningbreede6428
@henningbreede6428 2 жыл бұрын
@@WritersMoment No, this is the sole exception. I clicked on the youtube video because it was recommended and after reading the comments I'm not very motivated to watch it either. It doesn't seem to do a good job at addressing common misconceptions.
@ChiefKeefSA
@ChiefKeefSA 7 күн бұрын
Tone is sick dude - keep it up 👍🏻
@jannelukaswessendorf4672
@jannelukaswessendorf4672 2 ай бұрын
great work. definetly have to rewatch this more than once to understand, but it's a great video.
@matthewao
@matthewao 2 жыл бұрын
Can we just appreciate how well animated and produced this video is? God, so much effort.
@unripetomato4312
@unripetomato4312 2 жыл бұрын
everyother youtuber: animates their ideas to make it easier for the viewer vertasium: climes mountain with no context for a nice backround, spends hours making 3 words with a line through them and custom prints an entire set of cards just to express an idea, just to name a few.
@sunnyjim1355
@sunnyjim1355 2 жыл бұрын
Yeah, but that's irrelevant really - I read all this in a book already. It's the information that matters, not how nice it's presented.
@donegal79
@donegal79 2 жыл бұрын
@@unripetomato4312 He has a big team around him. Its not a one man show.
@user-feifei03
@user-feifei03 2 жыл бұрын
hey I recognize you from ut eng
@fredesch3158
@fredesch3158 2 жыл бұрын
@@sunnyjim1355 Uhhh... no, actually no. You, me, and a lot of other people may find it easy to understand written, objective, and scientific language, but many others don't. Some people understand artistic, subjective language easier, some others understand abstract languages easier (like the way sounds and colors relate, and "talk" to each other, like people who know how to use colors to tell a story, or people who write melodies, etc.). So probably a lot of people have a hard time with the math and stuff, and to help them have as fun as we have in this beautiful world of math, people (like veritasium) adapt the math to a more visual, artistic language. Your lack of empathy for people's different necessities helps no one, showing off you read books helps no one, belittling other people hard work helps no one. When you understand that reading books is just one of the many valid ways of acquiring information, and it doesn't make you "cooler" or "smarter", you'll definitely cringe looking back. :)
@ethang.9116
@ethang.9116 2 жыл бұрын
Veritasium: “Math has a fatal flaw” Me: So that’s why I failed my math test
@enveloreal
@enveloreal 2 жыл бұрын
your math test failed you
@Starstruck8970
@Starstruck8970 2 жыл бұрын
Bruh
@heyeso
@heyeso 2 жыл бұрын
@@enveloreal True, It denied the possible that your answer is concrete and relevant
@iamshane4960
@iamshane4960 2 жыл бұрын
@@enveloreal You are not taking a math test, but rather the math test is taking you
@sharonolsen6579
@sharonolsen6579 2 жыл бұрын
"Math has a fatal flaw" I believe this was my repeated assertion for the entirety of my school years... ; D
@thamersuliman4112
@thamersuliman4112 6 ай бұрын
Bro, I swear I sleep hearing your videos like hundreds of times. Your voice is so calm and one-pitched it helps me sleep every time.
@aarushi129
@aarushi129 29 күн бұрын
mathematics is so beautiful. i loved the way you were trying to explain the godel's number. having never heard of it before, i found it even more exciting.i am planning to persue a career in mathematics. would surely come back to this video once i have actually studied about it.
@MissesWitch
@MissesWitch 2 жыл бұрын
Simple Maths: Everything is certain. Complex Maths: *Nothing is real.*
@somelaser5906
@somelaser5906 2 жыл бұрын
very accurate hahahaha
@glircom
@glircom 2 жыл бұрын
Complex Maths: Everything has an imaginary component
@hilal_younus
@hilal_younus 2 жыл бұрын
This whole Episode has just thrown me into a very weird existential crisis:/
@Smo1k
@Smo1k 2 жыл бұрын
...or rather: Complex Maths: *Everything you can imagine exists. Not everything you can imagine is Real.*
@joelklein3501
@joelklein3501 2 жыл бұрын
@@glircom Im(religion) = God
@tux1468
@tux1468 2 жыл бұрын
"I'm right" "Okay, prove it." "I can't"
@monkestronk1227
@monkestronk1227 2 жыл бұрын
Prove that you can't
@richaellr
@richaellr 2 жыл бұрын
Trust me
@joundii3100
@joundii3100 2 жыл бұрын
@@monkestronk1227 Prove that you can prove that you can't prove
@jamesmonroe3043
@jamesmonroe3043 2 жыл бұрын
Is that you Al Gore????
