The Banach-Tarski Paradox
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- čas přidán 30. 07. 2015
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Q: "What's an anagram of Banach-Tarski?"
A: "Banach-Tarski Banach-Tarski."
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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.
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????
One of my favorite hobbies is clicking on a Vsauce video and seeing how long I can keep up before my brain overheats.
Been watching this repeatedly for 8 years now and it never fails to blow me away. Peak CZcams 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.
@@wet-read no
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!
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
Proud to say I fully understand all of this now! It only took half a math degree but after wishing I could wrap my brain around this since high school I'm very pleased :)
thats a huge achievement! congrats!
Same! I'm revisiting this video after learning about this paradox in my functional analysis class today
@@anthropomorphicpeanut6160 Isn't this part of measure theory?
Congrats bro, you are no longer a human🎉
We know we're grown up when Vsauce's tangents start making sense...
the hyperwebster introduction made it all click. absolutely mindblowing.
There is actually a variation on the internet called library of Babel. Just search it and it can give you a string of any number of words
when michael says "or can you" you know it's about to get real
every single time "my mind is about to be blown..."
Or as is usually the case with his videos, about to get theoretical.
haha yup
omg yes 😂😂😂
Yeah I love it
you know shits about to go down when he pauses and says "or can you"
😂
LMAO
yeah
You just go... "Fuck. He's off again, isn't he?" *Sighs*
I love that part
"you cannot cut up a chocolate bar and finish with more than you started with.. or can you?"
I immediately grabbed a chocolate bar because I know Michael's got me
Most CZcams videos are one time consumptions. Vsauce is that rare gem with rewatchability value.
"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
Cop: You’re under arrest.
Micheal: *Or am I?*
See what you don’t understand is...
Nice...
Michael*
uNo ReVeRsE cArD iN a NuTsHeLl
Cop: Ah shit, here we go aga-
*Vsauce music plays*
This video is so nostalgic to me. May very well be my favorite on all of CZcams
Same bro it’s been 8 years but I still look at it sometimes and feel how mind blown I was as a nerdy kid.
@@harambe9461did you understand this
haha same, it’s a classic
This is the first truly long-form Vsauce video. I still remember feeling that there was something different about this video when it was released 8 years ago, content-wise and format-wise. Sure enough, it was the start of long-form Vsauce.
“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)
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
I will come back and change my comment in 10 years
5 months in 👍
I’m here by year 8 😏
Oh you are also time travelling?
@@videos_not_found
That's aging! Not time Travelling💀
@@zuhaibzahoorx
Nevermind, young man:
Row, row, row your boat
Gently down the stream.
Merrily, merrily, merrily.
Life is but a dream.
I can't think of anyone who produces content that is more worth it to watch than Michael's. So much effort and passion are put into those videos that it's a crime not to watch them. Thank you VSause for making these.
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?
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 could watch any Vsauce video 20 times in a row and still learn something new every time.
Michael's mom: Micheal its bed time
Micheal: Or is it?
youtube man solves world hunger by giving everyone chocolate squares (2019 colorized)
Dude do you know if they are relatives? I meant Vsauce,Vsauce2,Vsauce3?
@@wrongparadoxscience1485 a mystery only god could solve.....
*or is it?*
And some fuckin dollar bills
2015*** my dood
2015*
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 🤨
Man I wish Michael would be my college professor it would be so cool to grasp all these profound things directly from him in a class
The Banach-Tarski paradox is like a mathematical magic trick
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
Bro getting frustrated by 0's at 4:20 is HILLARIOUS
I love how vsauce's videos stay nearly same as they were aswell as being just as entertaining as they were almost a decade ago.
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
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?
11:32 Wow, I'm very impressed with your freehand circle drawing abilities!
*asserts the Banarch Tarski paradox on your existence and multiplies your misery infinitely*
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
Imagine having enough brain cells to understand this.
Imagine having a brain cell.
Lol
@@MikeSmith-vz6nnI'm a man of taste
You don't want them. Now all I'm going to do for the rest of the night is lay here and stress about this. You can have mine. Please take them.
But don't think to hard because you don't have that many
It is so cool coming back to this video every few years. I remember when I was in middle school and I could only keep up for a little bit, but now that I am in 3rd year pure math, and it all makes perfect sense.
This video is such a VSauce classic
Teachers: The test won’t be that hard
The test:
It won't be that easy either.
