Math's Fundamental Flaw

[@rochestephan]

Ironic that Godel's death was the result of a self-referential paradox: he died in order to not die

[@TanyaNirielle]

This comment deserves more likes

[@DebdyutiBiswasdebbisful]

Underrated

[@reverieWithRupam]

Woah...

[@nDenTzMotionZztrujillo]

You nailed this comment

[@moazz5779]

This comment is just too good

[@mikejohnstonbob935]

Godel's friends: "No one's trying to kill you Godel" Godel: "You can't prove that!"

[@nbjornestol]

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]

@@nbjornestol he couldn't prepare his own food?

[@segmentsAndCurves]

@@lavabeard5939 He was a mathematician (logician) after all.

[@kindlin]

@@segmentsAndCurves Does that excuse a man from being able to provide for... himself?

[@kimochi5009]

@@kindlin It doesn’t excuse, but it explains why he didn’t prepare his own food.

[@lemond1649]

I don't know why but I love the idea of mathematicians gathered in a room yelling and hurling insults at one another

[@viacheslav7870]

"You are proof that one can actuality have a value of zero!"

[@sleepybraincells]

@@viacheslav7870 lmao

[@siinxx7656]

@@viacheslav7870 I'd rather listen to the first 10,000 digits of Pi than some irrational numble like you *crowd commotion intensifies*

[@emaanahsansarfraz1940]

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]

"You are more irrational than any number I've ever seen!"

[@vgamedude12]

Everytime people get into the weeds with math like this i feel like im just listening to philosophy with a different label.

[@mattiamazzanti8418]

Philosopher ask a question,Phisicists Turn questions into math

[@chetsenior7253]

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]

thats because they are philosophers, They are natural philosophers.

[@mafuchin]

PhD student here. Math is applied philosophy. You cannot have one without the other.

[@VoiceTotheEndsOfTheEarth]

Exactly, the foundation of mathematical proofs came from the Greek philosophers.

[@TylerJaneBronson]

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]

Where?

[@RAMBO14001]

Just like the human dimension...

[@Touay.]

@@RAMBO14001 It's simulations all the way down ....

[@TweaQAU]

So wait... if the camera kept zooming out on the game, it would continuously be simulating itself?

[@GaganpreetSinghKapula]

Same feeling 🤩

[@kyriakosmousias9009]

As a mathematician I haven't seen a more elegent presentation of these concepts,especially Godel's theorem. Amazing job thank you.

[@WritersMoment]

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]

@@WritersMoment well if he didnt do that contradiction then we wouldnt know the completeness of math

[@henningbreede6428]

@@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]

@@henningbreede6428 Wait, do you always comment in comment sections of videos you haven't actually seen?

[@henningbreede6428]

@@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.

[@amecha5368]

So basically... Can math prove itself? No. But math can prove that math can't prove itself.

[@Logan-zf1ft]

hahahahha good one

[@rob_olmstead]

well... you can't prove the rule using a rule because the rule is universal and immutable

[@kathanshah8305]

Yesn’t

[@Pineapple-hx9ty]

"math can't prove itself" to the power of -1

[@MsHellokitty666]

I was asking myself the exact same question

[@cah137-y4s]

“Is it Turing complete?” is the mathematician equivalent of “Can it run Doom?”

[@Gordy-io8sb]

Programmer*, but nice try buddy. You'll get it one day. Actually you won't, because you're a dimwit.

[@rich1051414]

It's the minimal necessary requirement to function as a programming language, so it's not exactly strictly a mathematical thing per-se. It's the computer science equivalent of 'can it run doom'.

[@stop8738]

No this is just nonsense.

[@BayesianBeing]

​@@stop8738how so?

[@stop8738]

@@BayesianBeing Math is fundamental to the universe, reality. Doom is coding to produce entertainment that enthusiasts obsess over trying to make it run on random machines not initially thought to be used in that way. Nonsense is when you’re so chronically online and out of touch with reality that you would essentially say running code for a game “compares” to reality itself.

[@anthead7405]

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]

Was waiting for P = NP after The Halting Problem. Maybe next time.

[@enemdisk6628]

Nice

[@DavidLiMusic]

Veritasium needs a video on P vs NP! Would be amazing.

[@pvic6959]

meanwhile me to my friend: Do you think dogs know theyre adorable?

[@codycast]

@@DavidLiMusic yeah because there isn’t enough n/np out there

[@DanielG03]

Me: *failing my math class* Veritasium: “they could be something like the twin prime conjecture” Me: go on...

[@tejasdeepsingh456]

Lmfao

[@SoumilSahu]

tbh the conjecture itself is pretty elementary to understand.

[@wildanimus2559]

@@tejasdeepsingh456 ditto

[@angryyoungman4389]

@@wildanimus2559 Charizard

[@crystalgiddens7276]

@@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.

[@matthewao]

Can we just appreciate how well animated and produced this video is? God, so much effort.

[@unripetomato4312]

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]

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]

@@unripetomato4312 He has a big team around him. Its not a one man show.

[@user-feifei03]

hey I recognize you from ut eng

[@fredesch3158]

@@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. :)

[@New_Genesis_dev]

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

[@Mackinstyle]

If you're a mathematician and you are labelled a "corrupter of the youth", you are doing something very right.

[@TheOOOOOOOOOOOOOOO]

nerd burns

[@Aereto]

@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]

I watched this video when its title was still "There's a Hole at the Bottom of Math".

[@tannerwitt3030]

@@Aereto wait whaaaaaat

[@theycallmealex454]

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.

[@kaushu42]

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]

I felt like i was going to start crying!

[@pushparahi5681]

What game? Can you mention time

[@Mackak_]

@@pushparahi5681 around 30:00

[@albanana683]

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]

@@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.

[@judypetree2589]

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]

I get my education from youtune videos:)

[@kebekbutcher]

@@carealoo744 Self education is better than forced education! Have a good day!

