The Banach-Tarski Paradox
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- Опубліковано 30 лип 2015
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Q: "What's an anagram of Banach-Tarski?"
A: "Banach-Tarski Banach-Tarski."
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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
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 UA-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.
@@wet-read no
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?
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...
"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
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
"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
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
This video is so nostalgic to me. May very well be my favorite on all of UA-cam
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
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.
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 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.
11:32 Wow, I'm very impressed with your freehand circle drawing abilities!
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!
“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)
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.
I could watch any Vsauce video 20 times in a row and still learn something new every time.
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 🤨
[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
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😉
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
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
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?
Michael's mom: Micheal its bed time
Micheal: Or is it?
When I was a kid watching this, I was certain I could make an infinite chocolate factory.
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
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 love how vsauce's videos stay nearly same as they were aswell as being just as entertaining as they were almost a decade ago.
Cant stop watching it, I never get bored of listening the same explanation over and over
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
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 come back to this video every few months, the idea fascinates me deeply
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.
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 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: 🤬 = 😡 + ➖ + #$!@
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 never fails to make me sleep. It’s really helpful with my insomnia. This is why I never actually understood the video topic.
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
Doctor: "You are in a mental hospital sir"
Michael: "Or am i?!"
Doctor: "Yes you are."
Micheal: disappears
@@lore644 Stop right there, criminal scum! You have violated the laws of physics.
😭😭😭
@@lore644 🎩🐇
No I’m a finite amount of time I can turn this place into a party
Doctor: Yeah he’s definitely high
This video is such a VSauce classic
- Kid: "Did you know you can you do chocolate out of nothing?"
- Dad: "That's impossible, little Tommy"
- Michael: **Actually...**
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.
This is my first Vsauce video I now see why everybody loves this bald man so much
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.
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
I’ve watched this video like 15 times over the years, and every time it’s recommended I’m intrigued
This has to be one of my favorite vsauce videos
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
The Banach-Tarski paradox is like a mathematical magic trick
this is by far and not even a contest, his best video
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*
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
I see this video in my reccomendations more than once a day for years. Why. I have watched it many times, but I have seen this goddamn thumbnail so many times it’s ingrained in my brain
Watching vsauce vids while being miserably sick is a fever sick. And i can feel my headache getting worse and worse
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
The part of the definition of the hyperwebster dictionary which no one seems to state explicitly is that it is simply what happens when you use standard alphabetization on a list of every combination of letters of any (finite) length. I assumed it was something more complicated and didn't figure it out till several hours later when I decided to try reverse engineering it from the recursive description suggested by the next part of the proof.
Every time I watch this video I figure out a bit more...
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.
"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?????
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!
*asserts the Banarch Tarski paradox on your existence and multiplies your misery infinitely*
One of the best videos in UA-cam history
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...
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 this video. Can't remember how many times I've watched it, but I feel like I'm getting close to understanding what he's talking about.
That Infinity wire grid segment felt like an acid flashback for a second, the music helped 😅
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
“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 ;)
Watching things like this probably made me who I am today as a math student in college.
This is a masterpiece
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
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
That's the lesser known Kerf-Tarski paradox, I believe. Or should I say, well known only to woodworkers, who make their career using that knowledge to transform shipping pallets into high priced furnishing.
Bro is the type of person to be in a totally casual situation with his friends and be able to make them question every speck of reality in under 17 seconds
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
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
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.
“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 is the science teacher we all needed
i always come back to relearn it
Me: trying to focus on what is being explained
My Brain: lmao did he just say „no hole will be left unfilled“
Lmao same though
😂😂🙌🏼♥️
😂😂😂
Graveyard
That's where you belong
*Micheal Scott intensifies*
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
Bro getting frustrated by 0's at 4:20 is HILLARIOUS
Ok so I think the flaw is when you describe "just rotate it", if you were going to move every particle in the universe at once I think it stands to reason you would have the power needed to clone every particle aswell
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]
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 !!
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
i love this guy saying , "or can you ?"
“What happened to Amelia Earhart”
“AAAAAAAAAAAAAAAAA”
Literally the most big brain comment
I cant stop laughing lmao
i think that’s what did happen
What didnt happen "ZZZZZZZZZZZZZZZ"
Ross: "The woman just vanished!"
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
Very epic Micheal
Any time “infinity” is introduced to the conversation, all bets are off.
-Michael stevens, do you take this women to be your wife
-i do
-...
-or do i?
and for that i tip my fedora to you my kind "insert here what you identify as"
@@cryingkiller1179 *inserts: fam*
Cue music*
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*vsauce music begins playing as he goes off on a tangent about the concept of marriage*
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
I think the reason this video is so popular is because the thumbnail just looks so cool lol
By rotating the spheres _after_ of the extraction, you are creating _new_ points, that weren't present in the initial single sphere. Then, after putting them back together these _new_ points allow you to double (or 'clone') the original sphere.
How does rotating create new points?
"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