Right😂
Correction:
Teachers: The test won’t be that hard
The test: *Video*
420 likes niceeeee
The test: deconstruct this test and make two tests
This year marks the 100th anniversary of the Banach-Tarski paper.
Why does he keep calling me vsauce
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
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: 🤬 = 😡 + ➖ + #$!@
Cheat codes be like:
It is truly interesting and impressive when Michael tries to guide us into some easier topics before delving into such of a beast. Can't find any other channels that can do this.
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'm not staying at Hilbert's Hotel if I have to change room every time someone checks in or out.
lol
#rekt
Oh shit I think my brain imploded
me too...Delfador999
I wouldn't, it would take infinite time to get down
we found the infinite money glitch
So crazy that I watched this video 8 years ago while procrastinating homework and now I'm watching this today while procrastinating homework. Very nostalgic to come back to this with much more time invested in higher level maths classes and fun maths videos and actually understand the explanation Michael gives.
1:05 - 1:14 "or can you...""
Me - ...And so it begins.....
I love this mystery sound that comes when he asks questions like this ^^
Prime Ninja me too, one day they'll use it in schools
Deadeyes especially when it comes down to more chocolate :D
Lyraniah ...yeah I also want to know the chocolate secret. How to do it at home. Buy one bar then start move them around and consume the leftovers. A chocolate 3D printer wouldn't be so bad either, starting with a 3D printer that makes chocolate 3D printers.
Deadeyes *inception noise*
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
I come back to this video every few months, the idea fascinates me deeply
This is my first Vsauce video I now see why everybody loves this bald man so much
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.
all I wanted was two bars of chocolate
Lol same
Alec Ryan but they wouldn't give it to me!!
Tell me you where quoting Suicide tendencies
Hos Delgatoes 3344 you got me there
Alec Ryan oh word
you can have a countable infinity amount of chocolatebars by simply rotating the chocolate into the right
its 8 years later and i wonder if they have new solutions to the problem
Me too
Solutions to what problem?
@@AndresFirte the mathematical Problem mentioned in the Video
@@gamerxp1887 the video shows a counterintuitive theorem, but it’s not a problem. It’s solved, proven. It is called a “paradox” because it’s counterintuitive, but it is known that the theorem is completely correct
I think the most applicable the Banach-Tarski paradox could be is to break down complex problems and see what is and isn’t necessary. Also maybe use an actual finite number of points to use in a more tangible way.
Everybody gangsta till Micheal says “Or can you?”
Lol
We need 1 more like till 100
Technically he isn't Vsauce, He's Micheal. We're Vsauce.
When did this get 289 likes wtf
Saw this when he said it.
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
I love this video for introducing me to the complex rabbit hole that is higher-level Math
This is mind-blowing! It took me a while to understand all of this. Thank you for making this knowledge more accessible to everyone. I appreciate your effort. Keep going😉
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
Micheal: I mean, come on, obviously you cannot cut up a chocolate bar and rearrange the pieces into more than you started with... or can you?
*proceeds to challenge my common sense*
AYE JUNGKOOK I SEE YOUUUU
The rule is, whenever he says "Obviously", it's somewhat followed up by him saying, "Or can..."
ARMY
he didnt! all those little missing pieces in the middle adds up to the piece of chocolate removed
+kamui Cage No shit Sherlock !!
from a professor in undergrad: an anagram of "Banach-Tarski" is "Banach-Tarski Banach-Tarski"
Lol idk why this has no likes
I'd imagine the guests in the hotel don't like moving rooms every day 😂
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
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...
10:56 If you look here, removing the first A the second word becomes A. Therefore, we can remove that one, but then look at the third: A. So we can remove tha- ect ect. What this means is that a hyperwebster (I think that's what he called it) doesn't have to have anything, a hyperwebster... can be nothing. I've made a hyperwebster, you've made a hyperwebster, we've all made a hyperwebster...
Idk how many times over my life I have to watch it before my feeble mind will grasp. I return every year or so to check
Same lmao
*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.
CZcams THE SUBREDDIT IS "r/Whoooosh, jesus christ
Imagine pulling up to an infinite hotel and being told “we’re full”
yeah that would be crazy especially if it involved infinitys being bigger then other infinitys and stuff
en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
Coincedentally, your thought is similar to a mathematican who lived in the 20th century.
