Want more brain food? Want your house to become a museum? Now you're thinking: www.curiositybox.com

Q: "What's an anagram of Banach-Tarski?"

A: "Banach-Tarski Banach-Tarski."

twitter: twitter.com/tweetsauce

Instagram: instagram.com/electricpants

Kevin’s Field Day video: frvid.com/video/vid%C3%A9o-1zARMZ08ums.html

Field Day: frvid.com/show-UCRPktNf5vnBR1J4e7t1RUVg

Deep dream animation by instagram.com/NaderMakki/

If you like it, you'll love this video also by Nader: frvid.com/video/vid%C3%A9o-fJ9j_z2kXI0.html

Chocolate illusion: mathandmultimedia.com/2014/07/22/explanation-infinite-chocolate-bars/

Chocolate illusion video: frvid.com/video/vid%C3%A9o-dmBsPgPu0Wc.html

related Numberphile videos:

sizes of infinity (includes diagonal argument): frvid.com/video/vid%C3%A9o-elvOZm0d4H0.html

infinity paradoxes: frvid.com/video/vid%C3%A9o-dDl7g_2x74Q.html

Vi Hart on types of infinity: frvid.com/video/vid%C3%A9o-23I5GS4JiDg.html

Countable & uncountable definitions:

mathinsight.org/definition/uncountable

en.wikipedia.org/wiki/Countable_set

en.wikipedia.org/wiki/Uncountable_set

Banach-Tarski on wikipedia: en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

Banach-Tarski proofs:

math.uchicago.edu/~may/REU2014/REUPapers/Robinson.pdf

www.math.hmc.edu/~su/papers.dir/banachtarski.pdf

people.math.umass.edu/~weston/oldpapers/banach.pdf

Banach-Tarski explinations online:

www.irregularwebcomic.net/2339.html

www.kuro5hin.org/comments/2003/5/23/134430/275?pid=5#10

skepticsplay.blogspot.co.uk/2010/05/doubling-sphere.html

austinrochford.com/posts/2014-05-14-banach-tarski-paradox.html

www.math.cornell.edu/~mec/Summer2009/Whieldon/Math_Explorers_Club%3A__Lesson_Links/Entries/2009/7/28_Lesson_6%3A__Whats_an_Anagram_of_Banach-Tarski.html

rachellevanger.com/index_files/BT%20Animated%20Presentation%20Web.pdf

quibb.blogspot.co.uk/2013_03_01_archive.html

blog.computationalcomplexity.org/2011/04/what-did-banachs-wife-think-of-banach.html

geopolicraticus.wordpress.com/tag/banach-tarski-paradox/

dgleahy.com/p47.html

www.math.hmc.edu/funfacts/ffiles/30001.1-3-8.shtml

Cayley graph animated gif: twitter.com/GIFsofWikipedia/status/624202342259240960

Hilbert’s hotel on wikipedia: en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel

types of infinity: www.xamuel.com/levels-of-infinity/

set theory and quantum physics: link.springer.com/article/10.1007/BF02213427#page-1

LHC gif: cms.web.cern.ch/news/lhc-data-be-made-public-open-access-initiative

Zermelo-Fraenkel axioms of mathematics: mathworld.wolfram.com/Zermelo-FraenkelAxioms.html

Is math invented or discovered?

phys.org/news/2013-09-mathematics-effective-world.html

www.scientificamerican.com/article/is-the-universe-made-of-math-excerpt/

more deep dream images: www.reddit.com/r/deepdream/

BOOKS:

The Pea and the Sun: www.amazon.com/The-Pea-Sun-Mathematical-Paradox/dp/1568813279

The Outer Limits of Reason: www.amazon.com/Outer-Limits-Reason-Science-Mathematics/dp/0262019353

Why Beliefs Matter: www.amazon.com/Why-Beliefs-Matter-Reflections-Science/dp/0198704992

Things to Make and do in the Fourth Dimension: www.amazon.com/Things-Make-Fourth-Dimension-Mathematicians/dp/0374275653

Music by frvid.com/u-JakeChudnow and

www.audionetwork.com

31 juil. 2015

Ma playlist

À regarder plus tard

Marina Marchese Il y a 32 minutes

Infinity +1 Yes but 1 is real, palpable, countable whereas Infinity is not. To me it's apples and oranges. Or should I say..it's all Greek to me! Sorry! No capish! I must have wandered in the rabbit hole ..again!

