i feel like the reason this is one of vsauce's most popular videos is because so many people come back to it every now and then cause they don't get it.
This one is reallly hard to understand if your brain is not accustomed to thinking in infinites and using assumptions to make other assumptions. Like I bet math majors would be able to follow this quite a bit easier than most people for that reason
This video is incredible. In only 24 minutes Michael took a concept that is utterly incomprehensible, separated it into a number of smaller parts, and turned it into a concept that is utterly incomprehensible. One might say he Banach-Tarski'd the shit out of it.
@@dudebuddy69that’s funny because my feelings didn’t make it to the video, my reasoning, logic, education, experience, they all made it. Also kinda backwards to have 69 in your name but you’re not nice.
I’ve been watching VSauce for the past 10 years, and some of his videos went over my head. I rewatch them and I understand things I didn’t before. What an awesome channel. I wish he did more lengthy videos instead of shorts.
Abstracted mathematics must be one of the dumbest, most pareidolia type of activities in the history of mankind. The number of atoms and the degree of force in a dollar bill and in a rotating unit is exactly the same before or after math nerds start their rants
I literally stayed home from school ND watched alot of his vids n took notes ND learned it went back to school taught my teacher den used this all in my reason why I dont need to go to school to learn
The funniest thing is that when we were kids, we would say that. Then as high schoolers, we thought infinity = infinity + 1 and made fun of people. But actually, in terms of ordinal numbers (where omega is the smallest infinity - countable infinity), omega is smaller than omega + 1, which is smaller than omega + 2, etc. This is different than cardinal numbers, like aleph-0, where aleph-0 + 1 = aleph-0. The whole point is that people have their own ideas about how to define everything, which is pretty epic in my opinion. Mathy explanation of the difference below: When defining the ordinal numbers, we take 0 = the empty set, and S(n) = n union {n}. Thus, the nth natural number is the union of all the natural numbers before it. Omega is the union of all the natural numbers, then. And then adding one more element to the set grows it, clearly. The cardinal numbers are defined as the distinct isomorphism classes in the category of all sets. That is, if you can map every element in one set to every element in the other set, they're in the same isomorphism class. So, as it turns out, when taking about these, we could totally map a set with omega elements to an element with omega + 1 elements. So in that sense, infinity + 1 = infinity. Weird, right? It's the best part about math, that the further and further we dive into trying to explain everything, we find more and more unanswerable questions.
If u watch it infinite number of times, the information u find is gonna keep increasing, as every time you watch it, your brain gets somethings that it didn't get the last time. Eventually, you will end up with infinite knowledge wtf It's 1:00 am. Don't you dare say I'm wrong. Actually..It maybe a hyperwebster... Caus' infinite knowledge can be divided into two parts: 1. Infinite knowledge 2. Infinite knowledge. Basically, U have infinite amount of infinite knowledge. I need to sleep.
I come back to this video once every year to see if I got smarter enough in order to understand the banach-tarski paradox. This is my 4th year, I finally understood
Oh, finally, someone who gets it! I’ve been stuck with so many questions, and I’d love your thoughts: 1- Technically every point may pas from polar parts of the sphere? So why don't we call each point as polar points? What does it mean to be close to those polar points? Ok this is the only question left that i didn't really get. Actually I have an answer. Polar points are the points doesn't act like we wanted. There are countable amount of them. But why? I think there can be uncountable number of them. If you can do that 14:56 image than you can do it on any point on the circle that point is on which is uncountable. And actually creating an image like that is impossible. But for example it is possible for the points 1 left away from the pole points for up and down movements to act like we don't want. For example we can apply those points left, down, down, right and we get to the point we started. Because when it is on the pole point of up and down it doesn't get effected by up and down. So when we do right we get to our starting point. This really is an issue. We need to fix it. This is just an example. And we can create multiple of them. So the issue here is understanding if the polar points are countable or uncountable. If it is uncountable then I think we didn't achieve anything. Because if it is uncountable the sum of up down right left and start pieces can be countable. Which means countable number of points. It doesn't even create a line. We can't guarantee to fill the space left for polar points with the points we have.
I cant believe that when i was younger i watched this video and it amazed me in so many ways, i thought about it and right now am studying it in my collage, time flies, and im happy that michael made this video that long ago, he actually inspired a lot of people, thats why i will always have high rispect for him
Daniel Grosch Yeah, I even mouthed along to it! BTW, this Paradox reminds me of how people used Key Black on cartoons, so they didn't have to use use too much Magenta, Cyan and Yellow. They took away colours, yet ended up with the same thing!
1) I can't agree with part one on "countable" infinity because I think that's just a misconception. When you say "we used up all the whole numbers", what you mean is "we reached the end of the finite list of numbers" but that list is NOT finite. Thus you will never end up "lacking" numbers. This is the same as saying "even numbers" vs "integers". You are just shifting your group definition. I think you grasp the idea when you say "lets start with 0.000 and add 0, when should we start ? We can't start because there is always one left" -> exact same with the whole numbers. You cannot end, you cannot say they are countable. You could say they are "iterable", but they are not countable because the "infinite set of numbers" has no length, because length means "head" and "tail". But "tail" means "the end" and there is no end to an "infinite amount". That's like saying "start by counting the length of an infinite universe, in kilometers, then ". You could start at some point and count : 1 km, 2 km, 3 km, 4 km, ... But you will never say 'hey i've reached the end, let's proceed with the next instruction" 2) Hilbert's hotel : You can't fill an infinite number of rooms. Imagine you have N the number of rooms = infinity. Now M. Smith comes to you and books a room. So you now N = infinity - 1. This notation is absurd but let's forget it for now. Next person would do N = infinity - 2. So having no rooms left would mean that when you count 1, then 2, then 3, then 4, ... you would at some point reach "infinity" but that's not how infinity work ! Because that would mean that there is a finite amount of numbers and that you reached the end. That would mean that there is a x value that solves x+1=Infinity. That does not exist, by definition. 3) "After an infinite number of those" -> not possible, because that implies that at some point, he would say "i arrived at the finite boundary of the infinite and will now proceed to AB". 4) Again, we cannot color all points because it is infinite ... Feels like this video misses the whole point of "infinite". This is a fairly difficult concept for us to grasp as it does not appear to us in nature, but saying "oh we were iterating to the infinite and reached its finite boundary" is just a problem of definition. Would be happy to debate around this and be proved wrong.