@jaystarr6571
@jaystarr6571 2 жыл бұрын
Said every YT comment ever.
@danielsupuruchukwu9561
@danielsupuruchukwu9561 6 ай бұрын
This is so fantastic Derek 👍 Thanks for going into details
@JohnKooz
@JohnKooz 3 ай бұрын
Agreeing with other praising commenters, I agree this video introduces and explores some of the uncertainties in math and computer science, but it concluded with an optimistic light. Thanks! Another great one from Veritasium!
@SuperStingray
@SuperStingray 2 жыл бұрын
Gödel: *Thanos Voice* "I used the math to destroy the math."
@DarshanGowda
@DarshanGowda 2 жыл бұрын
You deserve more likes!
@advocatesagainstabuse3556
@advocatesagainstabuse3556 2 жыл бұрын
My absolute favorite mathematics professor, whom interestingly was 'merely' teaching precalculus at a 2yr community college began his course with various proofs which illuminated apparent flaws in mathematics. I
@ryaaa__05
@ryaaa__05 2 жыл бұрын
😂😂😂
@voicelikemanywaters1017
@voicelikemanywaters1017 2 жыл бұрын
except the destruction didn't destroy it.
@pandakekok7319
@pandakekok7319 2 жыл бұрын
@@voicelikemanywaters1017 Bruh, did you just started another paradox
@pixelseeker
@pixelseeker 2 жыл бұрын
Seeing that "game of life" running inside "game of life" gave me goosebumps .... inception seems like child's play infront of it. The dislikes to this video are from people who are watching it sitting/standing upside down.
@MolecularMachine
@MolecularMachine 2 жыл бұрын
Agreed. It's like watching videos comparing the scale of astronomical objects.
@EGRJ
@EGRJ 2 жыл бұрын
It's like watching videos of Minecraft made inside Minecraft. Which several people have done, apparently.
@alvydasjokubauskas2587
@alvydasjokubauskas2587 2 жыл бұрын
And I thought, well if Windows exists inside Windows due to virtualization, and you could even run deeper layers, than it doesn't surprise me, that math's followed the same logic... A paradox that is working, by self referencing itself...Which gave birth to computers...
@howard8438
@howard8438 2 жыл бұрын
I didn't get that bit, I thought the game of life was essentially a set of rules, so what does that mean to see those rules running on those rules?
@StraveTube
@StraveTube 2 жыл бұрын
I physically exclaimed "OH DEAR GOD" and my wife heard me from the other room and yelled "oh no, what's wrong??" It's okay, she knew what I was watching and I just shouted back "MORE MATH" and she knew what was up.
@samvegsharma2675
@samvegsharma2675 8 ай бұрын
i literally clapped in a room I was alone..For the great men on whose shoulders we have build the modern scientific and technological world... Kudos to those scientific minds mentioned in this video...
@Cpt_John_Price
@Cpt_John_Price 4 ай бұрын
Man you are overreacting.
@DJGaming-co4il
@DJGaming-co4il Ай бұрын
You clapped, but while you were alone?... Does that mean you just clapped ursel-
@mathematicalpoetry4066
@mathematicalpoetry4066 6 ай бұрын
What a conceptualy beautiful video illuminating a wonderful part in the aesthetics of thinking.
@Pr1est0fDoom
@Pr1est0fDoom 2 жыл бұрын
This is one of the best videos on this channel ever. My brain hurts a little, but I thoroughly enjoyed the experience.
@PaulFisher
@PaulFisher 2 жыл бұрын
Hard agree. This is your best work. The animations, from the cartoons, to the 2D graphics, to the 3D models, were spectacular, and you and the folks that produced them deserve a huge amount of credit.
@l1mbo69
@l1mbo69 2 жыл бұрын
This and the one equation will change your life vid
@IndrajitRajtilak
@IndrajitRajtilak 2 жыл бұрын
I wanted to say the same thing. This video is giving me a dopamine hit like none other. So well researched and presented. I love how he's connecting all these concepts and theorems across math, computer science, and history. What an amazing journey through time!
