A Hole in a Hole in a Hole - Numberphile

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  • Опубліковано 24 тра 2024
  • Audible: www.audible.com/numberphile
    More links & stuff in full description below ↓↓↓
    Cliff's glassware: bit.ly/ACME_Klein
    Extras for this video: • Extra on a Hole in a H...
    More videos featuring Cliff Stoll: bit.ly/Cliff_Videos
    Cliff references A Comprehensive Introduction to Differential Geometry by Michael Spivak: amzn.to/2cwmdB7
    Animation: Pete McPartlan
    Note from Cliff:
    Original ideas & suggestions from Peter Nguyen of Coker College and Danny Stoll of U/Chicago
    Amazing glasswork by Tom Adams, George Chittenden, Lucas Clarke, and Xing Wei
    Support us on Patreon: / numberphile
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    Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
    Videos by Brady Haran
    Brady's videos subreddit: / bradyharan
    Brady's latest videos across all channels: www.bradyharanblog.com/
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  • Наука та технологія

КОМЕНТАРІ • 4,2 тис.

  • @sithlordmaster181
    @sithlordmaster181 7 років тому +6131

    I can't decide if I'm more impressed by the math or the glass blowing skills.

    • @urquix96
      @urquix96 7 років тому +93

      me too hahaha

    • @patsdude54
      @patsdude54 6 років тому +16

      sithlordmaster181 there was no math....

    • @kuco30
      @kuco30 6 років тому +286

      patsdude54 Topology has a lot to do with math. its like saying geometry isnt math

    • @Aspri987
      @Aspri987 6 років тому +8

      sithlordmaster181 that deserves a million likes brah

    • @RobertMinsk
      @RobertMinsk 6 років тому +32

      im more impressed by the glass blowing cuz forging a knife is already hard. but thats a whole 'nother level. if it were made of metal it would be even more impressive.

  • @Cr42yguy
    @Cr42yguy 7 років тому +4803

    at the beginning of the video i thought "oh nice, he actually made 2-3 things out of glass to show us something"
    and then it just escalated!

    • @RosesAndIvy
      @RosesAndIvy 7 років тому +162

      You should watch his klein bottle video, he's got hundreds of them!

    • @s0me1up
      @s0me1up 7 років тому +121

      +Renate vd Bent hundreds? HUNDREDS?!?! he has THOUSANDS if not TENS OF THOUSANDS

    • @lxathu
      @lxathu 7 років тому +138

      I doubt anyone else in the world has this kind of sentence in the dedicated wiki page: " He stores his inventory in the crawlspace underneath his home, and accesses it when needed with a homemade miniature robotic forklift."
      en.wikipedia.org/wiki/Clifford_Stoll
      It's a bit like Alice in Wonderland or Being John Malkovich.

    • @Cr42yguy
      @Cr42yguy 7 років тому +1

      Renate vd Bent don't worry, i've seen them all

    • @augustorodriguez743
      @augustorodriguez743 7 років тому +5

      that escalated quickly

  • @CraftQueenJr
    @CraftQueenJr 5 років тому +2374

    “ Is it okay I’m pointing with my nose?” And this man is amazing.

  • @aghaanantyab
    @aghaanantyab 5 років тому +3900

    The conclusion is topologists can't distinguish a donut and a cup of coffee

    • @evlredsun
      @evlredsun 5 років тому +86

      grats on almost paying attention in topology 101

    • @Twinspinner
      @Twinspinner 5 років тому +73

      But they both go great together in the morning👍

    • @VibratorDefibrilator
      @VibratorDefibrilator 5 років тому +41

      I bet they get dizzy from the view of a spaghetti bowl.

    • @AndresHernandez-lo9uy
      @AndresHernandez-lo9uy 4 роки тому +7

      (G)old

    • @MrEdrftgyuji
      @MrEdrftgyuji 4 роки тому +5

      Three handled coffee mug with a three-holed donut

  • @RealClassixX
    @RealClassixX 7 років тому +510

    He either made those all himself, or we have a VERY confused glass worker somewhere.

    • @evildude109
      @evildude109 7 років тому +74

      +Dritto1010 sizes? Like 0, 0.0, 0.00, 0.000, etc.?

    • @Maltanx
      @Maltanx 7 років тому +74

      +Dritto1010 a Klein bottle as no volume (v = 0), that's the joke

    • @The0Skeleton123
      @The0Skeleton123 7 років тому +6

      *but* this only goes for true four-dimensional klein bottles, not the ones he actually has, right?

    • @DerBullgod
      @DerBullgod 7 років тому +5

      Doesn't a Klein bottle have infinite volume minus all other actual volumes?

