How to Fill a Klein Bottle - Numberphile
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- čas přidán 7. 09. 2024
- In a 3D world, it's possible to fill 4D Klein Bottles - featuring Cliff Stoll.
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Cliff notes:
Cliff advises not to rely on his memory for the volume of a sphere. It's really 4/3 π r^3. Cliff also says that using a tube to break the vapor lock is challenging. Straws (even flexo-straws) kink when bent around narrow hairpin curves. And most flexible tubes (especially aquarium air tubing) have high friction against glass, so they're difficult to thread along the curve.
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Numberphile
Your videos are fascinating
Just Some Guy without a Mustache exactly I love watching them
Aren't you obsessed with those volume-less bottles.
Why doesn't the measuring jug have volume by virtue of the thickness of its glass? You can flatten it to a disc but if the disc is as thick as the glass of the jug, doesn't the disc have volume? Or is the idea that when you flatten it to a disc, you just keep flattening it until the disc is impossibly thin?
Thank you for your videos!!! Big fan! And your enthousiam makes it even better!
This man is evidence of "Growing old is mandatory but growing up is optional" and i love it.
Exactly
He gives me john Sturgess from young sheldon vibes
I love this comment
false..
I swear this guy is triple of my age and also triple of my youth.
Doc with 200% more chararacter.
He was unethusiastic until he was 50, and then looped around
its like he is on crack or something
How does he jump ten feet in the air when he hears someone say something like 'shapes'
Then you should lighten up a little
I love how he was super excited and happy, looked into the bag and completely stopped talking for a few seconds to eat a grape
Ahaha hey we all get distracted!
That was the cutest part of the video, he was so innocent there
I've never seen a person so happy to explain something. I want this guy to be my teacher.
Pop4eto he’s teaching you though
Bet
he's like rick if he weren't a narcissistic alcoholic
me 2
my old science teacher kinda was like this
"Be careful when you talk to mathematicians in the kitchen."
Solid life advice.
That's why I only use grams.
Ok.
even if ur eating chicken curry
Especially topologists.
They can either teach you how to eat pizza or tell you that holes are not real.
This man looks exactly like the person that i imagined was gonna tell me how to fill a kleinbottle
morbius??
🤔
"A disc has no volume."
Don't talk to me or my CDs ever again.
@Morris Sowards no leave my computer joke alone.
This is an agenda by big dvd
Ok pucci
*T U R N S I T U P*
About 60GB if you're taking about a blueray
Every other mathematician featured on Numberphile: "Here's my office"
Cliff: "Yo, welcome to my kitchen"
995 likes but no comments, this is very much a record
@@alxkeda you ruined it
@@ianparmley1566 indeed I did
@@ianparmley1566 can’t be setting the records to beat too high ya know
cliff is an amazing man, i must say
2:47
"So be careful when you talk to a mathematician in the kitchen" *Threatens with Pyrex cup*
Whoa, okay, sorry, please put that down!!
@@hunszaszist put the Klein bottle down and no one gets hurt!
As always, Cliff's joy and passion for topology is contagious.
He's so excited and it's so fun to see!
I agree
false..
My 6-year-old daughter be like: "What's the volume of this cup?"
- "Well, does it divide the universe?"
Yesn't
What kind of 6 year old asks about volume...
R/thathappened
Wish this video came out when I was in Geometry
@@blubee2289 r/ihavereddit r/youngpeopleyoutube r/woooosh
There is nothing in this world that I love more than a person who is genuinely delighted to teach others
"Because of the conservation of something"
- Cliff Stoll 2020
my favourite law of physics
6:12
I'd call it "conservation of physical volume"
Came looking for this
When a mathematician talks to a physicist
I love this video you can tell how excited this guy is about what he’s talking about and it’s just so wholesome.
He made my day
Wtf is that squidsmhirtz
@@FairArc it's dr doofenward squidshmirtz
He's a geek
Im reminded of Doctor Emmett Brown when I watch this guy.
I just graduated high school, and through all those years i really wish i had a teacher so happy and passionate to be teaching something he loves. All my teachers never really cared about their subject, this guy really gets passionate about how much he loves it, we need more teachers like him in schools. I mean he took something as simple as a klein bottle and made it so fascinating to watch and learn about.
Klein Bottle simple? in the same sentence? blasphemy xD
"This is not slow. THIS IS FAST compared to the age of the universe."
I like this guy
Time is relative..
Age is just a number. - My Uncle in jail.