@mfadhilal-fatih1427
@mfadhilal-fatih1427 2 жыл бұрын
Yeaaa it makes me feel cool
@Smo1k
@Smo1k 2 жыл бұрын
@@mfadhilal-fatih1427 XD
@alparius2
@alparius2 2 жыл бұрын
I got literal chills at the "It's the Game of Life... running on the Game of Life" part
@ringanmajumdar1949
@ringanmajumdar1949 2 жыл бұрын
Like our own life.
@Kabup2
@Kabup2 2 жыл бұрын
Like a matrix
@Ails1234
@Ails1234 2 жыл бұрын
But can it run Doom?
@Legobuild123
@Legobuild123 2 жыл бұрын
the game of life can be run on a game of life inside a game of life tho
@ShaLun42
@ShaLun42 2 жыл бұрын
@@Legobuild123 xkcd 505
@FelipeVRigo
@FelipeVRigo 4 ай бұрын
Blowing our minds. I love to watch your videos, because I always have something to learn.
@jaianeguimaraes129
@jaianeguimaraes129 3 ай бұрын
Bro, the flames you are lighting in my heart with these videos... Thank you so much
@XavierBergeron
@XavierBergeron 2 жыл бұрын
Seeing the game of life being carried out in the game of life was a really impactful moment in this video
@funkerdoo
@funkerdoo 2 жыл бұрын
FACTS, i don't know how to explain it but that was mind blowing
@a2rhombus2
@a2rhombus2 2 жыл бұрын
I actually cried. I'm not sure what came over me.
@dumnor
@dumnor 2 жыл бұрын
You can actually find files with game of life running on game of life that is in turn ran in the program. So its game of life all the way down.
@soulhacker63
@soulhacker63 2 жыл бұрын
I was reading about it 2-3 months ago so I my self made some patterns.... But then it because headache..... And not after watching this video I got to know why it was a headache....
@remivreuls6034
@remivreuls6034 2 жыл бұрын
So the game of life can run the game of life but that game of life can run another game of life but is the original game of life running on another game of life?
@Pants4096
@Pants4096 2 жыл бұрын
There was a brief moment while reading Hofstedter's *Gödel, Escher, Bach* where I felt I truly understood the concepts... This video brought me right back to that feeling! Very well written, presented, and produced! BRAVO!
@safeera5668
@safeera5668 2 жыл бұрын
Its such a good book
@Kachelator
@Kachelator 2 жыл бұрын
@Peter Jerde I just noticed your name. Almost same like mine, funny, don't you think? :)
@ilovecomputers
@ilovecomputers 2 жыл бұрын
Same, but for his other book I Am A Strange Loop. In honesty, I have a feel for what the Godel proof is about, but there’s no chance I’d deduce through its formal proof.
@vigilantcosmicpenguin8721
@vigilantcosmicpenguin8721 2 жыл бұрын
We could call this "Gödel, Hilbert, Turing"
@FatedHandJonathon
@FatedHandJonathon 2 жыл бұрын
@@ilovecomputers I felt much the same until I read David Berlinski's _The Advent of the Algorithm_. I highly recommend it; it makes the subject matter very approachable, and is a super engaging read.
@A.C.C.
@A.C.C. 23 күн бұрын
Fantastic, one of the best video I have never seen. Well done.
@scp_researcher953
@scp_researcher953 4 ай бұрын
thats byt far the best way anyone can ever conclude a study session. Like you professor
@LeonBlack666
@LeonBlack666 2 жыл бұрын
This was not a youtube video. This was a documentary. Loved it.
@The4stro
@The4stro 2 жыл бұрын
love it when that happens
@carpetperson5685
@carpetperson5685 2 жыл бұрын
as a cs student it feels like this video should be called "the origins of computer science"
@dirtytapwater1374
@dirtytapwater1374 2 жыл бұрын
@@carpetperson5685 the origins of computer science sounds like an essay no offense. It really only fits the second half of the video. I’m kinda mean ngl, sorry
@georgesracingcar7701
@georgesracingcar7701 2 жыл бұрын
It was an experience.
@LordofReason-cd8ug
@LordofReason-cd8ug 2 жыл бұрын
This is one of those videos where I know what he's talking about... But I also dont know what he's talking about.
@lordgod7269
@lordgod7269 2 жыл бұрын
Its unprovable lol
@alberteinstein3612
@alberteinstein3612 2 жыл бұрын
Ahhh yes quite the contradiction Now prove it
@whitewolf3014
@whitewolf3014 2 жыл бұрын
I know what you are saying... but I don't know what you are saying!
