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A mirror paradox, Klein bottles and Rubik's cubes

13625 ratings | 1538707 views
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: https://youtu.be/ZMC61C5tigA 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).
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Text Comments (2438)
the tessellater (3 hours ago)
squeezing things into tight spaces - nice!
Cool Cat (13 hours ago)
This is the nerdiest nonsense I've ever watched in YouTube. :(
john sosman (20 hours ago)
Can you make a 3D poiuyt?
Adrian Zamora (4 days ago)
Its not mirrored its upside down
Adrian Zamora (3 days ago)
Mathologer I wish we were 4th dimensional beings 😂
Adrian Zamora (3 days ago)
Instead of stopping half way and calling it mirrored, what if you go to the starting point, nothing will change right?
Mathologer (4 days ago)
It's mirrored. The mathematical Mobius strip has zero thickness, so does the man who is part of this Mobius strip. Apart from that it's really completely obvious :)
Steve Truthisoutthere (5 days ago)
Nice mental gymnastics buddy, the fourth dimension is all in your perception of said dimension
M-T (5 days ago)
I thought the video was cool, but what irks me the most is that he didn't show how he fit the rubik's cube inside. I thought it was going to be something special to the Klein bottle, but it looks like you can also do it in any beaker... Anyway, halfway through the video, I was curious if you were able to, and saw the dislikes. Of course any other person's first thought would be "oh so he can't fit it in" or etc. But my first thought was... "Oh my god, this is a troll video, he's going to fit the rubik's cube in by SMASHING THE CUBE INTO THE BOTTLE". But no, nothing happened.
Dawn Kamleiter (5 days ago)
Such an anti climax
Pockets MacCartney (5 days ago)
the illustration of the man strolling around the moebius strip is not correct.
chuck guerin (5 days ago)
Why would blowing a cube into a bottle even matter? To show off glass blowing skills? Cool bottles, but who cares if it has anything in it. I was more impressed with one sided loop myself.
Pete Tong (6 days ago)
Who invented the Klein bottle? Was it Calvin?
Richie Schneider (6 days ago)
Just FYI, a "donut shape" is called a "Torus".
Pete Tong (6 days ago)
Dunkin Torus doesn't sound as good though
Tamara Smith (6 days ago)
So it's a Möbius tube instead of a Möbius strip, which my high school geometry teacher actually discussed with our class over 32 years ago. But he didn't call it a Klein bottle. Why is it called that?
Pavle Pavlovic (8 days ago)
what is so strange here , its a bottle with hole on the bottom not at the top like usual , litrally that is all , it is very nice but its not any 4th dimension kind of thing its a simple bottle with enter point on the bottom rather then top , dong get it , 1000$ for that , no i wouldn't
Pirate's Piggy (9 days ago)
True mathematicians drink out of Klein bottles.
Unwindamind (10 days ago)
INCORRECT 7:06 he would NOT be a mirror image he would be facing the same way
Dean Young (3 days ago)
He has consecutive depictions A_1, ..., A_9 of how the little man would travel along the strip. If after traveling, he would not be a mirror image, then one of the steps A_i to A_{i+1} is wrong. Which do you propose is wrong?
Mathologer (9 days ago)
The Mobius strip as well as the little man have no thickness, the little man is part of the Mobius strip and is NOT hovering above its surface. There is NOTHING wrong with what I say in the video. Also, why do you feel the need to be so damn confrontational?
Thou shall not bear false witness
timwins31 (10 days ago)
Everyone bitching about not seeing him actually put the cube in the Klein bottle watched this video on a different level than everyone else. And you really missed the important stuff.
Gary Stango (9 days ago)
A crazy german guy who's a little too into Holes?
Nyein PYE PHYO (10 days ago)
wait.. what..?
Steve G (11 days ago)
I want to know how to get ketchup out of a ketchup bottle !
Adrian S (12 days ago)
A couple of thousand for a bottle... some people have more money than sense. Even more phantastic is I put a straw in a coke bottle..
Clint Estep (12 days ago)
What a waste of time. Show how you did it on camera you fraud.
jeff mancuso (12 days ago)
I only watched to see him put the cube in the bottle , what a gip.
Craig Sibley (12 days ago)
The mirror paradox is not a paradox. It is a mechanical point of view provided only in the case of a transparent material (or in a theoretical, infinite point, two dimensional mathematical plane... not the model shown here). You are viewing the image through the reverse side of the plane on which the "man" is traveling and therefore actually viewing his "other side". If you view the subject on the same side of the plane on which he is traveling, he is still facing the same direction in which he began. The same could be accomplished by simply looking on the opposite side of the mobius strip without the subject taking a single step.