It goes like this :
If the hotel is already full, and guest (from room) 1 move to room 2, guest 2 move to room 3 and so on, every guest will have a room to move into, and somehow from a full hotel you manage to create an empty room (room 1) out of thin air. Now you have a room.
Even if an infinite guest show up and the hotel is already full, guest 1 can move to room 2, guest 2 to room 4, guest 3 to room 6, guest n to room 2n. There will be an infinite number of empty room (room 1, 3, 5, ,7 ,9, etc) appeared for those new guest.
But, it does not just stop there. If you host a pyramid scheme in that hotel, everybody will gain and nobody will lose their money, because there are always more people to be involved in the scheme.
Stop copying veritasium bro
@@sameerbiswas2662 who?
@ChrisGD¹³ but what if an infinite amount of people go into the hotel and then you go in
I was waiting for the 😀 "or can you"🤨
This is the first time that I haven’t even come close to understanding what Michael is talking about. I lost him the second he started making rotations on the circle.
How did we go from chocolate to defining the universe
Ikr
but you dont. :0
@@roelofadema271 what
Or did we?!
Ro did we?!
Or idd we?!
Ro idd we?!
Or ddi we!?
Ro ddi we?!
Im too lazy to finish..
Or am I?
Ro am I?
Or ma I?
Ro ma I?
Or am ?I
Ro am ?I
Or Ma ?I
Ro Ma ?I
Welcome to Vsauce
If aliens ever show up we need Michael on the negotiation table.
Aliens: we want 1 million dollars
Micheal: but there are infinite numbers in between a million?!
The aliens would give up
Lmaooooo best comment so far
Vsauce : hey V-
Aliens : we surrender we are now your cattle allknowing being
MELT THEIR BRAIN
- Kid: "Did you know you can you do chocolate out of nothing?"
- Dad: "That's impossible, little Tommy"
- Michael: **Actually...**
i dont know what the heck ur talking about but im entertained
[At Michael's Wedding]
Michael: I do.
Guests: Awww
Michael: Or do I?
[Vsause music intensifies]
Leon Van Heerden *turns to guests*
Hey VSauce, Micheal here.
Lol
Haha good one.
I liked that.
Or did I?
Legend
Any time “infinity” is introduced to the conversation, all bets are off.
I’ve watched this video like 15 times over the years, and every time it’s recommended I’m intrigued
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
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
" Obviously you cannot cut up a chocolate bar and rearrange the pieces into more than you started with. 😀... *Or can you?* "
This is extremely interesting and I can explain infinity now. Due to your experience with science, physics and mathematics, you have combined my understanding and knowledge with yours and it has created a new subscriber for you. Thank you for putting your time and effort into this video.
Explain what he explained in the video, cuz I don't get it at all
@@g_g... I study in my free time about things I don’t understand
@@willgiles-tz8it I guess we're in the same boat then 😂
Maybe you should try it 👍
@@willgiles-tz8it I like to learn random stuff too. I should try to improve my habitual skills.
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
Start: INFINTE chocolate
End: THE UNIVERSE IS A LIE AND WE ARE ALL FAKE
The universe is a thought and everything that is seen or touched is Just Energy vibrating at different frequencies!
we will divide until we cover the earth’s surface
CHOCOLATE IS NOT EVEN MY FINAL FORM
@@kuliimjulischreiben I will destroy this planet in five minutes.. OR WILL I
He’s technically just saying theoretically our world is infinitely small and that we could duplicate things if we got the technology and if it was plausible
When your dog sheds enough hair to make a new dog
Yay, I can’t wait to flex my infinite points on a sphere
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]
"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?????
Cant stop watching it, I never get bored of listening the same explanation over and over
13:48 whoa whoa Michael you better be careful what sequence you do next that’s starting to look like a certain 1940s sign right there
"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.
“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
Ok, ok. This video has been in my recommended list for like 6 years. Tonight’s the night.
It's gonna be alright
@@extravagantpanda7962 stay away from my back door
How is he teaching more than my teacher and making it so interesting🥲
when he hits you with the "or can you"
😩
Me: OMG infinite chocolate
😣😫
I felt that
When the music hits
A guy gotta wonder...where the fook infinity came from and what type of physics glitch created it. Sometimes i wonder if the universe itself is the glitch. But for time to exist or, even be measured and conceived.. something has to be infinite and something has to not exist at all
Endless we are not a glitch u just described philosophy and the nature of GOD?!.
nightmare blunt rotation