@Excalibursin
@Excalibursin 2 жыл бұрын
+Cheesy Boi Basically there are several mathematical proofs that mathematicians made. The bulk of these mathematical proofs is setting up an entirely new, imaginary system of math, or numbers or letters etc. In the end, it turns out that none of these systems can ever resolve the following statement: This statement is false. Because of this, any system of mathematics or language that we know how to create will always have unsolvable problems.
@alrightyru
@alrightyru 2 жыл бұрын
@ 23:42 he says about the Turing Machine "...although this sounds simple..." ..um, No 😬
@andynguyen6668
@andynguyen6668 5 ай бұрын
I watched this in high school in 2020, and I did not understand a thing and thought it was really uninteresting. Now im watching this again in college, and while Im taking my first discrete Math class(Berkeley's CS70), I now understand and find everything interesting!
@nerd2544
@nerd2544 2 ай бұрын
same here a single CS semester course of discrete math + another foundational course on proofs, logic, sets in my math minor and boom everything in this video is familiar and understandable
@JinHansson
@JinHansson 3 ай бұрын
I read a book that introduced Gödel's theorem and didn't quite understand how mathematical statements were supposed to be expressed as numbers, but this video worked wonderfully on that.
@ryanjuvida1953
@ryanjuvida1953 2 жыл бұрын
I finally watched this after just ignoring it on recommended for a while, and it was glorious.
@B3RyL
@B3RyL 2 жыл бұрын
Same. It's been hanging there for weeks until I found the precise amount of free time in a day that I could devote to watching the video. Glad I did though.
@vinolicam4140
@vinolicam4140 2 жыл бұрын
i was doing an experiment: clicking on my recommendations and, don't paying attention to the video, but scrolling all the way down to the last video on the list of that one... I did it, 6 or 7 times and end up on this video, that called my attention. And like you, I am glad to did found it.
@celestiancyrillaryea3259
@celestiancyrillaryea3259 2 жыл бұрын
Same here😅😅... thought I would never watch it😅...loved it 🤗
@ammi300
@ammi300 2 жыл бұрын
Woah it’s crazy that we waited for the exact same time to watch this. After just ignoring it, knowing we would watch it eventually because it’s interesting 🤔
@abydosianchulac2
@abydosianchulac2 2 жыл бұрын
Mmhmm
@jherbranson
@jherbranson 2 жыл бұрын
I have to admit, seeing 'the game of life' running 'the game of life' was impressive. That's mind blowing.
@AleksandrStrizhevskiy
@AleksandrStrizhevskiy 2 жыл бұрын
Yeah, out of the whole video that part blew my mind more than anything else.
@uttie3408
@uttie3408 2 жыл бұрын
Wait. If the game of life can run its self, then the game of life will run its self that will run itself that will run its self... (edit) ...and so on.
@jherbranson
@jherbranson 2 жыл бұрын
@@uttie3408 I actually think it would be worth the effort to build one more iteration on top of the two. Perhaps I'm being unreasonable.
@HassanAhmed-rf9xr
@HassanAhmed-rf9xr 2 жыл бұрын
@@uttie3408 I dont get it is the game of life something that can run itself infinitely. It's just confusing tbh.
@danielb270
@danielb270 2 жыл бұрын
@@HassanAhmed-rf9xr you can write a computer program that simulates every computer component (that is what is called emulation), and you can make this emulated computer run windows with the same program running in it. this is the same thing: every next level of emulation requires large amount of setup, and takes a very long time to execute. but a turning complete system is not difficult to simulate: all you truly need is a way to do if-then and store a state, everything else (operating systems, games, hardware drivers, is just built on top of having a set of instructions in the memory modifying the memory and choosing between 2 option based on the memory)
@rodolforesende2048
@rodolforesende2048 4 ай бұрын
beyond saying that georg "discovered" that infinity is much more complex than anyone had imagined (7:13) , I guess the better approach is to say that aristotle prohibited to think about "complete" infinity! Aristotle prescribed that it would only be allowed to think in "potential" infinity! Georg was not intimidated by aristotle and decide to verify what happens when one set up criteria to tame the ambiguities in dealing with the concept of infinity!
@tamirlanger9479
@tamirlanger9479 2 ай бұрын
Thanks Derek, I *LOVE* your videos, and this one was no different!