[@palashrajput428]

@@kebekbutcher well said

[@scoogsy]

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]

I hope you live long and healthy 🙏❤️👍

[@blackdwarfrecords]

Oh, well done sir. Your closing line here very nearly sent a chill up my spine. Thank you for another well-spent half hour.

[@ArthurBCamara]

I'm a PhD in computer science. This is a full-on Discrete Mathematics intro course. This is amazing.

[@Kirmeins]

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]

Right on! A semester of DM in one video.

[@camrouxbg]

@@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]

I agree, this is also the key for appreciating the role of AI/ML theory. And randomised algorithms.

[@iamtheusualguy2611]

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.

[@J_Stronsky]

7:49 - 'corrupter of the youth' haha "Hey kids come here, you want to learn about some illicit infinities"

[@igorswies5913]

wanna learn how to divide by zero?

[@tilakmehrotra]

Noooooooo

[@mischief9499]

lmaoo

[@TheJanitorIsIn]

Socrates back from the dead

[@Sun-ut9gr]

@@igorswies5913 wait that's illegal

[@krissisk4163]

"There will always be true statements that cannot be proven." Oh yeah? Prove it. ....He proved it.

[@poorvisingh232]

Brains!

[@levibyler1132]

Plp are to smart

[@charlesballiet7074]

you mean like Epstein not killing himself

[@jenidu9642]

Proving something is impossible is also a proof

[@HerrCookienator]

Dis gave my brain a new wrinkle

[@wojciechlawniczak645]

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

[@OddNumber1524]

"How about you just hire another barber?" Said the engineer

[@Smitology]

And you only need two barbers to break the paradox. They can shave each other; the rules never said that wasn't allowed.

[@jamesflanagan6977]

Engineering student here, my first thought as well

[@jeffirwin7862]

2 barbers 1 town

[@kelpf0rest]

@@jeffirwin7862 IYKYK

[@ParadoProxia]

@@theknightwhosayn1 only the barber can shave anyone, that was one of the rules

[@michaelh4227]

Teacher: Your math is flawed. Student: No, math itself is flawed.

[@moncorp1]

dank meme

[@inthebackwiththerabbish]

lmfao

[@everyusernameistakene]

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]

@@everyusernameistakene ahahaha bro let me know what she says 😂

[@Rob-cm9jr]

@Repent!. I assure you math and time are constructs of man, not God.

[@Pants4096]

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]

Its such a good book

[@Kachelator]

@Peter Jerde I just noticed your name. Almost same like mine, funny, don't you think? :)

[@ilovecomputers]

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]

We could call this "Gödel, Hilbert, Turing"

[@FatedHandJonathon]

@@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.

[@dougieh9676]

It's disgraceful what they did to Turing. 😢

[@rl7012]

Zzzzzzzz......

[@louplayz752]

Haha the creator of the first computer was GAY.

[@mus_tard2183]

What trolls have done to the internet is so unfortunate

[@JuuuEmpathy]

it rlly is disgusting. luckily our modern society is changing that sort of behavior.

[@Eureka20043]

Praise to him

[@yhwh9778]

I love how the set theorists answer to self reference was "I changed the definition so that doesnt count."

[@dominicbonogofski]

It's like a kid on a playground saying they weren't playing when someone else tags them.

[@EonsEternity]

​@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]

@@EonsEternity I was just implying that it had the same energy behind it.

[@daarkdocumenter]

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]

​​@@daarkdocumenter@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.

[@Pr1est0fDoom]

This is one of the best videos on this channel ever. My brain hurts a little, but I thoroughly enjoyed the experience.

[@PaulFisher]

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]

This and the one equation will change your life vid

[@IndrajitRajtilak]

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]

Yeaaa it makes me feel cool

[@Smo1k]

@@mfadhilal-fatih1427 XD

[@Lalit-yw2tb]

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]

Veritasium getting philosophical. It's so important to take some time to think like that.

[@henryzhang7873]

@@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...

[@vipin7um]

Thanks Veritasium. The game of life is so much like the life itself. It would be great if you can further explore this topic. I have a gut sense that this is key to understanding how consciousness evolved in the universe and in fact how the universe evolved itself. Thank you so much for preparing content that is not only well researched but also so fundamental for our understanding.

[@Gromek999]

Masterpiece of a video

[@jacobnix9952]

Trueee

[@vaisakh_km]

You can't prove....

[@ctts8458]

fancy seeing you here

[@sinpi314]

Masterpiece indeed

[@jenshaglof8180]

Exactly what I was going to comment!

[@nickfosterxx]

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]

Yeah fr

[@garmind4868]

look closer at the bricks composing the castle what are the bricks composed of.

[@Zeru64_]

Derek: "... But for me, it was Thursday..."

[@barneyronnie]

I suspect that you are one of his groupies.

[@leowalan5463]

If only he is my math teacher or history teachers

[@cipherxen2]

Mathematicians: we must prove this equation Engineers: Eh, it's good enough, we'll just use it

[@mattstokes3881]

bridge collapses

[@cipherxen2]

@@mattstokes3881 and they learn from their mistakes, and makes better bridges

[@MarkAvo]

I feel seen

[@aloysiusvo318]

@@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]

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."_

[@Gaurav-pq2ug]

00:00 Undecidability is a feature of mathematics. 04:30 Not all infinities are the same size, shown by Cantor's diagonalization proof 08:28 Self-reference paradoxes in mathematics 12:18 Gödel's incompleteness theorem showed limits of formal systems in mathematics. 16:50 Gödel's incompleteness theorem shows that any mathematical system capable of fundamental arithmetic will always have statements that are true but have no proof. 21:13 Gödel's incompleteness theorem and Turing's halting problem are fundamental to modern computer history 25:10 The undecidability of the halting problem implies the undecidability of the general problem for determining whether a statement is derivable from the axioms. 29:56 The concepts and inventions of mathematicians like David Hilbert, Kurt Gödel, and Alan Turing changed the course of world events and led to modern computing devices.