    • @abyssaljam441
      @abyssaljam441 7 років тому

      but it it would have infinite volume then as 'all other actual volumes' are

  • @tristanridley1601
    @tristanridley1601 7 років тому +709

    I just imagined offering that first object to a pre-industrial King. If you weren't executed as a magician you'd probably be able to trade one of those for a whole life of luxury.

    • @numberphile
      @numberphile  7 років тому +132

      +Tristan Ridley love that thought

    • @finnberuldsen4798
      @finnberuldsen4798 7 років тому +2

      you have to imagine that if enough people attempt hit like some will accidentally dislike it.

    • @finnberuldsen4798
      @finnberuldsen4798 7 років тому +2

      you have to imagine that if enough people attempt hit like some will accidentally dislike it.

    • @Ezullof
      @Ezullof 7 років тому +23

      Why would you be executed as a magician ? A pre-industrial King would just be amazed by the fact it is transparent glass, and also probably a lot harder to break than ordinary glass.
      Otherwise, it's really not so weird. It's not because it has funny topologic properties that it would look like magic... (and it really doesn't).

    • @SebBrosig
      @SebBrosig 7 років тому +13

      You mean an item like this one?
      en.wikipedia.org/wiki/Cage_cup
      sure it was a luxury item fit for a king, but its maker was probably a slave and in no way entitled to a "life of luxury".
      Topologically it's also much more complex.

  • @marbleswan6664
    @marbleswan6664 6 років тому +1617

    Started with an advanced topology problem. Spent hours making multiple complicated glass spheres. Made them into a mug. Worth it.

    • @meekrab9027
      @meekrab9027 5 років тому +55

      Any advanced maths problem will invariably end with the mathematician at the pub.

    • @bonniejeandominguez656
      @bonniejeandominguez656 5 років тому +36

      @@meekrab9027 Oddly enough, he does not drink. The story goes that his dad told him that he would let him know when he is ready to drink alcohol. His dad died, never telling this mathematician when he was ready to drink, and so he never did. He tells it better.

    • @TheGauges420
      @TheGauges420 4 роки тому +4

      @@bonniejeandominguez656 is that really true? If so, I applaud him for sticking to his morals. That's a hard thing to find nowadays.

    • @bonniejeandominguez656
      @bonniejeandominguez656 4 роки тому +6

      @@TheGauges420 It is. It's in a Ted Talk he gave, if memory serves me right.

  • @Bread-yx2eg
    @Bread-yx2eg 6 років тому +1859

    5:21
    This guy is great. He's always smiling and you can tell he really enjoys what he's doing

    • @AHappyCub
      @AHappyCub 6 років тому +39

      Bread doing something you love so much will do that to you

    • @maxnullifidian
      @maxnullifidian 5 років тому +45

      I think he's used the same method to make a 3 holed bong...;-)

    • @arcalter6075
      @arcalter6075 5 років тому +13

      So adorable

    • @danielclaresmyth
      @danielclaresmyth 5 років тому +3

      Awesome

    • @TheRealFlenuan
      @TheRealFlenuan 5 років тому +8

      And he put so much work into this

  • @AgentMidnight
    @AgentMidnight 7 років тому +4026

    "Morty! Morty I *urp* I made a hole in a hole in a hole Morty, its *urrrp* hole-inception up in here Morty!"
    "Aww jeez Rick, w-why did you make so many holes, Rick?"
    "You ever try to drink from a mug with 3 handles? Its *urrrp* Its amazing Morty. Its topological magic Morty!"

    • @Snakeyes244
      @Snakeyes244 7 років тому +105

      HAHAHA! He does look like Rick!

    • @NickiRusin
      @NickiRusin 7 років тому +87

      You just made my day, sir.

    • @misteratoz
      @misteratoz 7 років тому +33

      I love you.

    • @Linkedblade
      @Linkedblade 7 років тому +9

      rick and morty is trash

    • @NickiRusin
      @NickiRusin 7 років тому +8

      Pablo Griswold Its' the oURRPnly way to hide it from space cops, Morty!

  • @GamesFromSpace
    @GamesFromSpace 7 років тому +1310

    So what I got from this is that a regular donut is topologically equivalent to a regular coffee mug (assuming the handle was hollow). That must be why they go so well together.

    • @OMGLYKEWOW
      @OMGLYKEWOW 7 років тому +82

      Policemen are geniuses!

    • @pedrocavalcanti46
      @pedrocavalcanti46 7 років тому +8

      Underrated comment! LikeLikeLike

    • @MerrillMath
      @MerrillMath 7 років тому +83

      One of the top 10 reasons for not doing your Math homework is that you took a break for a cup of coffee and a doughnut and spent the rest of the evening trying to figure out which one to dunk.