Yosen B. Mamma (12 days ago)
*!!!CLICKBAIT!!!* - This guy talks a whole lot, but says very little. I just wasted over a quarter-hour, waiting for this character to show me how he does it. What a letdown! - *!!!CLICKBAIT!!!*
Yosen B. Mamma (12 days ago)
+Mathologer - Look in the mirror, pal. Look in the mirror.
Mathologer (12 days ago)
Sigh, yet another comment from the very shallow end of the pool :) How did this video ever end up being a moron magnet?
Jamie Holocene (12 days ago)
Now THIS is a noodle twister.... my physiology professor once pointed out that the donut hole I was about to eat was goi g THROUGH my body not necessarily INTO my body. Sure, it breaks down, nutrients enter the blood stream by passing through cell walls in the intestine. But for all intents and purposes of this Klein bottle discussion, the donut hole goes in through your mouth, down your throat, through your digestive tract, intestinal tract, and finally exits via your waste disposal tract. All one long tube THROUGH the body. Check it, WE' ARE ALL KLEIN BOTTLES.
38alphaez (13 days ago)
Well. Bump the Klein bottle. Walking around in a twisty circle will transport you to the other side of the circle.
Mitchell Schubbe (13 days ago)
Robert Guerra (13 days ago)
what a dry sense of humor just cracks me up
Dainon McDuffie (13 days ago)
He talks completely over my head and now I feel dumb. Haha but I love how excited he is about this stuff! It’s cute. He’s definitely in the right profession 😁
Janelle honey-Badger (11 days ago)
You want to see someone excited about scientific stuff? Check out "Smarter Every Day" that guy is amazing & just so passionate about science. He's really amazing.
Switera Jaya (14 days ago)
Derek Johnson (14 days ago)
Since it's a Klein bottle, the Rubik's cube is already on the inside
TheRebelNine (15 days ago)
It’s awesome how excited he is about Klein bottles, I really enjoy listening/watching people talk about the stuff they love and are passionate about.
Keylup Veintisiete (10 days ago)
You should watch professor cliff from numberphile
Neil Aspinall (15 days ago)
This guy should be charged with false advertising. Click bait if there ever was some.
Charlie O'Malley (18 days ago)
Are they the first three chords of Kate Bush's Baabooska ?
Andy Low (18 days ago)
push something in a 4-th dimension, than pull it back at another place - and you have a portal!
Lee Watson (20 days ago)
Mobius 'Universe' explanation was wrong. You would not return to the same spot inverted, but in the same direction and orientation.
Mathologer (12 days ago)
The little man is part of the Moebius strip and is sliding around IN it. He is not hovering above the surface.
Terry Weaver (21 days ago)
First, what is the mirror thingy? 2nd... hmmmm... Only the "owner" should be able to disable the "reply link." I believe I would post the names of those disabling a reply link as doing so is at the least rude. Better yet... Stick them "inside" a Klein bottle.
Marvel James (23 days ago)
Your mobuis strip man is wrong way round
Mathologer (12 days ago)
Sigh, no he is not. The little man is part of the Moebius strip and is sliding around IN it. He is not hovering above the surface.
Andrey Novysh (23 days ago)
The best explanation ever how to "imagine" how to get rid of the clash. Especially for the kids! Our natural categories we "think with" does not help to "imagine" 3d -> 4d transition of course. But 2d->3d example is a good start!
Bob M (25 days ago)
The next time you go away, don't come back.
Yuki Endo (26 days ago)
Why so many dislikes? It's a nice video, huh?
Mathologer (12 days ago)
Yes, sadly this video has turned into what people in the biz refer to as a moron magnet. Lots of people here who usually only watch trash YouTube :(
Paul Wall (27 days ago)
...and the MIRROR was how Paradoxical on a Rubic's Cube?
Big B 501 (27 days ago)
Hummm? 🤔 Ancient Chinese secret I guess..... On another note... my hole high school experience....
Dean Finlay (1 month ago)
Zaubermann Inc (1 month ago)
wow this was very interesting until the point i realized that you will not explain how you got the cube in there. Now i am dissapointed af...:(
Aejaz Ul Bashir (1 month ago)
what is this... what is this all about... Klein bottle good for Mathematicians for what... nothing explained here...