Boom Planet that was Einstein
@@mailboxpipebomb no, that was Isaac Newton.
Boom Planet Newton was gravity and Edison was electricity. Einstein was relativity and time.
r/woooosh
I love how genuinely happy he sounds to be explaining things like this, as if he loves passing on his knowledge to the new generation.
Unfortunately the new generation, maybe besides us that are watching, don’t care.
@@ebbiebean9385 atleast we do
I hope my teacher, teach me like that
@@ebbiebean9385 I hate Gen Z 😂😭
@@ebbiebean9385 1.4 million cared
Most mathematicians: "A Klein bottle has no volume"
Me: *Bottle is bottle*
"Oh c'mon, its extremely fast compared to the age of the universe" That's such a great line
hes so a great person, i want to meet him
That's like a Douglas Adams quote!
@@sturmifan You can feel the passion in his voice
CCMarvMD i’m gonna use that in the future XD
Then he goes on: "This is spee compared to... Even something as rapid as global warming!"
"This is slow"
"Ah, c'mon, this is so fast compared to age of the universe" LOOL
best response ever
Got him!
that's something the doctor would say 🤔
Actually that was a bad smart answer as the age of the universe isn't fast/slow, but long/short (it isn't a rate)
@@rulekop He should had used "aging" considering channel's name and audience
I love how he put the champions league theme for Europe 3:22
"in the rest of the world"
Shows just Europe.*
(._.)
I love how he jumps! He's so excited! That's what science and mathematics does.
And not drugs!
@@billbosagginz740 Drugs do that too teehee
@@nykal1510 ik I was being sarcastic lol
It makes you crazy?
Or maybe his knowledge is rotting his brain?
If actual professors had this much enthusiasm during lectures, I might have love mathematics instead of having a panic attack lol
This dude is not normal. This level of enthusiasm would take 10 direct shots of adrenaline
@@SoumilSahu it's normal for a subject hes passionate about. My high school math teacher was the same way, and it made me love math even more that I already did. I get the same way when I talk about medicine and sometimes math.
Several of my professors had a great amount of enthusiasm -- and by proxy classroom to professor engagement -- when I was in college. It's not unheard of, especially when they're really passionate about what they're talking about.
My history and physics teacher was that way. That enthusiasm got everyone straight As on some complicated topics.
My dog isn't that enthusiastic seeing a bone
This man is literally bouncing with excitement and I love it.
I like to imagine this guy just came home from buying grapes and a cameraman was just waiting there and asks him about this stuff, and just, improvises
I like to imagine he bought exclusively grapes and also put them in that little paper bag
??...
He sounds like a cartoon character. He should do voice acting
Seiyuu
Like mario
He sounds like that guy from wreck it Ralph
that's just how old people sound
@@ethanrooney4110 Yeah he sounds a bit like King Candy from Wreck-it Ralph
Mathematics needs rigor but it also needs fun, lots of fun! I can’t imagine having a math professor like this gentleman! Simply awesome!
First minute in and i already love this guy. Hes so bouncy and he feels like he still has so much livliness in him, which i love. He reminds me of my biology teacher, he just have, genuine, legitimate love of teaching
I wanna be this lively when I'm this old :3
i was 20 seconds in and loved this guy
I mean why are biology teachers are supposed to be "lively"🤣
Love how the birds fly at 2:13
Makes him look like a wizard
Me at 6 PM: "I need to go to bed early tonight so I can actually get some sleep."
Me at 3 AM: "bUt hOw cAn a kLeIn bOtTlE bE fIlLeD wItH wAtEr"
The editor put in a lot of effort into those graphic sections and I just want them to know that they are appreciated
Guys this is just the back to the future dude in his early ages.
doc Emmet brown
Come on it's not that hard to remember the name "Doc"
GREAT SCOTT!
You mean Doc Brown
I didn’t know this guy could skate board?
This guy is *visibly* SO excited about explaining how to fill a klein bottle to us.
We all know people like this make the absolute BEST kind of professors.
6:43 "come on, it's not slow. This is fast compared to the age of the universe."
-Me, when I am procrastinating again with my thesis.
How come that CZcams knew I do too?
ErC0411 me while walking my 100m sprints at school
sometimes thats the best way, makes sure you got it exactly the way you want.
I can do 100 pushups pretty quick.
THIS QUOTE IS GREAT
Love how he just started pulling out grapes from the bag and started eating them 😂😂
"I could put stuff int... I put stuff into it !"