[@benjaminparker5044]

Ah yes, the iconic half way point of the video where I stop comprehending a single thing said

[@chronicles1192]

that feeling

[@Smo1k]

Read Douglas Hoffstadter and comprehend even less. In an entertaining way ;)

[@SoloPilot6]

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]

It is a proof which proves that not everything that is true can be proven after all ¯\_(ツ)_/¯

[@akhilaryappatt]

it's zone out time

[@jonasba2764]

As someone who majors in mathematics while minoring in computer science, this video is absolutely awesome. I've learned about a lot of these things in isolation, but this really connects them all.

[@alfredsharp239]

Ditto

[@PandemoniumMeltDown]

Math glue?

[@arnold-pdev]

If you want more of this story, I recommend the graphic novel Logicomox

[@MatthewElvey]

Thanks for confirming this is solid. (I’m not quite awake; need to re-watch when I am! For what I expect will be a more spine-tingly coolness, like when I understood the RSA algorithm. ) The book “Gödel, Escher, Bach” - This remind me to read it!

[@FinalWarrior591]

Hey, I'm the literal opposite of you! (Majored in CS, minored in Maths.)

[@temiolu3049]

OVER HALF AN HOUR OF CONTENT, youtube> TV any day

[@Medan1993]

and here I am, watching this on TV ;)

[@AxxLAfriku]

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]

@@AxxLAfriku Are you OK?

[@nothuman5335]

@@AxxLAfriku what

[@halfblood7]

@AxxL Some types of madness are beyond the limit of infinity

[@XavierBergeron]

Seeing the game of life being carried out in the game of life was a really impactful moment in this video

[@funkerdoo]

FACTS, i don't know how to explain it but that was mind blowing

[@a2rhombus2]

I actually cried. I'm not sure what came over me.

[@dumnor]

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]

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....

[@Dikkeboomstam]

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?

[@xrefor]

"This is the game of life, running on the game of life", together with the visuals and background sound gave me chills! Awesome video!

[@givemeahandle]

Did the same for me. I had an embolism, I think. ..... But seriously, maybe I did

[@AkshayKumar-ue1fp]

time?

[@girl6girl6]

He made math sexy

[@AkshayKumar-ue1fp]

@@girl6girl6 🙄

[@madladdie7069]

I'm wondering if that song's available elsewhere. It's glorious.

[@chenilleoneil1289]

I fell asleep to this video when you were explaining about Gödel’s numbers. In my nightmare, someone gave me a riddle. The answer needed to be yes and I could not lie or the nightmare wouldn’t end. I boldly said “Yes! Because there are an infinite number of integers between 0 and 1 and they are all real numbers!” Then immediately I woke up with a sense of peace and calm. It’s true what they say; falling asleep learning about a topic hardwires it to your brain.

[@kinokoman1207]

I finally watched this after just ignoring it on recommended for a while, and it was glorious.

[@B3RyL]

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]

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]

Same here😅😅... thought I would never watch it😅...loved it 🤗

[@ammi300]

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]

Mmhmm

[@Moersfreak]

For me, the biggest takeaway of the whole thing is this: how amazingly smart must Gödel have been to come up with that proof? Obviously, every other Mathematician mentioned here is also incredibly, incomprehensibly smart, but with the other mentioned proofs, I can kind of reconstruct how one might have arrived there. But with the incompleteness theorem, I just cannot fathom how one might come up with it. The guy must have been able to just straight see the matrix.

[@Blackoutwhiteout23]

He was only 25

[@tomwanders6022]

@Markman Dave Thanks a lot bud I have been in an argument with my brother and we clearly defend different ideas, I should probably do the research on it my self. Though it’s not completely about math only partly. Where arguing about videogame strategy, where when it comes to math we usually agree, but if it comes down to different strategies were clearly on different start ups we are clearly on different opinions.

[@ValMartinIreland]

It's cods wallop. Has anyone commenting here ever studied probability? In all scientific claims you must provide the figures to back your claim. That is not done here.

[@david-776B]

@@ValMartinIreland Are you referring to the video? Or the comment? Or someone’s reply to the comment?

[@kaia1962]

@Markman Dave While it's true that groups limit one's freedom, they also expand it. If there are no other people one would be one's own input and output. This would mean we'd never get other information besides the ones already existing in one's individual system. Thus we'd be systems of stagnation. On the contrary, the more people we listen to, the more information we can get. Especially if the others have a different point of view. Thus we have a lot of contradictory Information we can work with. Or in other words: "We have an abstract horizon". With this we not only have the chance to solve the contradiction, but also a synthesis. Whether a group is beneficial or obstructing for an individual, is based on the structure of the group and the level of self-confidence of the individual. Being self-confident means to stand your ground, but also being able to reflect on the critique. Only then you can find the most differentiated solution for your time. 0nly then you can build up on the horizon of your critics and convince them.

[@chorian5424]

mom: why did you get a B in math! me: math has a fatal flaw

[@cohensmith6100]

B is good

[@ALBINO1D]

@@cohensmith6100 and A is excellent.

[@cohensmith6100]

@@ALBINO1D ya but like why get mad abt a b when most mfs fail math

[@ALBINO1D]

@@cohensmith6100 is your benchmark just to be better than worst, or to be the best? Learn a lesson from Ash Ketchum.

[@cohensmith6100]

@@ALBINO1D Hes like over 20 and hangs with 12 yrs old girls ill pass man

[@andreselectrico]

This is the third or fourth time I've watched this video. I simply love it. I'm an economist myself, who used to despise the way basic algebra made economics abstruse and complicated. This was annoying because I love mathematical thinking, but not the way it was being employed in economics. Then I discovered complex systems, and everything changed. Indeed, the economy is a complex system par excellence. But then I realized that delving into the very idea behind complex systems actually helped me perfect the critique of algebra-based economics in terms of why it is futile to try to predict all outcomes. In fact, as an economist, mathematics helped me prove that math is not everything in life.

[@jeanlerondedamelbert9354]

If there was an Oscar for KZbin videos, I have absolutely no doubt this would be nominated. Well done sir!