Mathologer (12 days ago)
Sigh, "nothing explained here". Well, they usually say "I can explain it to you but I cannot understand it for you". In your case that has to modified to "I can explain it, but I cannot do anything about you not being able to recognise that what I am doing here is explaining some mindboggling maths". Absolutely remarkable :)
Thermalburn (1 month ago)
i want that as a wine decanter
Nicholas Granat (1 month ago)
Thanx for your time!
Omar Gonzalez (1 month ago)
¿Can anyone bring me the 3D design for a homework?
Richard Palmer (1 month ago)
What if the earth isn't flat or round...what if it's a **MOBIUS STRIP**
Ernani Savaris (1 month ago)
And I thought _I_ was nerdy...
sherwood 00 (1 month ago)
This guy thinks the eearth is flat and when you go around the track you comeback facing the other way as you flip over and do a 180 wow! What a ride that would be has anyone in the entire world experienced this! I didn't think so
Robert Morri (1 month ago)
Aesthetically where the neck meets its body there should be a tunnelling cuff and not the abrupt intersection seen .
Dr Dr (1 month ago)
Dum Mag (1 month ago)
Hugo Furst (1 month ago)
Thank you, Mathologer. I do not have the math background to "figure it out," but I nonetheless keep surfing YouTube in search of intellectual crutches that might - one bright day - convey to me an inkling of what you and the other uber-maths are able to apprehend. How curious that our senses can only perceive three spacial dimensions (and yet, know we are - femtosecond by femtosecond- propelled along an imperceptible, yet existentially experienced fourth dimension), only to have our minds inexorably compelled by the evidence to seriously consider as real psychedelic possibilities far beyond our individual and collective waking experience . Reality should blow our minds, right? The apprehension of mystery is the fundamental posture of the human intellect. Thanks again.
Mario Pineda (1 month ago)
Abhishek Vankit (1 month ago)
You deserved all the dislikes buddy 😑
Mathologer (12 days ago)
Absolutely fine with all the dislikes from the very shallow end of the pool if that has the effect of keeping a lot of fools from ever watching any of my other videos. On the bright side according to the YouTube analytics about 20k people subscribed to the channel after watching this video. 20k people who clearly see something in this video and mathematics in general that the fools of the world will never be able to get :)
#Banana#Republic#USA. (1 month ago)
Please don’t introduce this man to a gyroscope because if this gets him all giddy imagine what a gyroscope would do to him. Think I am kidding? Just search gyroscope in YouTube search Engine. There are people that spend their whole life thinking there is some magical power that could be harvested with the the right know how. 🤪 He was so happy I gave him a thumbs up. 👍🏽
Joseph Jores (1 month ago)
Wtf did I just watch. A guy sad obsession with a stupid twisted glass bottle. Doesn't even show how he puts cube in it. I'm reporting this is seriously misleading
Mathologer (12 days ago)
I let you in on a secret: Only fools do not spot at a glance what's wrong with the cube in the bottle. You see, the smart ones get it and are amused by this and all the rest of the mindboggling maths in this video and subscribe (20k have just based on this video). On the other hand, all the fools don't get a thing and never come back for more. Perfect, as far as I am concerned :)
Martin Moran (1 month ago)
Ha ha that's 16 minutes of my life I will never get back !
Jon Wardner (1 month ago)
Seriously what was that. The way he laughs as he reveals more and more “Klein bottles” is so unnatural it feels like a parody. Just when you think it’s actually un-ironic, “Klein bottle hat!,” “Klein bottle inside a Klein bottle.” But then out of nowhere a seemingly serious video brings rubix cubes into it for no reason other than its in the title? And they don’t even show it??? Am I missing something???
Mathologer (12 days ago)
Yes you are missing something :) I let you in on a secret: Only fools do not spot at a glance what's wrong with the cube in the bottle. You see, the smart ones get it and are amused by this and all the rest of the mindboggling maths in this video and subscribe (20k have just based on this video). On the other hand, all the fools don't get a thing and never come back for more. Perfect, as far as I am concerned :)
Aaron Singh (1 month ago)
U wasted my time buddy...n internet data.👎👎
Aaron Singh (12 days ago)
+Mathologer self praise is no praise buddy
Mathologer (12 days ago)
Yes, you did :) I let you in on a secret: Only fools do not spot at a glance what's wrong with the cube in the bottle. You see, the smart ones get it and are amused by this and all the rest of the mindboggling maths in this video and subscribe (20k have just based on this video). On the other hand, all the fools don't get a thing and never come back for more. Perfect, as far as I am concerned :)
Tavio Co (1 month ago)
I was curious & clicked on this video. After watching, I squeezed a bottle of ketchup in my mouth and pulled it out of my nose. In 13 secs.
stew mercer (1 month ago)
BIG E (1 month ago)
This is not a true klein bottle this is a two piece klein bottle it has 2 starting points and 2 finish points a true klein has no start or finish
iLLusion OTLUM ERP (1 month ago)
The Rubik's cube he put inside the klien bottle is magnetic.