Dreadnaught 1270 Il y a heure

So does this mean I could technically create a infinite money cheat

Mark Muster Il y a 3 heures

From my point of view: No And by the way: the "uncountable" infinety with fractions of numbers, is in fackt countable, if u count every step it needs to go to the startingpoint. So: 1: 0.1 2: 0.01 3: 0.001 And so on (infinite). So i guess its proven wrong, isnt it?

Mark Muster Il y a 9 minutes

@Tom Svoboda jer ofc. It isnt. If u look for the smallest decimal, u just add a zerro behinde the comma everytime, and count this.

Tom Svoboda Il y a heure

this doesn't enumerate all numbers. in fact, it doesn't enumerate almost anything. for example 0.2 is not on your list.

Matt Brooke Il y a 6 heures

Rotating a left rotation sphere to the right doesnt leave a residual point to be added to the new position. You will still always have the same spikey sphere only you are seeing it from another angle. If I step left then right my left step becomes a waste of time, not a residual me to my left to be added to the current me. Adding points on the circular plane to fill the poles is addition, last time I checked. If you feel you arent smart enough to understand this sort of thing its because there is a requirement to accept a "rule", these "rules" are applied by the theorist to take away the reality of the situation, and therefor it is no longer knowledge but faith, a want to believe. Truth is you do understand, its nonsense and simply not real.

Samar Grey Il y a 8 heures

This video is just proving that 1/2=2

Samar Grey Il y a 8 heures

How many ways can 2020 get worse? This video:

Firas Bsoul Il y a 8 heures

This has, indeed, strengthened my belief in almighty God, the most powerful, creator of the universe, the creator of things we don't know. I am pretty sure that the visible universe we know is like a sand grain in a big desert of what is out there. remember that our knowledge is limited but God's knowledge is limitless and eternal.

Josh Koop Il y a 9 heures

infinint

arno Il y a 11 heures

so in short, you need infinity, to have infinity?

Dahl Kalvi Il y a 13 heures

The people in the hotel getting shaked to oblivion by the constant of entering and leaving the hotel ahh shit here we go again

James Barralet Il y a 16 heures

Infinity is a circle, or a sphere, or cycles. Numbers and counting have nothing to do with it. Your dictionary could not be put into a volume. The volume would need to occupy infinite space. This is just taking flawed presumptions and making theories from them. Eg. Like presuming that human greed is not a choice, and that infinite greed is sustainable, and devising economic systems based on that. Brains are very limited - finite. But that is not your identity, who you are. Who you are is ok with infinity, it’s just a matter of stirring it into life.

Nik T Il y a 16 heures

Guys! There are no girls in the comments here... move on.

Aditya Bhattacharya Il y a 19 heures

The thing i understood is 1+1=infinity

Michael Bell Il y a 21 heure

5:14 "Forever isn't enough" that sounds like a Bond title

Nate Dawson Il y a 23 heures

damn i just wanted some extra chocolate

Olaoluwa Faleye Il y a jour

Hmmmm

NETB Il y a jour

I feel as if this paradox seems to be reaches for an explaination of god. Create matter, create something were there was nothing before. Interesting

Fizza Masood Il y a jour

Wow this guy makes me feel small yet smarter then my classmates

1281 - Vishwas Kulkarni Il y a jour

Dad: today was your test how many marks did you get? Sister: 99.999999999% Me: 4:07

goose green Il y a jour

Uncountable infinity in 2015: "the number of all numbers that there are" Uncountable infinity in 2020: "the number of proposed genders that there are"

Neil Kauffman Il y a 17 heures

I'd disagree, since because infinity divided by infinity is infinity, which would mean that the very countable number of people in the world would each have to have an uncountable infinity of gender identifications. Since each person can only have one identification, there cannot be an uncountable, or even countable, number of genders.

amphibia Il y a jour

4th graders memorizing 20th table be like: "Is ThE GuY iLlItEraTe?"