[starts eating grappes]
@@clementm5417 I loved that part I was hoping someone would comment about it
Professional CZcams content right there
oh, the world before coronavirus. Now you have to wash everything.
ChickenNuggetDinosaur ChickenNuggetDinosaur totally a mood right there
Coming from an engineering background all I have to say is, if he stuck a rubber tube down the hole in the Klein bottle that was smaller than the diameter of the Klein bottle tube, and long enough to reach the reservoir, water would be able easily enter and Air can escape.
Great, now explain the physics of it. This is also the fastest method to get water out of an upside down bottle, right?
"conservation of something" - ah, a true physicist.
It's because he doesn't want to say conservation of volume when he just said it does not have volume haha
Baddaby true
"You can see actual Klein bottles in the 4th dimension"
Cliff: *Happy topologist noises*
"They can't contain anything"
Cliff: *Sad topologist noises*
Doc has come a long way since he figured out how to time travel.
6:30
Cliff gets pulled over for speeding
the police officer tells him that he was going too fast
"compared to the speed of the sun through space, I was barely moving"
"Wrong, Officer! The Earth is actually moving in the opposite direction 10 times as fast! I legally had no choice...."
I can read this in his voice and its so fitting
Because of relativity, there's no such thing as the speed of the sun through space.
@@vojtechstrnad1
To clarify, yes. That notion is also called relativity. GALILEAN Relativity to be specific, formulated by none other than Galileo Galilei
(speed is always relative to another object so you can't have "the speed of the sun through space")
6:40
"Still pretty slow"
"I A M S P E E D"
:D
This dude has crazy mad scientist vibes and I mean that as a pure, genuine compliment
3:24 He used the Champions League theme for the european union. I'm not even mad.
*far from it, actually*
i was looking for this comment
...which is actually Zadok the Priest from Handel's Messiah with the lyrics changed.
@@adambis337 same lol
"Everywhere else in the world"
Shows Europe*
Eurocentrism is a disease.
"Conservation of something"
I guess you don't need a physics degree to be a topologist XD
Read this just as he said it in the video lol
This man is adorable, I love how he talks and seems genuinely excited to educate people. It makes me happy.
I need help. I'm training my baking skills for pi day but the recipe asks for 500ml of water and I don't know how to measure it.
I got a 500ml sphere but I didn't seem to be able to fill it with water because it wouldn't go through.
So I poked a hole in the sphere but now it has 0 volume.
This is a nightmare. There's no way for me to measure the water >
Make the water go through the 4th dimension and back to enter the sphere.
@@givrally7634 solid advice, works everytime
Buy a pi from the Bakrs shop.
Fix the hole after you've poked it. That should solve your problem.
@@policesquad That's clever
9:03 i'm confused.
If you get a Klein bottle nice and dry on the "outside", would that not automaticly make it dry on every side?
oh
oh yea
@@sturmifan Hey actually meant "some of the sides" maybe??
@@pratyushbhattarai5632 aren't klein bottles had only one side?
Well
At least from four dimensional being views
Well you can dry a measuring cup on the outside but a topologist would insist you missed a spot
When talking about holding volume like this video is, orientation and inward/outward facing parts of the vessel matter. Similarly you can MAKE a mobius strip have an inside/outside by wrapping it around your wrist--there is clearly a part touching the wrist and a part facing away from the wrist even when it only has "one side"
@@pratyushbhattarai5632 theres only one side on a klein bottle is the joke
I’m not usually interested in math and physics but this guy’s enthusiasm just makes me want to study. I wish my teachers are like this and if so I can study everything
Cliff: "Than, get it nice and dry on the outside." [9:02]
Me: "On the what?"
?
@@applepie1272 klein bottles visualized on 4d have no in and outside, due to it only having 1 side. I dont know if this is exact, correct me if im wrong
andarted: “On the what?”
Niiiice!
Yeah! They just have one side
@@peasg9839 if we think about it, don't most cups just have 1 side as well...
2:48
“So be careful when you talk to mathematicians in the kitchen”
In the... mathemakitchen?
@technix the fox thank you
oh cool, you made me laugh. Here, have a like!
@471LL4 YTB thank you boss
Underrated
Hey man, that was very funny. I laughed.
People: *Maths and Physics are boring and hard to understand*
This man: *I'm going to change this man's whole opinions.*
"Conservation of something"
Spoken like a true mathematician, never a special case and only general ones. Something can be mass... or whatever lol.
Hahahahaha
I was searching for this comment!