[@pottyputter05]

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]

Only if most human could understand what he is talking about 🤭

[@GabrielCarvalho-gd8op]

I was going to like your comment, but it says 404...

[@simonb6306]

So we have the rewind or whatever it is but we don’t have YT oscars? Ricky we need you

[@jeanlerondedamelbert9354]

@@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

[@Phr8]

Veritasium videos are starting to transcend into legendary content status.

[@peterhieuvu]

Seriously. The topics he presents are all well covered on youtube and in textbooks, but Veritasium manages to present it so elegantly. It makes it so interesting for topics that can sometimes be boring to a lot of people.

[@lightiamagay1625]

Modern day vsauce

[@ammaleslie509]

Starting?

[@LunaticTheCat]

@@lightiamagay1625 Vsauce with much more complex topics

[@rubik8529]

This video is a masterpiece. The content, the animations. Everything is out of this world

[@quinnipi2400]

The use of mathematical symbols as buildings is *chefs kiss*

[@macshyha]

Cardboards were very much from this world ;)

[@Founderschannel123]

This is a dream for every math teacher

[@jandelion404]

I've always been good at maths, but this video is what started me on the journey of truly loving it. I can honestly point to this video as what prompted me to start my mathematics degree!

[@jherbranson]

I have to admit, seeing 'the game of life' running 'the game of life' was impressive. That's mind blowing.

[@AleksandrStrizhevskiy]

Yeah, out of the whole video that part blew my mind more than anything else.

[@uttie3408]

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]

@@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]

@@uttie3408 I dont get it is the game of life something that can run itself infinitely. It's just confusing tbh.

[@danielb270]

@@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)

[@pixelseeker]

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]

Agreed. It's like watching videos comparing the scale of astronomical objects.

[@EGRJ]

It's like watching videos of Minecraft made inside Minecraft. Which several people have done, apparently.

[@alvydasjokubauskas2587]

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]

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]

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.

[@Brunoenribeiro]

This feels like the start of a new era for Veritasium. The production value is off the charts! And the topic is just beautiful. Congrats Derek and team S2

[@klobe9]

The graphics are off the charts, except for when he is standing outside with a literal flip board and papers taped together blowing in the wind with card board cut outs covering them. The conflicting statements, almost like Gödel theory

[@vishwarao6064]

they'd surpass Vsauce

[@afiffarhati4580]

@@vishwarao6064 a Vsauce vibe is exactly what i got from watching this (well , at least the old vibe) , hope this channel replaces the void left by that channel...

[@SarcasticData]

See I don't like it. Theoretical mathematical truths that aren't provable and/or practical are just neat to hear and that's it. It doesn't have a purpose. That's what I don't like. You can make up a story about a hotel with infinite rooms or tell me that there's an infinite number of twin prime numbers but do something with it. Show me an example on why it's worth knowing. This is what I'm talking about at 20:59. It's a paradox. Those can be neat. What did you do with the information though? What *can* you do with that information? I would MUCH rather Veritasium cover content like where he went into public and asked people things like, "Why does the earth rotate?" or "Why do two objects fall at the same speed?" but that's just my personal preference. I'm happy so many people like where his channel is going. I wish I was one of those people.

[@RationallySkeptical]

No, he's been at this level for quite a while now.

[@adam_musics]

I love how he uses “barber of Seville” muisc piece when he talks about the barber paradox in 9:30

[@rulerofelves746]

I first watched this video around when it came out. Now I am taking a final exam on logic and computability in 8 hours and I am back watching this to study. I didn't realize how much I'd learned until I realized all the topics here are familiar already. Still, it is an absolutely amazing explanation.

[@me9298]

Same here! I watched it back then as well and today I understand those concepts from my university course in logic for computer scientists. Hope your exam went well btw :)

[@CClausen85]

Listen to Alan Watts. He's more wrong than right, but that's to be expected when talking about an indescribable reality. The key to understanding lies in Eastern Philosophy. You can't grasp it, and you can't not grasp it. Those who know don't know, but those who don't know know. It comes from the knowledge of the meaning of words. Words are limited in their scope, We don't have words for metaphysical concepts, or non-conceptual realities - we can only reason within the framework of concepts, which is a something which is contrasted by a something else. Which - in a non-dualistic, non-conceptual reality means we are all very literally quite screwed, because we only deal in concepts.

[@shervinrad100]

How’d the exam go?

[@alparius2]

I got literal chills at the "It's the Game of Life... running on the Game of Life" part

[@ringanmajumdar1949]

Like our own life.

[@Kabup2]

Like a matrix

[@Ails1234]

But can it run Doom?

[@Legobuild123]

the game of life can be run on a game of life inside a game of life tho

[@ShaLun42]

@@Legobuild123 xkcd 505

[@tuomasronnberg5244]

"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]

It did remember 'God don't play dices' from Einstein.

[@JonathanHuertayMunive]

you might want to read mathematicians debates nowadays... nothing has changed

[@abhisheksoni2980]

Later generations are just making tiktok videos.

[@DevinDTV]

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]

Pythagoras beat them at their game though

[@voidentity4295]

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.

[@matthewyoung6263]

"1+1=2" "The above proposition is occasionally useful."

[@Jayess-c]

What's 3x+1?

[@Jayess-c]

Or y3X+1 it is impossible to get an answer it's like pi

[@kam9910]

@@Jayess-c lol dude they literally made a vid about that, it’s that where you got it from

[@Jayess-c]

@@kam9910 what are you referring to?

[@kam9910]

@@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

[@elif6908]

I didn’t get even a sixty percent of the math in the video but I’m grateful for those amazing people who thought about these things and still do.

[@sethmerczero9827]

I mean the whole video was about paradoxes and contradictions

[@shoam2103]

This is about the heart of mathematics, the most abstract thing that humans do. 40% is pretty good for a first try.

[@camrouxbg]

@@shoam2103 Definitely. Mathematical foundations are not for the faint of heart, but when presented in this way it can become quite accessible. You don't need to be able to DO the math here in order to appreciate it or even talk about it. I haven't watched very much of this channel, and I'm going to have to remedy that.