@Accursed Nature i geuss i added the part where you call him stupid, but what you said was that he didn't come up with this information by himself, he just researched it and repeated the topic which he read. Im saying every piece of info is based off of something though, physicists and teachers didn't just do experiments and figure out stuff all by themselves, they go through years of schooling, so you could say they don't know anything and are just repeating what they saw in a textbook.
@@zaahilibraahim7113 with infinity room's then there would be a infinity area in the hotel therefore the hotel itself is infinity so if you were outside the Hotel and tried to walk around the area of the hotel it would be endless
This is the only Vsauce video that genuinely stumps me. I eventually come back to it every year or so and understand it a little bit more, but I'm not quite at 100% just yet. This is such an interesting idea and Michael's ability to communicate the logic behind it so fluently is incredible, it makes those developments in understanding every time I come back feel so much more satisfying. Having grown up watching someone make learning truly enjoyable is honestly priceless, I hope Michael knows to how many people he is that someone.
Let's say you and your friend are playing "guess natural number", because there are countable amount of natural numbers, you will eventually guess your friend's number. Why? Because you can list all of the elements: after 1 comes 2, after 2 comes 3 and so on. In case of real numbers there is no "next" element. What comes after 1? 1.0001? Or maybe 1.0000001?
@@megrelikaci3380 To do so you don't need real numbers, rational numbers suffice, and they are a countable "number". Don't confuse continuous and dense sets: both 1.0001 and 1.0000001 belongs to the set of rational numbers Q. More, the real numbers that we can access to and use, i.e. that "exist", are _countable_, too bad Herr Cantor.
@@ferruccioveglio8090 What do you mean? We can list every rational number, but can't do the same for real numbers. The word countable means that you can count from one element to another, right?
Mine started when i began existing, or was it before i was existing? Could i have known of existence before existence? Impossible. Idk where i was going with this
Banach-Tarski K/D = infinity. Thanos = half of the universe/0.5 (referring to when he almost died by the hands of Thor)[haven't watched end game if it's even out, don't spoil anything for me fags lol]
@@friedec3622 if you move you move inside a sphere because the earths atmosphere is round contrary to the earth itself that is slightly larger at the middle point if you lost it at that point you have smol brain
The cool thing about VSauce is that every video you can still learn new things on every rewatch. There's things you didn't notice or remember or pay attention to, there's new connections you make with things you've learned since last time, you understand more from being an older smarter person now. I've been rewatching this for 9 years and I think I've got a pretty good grasp on it now yet this video still gets me thinking. Incredible.
or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you
@@tev5040i watched it before and it went over my head, but I got it this time. Youll get it if you think about it enough, i think what makes it confusing is infinities are hard for a person to think about.
Watch us one day create a machine to do the math for your heart which creates a complete separate heart. Would still be your crappy heart and you’d still need a different one though lol idk Im stoned because of this video.
I love how there are still comments from like an hour ago. It's been 5 YEARS. Vsauce will always be awesome, It's gotta be one of the coolest things to exist on the internet.
"In reality,i have not. You see,infinity plus one equals infinity,and as i have the right to eat an infinite amount of food,the five hours i've passed here are the same as not spending any time at all"
probably because its a useful mathematical fiction and is metaphysically impossible. Actual infinities are metaphysically impossible and violate the law of non contradiction.
currently studying the banach-tarski paradox for fun and rewatched this video, never really appreciated how informative it really is! also tysm for providing links to your sources, when i say it’s really helpful is an understatement.
I watch vsauce when I go to bed every night, I’ve never taken in the information and I don’t really care if I ever do, but I do enjoy his voice as I drift off
One of the Paradoxes proves that I can’t be actually arrested, if you divide 10 and 5 you will get 2, The 2 counting as a “N” Now if you divide 1 and 1 it would be 1, The 1 Counting as a “O”. You know where I am going to this? Now this is the place where the magic occurs, divide 8 and 2 which would be 4, The 4 counting as “U”. Did u see the magic happening in front of your eyes? (Sorry if this had no sense lol, I don’t speak english)
They released a patch, but I can't install it - it's incompatible with my axiom of choice. (I also heard that the patch causes a different glitch - it makes it possible to split a set into more subsets than it has elements. Anybody had the same experience?)
@@yourboy9236 he's reffering to the "days" (period) that they were regularly/semi regularly uploaded, I suspect you knew this and you're a piece of shit.
This man made me fall in love with learning when I was a child, I remember I used to hate actually studying when I was 13 and now I have just entered my phd physics program at 25 :) absolutely love him ❤
What happens when you love learning, but public school doesn't allow you to find your own path. I'm in a similar situation but still in high school, thank goodness for my English 101 teacher making me make my own learning topics, I would be very depressed otherwise.
@@zacharyswassing6741 lmao you'll be more unhappy when you're out in the real world. Enjoy every second of school if you can, and remember that feeling depressed is just a chemical hormone, you're in the best years of your life
I do not understand anything but I know, rotating in the right direction, specifically, particularly, accurately, and precisely, will make me create a clone of myself. Thank you Vsauce.
