# A mirror paradox, Klein bottles and Rubik's cubes

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**Published on Jun 21, 2015**- The Mathologer puts the latest $2000 addition to his Klein bottle collection to work. A couple of first-ever fun mathematical stunts in this video. This video finishes with a puzzle for you to think about. We posted a video with the solution on 1 August 2015: thexvid.com/video/ZMC61C5tigA/video.html

Enjoy!

Burkard Polster and Giuseppe Geracitano

P.S.: Most of of Burkard's glass Klein bottles as well as the Klein bottle hat were made by Cliff Stoll of ACME Klein bottles (www.kleinbottle.com). The metal 3d-printed Klein bottle opener was made by Bathsheba Grossman (www.bathsheba.com).

James Jenkins7 hours agoSadly this is more topology and physics than most people can easily understand.

jay715129 hours ago4th dimension? Sorry my brain only accepts 3!

Philip Eigen9 hours agoThe giggle when he puts the klein bottle in the klein bottle

Matthew Sivewright19 hours ago7:43 : Are you sure that diagram is right? I tried a practical method and the end at start there were the the same.

Kashn Itall2 days agoSo i didn't understand why was i watching this clip but then im thinking to myself like I'm sure this man not making this video for nothing and i start thinking why why why and BOOM it hit me

Free6ix9ine free694 days ago^{+2}Damn I was waiting for this guy to show how he got the cube in the tight hole and it never happens ššš¤¦āāļø

Ricardo montalban4 days agoWhere do you put the weed in?

you2tooyou2too4 days agoWhen Flatty on the Mobius comes back as mirror image, he has made the first half of a 'full' trip around the Mobius universe, and will return (to) normal if he continues and completes the 'full' trip.

wiplashsmile4 days agoAren't the bottles with the open intersection more representative of a 4D Klien bottle than the closed intersections?

Joda4 days ago14:09 Weird flex but ok

Oliver Kunkel5 days agoWhy does a drawed figure turn mirrored after walking the whole surface of a mĆ¶bius strip? This is not true.

Pete Skyrunner5 days agoThe best example of the 4th dimension I've seen.

Fordy McFord5 days ago*************DIMENSIONAL TELESCOPE************

Build a Ring out of neodymium magnets with spacing

You need to make a fractal invisible shape in centre with invisable magnetic forces , once magnets are placed correctly, the right shape will form then make it really cold and create plasma inside tube

You can use magnetic games youtube page with ferror magnetic field viewer to see these shapes

thexvid.com/video/x8zEWJzglN0/video.html

Inventors

Darrin Marshall

Nathan Anstiss

Magnetic Games

I FREE YOU FROM FAMINE AND POVERTY

IF THE EARTHS MAGNETIC FIELD ENTERS EARTH AT NORTH AND SOUTH THEN PUT A TESLA TOWER AT NORTH AND SOUTH AND HARNESS ITS POWER

THEN EARTH CAN ALSO BE USED AS A BATTERY TO OPEN UP WORMHOLES

Fakhrus Salhin6 days agowtf??????????? i saw that bottle i knew what i'm looking at and exactly how it was made within a couple seconds, i didn't know that the whole video was about explaining that. worst video on youtube EVER

Dmitri Lessy6 days agoWhat am i... Is it.. What.... Do you.... Why?

Caleb Cook7 days agoAt 10:30 "if you get that cube in that bottle..."

Caleb Cook7 days agoAnd how the fuq he get the cube in the bottle

Charles McMillion8 days agoIs there a psychiatric name for what's wrong with this guy?

Bruce David9 days agoNonsensical, and I hope he doesn`t have someone tied up in his Basement... or in a Klein Bottle!

Dan Finazzo9 days agoHe did not mention magnets at all . . . !!

johnrtrucker10 days agoIf you put a Klein bottle inside a Klein bottle inside a Klein bottle the 3 dimensional space we live in will suddenly divide by zero and you break physics

The Real 1noskcaj11 days agoIām watching a 4D object as a 3D model on a 2D screen.