Daniel Huddleston (1 month ago)
Haha mirror tricks and Klein bottles
Black Hawk (1 month ago)
I've never heard of a movie strip. I've heard of a strip of film but not a movie strip!
Daryl Re (1 month ago)
There goes a wasted 16 minutes of my life.
Reza Giovanni (1 month ago)
Shaved Heisenberg
eamonicker (1 month ago)
6:50 you are missing out half of the journey around the strip, he is still facing the same way going in the same direction. He hasn't traveled all the way around the strips one side, when he should disappear onto the unseen part of the strip on your diagram you have him appearing on the wrong part of the strip instead?! naff
Wally Wally (1 month ago)
Electromagnetic paradox in vacuum is more interesting
Michael Shaver (1 month ago)
Maybe he knows something about the 4th dimension that we don’t 🤔
Dwayne Page (1 month ago)
$20 says this dude gets off by sticking his junk into these.
P. S (1 month ago)
nuts ?
the giant midget (1 month ago)
That’s a cool looking bong. But I think you’re too stoned cause you’re supposed to put water inside not a rubix cube
Hafedh Ridene (1 month ago)
16 mn lost of my life... ended with a mister that will never be resolved...
dontusesoap (1 month ago)
i wasted my time on the video and now I'm wasting time on the comments.....the problem is me
LitFuses (1 month ago)
So it’s basically a glass tube with a thick end and a piece going through the side? So... a bong
Robinhema 3 (1 month ago)
Respected Sir ,I'm a student from India and I m really confused with a math problem and no one is able to define the solution process in an exact manner so can you please help me out with the problem and we Indian students love you to the core and we are really longing to question you a lot of questions I guess please help me
Michael Hiatt (1 month ago)
Why can't you show yourself putting cube in bottle? Are you from 4d?
Luis Eduardo HD (1 month ago)
Are we going to be reversed, or are we going to travel to a mirror universe ? It remembers me Alice through the looking glass.
Neander Heuri (1 month ago)
I guess its like the kings new clothes
Valiant 9 (1 month ago)
10 bucks says this guy has a dominatrix fetish..
Fox Kelly (1 month ago)
Clan Bottle aka Bong
Jeffrey Arnim (1 month ago)
This is becoming a most gooberish experience. I’m a bit fascinated with his fascination of his own fascination with some silly conceptual math humor...but now nodding off. How many times can you say “Klein bottle” in one sentence? Answer: too many! Seriously, any bottle has only one side, by strict definition... prove me wrong.
axe2grind911a (1 month ago)
What is the point of this video? Either show how you put the cube inside or do it front of our eyes in some cleverly cloaked or mysterious way... Was this supposed to be science or a magic trick? Too bad it was neither!
Henry Ford (1 month ago)
You didn't really do anything, one of the most boring videos I ever watched
Brandon Caldwell (1 month ago)
If u were to put something inside of it..it would also be outside of it as well
GRasputin91 (1 month ago)
Mad scientists talking about higher dimensions and have German accents. The stereotypes are true
GRasputin91 (1 month ago)
Lovecraft was right! Witches aren't really magic at all...they've just figured out how to access higher dimensions!
Mathologer (1 month ago)
Pretty much :)
Scott MacNab (1 month ago)
I don't think your mirror image thing worked as you jumped onto the other side of the strip in the last images which isn't right
Brian Travis (1 month ago)
Move it along faster
Kitt Crowley (1 month ago)
16 minutes of build up for a big dissapointment.
Jonian (1 month ago)
How can you have a 4th dimension when everything sits on only 3 of them?
AshTheZ0mbie (1 month ago)
>:/ an endless supply of 'um's 'uh's, and digressions. When presenting material, be precise and concise. This video could have been 11 minutes shorter and provided the same amount of actual content. Also, totally blueballed all of us who expected you to show how you got the cube in there
Don night (1 month ago)
-p Catalano (2 months ago)
2:09 There is the theory of the Moebius. A twist in the fabric of space. Where time becomes a loop. Where time becomes a loop. Where time becomes a loop...

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