Whenever I feel like I'm smart, I come and watch this video to get rid of that nonsense
Ever tried watching videos about space-time??? Or astronomical physics? Lol
one 2 heist
1 cespie . = 1 despite cheeeck, while it take
Yeah ! Right ?
@@ragecentral2861 Not Very Nice Earthling ?
So What His Point! I Already Knew you cant be like Buzz Light Year and go BEYOND INFINITY !! WE ARE FINITE!!
i feel like the reason this is one of vsauce's most popular videos is because so many people come back to it every now and then cause they don't get it.
Aren't those the best videos? haha
Yep, my second coming. Still dont get it.
This one is reallly hard to understand if your brain is not accustomed to thinking in infinites and using assumptions to make other assumptions. Like I bet math majors would be able to follow this quite a bit easier than most people for that reason
@@ogrim0 my 5th, and I'm still clueless
lol
Every time Micheal says “or can you” the universe reluctantly has to rewrites the laws of physics.
@@alexandramarberry1023 Or is it ?
But can you?
or can they?
"Ye canny change the laws of physics!"
-Montgomery Scott
Or will it 🤨
This video is incredible. In only 24 minutes Michael took a concept that is utterly incomprehensible, separated it into a number of smaller parts, and turned it into a concept that is utterly incomprehensible. One might say he Banach-Tarski'd the shit out of it.
That twist got me
That's what you're doing genius........ Education, hurts your feelings.
😂😂😂😂😂
@@dudebuddy69that’s funny because my feelings didn’t make it to the video, my reasoning, logic, education, experience, they all made it.
Also kinda backwards to have 69 in your name but you’re not nice.
HAHAHAHAHHAHAHAHAH
This is true pure mathematics. The kind that makes you feel smart, stupid and insane at the same time
Mostly makes me angry.
That is the perfect way to describe it, thank you!
@@n0denz 😤
@@stealthis 😤= 😠 + 😔 + 🙁 + 2 x 💨
@@asheep7797
Me when 1 + 1 = 2: 🥵 = 😰 + 😡 + 😊 + 😛 + 💧
Me when 1 + 1 = 1: 🤬 = 😡 + ➖ + #$!@
Chiropractor: I’m just gonna make a small adjustment.
*turns 90 degrees*
*accidentally duplicates spine *
Hah
Ok but like a Hydra
My mans did the shift + drag
Extra flexible
add bra kad add bra????
Feels like I've learned everything but nothing at the same time
impactofredemption r/im14andthisisdeep
That's maths for you.
that's called life
Vsause? More like Vegie sause! ! !
that's why it is called paradox
"It doesn't care; it's infinity"
Thats the level of confidence I want to acheive
It’s insane how he can go through half the video before he actually dives into the topic and still keep us engaged
half the video im already going insane
This explains how mars bars and Cadbury chocolate bars got smaller and retailers and manufacturers got richer .
They thought you wouldn’t notice !!!
@@johnnorris1983 Don't u mean Kit Kat?
Interesting to say the least
Start: Can you multiply a chocolate bar?
End: The Universe is both infinite and finite.
hah when u know why theres choco trick but u cant explain
You don't have to be smart to get its relative point, i gues :D
@@larswalzberg8486 9 divided by zero is infinite :D
@@phoenixjamirazucena5672 lol he spent a great deal explaining how you can make two spheres
@@larswalzberg8486 I know
Gave 1 star to Hilbert's hotel on Trivago. They kept shifting our room.
Feels like I've learned everything but nothing at the same time
Underrated comment!
This comment is just a cute joke and I love it
@Eric Lee thanks spelling is not my strong suit
@@eleanorbarryjhondersey7492 I hate to be the a**hole, but that was stolen from one of the top comments.
1:15 Michael... don't you dare... DON'T YOU DARE SAY IT. Michael--- 🤦 He said it..... HERE WE GO
Why did I read that in an indian accent 😂😂
@@paolalovescats I don't know, but now I did, too 🤣🤣🤣
I immediately thought of Vsauce's mom saying this 🤣
@@NASAnerd-bc2mx i can hear it! 🤣
*Queue the Vsauce music*
"Countable means you can count them"
michael you are so wise
Or is he
@@morpher728 ...Hey, wait a minute!
Ngl he spittin striaght fax
My name is Michael
Lmao idk why I needed this, but thanks
Most TH-cam videos are one time consumptions. Vsauce is that rare gem with rewatchability value.
Only because you didn't get it the first time
@mattb6646 not necessarily for me
@@mr.pineappler4269 I meant myself lol
@@mattb6646Alr mb
Soviet Womble and Cody ko that’s cringe
Michael: Obviously you can’t cut up a chocolate bar and have more than you had before.
Me: don’t say it
Michael: or can you
*groovy music starts playing*
I can. (Because I'll steal yours too. And Michael's, now that I think about it).
It's how Jesus duplicated bread
Once You know lyrics, You can't sing along!
Toom aroom, pam pom pam
Reals are Aleph_null to power of Aleph_null
I’ve been watching VSauce for the past 10 years, and some of his videos went over my head. I rewatch them and I understand things I didn’t before. What an awesome channel. I wish he did more lengthy videos instead of shorts.
“Countable means you can count them”
Man I’m glad I skipped school and watched Vsauce today.
pkcaleb Your 100th like your welcome 💯
Abstracted mathematics must be one of the dumbest, most pareidolia type of activities in the history of mankind. The number of atoms and the degree of force in a dollar bill and in a rotating unit is exactly the same before or after math nerds start their rants
same
I literally stayed home from school ND watched alot of his vids n took notes ND learned it went back to school taught my teacher den used this all in my reason why I dont need to go to school to learn
The only thing I understood from this vid
Michael: ...we are now ready to move onto shapes...
me: *you lost me at “hey vsauce”*
pupper_mint underrated comment 😂
Jeebuz thanks bro
🤣🤣🤣😂
pupper_mint hey vsauce?