[@koalanefelibato4365]

This Is the stuff I study everyday... I still don't get it. Math's are hard, but they wouldn't be so beautiful I they weren't

[@iamtheusualguy2611]

This is fine. It's a really abstract topic that most people will never have a reason to understand to begin with. But understanding the gist of it gives you this amazing feeling of having found out something so profound and fundamental about the world that is mathematics and any system our mind creates by applying logic. It's beautiful, awe-inspiring and depressing at the same time

[@ashwinjonathandias172]

👏👏👏👏👏I think Derek and his team deserves a round of applause for how good his graphics and editing has been recently.Content has always been top notch, but this just takes it to the next level...Brilliant stuff Derek!

[@dart1673]

Who's derek

[@prathamnishad1033]

@@dart1673 nice one

[@prathamnishad1033]

don't be like front benchers bro and editing was different not good.

[@ashwinjonathandias172]

@@prathamnishad1033 if you watch the original videos, u will definitely notice the difference...comment was just in reference to that

[@prathamnishad1033]

@@unicornhuntercg tf

[@ScienceSoSimplified]

This is one of the best videos on this channel ever.

[@XtecHubble]

I wasn't expecting to get goosebumps from this, but that game of life running a game of life.........

[@timeodaneosetdona]

Can I introduce you to the Simulation Hypothesis? ;)

[@ericdew2021]

Yeah, that was pretty damn cool.

[@nathan87]

Oh my god I got it too for real, wasn't expecting to find this in the comments!

[@eminence_]

Minecraft running Minecraft

[@AwesomeTheAsim]

Yeah...

[@wordedjewel5629]

Engineers be like: "Does is work tho?" "Well yes, but if you look closel..." "Then yes"

[@andres91cr]

Word

[@amanawolf9166]

Two principles I follow. KISS and IIWIAS KISS = Keep It Simple Stupid IIWIAS = If it works it ain't stupid

[@fftere]

@@amanawolf9166 that's enough for me, let's leave the puzzles for those who can bother

[@tarikbleak]

Mathematicians: Start crying uncontrollably*

[@jdotoz]

@@tarikbleak Don’t look at the way we do trig.

[@elchingon12346]

“1+1=2 The above proposition is occasionally useful “ I need this on a poster for my classroom 😂😂😂

[@PiotrKaszuba8403]

😂

[@sdgathman]

“1+1=2 The above proposition is occasionally useful “ It's also racist. smh

[@LIGHTISBURNING]

So trueee

[@ccgarciab]

@@sdgathman "I proudly and loudly misunderstand things"

[@DevinDTV]

@@ccgarciab sounds like you weren't aware that math and logic are constructs of whiteness which inherently oppress people of color

[@amongusztav655]

It is my favorite math related video. The things told in the video are so concrise and fundamental I often find myself returning to this video to help me understand Math and Life

[@iamdhrooov]

Here to appreciate how deep this guy gets into everything. The effort he puts in explaining and video making is tremendous.

[@every1665]

None of my maths teachers had anything like this guy's ability to explain. It's also my excuse as to why I'm lousy at mathematics!

[@whatarewaves]

@@every1665 i mean he's not really teaching math as much as he's teaching math history. learning set theory in university isn't as straightforward as listening to a video. you gotta do problems and proofs to really know it.

[@goblino9255]

that's what she said

[@НиколайОнов-л1ь]

Very true

[@iskandaralimubarok]

Godel : *refused to eat any food in order to not die* Master Oogway : "One often meets his destiny on the road he takes to avoid it..."

[@afiffarhati4580]

I just came from a Kong-Fu Panda video LOL What a coincidence...

[@atharvsharma7648]

@@afiffarhati4580 wow 🤩 😂

[@benediktwalch1605]

One can learn so much from movies that were intentionally made for kids.

[@Flashisgreatfr]

fun fact: did u know that more people die from pugs than from sharks!!!?? i will post regular videos like this so make sure to subscribe!! btw i'm a kid

[@atharvsharma7648]

@@Flashisgreatfr wow rlly

[@stevesether]

I very strongly wish mathematics was taught in a wider perspective like this video is. We teach mathematics as if it's a world onto itself, disconnected from everything. In reality, it's highly connected to history, philosophy, and nearly everything.

[@monkelettuce1799]

This is pure mathematics, if students were to be taught these concepts I'm pretty sure they or most of them will lose interest, I think these topics should stick to PhD/researchers and mathematicians

[@stevesether]

​@@monkelettuce1799 There's 18 million views on youtube that says that if explained properly, 18 million people can be interested in advanced mathematics. I'm about 99% positive most people viewing this don't have a PhD, or are mathematicians. I think what's great about this video is that it's not just about pure mathematics. If it was, it'd be boring, even for me. I already know about Godels incompleteness theorem. I knew a little about the history behind it, not in as much detail as is here. Instead it turns the mathematicians into real living people that have philosophical disputes with one another. When I learned math, you never really know who these people are, other than some mathematical tool you have to use, named after Euler. Even sticking some humanity and history in with mathematics makes it the most interesting. My best science teachers did that with science. I don't know why we don't do it with math.

[@sophi3006]

@@monkelettuce1799 we have an optional history and philosophy of sciences class at our school where we were taught in a few lessons basically the content of this video except for the Turing part. the class is full and not even half the students attending it take advanced maths and/or physics! sure its not for everyone out there but it does interest a lot more people than u might think :) it gives context to so many concepts you and makes them more fascinating imo (and idont even like maths that much in school, physics even less). the teacher does really have to be motivated and engaging though, but that goes for most subjects

[@Number6_]

@@stevesether we do at least in my school. Perhaps the flaw is you went to the wrong school or had the wrong teachers; or here's an idea , you take responsibility for your own education and stop blaming others for what you should be reading up on.

[@stevesether]

@@Number6_ That's more than a little rude.