@thenimalu
@thenimalu 2 жыл бұрын
This is basically my whole computer science studies in 34 minutes.
@tubz
@tubz 2 жыл бұрын
It took my OS prof a whole class to teach the barber paradox, this channel did it in less than a minute.
@hansolowe19
@hansolowe19 2 жыл бұрын
Is it less confusing for you than it was to me?
@TwoGuysOnePassion
@TwoGuysOnePassion 2 жыл бұрын
@@hansolowe19 yes
@tubz
@tubz 2 жыл бұрын
@@hansolowe19 yes, only because I was exposed to all of these concepts in a more in-depth and academic way before, so this video is just kind of a summary for me. But obviously if you haven't had that exposure it would be a lot more complicated. These are all pretty heady academic ideas without many real world equivalents. Totally understandable if it's confusing, a lot of students struggle with it
@gustavo9758
@gustavo9758 2 жыл бұрын
For a while I was wondering "Why is he calling them Good Old Numbers", lol (not native English speaker)
@kaushu42
@kaushu42 Жыл бұрын
The moment he showed the game of life running inside the game of life, I was totally blown away. Such a mind bending topic to contemplate.
@frazzled5791
@frazzled5791 Жыл бұрын
I felt like i was going to start crying!
@pushparahi5681
@pushparahi5681 Жыл бұрын
What game? Can you mention time
@Mackak_
@Mackak_ Жыл бұрын
@@pushparahi5681 around 30:00
@albanana683
@albanana683 Жыл бұрын
I wrote an implementation of Game of Life as an A level project on a Commodore PET. I had to use machine code as BASIC was too slow. I got a bad grade compared to others in the class who wrote simple stock entry systems, as the teacher didn't understand what I was trying to do.
@kaushu42
@kaushu42 Жыл бұрын
@@albanana683 That sounds great! If only this video was available back then, then the teacher would have definitely given you the best grade. The game of life is awesome.
@DavidHarrisActor
@DavidHarrisActor 6 ай бұрын
Excellent ancillary to Hofstadter’s “Gödel, Escher, Bach” Thank you!
@astro_penguin_
@astro_penguin_ Ай бұрын
I thought so too!
@germanic4316
@germanic4316 5 ай бұрын
Excellent video/audio presentation and explanation.
@danesorensen1775
@danesorensen1775 2 жыл бұрын
"Poets do not go mad, but mathematicians do." G.K. Chesterton.
@dara_1989
@dara_1989 2 жыл бұрын
poets accept flaws 👍
@zeitlichkeit5094
@zeitlichkeit5094 2 жыл бұрын
Very true. Ultimately it seems life is more like poetry and less like mathematical or logical certainty.
@alexvidzup9076
@alexvidzup9076 2 жыл бұрын
@@zeitlichkeit5094 language is poetry and language is human made. Anything human made assumes that we know something to be true so even talking about maths leads to proving it wrong. That’s me negotiating a price reduction
@alexeyvlasenko6622
@alexeyvlasenko6622 2 жыл бұрын
Plath, Villon, Wyatt, Wilmot, Byron, Crowley, Shelley, Pushkin, Lermontov, Swinburne, Chesterton, Baudelaire, D'Annunzio...
@jbolanowski1
@jbolanowski1 2 жыл бұрын
@@zeitlichkeit5094 not sure if it's true, but as a romantic by nature i have to give you like :)
@Lalit-yw2tb
@Lalit-yw2tb 2 жыл бұрын
This is the kind of brilliance that we achieve when someone asks what is the point of studying abstract Math? Turing made a machine to prove the decidability problem. That is a Big Brain move. I can't even imagine how much time and effort must have gone to make this video easy to digest. I'm truly blessed to have been a follower of your channel for years. Love you Derek.
@guillermo.mserrano
@guillermo.mserrano 2 жыл бұрын
Veritasium getting philosophical. It's so important to take some time to think like that.
@henryzhang7873
@henryzhang7873 2 жыл бұрын
@@guillermo.mserrano Because what the greats have found is ultimately there is a frontier of knowledge, and then you have to be satisfied living inside what might be a matrix, with no way of knowing whether you are or are not in the matrix, and without knowing if there is a higher power, if there is a purpose, etc. When you can't ask more questions of the outside world, you have to turn in, and figure out what your own meaning of life is, because you realize there might not "be a meaning". Stuff might be the way it is, because it is...