But hopefully not to a purple square. It is scary.
I have a lot of achievements in life but my biggest achievement is understanding half of what this video explains
The first part is easy, your mind decomposes once you start talking about the actual paradox
@@HassleHoffer372 mine wasn't decomposing infact it was never even there
That's some bold claim man.
Same
@@paulinoponcianotugonon2182 mine evaporated
Imagine eventually in the future when science is morre advanced, kids will be playing with banach-tarski sphere puzzles instead of rubik's cubes.
th-cam.com/video/9IKwPoNhP4E/w-d-xo.html
Did you really just say "Rubix"?
@@JonathanAufderheide-ln8pr oops thanks for pointing that out.
Did you really just say "rubiks"?
@jammyg1779 lmao
“countable means you can count them” is the only part i understood
same
ditto
:))))))
Lool
it means there exists a bijection between the set you're looking at and N (the set of natural numbers)
It's interesting to see that even after so many years none of the Vsauce videos seems old. They are ageless.
Just like him. Time will never catch up to either of them
Or are they? (moon men starts playing)
Why are you a red concrete block.
@@Immadeusbeat me to it 🙁✊
th-cam.com/video/zHL9GP_B30E/w-d-xo.html
6 year old: im infinite cooler than you
Another 6 year old: im infinitely+1 cooler than you
Michael popping out of thin air: actually...
Dunk Potato This is the most underrated comment on this comment section
The funniest thing is that when we were kids, we would say that. Then as high schoolers, we thought infinity = infinity + 1 and made fun of people. But actually, in terms of ordinal numbers (where omega is the smallest infinity - countable infinity), omega is smaller than omega + 1, which is smaller than omega + 2, etc. This is different than cardinal numbers, like aleph-0, where aleph-0 + 1 = aleph-0.
The whole point is that people have their own ideas about how to define everything, which is pretty epic in my opinion.
Mathy explanation of the difference below:
When defining the ordinal numbers, we take 0 = the empty set, and S(n) = n union {n}. Thus, the nth natural number is the union of all the natural numbers before it. Omega is the union of all the natural numbers, then. And then adding one more element to the set grows it, clearly.
The cardinal numbers are defined as the distinct isomorphism classes in the category of all sets. That is, if you can map every element in one set to every element in the other set, they're in the same isomorphism class. So, as it turns out, when taking about these, we could totally map a set with omega elements to an element with omega + 1 elements. So in that sense, infinity + 1 = infinity.
Weird, right? It's the best part about math, that the further and further we dive into trying to explain everything, we find more and more unanswerable questions.
😂
*vsauce music plays*
Me, an intellectual : I am cooler than you no matter what
Summery:
0:00 Chocolate
1:17 Intro
2:11 Infinity
- 2:50 Countable and Uncountable Infinity
- 6:50 Hilbert's Paradox of the Grand Hotel
- 8:08 Shapes
- 9:38 The Hyperwebster
11:16 Banach-Tarski Paradox
- 11:31 Sphere's Surface
- 15:33 Why 1+1=1
19:01 Conclusion
Imagine staying at Hilbert's Hotel, and every time someone shows up, you gotta pack everything up and move down a room
An infinite amount of people show up
@@isaaccrimmins968 I will just f**king leave the hotel and stay the night on a park bench
Definitely sounds like a Wes Anderson movie.
@@isaaccrimmins968 watch ted ed video about infinity paradox they have answered your condition there
Imagine the buffet of hookers
Michael could go clinically insane and no one would notice a difference.
maybe a little bit
Already is
Same goes for all mathematicians really
Please! Someone explain this part to me 13:50
Why is it that "UP" does not end at the same point as "RIGHT, UP, LEFT"?
Fr dude
I've watched this like 5 times now, I'll get it eventually...
I don't think I'll ever understand this...
@@easterlake I think I’ve watched this 5 or 6 times since it came out and I finally get it omg I guess I was just too young before lmao
It's my 6th or 7th time watching now and I just got it! :)
If u watch it infinite number of times, the information u find is gonna keep increasing, as every time you watch it, your brain gets somethings that it didn't get the last time. Eventually, you will end up with infinite knowledge wtf
It's 1:00 am.
Don't you dare say I'm wrong.
Actually..It maybe a hyperwebster... Caus' infinite knowledge can be divided into two parts:
1. Infinite knowledge
2. Infinite knowledge.
Basically, U have infinite amount of infinite knowledge.
I need to sleep.
lol
I come back to this video once every year to see if I got smarter enough in order to understand the banach-tarski paradox. This is my 4th year, I finally understood
good
Oh, finally, someone who gets it! I’ve been stuck with so many questions, and I’d love your thoughts:
1- Technically every point may pas from polar parts of the sphere? So why don't we call each point as polar points? What does it mean to be close to those polar points?
Ok this is the only question left that i didn't really get. Actually I have an answer. Polar points are the points doesn't act like we wanted. There are countable amount of them. But why? I think there can be uncountable number of them. If you can do that 14:56 image than you can do it on any point on the circle that point is on which is uncountable. And actually creating an image like that is impossible. But for example it is possible for the points 1 left away from the pole points for up and down movements to act like we don't want. For example we can apply those points left, down, down, right and we get to the point we started. Because when it is on the pole point of up and down it doesn't get effected by up and down. So when we do right we get to our starting point. This really is an issue. We need to fix it. This is just an example. And we can create multiple of them. So the issue here is understanding if the polar points are countable or uncountable. If it is uncountable then I think we didn't achieve anything. Because if it is uncountable the sum of up down right left and start pieces can be countable. Which means countable number of points. It doesn't even create a line. We can't guarantee to fill the space left for polar points with the points we have.