Szymon D11 days agoReally...? But why...?

Awesome Productions12 days agoP

Tim K12 days agoI was waiting for him to put his gerbil tube inside the Klein bottle. Thank God he didnāt go there

Auspicious Autonomous13 days agoOnly at 2 minutes it reminds me of some pictures I've been taking of rubber bands. Here is a link to one picture, but more are in the album. Just spontaneous art in ways. This one looks like a music symbol! facebook.com/photo.php?fbid=10213633485770805&set=a.10213474723761854&type=3&theater

Donel Mallory13 days agoDont do the Klein, (Rubic Cube deniers!) If u can't do the time..

Donel Mallory13 days agoJust subscribed..

Please correct the animation at the 6:55ish.. Love the decernible illustrations and instruction, but u have the cartoon creature going full-flip-mirror-gansta in a single not so apparent, single bound of super-too-cofuionist

ness..

lol hi13 days agoThat man turned a Klein bottle into a wine bottle

Lawrence Hoorman14 days agoTry a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a Klein bottle in a fish bowl.

Ben Birchman14 days agoIf you trace the man's feet along the line he shouldn't be upside down... Unless it's just seethrough strip and he didn't walk all the way around

Milind Shekhawat15 days agoTechnically the whole universe is inside that klein bottle.

Ana Almeida15 days agoYou nerdy man! I bet you paid the glassblower to put in!

Norman Plombe16 days agoThank you for the lesson....and I apologize for kinda wanting to see that big Klein bottle shatter.

Wojtek Tomalik17 days agoThanks for the totally awesome mirror paradox explanation. The rest, I blame myself for waiting for... I don't know what I was waiting for.. nice hat?... I dunno.

Nehmo Sergheyev17 days ago2K$ for a Kline bottle?! Someone suckered you inside out, Burkard.

Donnie Dollarhide Jr.17 days agoalgebraic topology is always cool

Gary Seven18 days agoAccording to your theoretical explanation of the Klein Bottle's properties the intersection should not be blocked up with a wall of glass. Later you state it should be blocked.. I don't understand this.

Ludwig van Beethoven18 days agoi dont understand the mirror paradox, your image of the 2d man walking through a mobus strip didnt fully go through the entire walking distance

Cephalopod_38719 days ago5:56 had me laughing so hard

Jason Nosaj20 days agoWhy didnāt you show how you got the 2x2 in there???? Thatās honestly the only interesting thing in this entire video. š

Steven Wunders20 days agowhen you have the example in front of you, you don't have to go through the 42 ways of how it's not something else. just explain how it is and what it is. didn't finish this video either.

troll20 days agoThe real paradox is that i am watching a 3D man showing a 4D bottle on my 2D monitor (and i am also ending the sentence with a NO-D dot).

Brayan Rodriguez21 day agoWhen iz over n realize waste of time

Jon Kinkopf21 day agohow did he put the rubiks cube in the klein bottle

sam lidgett22 days ago^{+1}U ok there bruv

Barry Evans24 days agoThese things don't make sense to me. Why do these clever people try to visualise things in four dimensions? Our brains are adapted to the way we see in three dimensions, so trying to put a three dimensional interpretation on a four dimensional object is never going to work. We'll just end up thinking about it wrong. I guess they are too clever to admit that they can't do it?

Snouie25 days agoThe man is not traveling around the mobius strip He IS the mobius strip

but its like trying to run around the block fast enough to look at the back of your own head

and if you could see the back of your own head with your own eyes it would be like being inside out

but we would also have to inhale the whole world and universe too through our feet as we throw up our inards

So if we are inside out now with the whole universe included on the inside of us

we would feel right side out again

(its difficult to explain in words but it makes sense to me)

Some people in the comments said "If we traveled the mobius strip we would be inside out/outside in" Yes to our mirrored self and No to our self but since our mirrored self is still the same person the answer is no because

we will always see our self as right side out

As we travel the mobius strip our mirrored self is also traveling the same so we just switch places with ourselves

