HomeОбразованиеRelated VideosMore From: Mathologer

A mirror paradox, Klein bottles and Rubik's cubes

12789 ratings | 1397264 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 (2290)
Christopher Brown (10 hours ago)
This guy is a delight
gareth5000 (11 hours ago)
Kate Bush
Bob Adkins (1 day ago)
I think Mathologer is Floki
What's the real use of this bottle? Or is it just an ornament?
Darryl Coleman (1 day ago)
I watched the whole vid waiting for you to put the cube in the bottle only to see u cut away and return with it in the bottle.... 26 (Too lazy to comment myself ,so i cut and pasted from Malcom Wiseman.Thanks Malcom)
Dimes (2 days ago)
This was a very interesting video. That said, I don't understand the hateful comments. Do you people want him to do a card trick? Or to pull something out of a hat? Don't listen to the people who came to "see how he got the cube in the bottle". The mathematical and geometric concepts you presented in the video are clearly too much for their feeble brains to understand. They can go elsewhere to have their elementary minds stimulated. Again, great video. You've just earned an interested subscriber.
whoscooldaddydre (3 days ago)
Super interesting, however I do have a question, isn't an everyday drinking glass, a 1 sided object? I'm so glad I stubbled upon this channel
Zineb Z. (3 days ago)
I always enjoy your videos. Glad I found your channel.
Tom Curtis (3 days ago)
Make a bong already 😂🤣
765tgbvc (4 days ago)
The vid begins interesting, then concludes delusional ...
APenker (5 days ago)
Why is it called "Klein Bottle". Klein was originaly talking about "Fläche" that means surface. But when they translated it, they used the word "Flasche", looks similar but means bottle. So it has originally nothing to do with a bottle. It was meant as a 4 dimensional surface. But now everybody, remembers it as bottle. (Sorry when I made some mistakes, my native language is german and not english.)
K'aman'Tur (5 days ago)
A couple thousand dollars? I'm a glassblower and could make one that big for less than a 100$...
Mathologer (4 days ago)
Cool, can I have two, please (I am serious :) How much for postage?
Gitesh Chaudhari (5 days ago)
What a dumb person
doghous3 (5 days ago)
Do you remember those over-enthusiastic creepy science teachers....
Kirk Calma (6 days ago)
I vant zee Klein bottle hat.
ASMRsoundsoflife (6 days ago)
Long winded and a totally useless and boring explanation of Möbius. You owe me 16 minutes!
Eugene Botchway (6 days ago)
This was like a full episode of inter-dimensional cable
Andrew Stephens (6 days ago)
Never seen one of those before. Is the 3 dimensional intersection both open and closed at the same time? Kind of a Schrodinger‘s cat kind of thing?
Riccardo Dell'Orto (6 days ago)
I clicked on this video thinking "let's see what is this mirror paradox". I was impressed and very curious about it, when he introduced it, and that's it, end of the part i was interested in in 5 second :(
Nico Steiner (6 days ago)
I like the presentation style of your videos. It is well thought, properly adjusted and perfectly "crafted" for each single topic. Presenting a Möbius strip or the calculation of infinite numbers is quite a challenge, not to speak about these "self including" inside-out Klein bottle creatures. But you are doing so very well for all these challenges, Sir. Each of your videos is a testament to your deep-rooted passion for mathematics.
Cook Leo (7 days ago)
What a nice way of comparing the dimensions. Well done
Texas Miller (7 days ago)
I love his giggle
Jabir Hassan (7 days ago)
Dis guy is a fucking dimwit ✌🏽
TheGhOuLGaLs (8 days ago)
Cesar Moreno (8 days ago)
Waist of time
WTF (8 days ago)
very good video thanks
FUSE (8 days ago)
What I don't understand about 4th dimension is, that you can represent the 3rd dimension in a 2 dimensional space, why can't I represent something 4 dimensional in a 3 dimensional space? I CANT ANSWER IT AAAHHHH
Steve 58 (8 days ago)
I need a couple of paracetamol- I still struggle with basic mathematics! Way beyond my comprehension but interesting nevertheless.
P Schmied (8 days ago)
The so-called glass klein bottle is NOT a paradox. It is topographically identical to an open cup, which ALSO has one surface, enclosing the material of the glass Making holes through a solid object does not change that fact that it is solid. A finite flat sheet of glass also has one surface because the "edges" are simply a portion of a continuous surface which is acutely deformed through space.
João Miguel (10 days ago)
Sorry but crap video. Waste of time.
Davi Trovon (10 days ago)
Interesting figure, but 4th dimension is actually the time
Carlos Robinson (10 days ago)
Your mirror image illustration of the Mobius strip is incorrect.
Carlos Robinson (10 days ago)
The Paradox exists because... Well, you can exist in more than one dimension at a time, but you always exist in one more Dimension than you can accurately perceive. For example, we know that we exist in at least the three dimensions that we have some measure of Mastery over. But we also exists and can probably be perceived from other dimensions as well that we ourselves cannot perceive because it is beyond our dimensional capabilities. Do we have an accurate understanding of what the 4th Dimension is? No, because although we exist in it and can perceive its effect upon us, we cannot accurately Define it. It is beyond our sensory capabilities, and therefore beyond our ability to deductively define it.