7:15
*another guest shows up
Everyone in the hotel: Aw shit here we go again
lol
That’s exactly what I was thinking lol
Imagine, you will move out of your room infinite times in a day.... ow sheet
Or like just give him the last or infinity+1th room which is infinity
Infinite numbers of Aw shit, here we go again
I love everytime he says something and then just goes “OR IS IT”
I hate when i stop understanding his explanation just after easily understanding the whols previous things he talked about.
I was just about to comment this hahaha
......or was I?
OR DO YOU?
Hi Ryan I am from the future, 2021
Banana man
when he said “the missing hole is forgotten, turns out we never needed it to be complete,” i felt that.
purple eve mood
im 14 and this is deep
I am that missing hole in life :((
9 years later, I'm still watching these old Vsauce again, going to that awkward silence part, and just like an instinct: Here we go again.
Landlord: Alright Michael, rent is due
Michael: *proceeds to explain to them why rent isn’t due until next century*
>rent is due
>OR IS IT?
Krakeon “michael please you do this every month give me the money and let me see my family”
No problem for Michael as this video has probably paid for his house -- no more rent.
😄
Like 667, saved you all from the devil.
This, is just simply how a cobblestone generator works.
This is an underrated comment.
Facts
This just made my day.
u are awesome dude
Lol
Let’s just appreciate how he writes this stuff down so we can somewhat understand it
I didnt realise that I understood it at all
I am the most famous man on YouTub! This is not bragging! This is the truth! The truth will set you free, dear du
@@AxxLAfriku no
Undestine,encx!
IfYoozDid...
I cant believe that when i was younger i watched this video and it amazed me in so many ways, i thought about it and right now am studying it in my collage, time flies, and im happy that michael made this video that long ago, he actually inspired a lot of people, thats why i will always have high rispect for him
dude imagine you’re in a argument with Michael and all of a sudden he says “or can you?”
at that point you know you’re done
Yep
“You can be alive. Or can you?”
Omg this comment is genius
@@oliviawilson4806
Or is it?
@@iiReTr0Z or are you?
It's pretty impressive that you guys found such a complicated glitch, hopefully the devs don't patch it
Lol
weeeeeee its time to use it and solve world hunger
Lol that's NPE for you.
compared to paper mario badge duplication, this is nothing
The dev space is in a bubble everyone is a software engineer lately because they went to a three weeks boot camp 🤣 so they won't pick it up 😕
I fear no man
But that line
"Or can you?"
It scares me
Or does it?
"Or can you?"
The question is most often rhetorical, but an existential gauntlet throw-down, nonetheless. >:^)
@@hlcepeda i have no idea what you just said but im scared
Mom come take me home please
@@glitchyart2120 That was my reaction after watching the film 'Hereditary'. And I don't scare easy. >:^)
1:15
13:50 bro is URR away from getting cancelled
nah its RRU
@@AimarDAGREAT he wrote it backward
you know you boutta learn some shit when michael says "or can you?" and the music starts
And you see that the video is 24 minutes long xD
Daniel Grosch He should put x-files music on when he says that xD
Daniel Grosch You know that the shit is about to get real when he says "or can you?".
When he says that, just know... YOU GON LEARN TODAY
Daniel Grosch Yeah, I even mouthed along to it!
BTW, this Paradox reminds me of how people used Key Black on cartoons, so they didn't have to use use too much Magenta, Cyan and Yellow. They took away colours, yet ended up with the same thing!
"No hole will be left unfilled." Now that is something I did not expect to hear while learning about math.
In a theory by Buttock Tarski? Why ever not?
( ͡° ͜ʖ ͡°)
This my friend is called MathPorn...
@TheFakeyCakeMaker 📸
9:16 yw
Teacher: the test wasn’t that hard
The test:
Paul Cimijotti right when I read this Vsauce said “That’s not possible to do in the real world.” Lmao
Yep
Right after I read “the test” Michael asked “what is infinity” like it was question no. 1
Same exact thing happened to me indie Jones lol
Copied
Every few years I come back to this video after I’ve grown up a bit to see if I understand it any more than I used to. Still working on it..
1) I can't agree with part one on "countable" infinity because I think that's just a misconception. When you say "we used up all the whole numbers", what you mean is "we reached the end of the finite list of numbers" but that list is NOT finite. Thus you will never end up "lacking" numbers.
This is the same as saying "even numbers" vs "integers". You are just shifting your group definition.
I think you grasp the idea when you say "lets start with 0.000 and add 0, when should we start ? We can't start because there is always one left" -> exact same with the whole numbers. You cannot end, you cannot say they are countable. You could say they are "iterable", but they are not countable because the "infinite set of numbers" has no length, because length means "head" and "tail". But "tail" means "the end" and there is no end to an "infinite amount".
That's like saying "start by counting the length of an infinite universe, in kilometers, then ". You could start at some point and count : 1 km, 2 km, 3 km, 4 km, ... But you will never say 'hey i've reached the end, let's proceed with the next instruction"
2) Hilbert's hotel : You can't fill an infinite number of rooms. Imagine you have N the number of rooms = infinity. Now M. Smith comes to you and books a room. So you now N = infinity - 1. This notation is absurd but let's forget it for now. Next person would do N = infinity - 2. So having no rooms left would mean that when you count 1, then 2, then 3, then 4, ... you would at some point reach "infinity" but that's not how infinity work ! Because that would mean that there is a finite amount of numbers and that you reached the end. That would mean that there is a x value that solves x+1=Infinity. That does not exist, by definition.
3) "After an infinite number of those" -> not possible, because that implies that at some point, he would say "i arrived at the finite boundary of the infinite and will now proceed to AB".
4) Again, we cannot color all points because it is infinite ... Feels like this video misses the whole point of "infinite". This is a fairly difficult concept for us to grasp as it does not appear to us in nature, but saying "oh we were iterating to the infinite and reached its finite boundary" is just a problem of definition.