[@l0l1p0p7]

I watched this video 3 years ago, fell in love with math and now I started my bachelor's program in computer science. The term social media influencer must be defined by people like you.

[@pirojfmifhghek566]

My first instinct would be to assume that the battle between Intuitionists and Formalists couldn't have been that dramatic. But then I remembered that there was an actual riot featuring thrown chairs and fistfights on opening night of Stravinsky's Rite of Spring over the timbre of the bassoonist. Man, nerds back in the day were hardcore.

[@HebbY_]

They still are. It's just harder to hide a murder

[@fftere]

Reading this really depresses me, how far we've fallen as a civilization. Look what we used to fight for, the greek requirements and essays about Virgilio just to enter universities, the academic debates in the common tongue, intelligence as something more than an industrialized misconception of public education ("nerds"), our music sensibility, etc. The idiots took over (I know, I'm one of them), the grandchildren of the Revolution, the City of Men, Rome.

[@mothra3477]

The fighting on the opening night of Rite of Spring was about much more. It is a very visceral work. It features a very unconventional choreography, with violent and sexually suggestive movements (far from a more traditional ballet, like the Swan Lake). The music itself is rather dissonant, and uncommon for the time. And, on top, it's about the ritual sacrifice of a virgin. Groundbreaking and controversial art always generate strong reactions; against and in favor. I would totally fist fight someone over the rite of spring. It's so riot worthy. And I think it's great if people are passionate about things and are willing to take stuff like music or math this seriously.

[@666Kaca]

@@fftere The hell does rome have to do with anything? Also you think we've fallen as a civilization? Elaborate.

[@thetrickster9885]

@@fftere wtf Drink some vodka dost

[@anilvips2978]

I’ve just finished a 3 month university mathematics module on Gödels theorems and you have managed to summarise the whole thing in impressive detail in just 30 minutes. Well done sir.

[@pinklady7184]

What math books have you read this year and last few years? I am curious as I am mostly self-studying maths.

[@anilvips2978]

@@pinklady7184 I haven’t read too many books as my modules are all self-contained. However all my modules have optional reading lists and I’d be happy to tell you what they are if you choose a subject area. My modules have all been in pure mathematics (logic, analysis, algebra, number theory etc.) so it would have to be in that area. I could even ask my lecturers for recommendations if you like :)

[@pinklady7184]

Anil Vips First off, I am a traditional artist with a growing interest in 3D realism & animation including physics simulations, which require lots & lots of writing maths inside node compositing & scripts. I am only intermediate in mathematics. I am not in college, but I can self-study at home, no problem. Only two years ago, I took up studying mathematics at home, as I had needed it for 3D realism, also for programming & scripting. Also, I have just recently taken up physics and engineering as well. I study those a little and maths more. Initially, two years ago, I had to relearn highschool maths at home as I had forgotten half of it. After having learned them off, I moved onto reading undergraduate books on calculus, analysis, linear algebra, set theory, number theory, abstract algebra, discrete mathematics, etc. I know just roughly 75% of them. I don’t know what other undergraduate maths I am missing on the list. Well, I will get there anyhow. At home, I have roughly 25 paper books in my collection, those on maths & physics. Half that number in Kindle. Of paper books, I have only one on calculus (metric version) by Ian Stewart, and I don’t know what next calculus books to read after that. Three books on linear algebra. One on discrete mathematics. One on vectors and tensors by Dan Fleisch. One on algebraic number theory. I’m always curious to know what books that undergraduate students read in college, especially in their first year & second year, and what they read thereafter. I understand just a little of topology, but I don’t know what prerequisites to study before moving to topology, category theory, and suchlikes. I regularly go exploring their internal topics inside Wikipedia, Mathematics Stackoverflow, MathOverflow, Quora, etc. I read what others are studying in colleges, what books they read for studies.

[@pinklady7184]

Hasan Tınaz Been there and done that. New maths is always a struggle. It is one step at a time. I treat each information like a gold nugget. Gather them and clump all the gold nuggets together and that is a gold bar, which is knowledge. Many gold bars gathered - a talent. I oftentimes learn math by brain-picking nerds social media like Twitter, Quora, Facebook groups, etc.

[@pinklady7184]

Hasan Tınaz I keep a study diary on all the tutorial videos that I watch in KZbin, Udemy, etc. A study diary hugely helps.

[@ativjoshi1049]

You just summarised two semester long courses. The visualisation for the first incompleteness proof was spectacular.

[@PiotrKaszuba8403]

I feel the same, but I would also say two semester of life.

[@SahilP2648]

A similar question to this was asked in my Foundations of Computer Theory course in my Master's degree. I don't remember the question itself but I solved it using contradiction of two self referencing black boxes (this video had 1). And I got 99.4% on that test, probably I was first in the class.

[@Digital-Dan]

@@SahilP2648 It is undecidable whether anyone could have done better?

[@SahilP2648]

@@Digital-Dan lol. Well it was the final exam and there were no classes scheduled later, otherwise I would have found out. Or if I had emailed the professor but he may have denied my request. I would say it's more likely it's me than not as it was a very difficult test and my professor Aaron Deever (who was at Cornell) is known to create his own homework questions and his own tests from scratch. Also I did ask a bunch of guys from my batch and none of them had heard anyone getting as much as my percentage.

I just rewatched this, and it's hands down my most favorite Veritasium video of all time.

[@JohnJohnson-vq7ze]

Fun fact: Einstein and Godel were close friends. Einstein once said later in life that he kept going to the Institute for Advanced Study (where they both had a position) just to go on walks with Godel. Godel once found a solution Einstein's field equations that he presented to Einstein as a birthday present. There's also a funny story where Godel applied for US citizenship, but his paranoia led him to conclude that the US constitution is inconsistent and allows for a dictator to take power. He then tried to present his discovery during his citizenship test, but the judge, a friend of Einstein, thankfully cut Godel off.

[@jopheonholzorf]

@@GarrishChristopherRobin777 I'm pretty sure every president has forced policies that not everyone was in favor of.