Conservation of bubbles.
@Kitsune 3.14 But the mass if air going out is not the same as the mass of water going in or is it? It's more like conservation of pressure. But pressure is not really constant, it just tends to an equilibrium so... consevation of something :D
Conservation of volume
It puts a smile on my face to see how enthusiastic he is
That attitude is learned. That means you can learn it, too, if you want to.
@@jonathanguthrie9368 Not necessarily learned, it wasn't taken out of him by the process of schooling etc. :)
It feels like he's like... Ooh ohh... someone wants to listen to me ramble on in my kitchen!!! Not that there aren't people who are interested, but the majority of people's eyes would glaze over.
@@VincentGroenewold I agree, I often find myself being similarly enthusiastic about (usually scientific) topics. It is sad that school systems manage to suppress the flame that is the curiosity we all have with boring and stressful everyday life. You would think that it's possible to interest almost anyone at least mildly in most scientific topics.
LordKekz Yep, I’m actually a father of a child with high iq and he couldn’t cope with a classroom. We ended up having to take him home as he got depressed, unfortunately that’s not allowed in the Netherlands so you have the super weird and stressful situation where you want to teach him at home, not going down the path of going the wrong way and still having to send him there. We couldn’t justify that for him, so we moved abroad. It took us a full year to get him interested again, at least he’s happier now and starting to get excited a bit again, but what he had before school, never really came back. I read that many famous scientists had the exact same experience. We definitely need to change that.
I love this guy’s energy. I can tell he really loves what he does
“How to fill a Klein bottle”
Just stick a hose in it
There it’s filled
Where will the air inside go?
The ALLrOUNDER SS imagine less like a garden hose, and more like thin airline tubing on a syringe or something.
@@mattschutt2340 That should work...... Wouldn't be as exciting as the mathematician wants it to be
It’ll explode
Because it’ll pressurize air and it will explode
2:12 I love how the birds in the background make for extra effects. Almost a cartoon.
Haha true
Imagine living life with this sort of excitement and enthusiasm for your work. Not about money or promotion, but just the art of the subject matter. It sounds like he almost starts laughing like an excited child on Christmas morning while he is talking. How wonderful and joyful must that life be? I envy him.
"This is fast compared to the age of the universe." Spoken like a true government employee.
2:13 omg the birds LMAO
random person hahaha oml
0:41 captions: [EXCITEDLY TAPS THE PLASTIC BALL] ...and an inside!
Me: *sees video*
Me: The only person who can adequately explain this subject is the same man who built a robot to fetch his catalog of Klein bottles in his basement
Me: *clicks*
Me: what a relief
My friends {∅}: So, can you drink out of a Klein bottle?
Me: well yes but actually no
With a straw maybe
I like that you're friends with the empty set. My set of friends is the empty set itself :(
Every time remember that Futurama episode!
@@Hampardo I wonder if mueez adam really intended it to be interpreted that way as a math joke, since he used {} instead of ().
Anyway, I really do love the set containing the empty set. Among other feats, it is the set-theoretic realization of the ordinal equivalent of the fascinating number Wau!
@@viliml2763 every course I've taken defines sets within curly braces instead of parenthesis
This man is the only person that’s over the age of 40 and can talk to young people in “our” language while not having it be cringy
As I am finally recovering from a 10+ year depression, I have a temptation to think "even if you are ready to live your life now, it's too late to feel feelings of exuberance, passion, and legitimate excitement. Those are reserved for people in their early 20s/late teens."
Cliff Stoll's mere existence has helped me so much by completely destroying this toxic idea.
so basically, we are all inside of every measuring cup in the world.
And every measuring cup is also inside all of the others measuring cups
Does this mean the outside of each measuring cup is inside the inside of each measuring cup?
josefu joestar
Except the ones that are currently inverted on countertops and other places that form a seal
I know that feeling of being so excited to explain something you love, even to people who might not be as interested as you are.
Dude legit has more movement than me, and I’m still a teen.
Same
Who wouldn’t be hyped for filling a bottle
@@Gator_nit Hmmmmmmmmmmmmmmmmmm
"Don't let the mathematicians touch your kitchen, don't let em near your recipe book"
He seems so happy to just pass on his knowledge and I want more.
I love that this man just has a bag of grapes
You mean you don't ?
is that uncommon?
**DANGER ALERT**
The excitement from this man is contagious
I love this guy, so charming. I wish I could have him as a teacher.
He's so joyful when talking about Klein bottles, like me when I go outside and see the stars!