Would be happy to debate around this and be proved wrong.
I wasn’t in the mood for an existential crisis today, but here we are.
I didn’t even know I was a having a existential crisis till I google the meaning of the word
Ikr
❤
i-it's 1:30 but I feel you
Haha!
Made me contemplate what 'mood might invite and existential crisis.
*1st grade teacher*- so kids 1+1=2
*Michael in 1st grade* - umm not really see if you take a 3-D sphere and mark every point.......
@Accursed Nature but he's pretty fucking smart for understanding that lol...he lost me at "Hey Vsauce"
@Accursed Nature everything is based off of at least one small thing, so you are saying that everyone is stupid and can't do anything
If you substitute the word "Michael" in the example to "person who understands this", would that make you happy? Accursed nature
@Accursed Nature i geuss i added the part where you call him stupid, but what you said was that he didn't come up with this information by himself, he just researched it and repeated the topic which he read. Im saying every piece of info is based off of something though, physicists and teachers didn't just do experiments and figure out stuff all by themselves, they go through years of schooling, so you could say they don't know anything and are just repeating what they saw in a textbook.
TH-cam THE SUBREDDIT IS "r/Whoooosh, jesus christ
Michael: “Or can you?”
The laws of physics: *sighs*
Ha.
*Yes*
Michael written the laws of physics !
In future they will say Vsauce the god of Or can you
SamTheMa'am you stole this didn’t you
Or do they
6:35 Fun Fact: Every odd number that matches with the even is x2 the original number. 3+3 =6 😮
when he hits you with the "or can you"
😩
Me: OMG infinite chocolate
😣😫
I felt that
When the music hits
Imagine being the person who cleans all the rooms in Hilbert’s Hotel
Theres no reason for one person to clean the room because there are infinite numbers of cleaners . Sorry, Vsauce has gotten in my brain.
@@zaahilibraahim7113 with infinity room's then there would be a infinity area in the hotel therefore the hotel itself is infinity so if you were outside the Hotel and tried to walk around the area of the hotel it would be endless
@@emmanuelnethery9498 yea
But who has to buy the Lemon Pledge?
why clean a room if you can always use a new one whenever you want ? their are infinite after all ?!
This is the only Vsauce video that genuinely stumps me. I eventually come back to it every year or so and understand it a little bit more, but I'm not quite at 100% just yet. This is such an interesting idea and Michael's ability to communicate the logic behind it so fluently is incredible, it makes those developments in understanding every time I come back feel so much more satisfying. Having grown up watching someone make learning truly enjoyable is honestly priceless, I hope Michael knows to how many people he is that someone.
Calculus 2 can help understand if you’re looking for more reading material
@@RyderB26 thanks for the suggestion!
@@RyderB26? Banach tarski is in the field of abstract algebra
@@JohnDoe-vt3vz series and sequences is the foundation of it
@@RyderB26 no, not at all. The proof is entirely group theoretic. It's on the Wikipedia page if you care to look.
13:48 bro michael be wildin i really thought he was about to draw it
RRU 😭
Got to Hilbert's hotel and could only think of the logistical nightmare of moving infinite guests up a room or down a room number.
Easy, when they move up they tell the person in the room they are moving into to move into the next room, and the cycle continues.
@@dj4972 bold of you to assume everyone will comply
What a terrible customer service policy to make EVERYONE move every time a new guest arrives!
0/5 stars!
Use ur PA
Lmao service workers biggest nightmare, trying to get an infinite number of people to listen to your requests
“Countable means that you can count them” the only thing I took away from this vid
"Countable means that you could count them " only if you have an infinite amount of time
Let's say you and your friend are playing "guess natural number", because there are countable amount of natural numbers, you will eventually guess your friend's number. Why? Because you can list all of the elements: after 1 comes 2, after 2 comes 3 and so on. In case of real numbers there is no "next" element. What comes after 1? 1.0001? Or maybe 1.0000001?
@@megrelikaci3380 To do so you don't need real numbers, rational numbers suffice, and they are a countable "number".
Don't confuse continuous and dense sets:
both 1.0001 and 1.0000001 belongs to the set of rational numbers Q.
More, the real numbers that we can access to and use, i.e. that "exist", are _countable_, too bad Herr Cantor.
@@ferruccioveglio8090 What do you mean? We can list every rational number, but can't do the same for real numbers. The word countable means that you can count from one element to another, right?
Countable means there’s a bike toon between the set and the inductive set
Therapist: how did your existential crisis begin?
Me: Hey Vsauce Michael here
Tom Powwell oh I thought therapist said " the rapist" lmao
You're not helping.
Mine started when i began existing, or was it before i was existing? Could i have known of existence before existence? Impossible.
Idk where i was going with this
Tom Powwell z
Lol! Great comment!
4:26 he drew among us before it existed
It's just Micheal showing us his true power.
Kinda questionable why he did it through a dead meme, though
Goddammn you
Unfortunately, my mind melted before it could get blown
Haha I started with the hope but my mind melted too.
Thank god it wasn’t your dilzy
imagine having a mind
*my brain is a peice of mush*
That's some serious medical condition, good that your mind melted before
Thanos: The universe is finite, its resources finite.
Banach-Tarski has entered the chat.
And about time, too!
Banach-tarski :*explained the paradox
Thanos : impossible
OSCAR!!!! THIS shit is funny af😂😂😂😂😂😂😂😂 👌👌👌👌 gg man
🔥😂🔥
Banach-Tarski K/D = infinity.