    • @Drecon84
      @Drecon84 7 років тому +55

      It gets better. Humans are topological donuts as well.

    • @colt4667
      @colt4667 7 років тому +26

      +Drecon84 President Kennedy said "Ich bin ein Berliner." A Berliner is a donut. JFK knew some topology.

  • @thegeneralissimo470
    @thegeneralissimo470 4 роки тому +177

    "at 1200 degrees Fahrenheit, it is flexible glass"
    I love you Cliff, you're so silly.

  • @stuberosum1
    @stuberosum1 5 років тому +595

    THIS MAN JUST TURNED A HOLE-CEPTION INTO A 3 HANDLED COFFEE MUG.
    THE GUY IS ABSOLUTELY AMAZING

    • @a_common_weeb
      @a_common_weeb 4 роки тому +13

      in addition the mug is also insulated because it has 2 walls

    • @username_not_found6926
      @username_not_found6926 3 роки тому +2

      You should thank topology for being able to do that.

    • @asheep7797
      @asheep7797 2 роки тому

      @@username_not_found6926 thank

    • @mk_rexx
      @mk_rexx Рік тому

      I'm surprised he didn't turn it into a beanie

  • @alexeysaranchev6118
    @alexeysaranchev6118 7 років тому +2344

    I refuse to believe someone actually disliked this video.

    • @numberphile
      @numberphile  7 років тому +141

      +Alexey Saranchev it happens

    • @dlee645
      @dlee645 7 років тому +4

      Ikr

    • @nicholaslau3194
      @nicholaslau3194 7 років тому +11

      You are seeing things. Maybe an eyecheck and glasses will make the dislike bar that magically appeared go away?

    • @TheGreatSteve
      @TheGreatSteve 7 років тому +4

      Probably theists.

    • @Abdega
      @Abdega 7 років тому +4

      +joseph crosby mecham So what you are saying is this is like a Turing test, but based on topology… a "Torus test"?

  • @thepoopenator7341
    @thepoopenator7341 7 років тому +383

    5:20 is why Cliff Stoll is the best person on Numberphile

    • @TheSweBoo
      @TheSweBoo 7 років тому +28

      It makes one so happy ^^

    • @guyhommeki
      @guyhommeki 7 років тому

      Exactly what I thought haha

    • @unvergebeneid
      @unvergebeneid 7 років тому +3

      +PlexyPanda Get a life!

    • @Madsy9
      @Madsy9 7 років тому +9

      I agree. His enthusiasm and charm is infectious :)

    • @Madsy9
      @Madsy9 7 років тому +1

      +Penny Lane You deserve 1-up vote

  • @Mel-bq4jd
    @Mel-bq4jd 4 роки тому +27

    I know many have already mentioned how wholesome his enthusiasm is, but at 5:21 when cliff goes "hee hee hee" excitedly is the most wonderful thing ever

  • @steelstriderq7801
    @steelstriderq7801 6 років тому +131

    The enthusiasm is infectious, never have I ever been so interested in so many holes in all my life.

    • @braxtonbarfriquaorme8703
      @braxtonbarfriquaorme8703 3 роки тому +14

      Yeah, one time I saw my step sis get stuck in the washing machine, let's just say I was busy explorin' some holes too.

    • @youngflamer1667
      @youngflamer1667 3 роки тому

      So.... you stopped being an asexual?

    • @henrikljungstrand2036
      @henrikljungstrand2036 2 роки тому +6

      @@youngflamer1667 I saw that comment coming. 😂
      Suppose the absolute majority of us are interested in holes of some kind, especially since both sexes have them. 😏🤭
      Unfortunately (?) they are not real topological holes, but merely "caverns".

  • @jaredhoeft2832
    @jaredhoeft2832 7 років тому +358

    This man is precious.
    He makes topology, a notoriously daunting subject, sound whimsical.

  • @inwemeneldur2025
    @inwemeneldur2025 7 років тому +345

    "Is it okay if I'm pointing with my nose?"

  • @TheOfficialCzex
    @TheOfficialCzex 5 років тому +313

    Find someone who looks at you the way this guy looks at a three-holed taurus.

    • @angelmendez-rivera351
      @angelmendez-rivera351 5 років тому +27

      TheOfficialCzex torus, you mean. Taurus is a whole scarier thing.

    • @Adahn99
      @Adahn99 4 роки тому +12

      @@angelmendez-rivera351 I would be more scared by a three holed torus charging at me at 35 mph

    • @yazajag
      @yazajag 4 роки тому +1

      🐂😣😃

    • @elysia4982
      @elysia4982 4 роки тому +2

      @@angelmendez-rivera351 I'm a Taurus and I can confirm this statement 😏

    • @tanveer_badar_
      @tanveer_badar_ 6 днів тому

      *torus. Not the bull.