@JorJorIvanovitch
@JorJorIvanovitch 19 күн бұрын
Thank you for having a channel that contributes something positive to the online community. It is very rare to find a channel like this compared to all the other noise online. Did you get an advanced degree in mathematics at some point?
@chrisc9769
@chrisc9769 5 ай бұрын
What happened to Turing was a tragedy, then and now. While i am an American i love Military History, specifically WWII. So i am familiar with Turing and the work he did during the War. (Not so much his other work which is fascinating) It has always bothered me how he specifically was treated after the war and it was good to see him get his Roaly Pardon in 2013.
@jeanlerondedamelbert9354
@jeanlerondedamelbert9354 2 жыл бұрын
If there was an Oscar for KZbin videos, I have absolutely no doubt this would be nominated. Well done sir!
@pottyputter05
@pottyputter05 2 жыл бұрын
Wait... why isn't there? You'd figure it would be better than they way current award shows are going. Not a dig at how awards are given just an observation on the criticisms they have received.
@mrashikhan19
@mrashikhan19 2 жыл бұрын
Only if most human could understand what he is talking about 🤭
@GabrielCarvalho-gd8op
@GabrielCarvalho-gd8op 2 жыл бұрын
I was going to like your comment, but it says 404...
@simonb6306
@simonb6306 2 жыл бұрын
So we have the rewind or whatever it is but we don’t have YT oscars? Ricky we need you
@jeanlerondedamelbert9354
@jeanlerondedamelbert9354 2 жыл бұрын
@@pottyputter05 I commented without much thought but I absolutely agree. Some (emphasis on some) of the content on KZbin is absolutely on par with Oscar nominated films, especially some of the lower budget ones
@nickfosterxx
@nickfosterxx Жыл бұрын
I suspect that for many people, making this video might be considered a lifetime achievement. But for Derek, just one more brick in his incredible, historic castle of outstanding teaching.
@Avisha_Jain
@Avisha_Jain Жыл бұрын
Yeah fr
@garmind4868
@garmind4868 Жыл бұрын
look closer at the bricks composing the castle what are the bricks composed of.
@Zeru64_
@Zeru64_ Жыл бұрын
Derek: "... But for me, it was Thursday..."
@barneyronnie
@barneyronnie Жыл бұрын
I suspect that you are one of his groupies.
@leowalan5463
@leowalan5463 Жыл бұрын
If only he is my math teacher or history teachers
@felipevanhartz5756
@felipevanhartz5756 6 ай бұрын
Facilmente o melhor vídeo sobre matemática do mundo.
@johnrobinson1916
@johnrobinson1916 Ай бұрын
It is important to note that in the "incompleteness theorem" that even though it is possible to create a "well formed" statement within the context of a specific axiom system, that may not be provable within that axiom system, it does not preclude proving or disproving the statement in a "larger" axiom system . Some problems formulated in the context of geometry may not be provable with axioms of geometry, but may be provable in the context of algebraic geometry.
@Djaytaur10
@Djaytaur10 2 жыл бұрын
Hilbert: I proved everything Goudel: I am about to end this man's whole career
@msew
@msew 2 жыл бұрын
lolololololololol
@GabrielLima-gh2we
@GabrielLima-gh2we 2 жыл бұрын
Actually no, Hilbert didn't proved everything, he created a system of proofs, a formal way to prove everything in mathematics and every other field. On the other way, Gödel didn't want to disproof all mathematics, he proved that not ALL mathematical statement can be proven, that is, there will be always some true statement that we will not be able to prove, but still there will be mathematical statements that CAN be proven, till this day we prove new and old mathematical laws, the problem is we can't know which statement can be proved or not, we might not find the answer right now and say that it is unprovable and 500 years later someone prove it, it is just undecidable, that's the point of Gödel's study.
@utkarshsaini5650
@utkarshsaini5650 2 жыл бұрын
@@GabrielLima-gh2we ikr
@edwardhuang5885
@edwardhuang5885 2 жыл бұрын
Godel: Can you prove yourself tho?
@gabriellarosa7159
@gabriellarosa7159 2 жыл бұрын
@@edwardhuang5885 Descartes: Yes
@desperadox7565
@desperadox7565 2 жыл бұрын
It's not surprising that so many mathematicians get crazy.