Thanos = half of the universe/0.5 (referring to when he almost died by the hands of Thor)[haven't watched end game if it's even out, don't spoil anything for me fags lol]
I feel like I just learned something incomprehenable
Welcome to vsauce
I don’t wanna be that guy but.... one of those words was no spelled correctly
@@a.k.alight8065 Yeah lol, I just realised that when HBPencil commented
@@a.k.alight8065 oh man the irony... You misspelled "not"
Samvrit Check Mate.
vsauce videos are perfect to play in the background because it doesn't matter if you pay attention or not, you won't understand anything either way
“Hilbert’s Hotel can be applied to a circle.”
Thats it I’m officially lost
No, I still not lost it.
The moment he said about left right on sphere is I lost it.
I lost it when he started talking about why up down something didnt work so we had to move some parts of the sphere somewhere or something
@@friedec3622 if you move you move inside a sphere because the earths atmosphere is round contrary to the earth itself that is slightly larger at the middle point if you lost it at that point you have smol brain
@@TheFagerlund What? Does the video talking about Earth?
I think it's about geometry and placement.
@@friedec3622 smol brain ;)
''you can't duplicate chocolate.''
michael: *OR CAN YOU?*
**surprised Pikachu face**
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞
That line got me hooked honestly
That got the women listening
he just had to press ESC when the item appeared in his hotbar
"The Universe isn't strange... We are."
I love this quote
We are part of the universe he didn’t think about that.
Vsauce: *Or did I?*
Doctor strange
The cool thing about VSauce is that every video you can still learn new things on every rewatch. There's things you didn't notice or remember or pay attention to, there's new connections you make with things you've learned since last time, you understand more from being an older smarter person now. I've been rewatching this for 9 years and I think I've got a pretty good grasp on it now yet this video still gets me thinking.
Incredible.
You obviously cannot stop Michael from saying, "Or can you?", or can you?
J Fidel Yes ahhahahahhahaha
or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you or can you
" *Hey sir? Mr. Trump would like to know your destination* " or would he?
@Geo Metric Yoshi, He would OwO
I read this just before he said it at 1:15
Hotel designer: so how many rooms do you want?
Hilbert: yes
7:42 " u n l i m i t e d s u p p l y o f g u e s t s"
why Yes?
@@paulscottfilms because yes
He gonna have a hard time filling that hotel during this pandemic
Who the **bruh** is Hilbert lol
Me: Trys to understand what he's saying
Michal: 1+1=1
Me: Yes i agree. Wait
Lol
Waiting for someone to correct him/her, then someone to reply to that and incorrectly say r/whoooosh
BeansNToastYT whhaaaaaaa.............
@BeansNToastYT ok then..
BeansNToastYT wut
2:17 that was the best blah blah blah I’ve ever heard
Sir, Sir excuse me, I only asked if you wanted cream in your coffee...
😂😂😂
Lmao
Or did you?
Sauce?
Oh sorry sorry, yes i would like cream in my coffee
Or do I?
What even IS cream?
"There's endless refills, sir"
Vsauce Michael:
"I can drink infinite soda. Or can I?"
HERE!!!
Timo Dirrigl I have an infinite bladder....
....or do I?
Tell that to McDonald's when dining in!
i had no clue what the title of the video meant i just came for the fluffy ball thing in the thumbnail...
oooooof
Same omg
same
Same
• oOf •, unfortunately I did the same thing.....
3:53 I just realized (like 10 watches in btw) Micheal put one half between 1 and 2 lol
1:17 you know shits about to go down when the song comes on.
Lmao Ikr!
***** lol
***** I literally take my serious chair stance when that song comes in. Hand below chin, squinted eyes and all.
***** loooooooooooooooooooooooooooooooooooooooooooooolll
so true hahhaha
When Michael makes a statement then stares at the camera with a long pause.
“Ah shit here we go again.”
Or can you?
Michael playing Gta San andreas:
Or do we go again?
Or do we?
haha😂😂🤣 btw thanks for 130 now lets reach 140 pls 🙏😀😀
It’s more like forget everything you think you know from doctor strange
Been watching this repeatedly for 8 years now and it never fails to blow me away. Peak TH-cam and peak Sauce content.
this is that one vsauce video i come back to like once a year and hope that this is the time i actually get it
I watch this video again when i feel im starting to forget some of it hoping the spaced repetition affect to take place
Maybe you should lay off the Sauce.
Yeah I saw it a few years ago, im watching it again to see if it makes anymore sense
@@tev5040i watched it before and it went over my head, but I got it this time. Youll get it if you think about it enough, i think what makes it confusing is infinities are hard for a person to think about.
9:16 "no hole will be left unfilled😂
I see you already wrote my comment for me. Thanks.
Gotta be mentally prepared for that
@@RationallySkeptical gotchu bro
"No hole will be left unfilled"
-Vsauce
sounds like my honey moon
Except the potholes in my home state!
@@arakbmt2379 Michigan?
The words my dad muttered on my 7th birthday party
@@arakbmt2379 sweet home Alabama?????
doctor: we're still trying to find a heart for your heart surgery
me: just rotate mine
xD super underrated
Watch us one day create a machine to do the math for your heart which creates a complete separate heart. Would still be your crappy heart and you’d still need a different one though lol idk Im stoned because of this video.
Did you learn nothing? You’d just end up with a copy of the original including whatever the problem is.
@@iamme4552 it'd still be cool tho
I Am Me you know what a joke is?
Me: 'mum i just learned something new'
Mum: 'what'
Me: ...
Or did you? ***Vsauce theme plays***
@@farr2600 or did he?
I just learned how to hack chocolate
Mum be like wtf
Cool pfp
For me, this channel is the best on TH-cam. Thank you Sir Michael.
I love how there are still comments from like an hour ago. It's been 5 YEARS. Vsauce will always be awesome, It's gotta be one of the coolest things to exist on the internet.
makes me happy that this has like 29mil views, theres hope after all for humanity
@@internetenjoyer1044 you actually don't realize the earth is dying fast, or do you?
@Gary Garretson yeah yeah forget about the Uno reverse card existing.