  • @TheMartian11
    @TheMartian11 4 роки тому +252

    The moment I saw his hairstyle, I knew he meant buiseness.

  • @canyousmoketho
    @canyousmoketho 7 років тому +936

    He's so proud of himself, he seems so happy.😊

    • @HosamSherif
      @HosamSherif 7 років тому +79

      Yeah, it's great to see someone so passionate about a subject.

    • @jacobmock6682
      @jacobmock6682 6 років тому +1

      I Lost My Halo yeah and he just wasted 13 pounds of glass on this video

    • @Assultmaster1
      @Assultmaster1 6 років тому +7

      Jacob Mock wasted?

    • @Assultmaster1
      @Assultmaster1 6 років тому +1

      Jacob Mock i mean, have you Seen techrax?

    • @mikesekulovski7966
      @mikesekulovski7966 6 років тому

      Word has it he's been playing with glass for the last six months, this is his first contact with the outside world in over a year.

  • @TheDiscoMole
    @TheDiscoMole 7 років тому +433

    That smile and excitement signify a magician level mathematician.

    • @zerogenic
      @zerogenic 7 років тому +1

      TheDiscoMole Everytime we go into Math class, I'm hyped.

    • @ThousandStars1000
      @ThousandStars1000 6 років тому +14

      You mean a mathamagician

  • @3buffalo13
    @3buffalo13 6 років тому +397

    That's stretching things a bit, wouldn't you say?

    • @MrCubFan415
      @MrCubFan415 6 років тому +11

      3buffalo13 badum tss

    • @fidelio6311
      @fidelio6311 4 роки тому +2

      the day he stretches things a bit is the day we move into the second dimension
      I'm obligated to say I am aware of the pun. I liked it 🙂

    • @lkkoller
      @lkkoller 4 роки тому +1

      I see what you did there... lol

  • @DeannaEarley
    @DeannaEarley 4 роки тому +31

    And this is *EXACTLY* why I’ve loved topology and mathematics since I was a child!

  • @avihenriksen3947
    @avihenriksen3947 6 років тому +1351

    I love how excited the people on this channel get about math

    • @Aleksandar0100
      @Aleksandar0100 5 років тому +22

      *meth

    • @Ivan_1791
      @Ivan_1791 5 років тому +2

      Lovely.

    • @IETCHX69
      @IETCHX69 5 років тому

      Giggity

    • @stipser1
      @stipser1 5 років тому

      especially that one guy that looks like oscar isaac

    • @KordintheHusky
      @KordintheHusky 4 роки тому +5

      Math is awesome when it's not shoved down your throat and taught in the most boring way possible

  • @JamesRevan
    @JamesRevan 7 років тому +600

    I love this man, his enthusiasm is just fantastic. If I had a teacher like that back in school maybe I wouldn't hate math so much.

    • @JamesRevan
      @JamesRevan 7 років тому +5

      Yes, indeed. Made a mistake.

    • @TheRedstoneTaco
      @TheRedstoneTaco 7 років тому +3

      Our world geography teacher is like this and it's awesome. I definitely think it's helping our grades

    • @JamesRevan
      @JamesRevan 7 років тому +6

      ***** Well I meant that kind of enthusiasm that makes you happy to learn something. Not many teachers like that.

    • @cellina.starfire
      @cellina.starfire 7 років тому +3

      Everybody loves Klein Bottle Guy :D

    • @MrRobinhalligan
      @MrRobinhalligan 7 років тому +1

      We had a Chemistry teacher in secondary school like him and a math teacher as well made you want to learn.

  • @gaarathesandslayer
    @gaarathesandslayer 5 років тому +36

    At least once in my life, I want someone to look at me the same way this guy looks at math.

    • @henrikljungstrand2036
      @henrikljungstrand2036 2 роки тому

      Then cultivate your mathematical interests, do some hobby research, and date an enthusiastic mathematician! 😄
      We do have a childlike enthusiasm for beauty and life, and lots of us have charm, humor and some seductive skills. 😊

  • @rannov.4707
    @rannov.4707 6 років тому +117

    You could say this takes topology to a HOLE new level!
    No?
    Okay, I'll leave...

    • @Sztefa001
      @Sztefa001 4 роки тому +2

      WHY DOESN'T THIS COMMENT HAVE MORE LIKES

    • @ChaoticTeen16
      @ChaoticTeen16 3 роки тому +2

      @jokar jokar I think you mean a "hole-some" pun

    • @pranavlimaye
      @pranavlimaye 3 роки тому

      While I read this pun, the only hole I'm interested in making is a BULLET HOLE through my skull

    • @gallium-gonzollium
      @gallium-gonzollium 2 роки тому +1

      Hole-y me!