[@rowenlampe7426]

@@GarrishChristopherRobin777 imagine beleiving someone a dictator and a facist just because they don't agree with you, its beyond me.

[@Maxatal]

@Gerrie van Boven Biden is hardline against China lol

[@Maxatal]

What was this loophole? I’m curious now.

[@Enonymouse_]

Einstein was very particular about who he spent his leisure time with.

[@Djaytaur10]

Hilbert: I proved everything Goudel: I am about to end this man's whole career

[@msew]

lolololololololol

[@GabrielLima-gh2we]

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]

@@GabrielLima-gh2we ikr

[@edwardhuang5885]

Godel: Can you prove yourself tho?

[@gabriellarosa7159]

@@edwardhuang5885 Descartes: Yes

[@MrEmayhew]

“We must know - We will know” And we do know. We know that we cannot know. And that is still knowing.

[@jakubdaraz4138]

Socrates :D

[@JasonJason210]

Isn't that a contradiction 😜

[@nias2631]

@@JasonJason210 its kind of like knowing the empty set.

[@j.dragon651]

I think, therefore I am, I think?

[@KasumiRINA]

@@j.dragon651 you've got another think coming!

[@VicJang]

Amazing video! I’m not able to understand it fully obviously, but the ideas are presented in such a way that’s so clear and precise yet easy to understand. Veritasium is incredible!

[@alexander1989x]

When he showed "It's the Game of Life... running on the Game of Life" it literally blew my mind.

[@ritwikism]

Can someone explain that better? It was cool but I think I don't fully comprehend what is happening

[@amineabdz]

@@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]

@@ritwikism they basically built a computer on the game of life that runs the game of life

[@cookiecan10]

@@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]

@@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

[@Nethender]

Its moments like these where im glad other people did the hard thinking for me, because there's no way id think of any of this

[@Wabbelpaddel]

You'd just have to look close and abstractly enough

[@wassuprocker892]

even if you could you'll likely became crazy, theses logical problems are really for certain rare and random type of personalities and life environements. starting your day by deciding to solve an unsolvable puzzle and doing it seriously for science... personally i see theses fields as almost auto mutilation.

[@panloon7776]

Absolutely

[@BiLLY_KaSh]

@@wassuprocker892 That's where the fun is. Basically life itself is a paradox. Escaping the loop is freeing, but you strip yourself of fun, while staying in it keeps the fun there. Simple solution to the paradox of life is our free will. We can make a choice whether to stay or leave. :) Edit: "Fun" was kind of the wrong word. Satisfaction/pleasure is a better one I think.

[@leviathoncannon]

Godel just told us that we can't know everything about math. Which is obvious. Cuz you can just keep talking about math forever...

[@LordofReason-cd8ug]

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]

Its unprovable lol

[@alberteinstein3612]

Ahhh yes quite the contradiction Now prove it

[@White.W0lfz]

I know what you are saying... but I don't know what you are saying!

[@Excalibursin]

+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]

@ 23:42 he says about the Turing Machine "...although this sounds simple..." ..um, No 😬

[@tonylikesphysics]

This video was amazing. I wanted to comment specifically, but learning Alan Turing killed himself and the circumstances surrounding that just destroyed me inside. I hope he rests in peace 😢

[@rodrigoferreiramaciel4815]

The fact that the game of life can simulate itself has is kind of beautiful

[@_.-_.-_.-_.-_.-_.-_.-]

no dude, javascript is an ugly nightmare

[@thefran901]

@@_.-_.-_.-_.-_.-_.-_.- You can program Conway's Game of Life in any language though, in fact, you can play in on a physical board where you are the one switching each cell in each iteration (which would be nightmarish yes, but Conway used to do it).

[@DBrentWalton]

It sure does. Much like real life itself.

[@ebicman1351]

minecraft in minecraft les goo

[@ryanpwm]

@@thefran901 you can even program the game of life to play musical notes and it makes quite an interesting random pattern/note generators. It’s one the of the few random generation algorithms that can make interesting music while not needing to combine separate algorithms for pitch and time based randomization to be musical. And it generally plays music in a way that is like someone purely improv noodling vs something that sounds either too random or too mechanical.

[@emilyrln]

"19th century mathematicians HATE this one weird trick!"

[@gmarais1986]

Haha when will those ads stop being a thing? Gödel would have known

[@splifstar85]

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]

Oh, look. A meme.

[@FlyoviaUSA]

You won't believe what Kurt Gödel looks like at age 115!

[@Jnglfvr]

Comment of the year.

[@ethang.9116]

Veritasium: “Math has a fatal flaw” Me: So that’s why I failed my math test

[@enveloreal]

your math test failed you

[@Starstruck8970]

Bruh

[@heyeso]

@@enveloreal True, It denied the possible that your answer is concrete and relevant

[@iamshane4960]

@@enveloreal You are not taking a math test, but rather the math test is taking you

[@sharonolsen6579]

"Math has a fatal flaw" I believe this was my repeated assertion for the entirety of my school years... ; D

[@KipIngram]

Turing was an amazing person - definitely one of my intellectual heroes. The way he was treated after the war was criminal.

[@Efreeti]

I spent many hours playing with The Game of Life back in the mid-90s. The fact that The Game of Life is playable in The Game of Life... blew my mind.

[@henningerhenningstone691]

I know right, seeing that literally brought tears to my eyes, so beautiful. Seeing that I realised I had never quite grasped the full extent of Turing-Completeness - any Turing-Complete system can simulate itself, using only itself to do so.

[@God-gi9iu]

O

[@jacominnaar]

@@henningerhenningstone691 I'm glad I'm not the only one that starts tearing up at random stuff like that haha

[@pereraddison932]

@@God-gi9iu ... hIrOnIcAl... Shrodinger...

[@krishnannarayanan8819]

I am just a High school Algebra 2/Trig student, I really want to learn science and math but it's all such a vast world, one of the reasons I also tear up. However, my question remains: Is it possible to play doom in the Game of Life?

[@AlexTuduran]

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!