@pereraddison932
@pereraddison932 2 жыл бұрын
... Dearest, Desperodox... is why it's best to begin crazy for the possibility of a cure at some point along the way, though, that's doubtful...
@souhung69
@souhung69 2 жыл бұрын
Or are they mathematicians, because they are "crazy"? 😏
@MrLaz0rz
@MrLaz0rz 2 жыл бұрын
They only become crazy when they begin or fully understand.
@Schwolfstain
@Schwolfstain 2 жыл бұрын
Isn't it why we also have creativity aspects and imagination?, I mean, if you're relying all your mind on pure mathematics it's obviously gonna break your entire perception of reality, becouse like it or not, our brains can't begin to fully understand one without the other (maths and creativity) since that's how we humans are built and perceive reality, in a way, one feds the other, if these mathematicians had enough imagination, they, instead of going crazy, would start to build a better way of doing another type of maths, perhaps one that would unterstand the limitations of language or the posibility of two opposite states like in quantum mechanics.
@Zenovarse
@Zenovarse 2 жыл бұрын
@@souhung69 craziness does not imply mathematician but mathematician implies craziness.
@stevegoralski7247
@stevegoralski7247 4 ай бұрын
I legit thing this is one of the greatest educational KZbin videos of all time. If there was a KZbin educator hall of fame, this would be in it.
@shiaakatsuki7865
@shiaakatsuki7865 5 ай бұрын
19:56 I love how this is just a slightly different variation of the Liar's Paradox or the Russel's Paradox.
@astro_penguin_
@astro_penguin_ Ай бұрын
And Godel knew this! The Epimenides paradox was the idea that motivated it all. Godel went through all the trouble of constructing his system because he knew that he needed to work that paradox in somehow-though a little bending and twisting was needed in order to force mathematics to refer to itself. :)
@EdgyShooter
@EdgyShooter Жыл бұрын
Meanwhile in physics: "Can you prove this statement is true?" "I'm just going to assume it is and continue from there"
@bugdracula1662
@bugdracula1662 Жыл бұрын
I mean that is how the halting problem works
@TheOriginalFaxon
@TheOriginalFaxon Жыл бұрын
A lot of why we do what we do in modern quantum theory (physics, mechanics, gravity, etc...) is entirely based on knowing these principles as well. Once you establish that there are some things you may never be able to prove, you can assume that if your model is in fact flawed, you will be able to prove that it is flawed eventually with enough evidence and research or computational power, or the correct real world simulation that answers the question, just as everything in this video was more or less shown conclusively (except for the things which conclusively couldn't be, because yay uncertainty principle). If your assumptions are in fact correct, it should actually be easy to prove they are, even if you don't know WHY they are. There are actually numerous technologies which we know work, but have no idea why, and the same goes for systems within the human body and specifically the nervous system in particular. Some of the imagery you'll see or otherwise experience mentally, while on psychedelic drugs like mushrooms, LSD, DMT, and even dissociatives like ketamine and phencyclidine, match up with the kind of fractal geometry you'll see when you feed certain known mathematical patterns into a computer visualization system. On some level our own brains may in fact be Turing Complete computing systems. I suspect as we go further and further with the research into neural networks, and simultaneously try to properly understand the method of functioning behind the biological computer we all use to think, which simultaneously gives us our sense of self, and the ability for meta-consciousness, the ability to be conscious of one's own consciousness. You can dive off the deep end into theory all night on that one and at the end you'll be even more confused than you were when you dived in to begin with, what with everything you learned, but someday somebody is going to figure it out, and completely revolutionize the world yet again. After the ascension of quantum computing, that will most likely be the next major computer revolution, assuming they don't happen simultaneously in some ultimate singularity event.
@joseromero99
@joseromero99 Жыл бұрын
@@TheOriginalFaxon a00
@Number6_
@Number6_ Жыл бұрын
This is why physics has become more of a religion than a science. This is why these branches of physics haven't seen any progress in the last 70 years.
@ChristAliveForevermore
@ChristAliveForevermore Жыл бұрын
Physicists rarely question whether or not they *should* assume such and such to be true in the first place. Einstein at least had an axiomatic criteria (least number of assumptions in the simplest possible form which frames the most general kinds of problems). Even then, his long talks with Gödel likely helped him to come to terms with the fact that axiomatic (assumptions-based) mathematics which has prevailed for 3000 years is fundamentally flawed.
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