@Gary Garretson "I SHOULD NOT EXIST FROM THE TRUTH."
The dude is legitimately brilliant. 99.9999% of brilliant people are not legitimate.
"Sir, you need to leave. You've been eating at this buffet for 5 hours now..."
Michael: "Or have I?"
I'm crying lol
LoL 🤔
"In reality,i have not. You see,infinity plus one equals infinity,and as i have the right to eat an infinite amount of food,the five hours i've passed here are the same as not spending any time at all"
You go now
You have sir, you blocked the toilet.
When I first learned about the Banach-Tarski paradox, it made me so mad that I was completely beside myself.
underrated
Underrated comment ☝️
probably because its a useful mathematical fiction and is metaphysically impossible. Actual infinities are metaphysically impossible and violate the law of non contradiction.
@@Raiddd__its a joke "beside myself"
@@Raiddd__yes the entire premise assumes infinitesmal is a thing
currently studying the banach-tarski paradox for fun and rewatched this video, never really appreciated how informative it really is! also tysm for providing links to your sources, when i say it’s really helpful is an understatement.
I may need to watch this an infinite amount of times to understand
I watch vsauce when I go to bed every night, I’ve never taken in the information and I don’t really care if I ever do, but I do enjoy his voice as I drift off
Jordan Wills 🤣
Nothing to understand, it's intellectual masturbation..
So you will never be able, to understand this fully
@@2.SPIRITED I could, but if I paid attention then I would get bored of listening to it during the night
Cop: You’re under arrest.
Micheal: *Or am I?*
See what you don’t understand is...
Nice...
Michael*
Cop: Ah shit, here we go aga-
*Vsauce music plays*
One of the Paradoxes proves that I can’t be actually arrested, if you divide 10 and 5 you will get 2, The 2 counting as a “N”
Now if you divide 1 and 1 it would be 1, The 1 Counting as a “O”. You know where I am going to this? Now this is the place where the magic occurs, divide 8 and 2 which would be 4, The 4 counting as “U”. Did u see the magic happening in front of your eyes?
(Sorry if this had no sense lol, I don’t speak english)
Hopefully the new duplication glitch doesn’t get patched soon.
Ye
That was a hard 9/10 math/online video game joke congratulations
They released a patch, but I can't install it - it's incompatible with my axiom of choice. (I also heard that the patch causes a different glitch - it makes it possible to split a set into more subsets than it has elements. Anybody had the same experience?)
I rarely comment on a video, but you Sir made the most OnPlace gaming joke ever!
Yes, I want my chocolate first!
this man doesn't even need cool clickbait for videos
I miss the days of these trippy, random and thought-provoking Vsauce episodes!
Do they not exist anymore?
@@yourboy9236 he's reffering to the "days" (period) that they were regularly/semi regularly uploaded, I suspect you knew this and you're a piece of shit.
Cyrsclin idk if this has anything to do with his absence but I think he just became a father
@ Look up D!NG.
@@bliss9280 wait I thought it was dong.
When you say "can you?" i dont sleep for 16 days
Or... do you?
Can you
Are you
Or am i
0|
(
0|
Great video, but the sphere part went really over my head, still enjoyed it though!
xisumavoid Good to find you here ! :D
Wow you? Here? Awesome! I like your vids
Hey X. Not surprised to see you here.
Hey Xisuma! :O
Hey X! How are you doing?
I feel like this is what Gojo’s domain expansion is like; just bombarded with information you’ll never understand
I dunno, it seems like a rather concise and clear explanation
"We apparently never needed it to be complete"
9:20 This is exactly how I imagine Micheal breaking up with someone.
I literally got this far and went straight to the comments
@@zacszczepanski4192 Seems you know what's worth talking about!
😹😹😹
This man made me fall in love with learning when I was a child, I remember I used to hate actually studying when I was 13 and now I have just entered my phd physics program at 25 :) absolutely love him ❤
nice
What happens when you love learning, but public school doesn't allow you to find your own path. I'm in a similar situation but still in high school, thank goodness for my English 101 teacher making me make my own learning topics, I would be very depressed otherwise.
@@zacharyswassing6741 lmao you'll be more unhappy when you're out in the real world. Enjoy every second of school if you can, and remember that feeling depressed is just a chemical hormone, you're in the best years of your life
@@StoneTheCr0wyou can still enjoy life when you are older though it is hard to do
Congratulations!
Kindergarten teacher: 1+1=2
Michael: or is it?
Collage teacher: ok so class i have a question. What is 1+0?
Class:*laughs* 1
Collage teacher:* pulls mask off *
Michael: WRONG ITS 2 CLASS DISMISSED
HEHEHE I AM A SUPASTAR WARRIOR lmao
Shailesh Rana o
This was actually a real problem that mathematicians faced when trying to define the foundations of mathematics.
Well, it could be IIIV or 01 or even impossible to solve...
It feels like this video was made a few days ago..
His videos are timeless
I do not understand anything but I know, rotating in the right direction, specifically, particularly, accurately, and precisely, will make me create a clone of myself. Thank you Vsauce.
Reality has the problem of the Planck length
There is no infinity in the physical world
and you can also create a new saint every time you fail the white flower quest
Keep spinning, little vessel
@@tuluppampam That's why infinity is unrealistic.
Not unless you're a sphere
At the start of the video I was like, “I’m getting this!”
And then came the sphere, and it all went downhill.
R.A.S.K same
Their u go guys starting of a HORROR MOVIE - 1:06
The new list hat has the old list in it
This is why I got a numerics degree XD
1+1=1
"No hole will be left unfilled." - Michael 2015
Child: NO Jeffrey Epstein: YES
😂😂 sorry but that sounds so wrong
Michael after the isolation chamber
*AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH*
Hahahahah
This was truly the golden age of Vsauce.