the diagonal proof doesnt apply to an infinite list imo. to me thats not a proof at all but trying to apply a concept that might work in the finite realm to the infinite realm
This was the best add for game of life I’ve ever seen
Absolutely best science show! Thank you for inspiring us!
One of the most interesting videos I have watched in a long time, although I have to admit I got lost in a couple of passages.
The past waiter unexplainably fool because bracket immediately twist before a decorous luttuce. noiseless, holistic ghana
This video shows me why there are only a few Turings in this world while the plentiful of mostly hairless apes on Earth have ignorance and violence instead.
0 doesnt exist in the real world. only in math. there is never nothing. only equilibrium.
This video is really going to make me switch my major
Pls explain tht how godel proved true statements can't be proven
I'm fan of conways game of life
I think that's where god enters the chat.
Pretty sure Alonzo Church published his proof prior to Turing.
Pre pubic Gents Barber Required. must be prepared to take early retirement. 🤔😌👍😁 🤣
Then why Odifreddi is still trying to convince us that God does not exist?
There are infinite integers. However, if you pick any integer and its neighboring integer, there are infinite real parts between them. So between every integer there are infinite real numbers. Jesus.
Actually also between real numbers. Pick two that are really close but not the same: x=0.00...01 and y=0.00...012. There are also infinite real numbers inbetween these, kind of freaky.
Yes that's true, but that fact alone is not enough to conclude they have different cardinalities (i.e. they are infinities of different sizes).
Why didn’t you choose coloration that more people can see?
took me 5 minutes to understand the R set line😂😂
What is the pink blob below Australia on your globe, when you are holding up the Godel cards?
If are some trues that can't be proven, how we know these truths??If can't be proven we can't know it's true. We can only have a guess??like faith?? Edit: truth exists, but we don't have access to it
Ah homophobia, ruining math, science, and engineering..
10:45 Wang Hao is a chess player
You realized math doesn't make sense. A realization we've all made
Godel: "ill finish quick this h+ code, then i eat something... "
Self-referent statement: "X is not X". What wisdom, so appropriate for the year 2020 (which equals the year 1984 of Orwell).
6:30 im not convinced we couldn't find the same number anywhere on the list, can someone explain me please?
@Релёкс84 ah thanks if it's simply defined as such then yeah sure
It is defined as being different from every number on the list. So if it ever were on the list, it would be different from itself, which is quite impossible.
6:36 Why does the proof concludes this as you will also get an index for this new number?
Hilbert is wrong.
my brain hurts
no jocking the fatal flaw is that humans invented math, so stupid to believe that the universe all of the sudden after billions of years will just follow those rules.
thank you well, much obliged
8:00 "informal leader of the formalists" - sounds funny
who wants to be a next gen parasite ?
But if an axiom is unprovable, then how can we know that it is true???
The fatal flaw of this "Math Has Fatal Flaw" video is math only has a fatal flaw when you put fatally flawed restrictions on it. For example - the barber at 9:35. The paradox comes from the set of fatally flawed rules. Why must the law say the barber can't shave himself? Most of the range in which these kinds of questions are being asked is beyond where it provides practical usage. For example Newtonian physics works within a certain range and then at some point General Relativity has to be used. Or you can make up a problem that is not answerable,.. such as,.. "Which came first the chicken or the egg?" or more specifically "which came first, the chicken or the chicken egg?" The question has a fatal flaw that restricts the answer to only two possible outcomes,... when neither is true. On an evolutionary scale, the egg obviously came before the chicken. But regarding the chicken and the chicken egg question,... the answer is they both came at the same time. The chicken evolved with the chicken egg simultaneously. This kind of metaphorically proves that if something proves to be unprovable, we just may be using the wrong tools to prove it or asking a fatally flawed question.
Maybe contradictions are true 🤔
Next possibility: Does not exists such a g. Proove: g contains g, it means, that g must be more complicatued than g. It is'nt true. Indirect proove.
and this is why people take such comfort in systems of faith. Even within the video itself, if people couldn't have faith (faith is the assurance of things hoped for, the evidence of things not seen) that one day the hole would be filled, they would go crazy thinking existence shouldn't be possible.