  • @Inertia888
    @Inertia888 6 років тому +3582

    this person's dreams must be fantastic!

  • @aidanfuge2108
    @aidanfuge2108 7 років тому +574

    I love how this guy takes interesting topological concepts and turns them into useful everyday items like hats and mugs

    • @sender1496
      @sender1496 7 років тому +11

      Where on earth would we be without three-handled coffee mugs?

    • @VAFFANFEDE18
      @VAFFANFEDE18 7 років тому +17

      You can more easily win some beer-drinking competition, you would have more grip on the glass

    • @chronosorion6911
      @chronosorion6911 7 років тому +1

      Not if the handles are hollow!

    • @razpootis5802
      @razpootis5802 7 років тому +2

      OMG a recent post on an old video.

    • @IronSmeltery
      @IronSmeltery 7 років тому

      Grimlock - and this makes u happy?

  • @GweiTheLeafChild
    @GweiTheLeafChild 5 років тому +46

    Glass Blower: I'm sorry Mr Klein, you want *WHAT* in *WHERE* in *WHAT* , _this time?_ Maybe you should take over.

    • @Xthis1s4youX
      @Xthis1s4youX 4 роки тому +4

      on his first klein bottle video he said he had a friend that had made a klein bottle out of glass with him, the thousands of klein bottles were ordered to a company, but these... these are just too specific, I'm pretty sure he's his own glass blower now, and a master at that

    • @hamiltonianpathondodecahed5236
      @hamiltonianpathondodecahed5236 4 роки тому +3

      btw fyi he is Cliff Stoll not Felix Klein but It doesn't matter anyways

    • @omikronweapon
      @omikronweapon 4 роки тому

      @@Xthis1s4youX I always assumed he enjoyed doing glass-blowing and never stopped. Just decided that he couldn't make a 1000 Klein bottles by himself, so outsourced.
      There's no wáy that anyone else would make all these for him :P

  • @JK-wt7rc
    @JK-wt7rc 6 років тому +36

    This is mathematical art! You should display these as a sculptural art piece, and when people ask what it means, you can blow their minds by pointing at the last one in the sequence and saying, "This one with the handles is exactly/technically the same as," -points to the first one in the sequence- "this one"! Then you can go into this explanation to both blow their minds even more as well as educating them!

  • @unfig3034
    @unfig3034 7 років тому +521

    This guy gets so excited, I can't help but smile :)

    • @t1glistenerelf
      @t1glistenerelf 7 років тому

      ( ͡° ͜ʖ ͡°)

    • @JeyPeyy
      @JeyPeyy 6 років тому +1

      I'd be happy too if my job was tearing up holes

    • @mothcatcher893
      @mothcatcher893 6 років тому +2

      Remember the rules... you can't tear only stretch

    • @cs4all670
      @cs4all670 6 років тому

      H

  • @craigroberts7013
    @craigroberts7013 7 років тому +560

    how does this not end as Klein bottle???

    • @numberphile
      @numberphile  7 років тому +72

      watch the extra footage!!!

    • @Bl00drav3nz
      @Bl00drav3nz 7 років тому +56

      Wild guess: A torus with 3 holes has an inside and an outside, while the Klein bottle doesn't - so it's impossible for the two to be homeomorphic.

    • @craigroberts7013
      @craigroberts7013 7 років тому +4

      @Bl00drav3n after watching the video im sure youre right but it wasn't obvious to me as i was watching the video. i thought for sure i knew where it was headed.

    • @Theraot
      @Theraot 7 років тому +1

      make more of these!

    • @lxathu
      @lxathu 7 років тому +35

      There are times in life when you have to put away the bottle and start a hole new life.

  • @BritishBeachcomber
    @BritishBeachcomber 3 роки тому +4

    Your glass creations belong in a museum. Far better than any computer graphic morphology. Absolutely mind-blowing.

  • @DreckbobBratpfanne
    @DreckbobBratpfanne 6 років тому +266

    HOW MANY OF THESE THINGS DOES HE HAVE??? 😆👍

    • @radulescubg
      @radulescubg 5 років тому +36

      He has a basement full of about 1000 Klein bottels

    • @brandonwithnell612
      @brandonwithnell612 5 років тому +19

      just 1, hes just pulling on holes like magic

    • @eurickevardone2976
      @eurickevardone2976 5 років тому +3

      Yes.

    • @nickramirez5310
      @nickramirez5310 4 роки тому +1

      I thought he put the Klein bottles under his house

    • @clickrick
      @clickrick 4 роки тому +4

      @@nickramirez5310 But is the house outside the Klein bottles or inside them?