The dimension to our mirrored self is not out in space its inside of each and one of us

So right now I am inside my mirrored self and my mirrored self is inside me I am unable to tell which one of us is actually inside out because we see ourselves always as right side out and we are the same person

Amigo Secreto25 days agoŠŠ«Š”Š«Š ŠŠŠŠŠ ŠŠŠ Š„Š£Š Š”ŠŠ”Š

Micheal Bodnar25 days agoI was a

Watching to see how he put it in then he just cuts it out so we dont know

Blackheart Darkstar25 days agoAt 7:30, he claims the man would be mirrored, but he hasn't made a full loop yet.. At that point in the 'travel' he would he on the opposite side of where he began, he still has half a trip to make.

The guy pulled him through the strip to his starting point when he was only halfway.

((I'm only at the posted time, pardon me if he explains this, I posted now because I have a bad habbit of forgetting what I wanted to say))

Snouie25 days agoHe is implying the man Is the piece of paper on a 1 dimensional path but even if he is actually inside out or mirrored The Man will always see himself as right side out

and he was not pulled through the strip because he is the strip

ViiRal25 days agoCOUPLE THOUSAND? Youāre saying it like thatās cheap for fucking glass

Leng Thor25 days agoWtf dude....jacked off for 16 mins and 10 seconds of it inside. Tou will never reproduce that way.

Richard Phillipps25 days agoHaha, love the klein bottle in a klein bottle world first :D thank you for your vids! Great job

music school25 days agoHow he get rubix cube into that bottle

JKazama18225 days agothe major flaw in his explanation is when he talks about the 4th dimension! Every one knows that 4D = Time! He totally re-invented the definition to fit his narrative. He essentially tried to explain 2 dimensional objects as 1 Dimensional, so when he factors in āAnotherā dimension he exclaims 4 dimensions! When its really just 3! Heās a failed professor in this! Heās using descriptive illusion to rationalize optical illusion into a 3D environment/object! Its not 4D! Soooo this is false, and he just has a fetish for something that is NOT mathematically complex! Its just a cool glass blowing technique

raghul deva26 days ago@6:56 the concept is wrong.. he will be coming to finish how he started.. just think on it

Snouie25 days agoThe concept is correct because people think the man is pulled through the strip but Really the man Is the strip itself

Jon Page26 days agoThe most disappointing video I've ever watched in my entire life

Trollface 10126 days agoSo in the 4th dimension we are just on a strip of paper

Julie-Anne Teresa Lanham26 days agoWow that showed me NOTHING.

AleÅ” Tomis26 days agoI just waisted 16min of my life.

Kenny Westone26 days ago14:59 that nerd laugh, that was the thing that you've been beat up by bullies in school and made you a great man that you are today.

Kettenraucher HD26 days agoI want someone to be as enthusiastic about me as Mathologer is about his Klein bottles

Joe Eagar27 days agoAre klein bottles technically closed surfaces?

EspectroUrbano27 days agoSo much hate in the comments. But I really love this guy's enthusiasm about Klein bottles. It's cute and the collection is adorable.

SURAJ KUMAR27 days agoF***ing stupid just wasted my time here

bigbassjonz27 days agoSo a real Klein bottle has no entry into the larger bulb? Sounds like it's not a bottle at all.

Deepansh Bhargava27 days agoHe somehow reminds me of Buster Bluth and Walter White

I love him!!

VJ Kay28 days agoI canāt believe I watched this, what a lossssser

Altair461128 days agoanswer:

just use the keychain cube version and slip that sucker in there

Altair461128 days ago>says they cannot exist in our third dimension

>proceeds to show his collection of klein bottles

lollmaooo

FleidHD Lp28 days ago7:05 why would the man be upside down? In the part he has to walk which isn't seen in the picture he would turn so he'd stand normal again, or did i missunderstood anything?