So Math itself is infinite. And Math's infinity could be only proven by Math itself. So Math's biggest flaw is itself being a Self Reference Paradox.
i come here when i'd like to get a migraine
The statement below 👇 is false The statement above ☝️ is true
Sounds like a lot of these guys could of had better lives if they hadn't of taken "show your work" a little to seriously
"Not all infinities are the same size" 😂😂 Size means that something is finite and has dimensions to it. This statement is so wrong in itself!
In an infinite row of numbers, you cannot know for certain that the new number you created will not appear, how in the world one could prove of disapprove this? Nobody could write down an infinite list to begin with.
Or there’s a third alternative to the goodle number g It’s not a number, thus it doesn’t prove anything at all other than that this guy was a tad off his rocker
But………….if the index were made with the real numbers instead then you could make the same statement in reverse…….
Hello, veritasium. So if 'trueness' and 'provability' are seperate, then: (While A= a statement) A can be true but can be unprovable A can be true and provable A can be false but unprovable A can be false but provable So if the statement with godel code 'g' is false, could it be that it's not a contradiction? Since if that statement is false, then it means that proving is true. Proving it as false means it's guaranteed that it's false, and there's no contradiction. Proving is proven to be true. Can anyone share some insights pls
wait what did you use to play the game of life like that? or is it all just animation?
Cool but ........ what???
Godel's parents were cousins?
Seeing the game of life run itself honestly amazed me
God: "hehe, I remember when I was in pre-school"
Prinkipia or prinsipia..?
Hilbert - I'm gonna probably win a nobel price for this... Godel - Hold my beer while I wreck this guy's whole career!
How the hell are there over 6K dislikes of this video? What morons.
The whole Turing punishment is very misunderstood. Like, imagine if a person created a device that could do the 1940s equivalent of cracking nuclear launch codes. Now imagine that person keeps getting drunk, keeps picking up (very socially unacceptable) prostitutes, is continually arrested for causing disturbances with these prostitutes, and continually bailed out by his friends in government. Do you think this person can keep the device or its workings secret? Do you think that such a person could be blackmailed into giving his secret device up? Do you think this person's role in the device could be found out, and that could then be manipulated or kidnapped and forced to work with "the enemy"? That's almost literally the situation. I mean, if he just chose to live a quiet (though yes, somewhat secret and discrete) life with one gay lover, I'm 99% certain the government would have looked the other way, as they usually did with important men who were gay, even back then. Or do you think that there were no important, secretly gay (but known to the higher ups) men ever in Britain before the 1990s...
Very good video. Good work. When I was in basic school I wasn't very good. In secondary school I realised that some subject could actually help me understand, improve and do the tasks of the most ordinary routines of live. By "college" I notice that I was pretty much surrounded by knowledge and everything around me was almost cared for a different subject. Math's there too. But then a teacher had a sort of a public discussion about life and death and for a few days I had my brain wrap and immersed in all the knowledge I have learned so far. Unsurprisingly I came to the conclusion that every subject has its own development but as close that you get to the edge of it's circle the more that knowledge gets more and more mixed with the circule that is next to it. I think that this video is all about that as well. Is about the filosophy of maths. A sort of grey area between maths and filosophy. Or perhaps other subject. I always been convinced that is an area development by the best of maths but also by the ones more unsettled with the 1+1 is 2 who seek arguments in different subjects is order to support their ideas using their knowledge from another subject. It will certainly leave me unsettled for a few days.
The thing is, if our math is so incomplete and flawed, how do any of our modern equipment work...at all? Since it's so dependent on accurate mathematics?
It's more of that it was shown that there is no fundamental system of mathematics which can be complete or decidable and completeness is not provable. So, it's not that every computation in mathematics is wrong just that there are some statements that are unprovably true and that not every problem is actually solvable. It could be proven that it is not (such as the twin primes conjecture). Tbh this is what I understood from the video I could be misinterpreting.
Can someone please explain to me again the part when Derek says that proving the g card makes no proof? I understood everything else but i keep watching this statement and I can't seem to get it
9:55 is a meme.
Isn't the diagonalization proof wrong? It seems that in order for it to work you must get to the end of an infinitely long list, which can't happen since it is infinite in length, right?
I need to say: this video makes me cry. About math, but so touching and personal at the same time. Thanks for that.