  • @tommythai1043
    @tommythai1043 7 років тому +627

    A 3 handled mug?! Let Tadashi tap it with his spoon

  • @dan339dan
    @dan339dan 7 років тому +424

    The typical "mad scientist" laugh :D

    • @VidkunQL
      @VidkunQL 7 років тому +47

      If he smoked he'd get the mad scientist laugh. Now he has the merry old elf laugh.

    • @Roth-kana
      @Roth-kana 7 років тому +42

      5:22

    • @zlsoypalomocojo1659
      @zlsoypalomocojo1659 7 років тому +3

      VidkunQL jjajajajjajaja

    • @MichaelRWolf
      @MichaelRWolf 7 років тому

      Dan thanks for sharing such a passion.

  • @chrischiesa3253
    @chrischiesa3253 6 років тому +36

    It must be great fun to be able to just "go into the glass shop" and *make* these things. :-)

    • @robertnett9793
      @robertnett9793 5 років тому

      This made me whish to become a glassworker myself. Just for the minute chance, that someone like him pops in my shop, demanding me making such amazing things :D

  • @slinky6481
    @slinky6481 5 років тому +10

    Just when I wouldn't think it possible, he'd pull out yet ANOTHER glass construct. That was the most mind-blowing part of this video, if you ask me.

  • @diegofonseca5096
    @diegofonseca5096 7 років тому +722

    I was waiting to see thousands of these spheres under his house :(

    • @The_Blog
      @The_Blog 7 років тому +28

      Well he has a couple (hundred) of Klein Bottles lying there already :P

    • @diegofonseca5096
      @diegofonseca5096 7 років тому +27

      +BloggingLP That's why I said that xP

    • @OwenPrescott
      @OwenPrescott 7 років тому +5

      He can't enter or leave his house.

    • @The_Blog
      @The_Blog 7 років тому +1

      Diru
      I suspected so. Sry if it came off that way, wasn't intended.

    • @diegofonseca5096
      @diegofonseca5096 7 років тому

      +BloggingLP I don't speak too much english, so was my fault, I didn't understand very well

  • @BigMobe
    @BigMobe 7 років тому +1308

    This is distracting me from my video-games.

    • @TheGanamaster
      @TheGanamaster 7 років тому +1

      Games? What video games? xD

    • @BigMobe
      @BigMobe 7 років тому +16

      TheGanamaster
      I was trying to play GTA V but I kept turning my head to watch this video