F M28 days agoTake some LSD and you trip through the Universe and come back reversed, not just theoretically :-D

Unslaad Krosis28 days agoA 4th simensional beings child toy is magic to us 3 dimensional beings :(

Unslaad Krosis28 days agoAlso can this explain doppelgangers?

Jason Rhodes29 days agoEvery time he drops something into a Klein bottle, it is probably fucking up the universe somewhere.

Jason Rhodes24 days ago+Snouie If you were meaning me, I was being facetious.

Snouie25 days agojust reading the comment section is proof

Aaron Fingerle29 days agoIs the freakin' getman?

His accent is just germanš

I'm german too

Stephen Needham29 days agoThey don't want answers, they want attention?

ComedicEinstein29 days agoBut can you smoke out of them?

Orion In The SkyMonth ago15:00

Klein-ception

Franklin BarnesMonth agoHi

Jharna MandalMonth agoYou are really mental but I love your videos very very much.Plz don't mind

Hopeson LouisMonth agoš±you didn't show how you put that cube in the bottle???

Steven HernandezMonth agoH.P. Lovecraft wrote about a mirror that had such properties!

GuĆ°mundur Ingi GuĆ°mundssonMonth agoSo if you go one time around youre strange after.. but if you go second time youre normal again?

Robert GiftMonth agoWhy not show assembling the cube inside the Klien bottle?

Gary SozaMonth agoHow did I get here? Klein bottle effect? I was really not into this stuff and now I am! So in my 3D thinking I was outside the Klein bottle stuff but really as this is a 4th dimensional creature I was in all the time!? Where is my Klein bottle hat?!

ŠŠ½Š“ŃŠµŠ¹ ŠŠ³Š¾ŃŠ¾Š²Month agoYou have a mistake here. Your person on a mebeus strip will not get mirrored. In the video you forgot to walk him on not visible side of strip. He will be at same pose on the end of his trip along strip.

ŠŠ½Š“ŃŠµŠ¹ ŠŠ³Š¾ŃŠ¾Š²Month ago+Mathologer so he is like drawn through it? Then I get it. But its unclear in the video.

MathologerMonth agoA mathematical MS just like a plane has not thickness, neither has the little man who is part of this MS. He does NOT slide around on the MS he is part of it.

CombraStudiosMonth agoIf you paid attention in Futurama S05E03 you could see "Klein's beer" packaged in klein's bottles, one of my favorite background jokes

mastaluk5Month agoGo outside and have a Klein orgy. Smh

mastaluk5Month agoGuy has to much time on his hands

Damogan gMonth agoI don't get it

David Alonso PĆ©rezMonth agoI'll never get back these 16 mins of my life...

Liam SnaithMonth agoWhat if the universe was the shape of a Klein Bottle?

chekicktuschetan sharmaMonth agoI was watching something stupid and then baam!! I am here

Going back to parallel universe

Olli TeirikkoMonth agoDid I just watch 16min of this nonsence?!

SCARLETā STARMonth agoDoesn't EVERYTHING basically have only one side? I mean even a normal mug. The rim is not really an "edge" it's a curved surface that connects the "inside" with the "outside". "edges" don't really exists right?

Mark ArnottMonth agoNext time your out camping MAKE YOUR OWN ashtray type - put a bottle in the fire when red hot push the middle in with a stick BUT removed too fast it'll crack some campfire fun take an old flagon bottle or so so try 1st make a dip in ground for safety a fire with a dip keeps hot over night as the night breeze passes over \-|-|--|--/ u wake up with Embers STILL BURNING

Tony DrizyMonth ago^{+1}i think that the Rubik`s cubes are magnetic and you enter each single piece separately before the combine into one when inside

Freddy Kruger20 days ago^{+1}good solution, even if you're wrong, it would work. The question is, why does this guy choose to make an obviously long winded and aggravating video without showing HIS solution.

Justin HalfordMonth agoThis is gay

markus martinMonth agoThat would be a good bong ššš

manish lambaMonth agoBhoadika chutiya bana diya.