"This... is the game of life. Running... on the game of life." My response. "F..k". I don't know why that was my response.
@Veritasium, please consider doing an episode that goes through the proof of why computers use binary. In one of my college courses that was mathematics for computer science majors, we had to go through that proof. The number that came out was the natural logarithm e (2.71828). The following class when we went over the assignment those of use who came up with e (and were also confused as to how you can have a computer system that is BASE e) got our answer. He explained that e was correct, but would be impossible to physically do that. So he rounded both up and down. Hence, BASE 2 and 3 were both good number bases for computers. Few people know this because we also think of computers as using 1s and 0s, or electronically positive voltage or zero voltage (usually +5v and 0v). But there have also been tertiary chips using +1, 0 and -1. (negative voltage, 0v and a positive voltage) Thus, both are equally efficient but the industry rapidly settled on binary.
That does not make sense
When I was in a computer class back before PCs, we had to write a game of life program in FORTRAN. There's much truth out there that can't be proven by the means we know now. That's the beauty of truth. Someday we'll learn the proof, but for now, we're just not there. It's also the beauty of live (as in real life) itself. :) Also, my first degree was in mathematics. In one of my classes we had to show examples where x divided by 0 is undefined. So many people think it is infinity, but that's not always the case. I sure wish I would have saved that paper. But, after many decades, all that stuff is somewhere in a landfill.
Those who know how much wealth they have in bank should not stay here too long or else they might not have any brains left after trying to make sense of this maths-match here.
I didn't quite understand Bertrand Russell's argument about R - why if it does not contain itself then it must contain itself, and vice-versa. Can anyone explain the logic? Thanks.
I love this guy's videos.
I stopped understanding this video at 14:00 😂🤣
Math doesn't factor in chaos and consciousness probably because it can't and reality has shown time and time again to contain both.
How the hell did anyone come up with this and actually understand it. It’s so fascinating but I don’t understand it lol
press f for the barber
Whenever I hear about this kind of thing, it really makes me wonder if part of the problem is that our current understanding and use of mathematics is fundamentally flawed even right down to arithmetic. But then I realize how impossible it would probably be to come up with some system of math that didn't work with arithmetic as a base, and my head ends up hurting.
Hilbert: "Math is complete." Gödel: "Well actually..." Hilbert: "Ok, fair enough, but math must be consistent." Gödel: "Ackchyually..." Hilbert: "Oh for fuck's sake, but it has to be at least decidable!" Turing: "LOL"
As a object oriented programmer used to deal with composite objects that has references of itself, the R set blow my mind
Man I have seen this thrice now
This self referencing is the cause of me not understanding flipflops.
29:56 which music is this??
The secretive invoice optimally taste because milk lately carry unto a shocking dock. beneficial, soft retailer
Language is not a math! Car can be different pronounce and some people thinking about car call it a motor :-)
How fortunate is it that you can apply these mathematical principles to other systems
A potentially stupid question: Why would you bother to create H+? Why wouldn’t you just create H and call it a day? And would the answer still be the same if you did? 🤔
Why do people assume they need to count every vain of each leaf on a tree to know it's a tree? If red or green round things grow off twiggs attached to branches, it's a red or green "Apple" "tree". You do not have to count how many apples have worm holes to know it's an Apple tree, and worms like Apple too.
Lol just found the meaning of consciousness
I swear he makes this sound so simple but at the same time my brain cannot comprehend anything he is saying
Me too the card part is too much
So sad about Alan Turing...❤️
Okay, that's the same explanation for the hotel with infinite numbers, My question is what if Cantor's"Diagonalization proof" is Wrong? What if in the set of infinite numbers there are infinite numbers with all the infinite possibilities of the diagonalization proof? I mean what if there are indeed numbers that are greater (and less) than the numbers in all indexes of all numbers with all different possibilities (antidiagonal)? Given the nature of infinity, this is a legit question. P.S I'm not trolling, I truly need an answer.
@mohamed mada Not, it is not the same as Hilberts hotel. There you have only 1 infinity. The infinity of natural/rational/integer numbers. In Cantors diagonalization argument occur 2 infinities. One is bigger.