    • @Chelsea2009FC
      @Chelsea2009FC 7 років тому

      BigMobe lol

    • @SamuelHabekotte
      @SamuelHabekotte 7 років тому +1

      same

    • @prajnaprajna1923
      @prajnaprajna1923 7 років тому

      This is my best proof about Flt
      Define
      Sx=1+2^2+3^2+4^2+....+x^2.=x(x+1)(2x+1)/6=(2x^3+3x^2+x)/6
      Sy=1+2^2+3^2+4^2+....+y^2=y(y+1)(2y+1)/6=(2y^3+3y^2+y)/6
      Sz=1+2^2+3^2+4^2+....+z^2=z(z+1)(2z+1)/6=(2z^3+3z^2+z)/6
      So
      2x^3=6Sx-3x^2-x
      2y^3=6Sy-3y^2-y
      2z^3=6Sz-3z^2-z
      so
      x^3=3Sx-3/2x^2-x/2
      y^3=3Sy-3/2y^2 - y/2
      z^3=3Sz -3/2z^2-z/2
      supose
      x^3+y^3=z^3
      3Sx-3/2x^2-x/2+3Sy-3/2y^2 - y/2 - (3Sz -3/2z^2-z/2)=0
      or
      2Sx-x^2-x/3+2Sy-y^2 - y/3 - (2Sz -z^2-z/3)=0
      or
      2Sx+2Sy-2Sz-(x^2+y^2-z^2) =(x/3+y/3-z/3)
      So
      Sx+S(x-1)+Sy+S(y-1)-Sz-S(z-1)=(x+y-z)/3
      So
      (x+y-z)^2=[3Sx+3Sy+Sy+3S(y-1)-3Sz-3S(z-1)]^2
      because
      (x+y)^2=x^2+y^2+2xy
      (x+y-z)^2=(x+y)^2+z^2-2z(x+y)=x^2+y^2+2xy+z^2-2z(x+y=x^2+y^2-z^2+2xy-2z(x+y )+3z^2
      So
      (x^2+y^2 - z^2)=(x+y-z)^2+2xy-2z(x+y )+3z^2=[3Sx+3Sy+Sy+3S(y-1)-3Sz-3S(z-1)]^2+(2xy-2zx-2zy )+3z^2
      And
      (x^2+y^2-z^2)=(2Sx+2Sy-2Sz)-(x+y-z)/3
      So
      [3Sx+3Sy+Sy+3S(y-1)-3Sz-3S(z-1)]^2+(2xy-2zx-2zy )+3z^2=(2Sx+2Sy-2Sz)-(x+y-z)/3
      So
      (2xy-2zx-2zy )=(2Sx+2Sy-2Sz) - [3Sx+3Sy+Sy+3S(y-1)-3Sz-3S(z-1)]^2-(x+y-z)/3
      Named
      (2Sx+2Sy-2Sz) - [3Sx+3Sy+Sy+3S(y-1)-3Sz-3S(z-1)]^2 is a
      Note a is an integer.
      So
      (2xy-2zx-2zy )=a-(x+y-z)/3
      So
      6xy=[3a-(x+y-z)+6zx+6zy.]
      So
      x=[3a-(x+y-z)+6zx+6zy.]/6y
      Because x is integer so
      [3a-(x+y-z)+6zx+6zy.]=K6y
      This is the first condition that to be added
      And
      6zx=6xy+-2zy - 3a-+x+y-z
      So
      x=[6xy+-2zy - 3a-+x+y-z]/6z
      This is second condition that to be added
      And
      6zy=6xy-6zx-3a+x+y-z
      So
      y=[6xy-6zx-3a+x+y-z]/6z
      Thie is third condition that to be added
      And
      z=[6xy-6zx-3a+x+y-z]/6y
      This is fourth condition to be added
      Total have 4 conditions that to be added
      6zx=6xy+-2zy - 3a-+x+y-z
      x=[6xy+-2zy - 3a-+x+y-z]/6z
      y=[6xy-6zx-3a+x+y-z]/6z
      z=[6xy-6zx-3a+x+y-z]/6y
      [3a-(x+y-z)+6zx+6zy.]=K6y
      [6xy+-2zy - 3a-+x+y-z]=h6z
      [6xy-6zx-3a+x+y-z]=g6z
      [6xy-6zx-3a+x+y-z]=f6y
      Attention! they are different
      With 4 conditions added It will definitely hinder the problem solving.

  • @Speireata4
    @Speireata4 4 роки тому +4

    I love how he giggles and enjoys what he has done. It gives so much life to a dry subject.

  • @argonman1
    @argonman1 5 років тому +14

    Beyond the number/math interest, this guy is a fantastic glass blower! Superb! Well done Sir!

  • @ilghiz
    @ilghiz 7 років тому +349

    That’s how Professor Emmett Brown invented his time machine :)

    • @ezequielblanco8659
      @ezequielblanco8659 7 років тому +10

      Came to the comments looking for a Doc Brown reference. I think the character was based on this guy.

    • @HideoMatsuoka
      @HideoMatsuoka 7 років тому

      ikr

  • @metleon
    @metleon 7 років тому +336

    Now put coffee into your 3 handled mug and dunk a 3 holed doughnut into it.

    • @strafeae4618
      @strafeae4618 7 років тому +8

      Second best comment so far, only to the Rick and Morty comment lol

    • @143TYAGI
      @143TYAGI 7 років тому +2

      hahaha creativity peaked. getting flashes of the situation.

    • @HanibiSW
      @HanibiSW 7 років тому

      why not dunk a 3 handled doughnut? it can be done

    • @metleon
      @metleon 7 років тому

      RNG How are you going to make a 3 holed taurus mug work? It won't be able to hold anything.

    • @samajammy
      @samajammy 7 років тому

      The 3 holed taurus mug was in the video @ 8:10. Take the sphere with 3 handles, push the top down into the bottom and it actually makes a vacuum mug - in that it has an empty space between the inside and outside walls of the mug... 3 holed doughnuts, also totally do-able.

  • @Kapin05
    @Kapin05 6 років тому +46

    This man is amazing! I love the enthusiasm, this video just made me think 'woah, that's totally a thing! COOL!'

  • @e4htysybvgtjyevbdehybrjeb469
    @e4htysybvgtjyevbdehybrjeb469 6 років тому +141

    How much did all that glass cost?
    Edit: Also where will he put all of them?

    • @jameshughes3014
      @jameshughes3014 5 років тому +21

      Fill them with glitter, never buy another Christmas tree decoration

    • @aedile2819
      @aedile2819 5 років тому +50

      Under his house

    • @Alex-wi1mx
      @Alex-wi1mx 5 років тому +19

      e4htysybvgtjyevbdehybrj eb48 ihuter IDK, he makes them himself.
      Under his house with the 1000 Kline bottles

    • @EricH928
      @EricH928 5 років тому +24

      He puts them in a hole. Duh.