YouTubes best station Il y a jour

who elce wasted a perfectly good dollar :(

Sandy Reed Il y a jour

This guy is a genius

Sandy Reed Il y a jour

So when would you end infinite?

Sandy Reed Il y a jour

I just want to point out that all of those dollars are different the one he ripped.. and the two on the table all the numbers are different .

Релёкс84 Il y a jour

No shit Sherlock

Sandy Reed Il y a jour

Just saying.

BuildTest/ExplosionTest Il y a jour

But who would take the time to think about this

Jeremiah Reeves Il y a jour

did he just say the buttock tarski paradox

Chiliwangchang 123 Il y a jour

If we could duplicate ..... This way I would be very rich A portion of this comment was removed by the us government the portion of the comment that was removed is replaced by periods

CyberSnake100 Il y a jour

My brain hurts ...

Gary Hasch Il y a jour

Wait.... What if you take infinity from infinity ()()-()()

Rebotxd Il y a jour

1:15 I love when he does this 😂😂😂

Peter Parker Il y a jour

9:16

Wade Wilson Il y a jour

This is the most roundabout way of telling me I'm weird that I've ever received.

DiceDodo Il y a jour

10:08 The dictionary just got a little sleepy.. 💤

William S Il y a jour

I feel like the Banach-Tarski Paradox just kinda suggests that the axiom of choice is probably incorrect, since you need to take that axiom as truth to even get the paradox in the first place, and the paradox leads to non-sense when viewed from our perspective in the physical world (except colliding particles as you mentioned, but I feel like thats not solid yet). But if I considered that as absolute evidence that the axiom of choice is bullshit, I'm sure our version of Star Trek's Q would be really annoyed with me.

Your Homie Il y a jour

2:44 are we watching buzzfeed unsolved or vsauce

Jose Moraga Il y a jour

couldn't the proof at 5:30 work the other way around (swapping both sets of numbers), hence proving that there are more whole numbers than real numbers between 1 and 2?

Leruo Monang Il y a jour

Bruh this guy just said there's more than forever

Brian Arborio Il y a jour

CAUTION: INGESTING THC AND WATCHING THIS VIDEO MAY CRUSH YOUR MIND. PROCEED AT YOUR OWN RISK

xQualifieDx Il y a jour

whenever i see this thumbnail all i think is anything is possible if we look at it differently. or something like that...

xQualifieDx Il y a jour

ive watched this about 5 times i still dont really understand much more

Pedro4816 Il y a jour

I think humans found a glitch with the world 😂

C&C Phx Il y a jour

This must be how this guy feels when he checks his account balance...... this guy definitely a multimillionaire from FRvid

Zachary Kruger Il y a jour

could this be used for digital storage?

Nikhil Mahajan Il y a jour

This video called me dumb in infinite different ways 😭

John Viggiano Il y a jour

Sorry. But I can not believe someone who thinks 7+2=9 🙄 @ 5:46

毛歌凡 Il y a jour

I don't smoke weed but damn *Windows Xp starting noises*

Prachurjya Ghosh Il y a 2 jours

This butchers every single bit of my self esteem.

Objectivity1958 Il y a 2 jours

I've watched this video about 28 times now since 2015 and I still keep running out of chocolate. WTF?

Happyk1nGG Il y a 2 jours

Vsauce: *becomes smart* Impossible stuff: _adios_

Mariano Barros Il y a 2 jours

9:48 6 year old me thinking what it would be like to scroll right infinetely on excel

um cara aleatório eggs333 Il y a 2 jours

nice taste of music! greetings from brazil 🇧🇷

Emil Tildelöv Il y a 2 jours

“No hole will be left unfilled” 😂

aaaaaaaaaaaa1111a Il y a 2 jours

Fucking

TXLAdventure Il y a 2 jours

Petition to make a point the size of an electron, because that’s as small as things are ever going to get, unless it’s a black hole, but in that case who cares anymore your not going to need to do your math homework in a black hole.