Carlos Robinson (10 days ago)
Let me explain. You are thinking of a Mobius strip as a two-dimensional object when it requires at least three dimensions for it to be created. You erroneously continued the upside down figure of the two dimensional person on the wrong plane; it would take two revolutions of the Mobius strip for the person to end up at their starting point. The real Paradox is that you never occupy the same space even though you are traveling along a single plane without turning to return to your original starting place. But your orientation would still be the same. The mirror Paradox is that when you are at the same "point" of the Mobius strip after one single revolution, you wouldn't be in the same "place", and it would be at that point that you are a mirror of yourself, albeit not existing in exactly the same space.
kimura kano (12 days ago)
Ahh ok. And his point is? Are you a magician? A nerd? The 2d guy walking around didn't even make sense. He doesn't suddenly reverse. I don't see it at least.
HABIBI Z ONE (12 days ago)
what's the point of a Klein bottle? it provides no mathematical proof or solve any theory, its simple creating a solution to a problem you've created... this renders it useless....
Bogdan N (13 days ago)
That example with the 2 dimension man walking on the Moebius strip is WRONG! If you start from a point on the strip and follow along it, you will reach that point periodically, and facing in the same direction. In the example provided, you cross the boundary of the strip, on left side of the picture. I believe you found a way to defy the laws of thermodynamics, too?
Milan Orlovszki (14 days ago)
*Insert surprised pikachu meme*
Jay H (14 days ago)
We have a Klein Bottle shop in my area, they sell all sizes and colors and designs. Okay not really.
Karen Reddy (16 days ago)
Without showing the process of getting the cube in, the video is a bit wasteful.
Spaceboyy (18 days ago)
This guy kleins
Noneya Fukov (18 days ago)
I missed the entire point of whatever the hell you were babbling about.. I'd like my 16 minutes back ... Can you put that in a bottle?
Aditya S (20 days ago)
Hey i love your videos...please do one on gabriels horn
Jonathan Castillo Zea (20 days ago)
14:55 - 15:10 there is never seen before. I love it. Just for that you got my like.
Rubiksmaster02 (22 days ago)
dude they are not called nano cubes
TheJudge01 (24 days ago)
A klein bottle?.....right. Like the ones used in meth labs. Just kidding. These bottles can't be used for anything but take 2000 dollars from someone who thinks they're absolutely amazing. Whats amazing is the steam engine made of glass to see how the internals work. That was neat especially if turned into an automatic bong pumping smoke into your lungs. Choo choo. Holy shit! Put that on ebay for $2000 and that shit would be sold within a minute of it being posted.
Paul van Gemmeren (24 days ago)
Möbius loses job Möbius loses house Möbius loses husband *Möbius strips*
Russell Wen (25 days ago)
How do you extend it into the fourth dimension practically anyway
Russell Wen (25 days ago)
'Rubik's cubes' YAY
Edu.RC (25 days ago)
Awesome! Who doesn't like Klein Bottles and Rubik's: https://youtu.be/-BHfsPC1pSY
lewie snyder (25 days ago)
Anyone feel like South Park already did this bit? Step 1: Get Klein bottle and Rubix cube Step 2: Step 3: Rubix cude is in Klein botttle
Ray Quinn (26 days ago)
Thank you for your passion for math, and the labour of creating these videos for curious folk like myself. I appreciate your efforts to explain and visualize these concepts. I must admit my confusion regarding the 2D man travelling upon the mobius strip [6:25 > 7:55], at 6:56 in particular when he is rotated to an upright and left-facing position. To us, in one revolution (half a cycle?) he would be upside down and on the reverse side, but in two he'd be at his origin in the same orientation. Sadly I don't follow why he rotates to become a mirror image in the example just by travelling halfway around the mobius strip, facing the way portrayed (to the left) against his vector in particular. The lower left image would be correct to another observer for across from us seeing the reverse from our perspective, and should that portion of the strip (bottom left as shown in video) not be filled with images of him head up and facing toward the right to complete the cycle? If this all seems like nonsense - no worries - it is likely related to why I don't understand the notion of travelling the universe only to return inverted or a mirror image. If anything, to me as the traveler, the universe would be the mirror image. Happy Holidays from a dullard!
burakan (28 days ago)
I wish i read the comments before watch it.. 😔 ❕Warning! This video is a clickbait and a waste of time❕
Mary Mc (28 days ago)
Hey today I found your channel & it’s Christmas! ☺️
Danny B (29 days ago)
15:30 thank me later lol
ryanguit (25 days ago)
S Tra (30 days ago)
If you pay a couple of thousand dollars for a glass bottle, your IQ can’t be very high.
Matthew Wheeler (1 month ago)
I think you're a Klein bottle baby
jim mcewan (1 month ago)
My guess is that its just single blocks and they have magnets on at least two sides with attracting poles to the other blocks so they automatically are drawn together if you put them inside in the right order ! I,d put money on it! Who,s a clever boy then? Tell me I,m wrong!