[@mungaikariuki4252]

These were incredible They wrote a whole book to say 1+1=2 Unbelievable am in awe

[@annoy4nce648]

Honestly, my favourite part of him describing that part of the book is the joke. You can feel how fed up the authors were with the amount of rigor and pointless proofs. And yet, they still acknowledged that there was some level of importance to it.

[@locklan4874]

That is not true, they simply happen to prove 1+1=2. They ddint write the book for that sole purpose

[@NikSchiffmann]

Yah. Touches on the foundations of mathematical knowledge. Kinda wrong though. Bad headline too.

[@TheSpacePlaceYT]

@@locklan4874 True, however I'm sure you know the intended message of the comment.

[@musaiyabmirzaali]

@@annoy4nce648 Pointless is the exact opposite of what they did in that book

[@Coderboyhtml]

The best video I have ever watch hands down. Thank you!

[@stencilman5030]

I can HIGHLY recommend "Gödel Escher Bach" by Hofstadter at this point.

[@mohitlilhore1793]

👍🏻

[@tomisaacson2762]

I've never read a book that explains incredibly complex ideas in such a fun and clever way. It's challenging but amazingly rewarding.

[@danielabbey7726]

Yes, excellent book!

[@professorxgaming2070]

Have it on my stand! The Eternal Golden Braid

[@utroba3108]

Gedel ešer baher popper pen plotter ergometar?

[@amithattimare834]

This video is so professionally made that I am grateful to see it for free on YT. From the animation to the content, everything is beautiful.

[@PiotrKaszuba8403]

Word.

[@ccgarciab]

I know! PopSci tv channels have never gotten to this level of rigour+clearness+production value at the same time!

[@PippPriss]

Wow, can we just appreciate the production value of this video? Veritasium really fulfilled his dream of creating compelling videos of informative nature, but yet touching and following a great "storyline", if you will. He has the perfect blend of his creative dream, being a filmmaker, and his profession/academic degree as an engineer.

[@vSilverXXProduction]

I'm so proud of him

[@dr.strangelove5622]

This is one of the finest videos which I have watched on KZbin. I am always on lookout for sourcebooks: resources which expand on the subject in chronological order while going from lowest to highest level of difficulty for each concept. This video did just that. I wish that there were books which explain the theory of computation in this manner. (I could find only one book which dealt with the subject in this way: Computability, complexity and languages by Martin Davis and Elaine J. Weyuker).

[@agusc5117]

This is just out of this world man. A sincere congratulation to everyone that worked on this piece of art. A great way to convey an extremely complex topic. Thank you for publishing this for free. This is the stuff the next great scientific generations will be built on.

[@lawrencetchen]

Don't think enough credit was given… the art in this episode is spectacular!

[@Vitae_]

credit to who?

[@IskanderVFX]

Impressive

[@jesusmgw]

This video was the only source that made me understand the theorem, and it did it in one go, without even needing to pause or re-watch it. Derek is getting more and more proficient at teaching with each video he makes.

[@nateiverson8681]

Yes! This video is so good!

[@renagonpoi5747]

Which theorem? The incompleteness theorem or the undecidability theorem? Me personally was just so close to understanding Turing Machine, but somewhere right near the end. I may need a few more gos.

[@jesusmgw]

@@renagonpoi5747 The incompleteness theorem in my case, the prime number factors encoding part is very hard to explain usually, and Derek did it super smoothly.

[@jeremyn4397]

For real. I have tried so many times to really wrap my head around what he was doing, but this video helped me see it in a new way.

[@ericmesaros7747]

I had to watch this video twice over a two-day period to comprehend Canter’s diagonal proof. Thank you again Veritasium for explaining complex math and science in layman’s terms.

[@Turtle1631991]

15:15 - The fact that it was Neumann who paid attention doesn't surprise me. The guy was genius among geniuses. In fact upon hearing Gödel he quickly realized and proved inconsistency by himself. Only when he took it to Gödel, he was informed Gödel already submitted work on that also.

[@manager0175]

I am sure Godel said "Hello Newman" in tolerated disgust. 🙂

[@xcruzz]

I can’t believe this was +30 minutes. At some point I was like: “How many of these I’ve seen today?” This was a huge class!!! Loved it!!

[@EdgyShooter]

Meanwhile in physics: "Can you prove this statement is true?" "I'm just going to assume it is and continue from there"

[@bugdracula1662]

I mean that is how the halting problem works

[@TheOriginalFaxon]

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]

@@TheOriginalFaxon a00

[@Number6_]

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]

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.

[@7ismersenne]

A most informative vid looking at some of the more fundamental issues faced in the last 150 years. Many thanks.

[@UltimateDuck97]

I like the first title tbh. "There is a hole at the bottom of math" sounds wayy more interesting. I just wish youtubers experimented with abstract titles like that, but it changed to something much more bland and clickbaity. Like I get it, just a little sad tho.

[@TLHobnobs]

That wasn't even the first title. The first one was "You can't prove everything thats true". I think Derek is changing to to test different title strategies.

[@kaynex1039]

@Angelspawn I would say that "Fatal flaw" is clickbait. The facts in this video will never kill math lol.

[@cybercery5271]

@@kaynex1039 it is a fatal flaw, because once you think about it, everything you do in maths is being questioned by my brain

[@NM-zb6pd]

"hole at the bottom of math" like we all do, math too 🤣 may be for decency purpose he changed it.

[@benjaminjagersma]

@@NM-zb6pd And changing from the first title "You can't prove everything that's true" may also be for decency purposes, as it's indecent for scientists to touch anything close to religion, to treat religion as they were one's private parts.

[@steelfirebladez1081]

Mathematicians: “I used the math to destroy the math”

[@hisxmark]

Math is not destroyed. It is a science. It improves itself.

[@caber1487]

@@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]

@@caber1487 that is not how it works

[@larrycarter1192]

0 is like infinity and infinity and is like 0?

[@goodgoyim9459]

@@hisxmark race and IQ proves many things regardless of what you want to believe lots of anti science ppl here. odd.