Sacul Selasor Il y a 22 heures

@TXLAdventure lol what sorry defeats the point of what nb

TXLAdventure Il y a 23 heures

Sacul Selasor if they have zero dimension than that defeats the point pun intended

Sacul Selasor Il y a 23 heures

@Parker Brewer uh... as i said, they are said to have zero dimensions, so they arent "made" of anything, id reccomend just waching a video

Parker Brewer Il y a jour

But what are quarks made of?

Sacul Selasor Il y a jour

aaacctually no... the smallest thing that we get, is acctually a quark, not an electron. a quark is basically the things that connect protons and neutrons together, and people HAVE suggested naming that as the perfect 0 dimensional point

TXLAdventure Il y a 2 jours

wouldn’t infinity in the case of infinity+1 just be an an unsolvable equation such as y=5x sure it can be graphed, but not solved so there would still be twice as many. I have no clue what I’m talking about but could it?

Tony Dimaric Il y a 2 jours

It's just like creating infinite amount of something out of that something.

Abdo Il y a 2 jours

30M views wow

Ryan Huffman Il y a 2 jours

This isn't even a paradox. This only applies to a sphere because there is no correct up or down, left or right. This just exposes some quarks of infinity. With infinitely many points left is right and up is down. In the real world, up is up, down is down, left is left and right is right. This has no real world implications. This is just pretentious philosophy crap.

Tom Svoboda Il y a jour

@Ryan Huffman no offence but you're talking out of your ass. what you're saying is complete nonsense, mathematically speaking.

Ryan Huffman Il y a jour

@Tom Svoboda not really. A sphere is just the physical manifestation of infinity. There is no correct up, down, left, right, beginning or end. If you added extra directions for the moves, you could end up with more spheres. If you added infinitely more directions for moves, you would end up with infinite spheres.

Tom Svoboda Il y a 2 jours

you sound like you know what you're talking about

Gio Il y a 2 jours

Chocolate to numbers

Dylan Wyatt Edquiban Il y a 2 jours

almost 30 mil boisssssssssss

Edber Balzatv Il y a 2 jours

I literally searched hairy ball to find this vid ✨💕👏👁👄👁👏💕✨

Martez Araya Il y a 2 jours

It’s sort of obvious

Martez Araya Il y a 2 jours

Due

Erza 13 Il y a 2 jours

If the hotel is fully booked doesn't that mean that the infinity of the guests in the rooms = the infinity of the hotel rooms? So how can the owner provide a room for the new guest? All the infinite known rooms are already booked for all the infinite known guests !! If oo = oo so how does oo + 1 = oo? 🤔

TITANIUM HORNET GAMING & Stuff Il y a 2 jours

Almost all of these are just functions

TITANIUM HORNET GAMING & Stuff Il y a 2 jours

@MikeRosoftJH haha, i understood nothing you just said.

MikeRosoftJH Il y a 2 jours

Of course! Translation and rotation are functions (in particular, a special kind of one-to-one functions which preserve lengths and volumes). Assuming axiom of choice, it is possible to split a solid body (such as a single solid ball) into finitely many subsets, which can be moved around by translation and rotation to form a solid body with a different volume (such as two copies of the original solid ball). (The problem is that the pieces in question are not solid bodies and don't have any well-defined volume; the volume can't be zero, and it can't be non-zero either.) Or, to put it differently: there exist two finite collections of sets A and B, such that: sets in collection A can be moved around by translation and rotation (without overlap) to form a unit solid ball; sets in collection B can be moved around to form the same solid ball; but the sets in the union of A and B can also be moved around without overlap to form a single solid ball of the same volume.

Starz Toons Il y a 2 jours

im going ape shit over this

Lionel Messi Il y a 2 jours

นึกว่าเพลง paradox 555

Tarrrantula Il y a 2 jours

What?

Laceluz 666 Il y a 3 jours

3:13 Michael has spoken, this is how we pronounce seven now

7duality7 Il y a 3 jours

My brain feels like it just checked out of Hilberts Hotel and checked into Bates Hotel 🤯

***Mingot Army*** Il y a 3 jours

We were so close to make infinite water sourse

Tan Thien Nguyen Il y a 3 jours

Werbungen darf nur 1.Min.