Sweating Dynasty (1 month ago)
drenatomja (1 month ago)
One of the germans in Dude wheres my car, years later
Юра Рябов (1 month ago)
Do you indulge in speedcubing?
verliba (1 month ago)
I'd like to point out that the man on moebius stripe, does not come around mirrored.. He only comes mirrored if he passes through the paper from one side to the other one when he's half way. If he went all the way to the starting point, he would not be mirrored. Try that with a paper guy on a paper moebius stripe.
Ty BB (1 month ago)
7:20 feels like he missed a detail here or that he didn't Double check his workings
Ursadon (1 month ago)
So if I somehow come back as my mirror image...would every single one of my action and physical beings (such as my heart) be located on the opposite side? Like I'd become from right-handed to left-handed? And my heart be located on the opposite? *:thinking:*
John OBrien (1 month ago)
No idea how I got here, almost a Klein bottle enigma in itself, I was traveling through YouTube and inverted to this.
Jeremy Smith (1 month ago)
But he's also now on the other side of the same side
Joose Kantola (1 month ago)
Rubik's cube in title Clicks Cubing is such a great hobby. It's just about learning and improving.
Rana tabu (1 month ago)
What a waste of time !
Kenny Arias (1 month ago)
What if the universe is a klein bottle
Venkatesh babu (1 month ago)
How do you get clustering. KB. I mean how one KB can pass through each other in separate ways.
Venkatesh babu (1 month ago)
The cross over place is black shade or seems black holes.
Venkatesh babu (1 month ago)
Water flow patterns over Klein bottles with a spin.
Venkatesh babu (1 month ago)
How do we order numbers in terms of Klein model structures. Mean where do numbers fall.
Ash Ketchum (1 month ago)
Why I'm watching this 😒😕, this guy is stupid, doesn't know dimension thinga at all.. Saying it'll vanish in 4th dimension and we can't see lol, we're living in 4th dimension nd 4th dimension is time...
PowerPro Films (1 month ago)
Lost me with the 4th dimension stuff..
Colin G (1 month ago)
13:19 a world first? So impressive. Call Guinness quick. Jk i like these videos good stuff but i need to tease ya on that world first thing like wowwww ammmazing
Definitely worth it
Filipe Anastassopoulos (1 month ago)
triggers my misophonia.
Erald Buneci (1 month ago)
what mirror! he is in the back. he is not mirrored
So it's technically a three dimensional mobius strip!
James Jenkins (1 month ago)
Sadly this is more topology and physics than most people can easily understand.
jay71512 (1 month ago)
4th dimension? Sorry my brain only accepts 3!
Philip Eigen (1 month ago)
The giggle when he puts the klein bottle in the klein bottle
Matthew Sivewright (1 month ago)
7:43 : Are you sure that diagram is right? I tried a practical method and the end at start there were the the same.
Kashn Itall (1 month ago)
So 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 free69 (1 month ago)
Damn I was waiting for this guy to show how he got the cube in the tight hole and it never happens 😔😔🤦‍♂️
Joel Vautour (23 days ago)
Very boring video,about something that could have been interesting
Gea Zom (30 days ago)
+S Tra nice! so that i can learn something about 4 dimension on pornhub!
S Tra (30 days ago)
There’s a lot of videos on pornhub that explain how to put things of different shapes in tight holes. Much better than this one, too. If you like German accents, they have that, too.
jim mcewan (1 month ago)
My guess is that its just single blocks and they have magnets so they automatically are drawn together! I,d put money on it! Who,s a clever boy then?
Free6ix9ine free69 (1 month ago)
+Vicmo I think he just used butter to slide it through.
Ricardo montalban (1 month ago)
Where do you put the weed in?
you2tooyou2too (1 month ago)
When 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.
wiplashsmile (1 month ago)
Aren't the bottles with the open intersection more representative of a 4D Klien bottle than the closed intersections?
Joda (1 month ago)
14:09 Weird flex but ok
Oliver Kunkel (1 month ago)
Why does a drawed figure turn mirrored after walking the whole surface of a möbius strip? This is not true.
Pete Skyrunner (1 month ago)
The best example of the 4th dimension I've seen.
Nathan Anstiss (1 month 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 https://youtu.be/x8zEWJzglN0 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 Salhin (1 month ago)
wtf??????????? 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 Lessy (1 month ago)
What am i... Is it.. What.... Do you.... Why?
Caleb Cook (1 month ago)
At 10:30 "if you get that cube in that bottle..."
Caleb Cook (1 month ago)
And how the fuq he get the cube in the bottle
Charles McMillion (1 month ago)
Is there a psychiatric name for what's wrong with this guy?
Bruce David (1 month ago)
Nonsensical, and I hope he doesn`t have someone tied up in his Basement... or in a Klein Bottle!
Dan Finazzo (1 month ago)
He did not mention magnets at all . . . !!
johnrtrucker (1 month ago)
If 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 1noskcaj (1 month ago)
I’m watching a 4D object as a 3D model on a 2D screen.
Szymon D (1 month ago)
Really...? But why...?
Awesome Productions (1 month ago)

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