@mohamed mada _"You didn't quite capture the essence of my question,"_ I did: Cantor was not wrong. _"I didn't say that there could be a number greater than another number in one set "_ You said: "I mean what if there are indeed numbers that are greater (and less) than the numbers in all indexes of all numbers"- There are the natural numbers. Those DEFINE the term "countable". It doesn't matter if there are other numbers. There are of course. The rational numbers for example. But those are not really more. And there are the real numbers. Those are "more". So we are already talking about this. _"My question simply is what if such a number already exists"_ There exists no such number. A number is not a set. And there is no natural number "greater than all natural numbers". _"and our list which contains infinite numbers having infinite possibilities?"_ All possibilities do not contain all real numbers in [0,1] as the proof has shown.
@Andre You didn't quite capture the essence of my question, I didn't say that there could be a number greater than another number in one set even though in an infinite set of numbers that could easily happen, I mean since the diagonalization proof says that in the list a different number would be created changing the index of each number increasing it by one ergo it won't belong to our list. My question simply is what if such a number already exists and our list which contains infinite numbers having infinite possibilities?
_"My question is what if Cantor's"Diagonalization proof" is Wrong?"_ It is not. Next question. _"what if there are indeed numbers that are greater (and less) than the numbers in all indexes of all numbers with all different possibilities "_ A number cannot be greater than all numbers. This is trivial to prove. _"Given the nature of infinity, this is a legit question."_ No, it is not.
I couldn't agree more, it's convoluted, isn't taught in ways most understand, and it doesn't olve man's greatest problem: stupidity.
This is so much better explained than everything else that it's the only one that actually says the problem how it is
I have a Doubt Derek. If the Machine h has to produce some kind of output, It has to first run a code and an input for which the sequence of the output may or may not terminate. Then the machine h+ comes into play, Which implies that the sequence of the program and the input which was already coming is inverted completely which follows a loop around the machines h and h+ and I don't see why this creates a contradiction(like if the machine h gives out the output that the first inserted program and input produces a sequence that terminates. Then the not gate put inside h+ reverses the sequence and terminates it which in turn produces a inverted loop. In which the steps of procedure are inverted with respect to the steps mentioned before.)Which implies that the machine h when working in conjecture with the machine h+ never produces a stable output when it is fed with h+'s program code and the recurring input. Then I don't see why they simply assume that the machine h is impossible to make.
This can go in either one of two ways. 1) Either I am Stupid.2)Or You are a Genius to Understand this.
We are immortal until the day we die
One issue here is that any "solution" for Russell's Paradox is probably translatable to a homologous "solution" for Godel's Incompleteness Theorem. My understanding is that there have been at least 3 PhDs generated in the last 100 years purporting to "solve" Russell's Paradox, in 3 different ways. Thus one (I) would expect that there are at least 3 corrective counter-theorems to Godel's Incompleteness Theorem. Hilbert might, and probably would, content himself with these, since if memory serves, these are more or less formal ways of encapsulating and manipulating Russell's Paradox. [Note that I would conjecture that homotopy theory implies there exits an (uncountable) infinity of such solutions to Russell, translatable to an infinity of solutions to Godel incompleteness. Cheer up, dead Hilbert, no need to twist in your mathematical grave; your glorious formal headstone still marks your intellectual location for would-be visitors.]
The problem with infinities is a problem of the human brain, not of mathematics. Consider : humans cannot truly understand what infinity is because our brains are finite. Stop considering infinity as a static object, and think about them more as multi-dimensional like space-time. The set of real numbers is infinite, as is the set of integers, but the real number set "grows" faster than integers. So they are both infinite but not the same size at the same point in some (newly defined) dimension.
5:47. I think if we can get this new real number then we didn't actually write all the real numbers in the first step (we wrote all the real numbers minus one).
_" then we didn't actually write all the real numbers in the first step (we wrote all the real numbers minus one)."_ And that is the reason why it is not possible and therefore there are more real numbers than natural numbers.
Turing was essentially killed for being gay. Lot's of wonder and beauty presented in this video balanced with some dark stuff.
I love how much I hate this, but I also hate how much I love this.
4:06 I wonder how to search through all the comments and find out why a set of nothing is inside the set of everything?! >search:?
i'm new here.. why the heck are you explaining math in the middle of nowhere? :D
That is why man as a part of creation, will never be the creator god of everything.