Tan Thien Nguyen Il y a 3 jours

Erklären Sie für Apples Apps auch.....? Wie vieles Flugzeugen schon Abgestützt....?

Tan Thien Nguyen Il y a 3 jours

Komischerweise, seit Sie mit VIRUS sind Jogourt Sorte Milch Produkte weniger Verkaufen können. Trotzdem Käse sind Belieben... ..Was ist passiert mit Mars Mensch ?

Kyri Papapetrou Il y a 3 jours

i dont like the way you write the number 8

Bradley Mann Il y a 3 jours

"INFINITY TELLS US?...

sam sto Il y a 3 jours

what happens if you add or subtract infinity to infinity

Afra Afsara Il y a 3 jours

I can't be the only one who thinks that he's gonna talk about some weird planets after seeing the thumbnail 😹😹

Legend Il y a 3 jours

18:59 Imagine doing 2 + 2 = 2

Legend Il y a 3 jours

1:14 you used to, back when cutting up chocolate was still new

Martin Wood Il y a 3 jours

I know nothing about this. But that's not going to stop me talking about it. Surely you can always pair up the whole numbers with the randomly generated numbers between 0 and 1 and their augmentations because.....................you will never....................that's......... never....................and once again for the listeners at home..........never...................run out of them.

Night and Day Marine Il y a 3 jours

24 minutes of my life I will never get back...

LacrimarvmValle Il y a 3 jours

My brain hurts

Iliketacos123 Il y a 3 jours

i think im just going to work an extra couple days to double my paycheck instead of attempting the Banach Tarski.

SLAM POLICE Il y a 3 jours

hey Simon

I'm In A Vegetative State Studios Il y a 3 jours

"Hilbert's Paradox of the Grand Hotel" That sounds like it would make a great tim burton psychological thriller

GudanCraftYT Il y a 3 jours

10:07 , now that's a lot of sleeping 😂😏😏

GudanCraftYT Il y a 3 jours

CEO of "Or can you" CEO of "Infinite" number" of BlAblAHhabla"!

Saucey Sauce Il y a 3 jours

1:17 when that music starts you know Michael bouta spit bars about science

Mr. Garden Il y a 3 jours

There once a time was accountable Infiniti called Aleph null The next biggest infinity was called omega

MikeRosoftJH Il y a 3 jours

ω is not the next infinity after aleph-0; ω is the same set as aleph-0. Aleph-0 is a cardinal number (the cardinality of the set of all natural numbers), ω is an ordinal number (the order type of the set of all natural numbers under the usual order); and in the standard definition, cardinal numbers are defined as initial ordinals (the smallest ordinal number with the same cardinality). There are many countably infinite ordinal numbers, and the ordinal number ω is the first or smallest of them (all ordinal numbers which are less than ω are finite); so the corresponding cardinal number aleph-0 is identified with the ordinal number ω.

House Owner Il y a 4 jours

We just going to ignore how Micheal bullshits us with the money trick

Ans Hakim Il y a 4 jours

I don't even understand but this is cool

Bartosz Kaczmarek Il y a 4 jours

So the space is infinite in small and big scales? Does that make any sense? No! But it dosen't need to make any sense.

Funk Kyno Il y a 4 jours

Nobody talking about how Michael vandalised a 1 dollar US note?

Hayden Richards Il y a 4 jours

VSauce ...Please Do a Video On How Man Would Navigate in Space..It Seems to me that based on the "FACT" that the Earth is moving, the Sun is Moving, the Milky Way is Moving..How do we find our way back to earth If we leave Earth & the Galaxy at High Speed(Close to or At the Speed of Light). It seems to me that since there No Up or Down, East or West, North or South..and everthing seems to be Spinning Relative to Each Other.. When the earth fades out of visual/ electromagnetic view or detection.. One navigation degree of error in an infinite amount of spherical planes or dimensions will translate to..upon trying to return to earth..being millions/trillions of km / light years off course..ie. Lost in Space...The Only Solution I see is to have supercomputers to navigate...So Please If You Somehow See this Message..I'm Looking Out for Something from You Guys Soon...&..Once Again You Guys at VSauce U Definitely & Absolutely.. 😎ROCKMAN😎