I hope no one ever hates on this guy he is a funny, nice and excited science guy. I would want him to be my teacher
Orange Stone where’s your brother redstone
@@jasonmintzchannel8902 That traitor kicked me out of minecraft and replaced himself in my place so I made a CZcams channel to win back my spot.
"this is fast, compared to the age of the universe!"
Yeah, so is the human aging process.
@Dylan Parker ... And so is the age of our universe...
"In America, it is possible to put 16 ounces of water in it"
Did he just-?
I love how disgusted he sounded when he saw it measured in pounds
There are only 2 countries in the world that use imperial. USA and Mianmar do only 4.5% of the population.
Jay Best what about Liberia
@@defaultkid99 I thought that pretty much everyone there used metric even though not officially changed over yet.
The key point, a country being weird and wanting people to use their 16 times table on order to count out 2 cups...
@@jaybestnz No. Only USA and Liberia use imperial system. Myanmar uses a traditional system of units, not imperial.
That was truly interesting. He brought life into what many consider a dry, tedious discipline. Really enjoyed listening to this
This is the best illustration of a bottleneck I've ever seen. You can perfectly illustrate how a job that should be easy and quick takes so much work and is impossible to speed up if the system is overcomplicated
I’ve been really interested in the topic of Klein bottles because of this channel
Lol I see u everywhere ur the next Justin y lol
@@aninditachakraborty8856 There's a thing like that, people like him are called commenters
I really don't know why people rage at some commenter just appearing everywhere, do they not know about the notifs?
It's probably because of Cliff's enthusiasm.
Ayy mah guy
So excited. So wholesome. I came for the Klein bottle but stayed for his excitement.
I’m constantly scared he’s just gonna drop something with all that energy of his
I got immediately excited when Cliff appeared on my screen.
so did I lol. I think we all did.
@@butterscotchdoesthings1126 I think it's impossible not to. Excitement flows from high pressure to low, and Cliff Stoll is an excellent source of high pressure excitement.
@@mal2ksc I've never seen him before, but I liked him instantly.
I love how jumpy and energetic and just excited he seems about the topic. He should be a teacher
Cliff Stoll is like a real-life Cave Johnson. We need to give him an Aperture Science and he'll work his magic.
To think about it: topology is most concerned with number of holes in the object, or saying scientifically, number of APERTURES :) So yeah, he's exactly the guy we need!
And we must keep away from lemons or it will be explosive video.
Moon Rocks!
We do what we must because we can. In the background: I don’t want your lemons
I want someone to love me as much as Cliff loves klein bottles
Lots of mathematicians and physicists greatly appreciate Greek letters; I'm sure someone does.
SplinterDragon Ah yes, the well known letter "Yangtra" from the Greek alphabet.
@@yangtra2534 μ or mu, the Greek letter.
@@kuttlefish225 Ooh no it was a typo lool
@@kuttlefish225 i am going to university to study physics, learning greek has been a bonus
Every professor should be this passionate and cheerful. Thank you for a great lesson sir.
I love his passion. I just hope I can be that passionate about anything at that age. Heck, I can rarely find that kind of compassion even now.
It actually gets better with age
1:01
"Likewise a bag - I can put stuff int..." (ohhh there are the grapes I bought some days ago...are they still eatable? :eats one: Yeah, they are...where was I?) "...put stuff into it" - I love those moments 😍
surprise grape!
I love his enthusiasm, he seems so happy to teach us how to fill a Klein bottle
I love this guy. He’s just so passionate and happy about doing maths.
And his happy little Klein bottles too.
I ordered a Klein bottle opener to open and fill mine. Of course it cracked.
I think there was a misunderstanding about the terms "Klein Bottle - opener" & "Klein - bottle opener"
I love this man's energy so much. Wish I could've had him as a teacher.
"Be careful when you talk to a mathematician in the kitchen."
Ironic.
6:04 "Conservation of something" is my new favorite physical law
I have one of his Klein bottles on my shelf! He included a photo he took of it next to the first daffodil of the season and a letter describing how he was about to ride his bike to the post office to send it. Very wholesome guy.
2:13 the moment when the mathematics scares away birds.
He is back. The man The myth. The legend.
The man
The myth
The legend
T H E G R A N D P A
The excitement in this guy is everything we can hope for from a teacher.
"Likewise, a bag ! I can put stuff into it !"
reaches in...
"I put stuff into it"
"i can also put stuff with volume into it"