ReesSoft Il y a 2 jours

Hayden Space probes and satellites can already navigate themselves in space by using star trackers. www.space.dtu.dk/english/Research/Instruments_Systems_Methods/Stellar_navigation If we ever go to the nearest stars or beyond then the concept would be the same. A mission called GAIA launched in 2013, and has mapped the positions and motions of hundreds of millions of stars. frvid.com/video/vid%C3%A9o-648xGDdNz_g.html Any starship would have a similar map built in to its navigational system. You can always orientate yourself in space by using x,y,z coordinates. In maths the y axis usually denotes "up" or "down". In our Milky Way we could define up and down along the y axis as being above or below the galactic plane. We're probably a couple of centuries away from being able to go to the stars, and by then we'll have far more powerful navigational computers than we have now. I don't think there's much chance of getting lost in space, as long as the navigational system stays online. No direct contact with Earth would be necessary, as the navigational computer would always know where the spaceship is, relative to its star map. Hopefully vSauce will see your question and reply to you.

Hayden Richards Il y a 4 jours

Beautifully Produced... Expertly Narrated.. Concepts I've fought with for the latter part my Life..Concepts that are constrained by traditional scientific thinking..From about Age 36 I've Always been grappling with the concept of Infinity, Life..Death..Consciousnes...With the coming of this New Age of Connectivity and Information Sharing I/We All can Rise Out of the Age of Ignorance & Embrace the New, embrace the truth, embrace the Real. I've always argued that when scientist keep saying we have a trillion stars or a trillion trillion stars/planets etc..they were not thinking correctly..the concept of infinity is so beautiful that it terminally gives an explanation to everthing and our (lifeforms) "arrival/birth" into the universe was a simple an inescapable "will" of the inanimate desfire.. to be come animate..We keep thinking of the Existence of Life on Earth & Our (Mans') Existence as Something that has to be Repeatable somewhere else in the Universe..But What If We are just a Strange Phenomena..What If we are just a chance phenomena..something that occurred over the infinite eons of time..only a natural or supernatural mistake..What if We Are the Gods.....and We are Here to Give Account..To Keep Record of the Endless Infinite Beauty & Possibilities of a Scientific, Infinite & Matematically Regulated Universe..Man has Only Recently Come out of its Infancy..Its Father being the Unthinking & Lifeless Cosmos..It is for Us to Rise Up out of the Cradle and Explore & Give Account to the Universe of the Gift that it had bestowed on/to Us.. the gift that it has bestowed on itself...Life..Man..The Supreme Being...the Universe has been and Always Will ..Be. However Man..Life... has Only Recently Come to Being..In desrespecting our selves and our cradle(earth) we disrepect the universe..the One ..the Universe Always Equalises..Let Evil Believe It is Winning the Supreme Be..ing..If Man Extiguishes Himself..The Supreme Will ultimately Try Again..to become Aware of It ..for Life Is the Only Means the Universe has..to become aware of itself.. Again.. VSauce...You Definitely.. 😎ROCKMAN😎

Me name Was taken Il y a 4 jours

1:08 that got me scared

hisxmark Il y a 4 jours

But any point "X" in an open n-ball can be taken as the origin since there will always be a scalable distance (less than infinity) between any two points. That is to say, that for any n-ball where the radius is 0 < r < 1 the "center" will be arbitrary. That's why, for instance, that the universe "expands" (or contracts) away from (or towards) any point chosen as the "center". When an n-sphere is projected onto a Euclidian manifold the arbitrary zero point of the sphere maps to infinity, but every other mapping transforms to a distance greater than zero but less than one. This is one understanding that is necessary to understand cosmology. All distances in spacetime are greater than zero but less than one, where one is the radius of the spacetime n-sphere.

A K Il y a 4 jours

Infinite universes.

just a non-yter Il y a 4 jours

"1 + 1 = 1" My life is a lie...

Erza 13 Il y a 2 jours

😂🤣

Anthony Werkmeister Il y a 4 jours

"No hole will be left unfilled."- Michael

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