    • @IndigoGollum
      @IndigoGollum 5 років тому +6

      Under his house with the hundreds of Klein bottles he has.

  • @fawnjenkins5157
    @fawnjenkins5157 7 років тому +122

    Gee, Doc, that's wild. Can't we get back to saving our future though? --McFly

    • @bibasik7
      @bibasik7 7 років тому +8

      This made my day.

  • @bstoppel1
    @bstoppel1 7 років тому +120

    someday an archeologist is going to find these and be fully confused.

    • @valeriobertoncello1809
      @valeriobertoncello1809 7 років тому

      ahahha indeed

    • @iota-09
      @iota-09 7 років тому +5

      i'm not sure if they would resist the test of time...

    • @soufang
      @soufang 7 років тому +4

      Glass does not decay, so as long as they are in a safe place they will last forever

    • @Hedning1390
      @Hedning1390 7 років тому +6

      They would probably say it had ritualistic use, just like todays archaeologists say to cover up what they don't understand.

    • @MercurySG3M
      @MercurySG3M 7 років тому

      soufang what if it's more than 1 million years into the future? then it'd decay

  • @subven69
    @subven69 5 років тому +23

    Bless his heart.

  • @chilling_at_pontiff
    @chilling_at_pontiff 4 роки тому +8

    This man made 18 different glass globes to prove a solution theorized some 100 years ago

  • @oceanblue2358
    @oceanblue2358 7 років тому +242

    This man makes the sun shine.

  • @tally9542
    @tally9542 6 років тому +573

    I love this guy, he's like the crazy old professor I never had.

    • @CraftQueenJr
      @CraftQueenJr 6 років тому +14

      Chloe Dropbear I know, he is the perfect image of the crazy old genius who everyone thinks is insane!

    • @hirokatsuvictor8755
      @hirokatsuvictor8755 6 років тому +11

      Great Scott!

    • @yazajag
      @yazajag 4 роки тому +1

      Yes I agree, you now have 360° of likes ☺👍🏽

    • @madide3978
      @madide3978 4 роки тому +1

      Reminds me of Doc from back to the future (an old movie)

  • @TheZANCAT
    @TheZANCAT 5 років тому +32

    This guy seems like he's about to pop into a hole himself, taking Alice to wonderland

  • @Thomas-hv1xh
    @Thomas-hv1xh 6 років тому +63

    Be careful where you put the handles, otherwise you'll end up with a two-handled mug with a hole in the bottom.
    Or if you're crafty, you could instead fashion a one-handled mug with two drinking straws built-in, perfect for sharing a milkshake.

    • @XenophonSoulis
      @XenophonSoulis 5 років тому +3

      Milkshake from under the bottom of the mug...

    • @leddaudet2350
      @leddaudet2350 4 роки тому

      Gotcha

    • @TyneMint
      @TyneMint 4 роки тому

      ...so as long as it is a shape with 3 holes. The answer will be correct?

    • @henrikljungstrand2036
      @henrikljungstrand2036 2 роки тому +1

      @@TyneMint Yeah kind of. The important answer is that all these three holed shapes are topologically "the same", because they are homeomorphic. For 2dim surfaces (bended in 3dim or 4dim space, higher surrounding space makes no difference), the number of handles and the orientability are the only topological variants for compact (finite) real manifolds, except when we have linked holes (like an external hole going through the center of an internal hole), which means there are several surfaces disconnected from each other. Linking is only relevant for 2dim manifolds embedded in 3dim space, because the holes/surfaces can always be unlinked in 4dim space.
      Topology is trickier for bended 3dim bodies/"surfaces" though, and it gets worse in higher dimensions.
      And non-compact manifolds are also different, especially if they have an infinite number of handles going through each other.
      Also there are topological spaces that are not real manifolds, and some that are not even chain complexes composed of real manifolds of different number of dimensions.

    • @TyneMint
      @TyneMint 2 роки тому

      @@henrikljungstrand2036 Huh... That is a lot to process... Woah

  • @adamtaylor1739
    @adamtaylor1739 7 років тому +404

    Thumbs up if you want Klein bottle man for president!!

    • @mecca4521
      @mecca4521 7 років тому +4

      +++

    • @isaacbriefer193
      @isaacbriefer193 7 років тому +3

      YES!

    • @isaacbriefer193
      @isaacbriefer193 7 років тому +12

      For some odd reason though, Trump Klein bottles are unusually small.

    • @deralmighty8011
      @deralmighty8011 7 років тому +10

      It's not the size that matters. It's how you use it.

    • @MrCubFan415
      @MrCubFan415 6 років тому

      Isaac Briefer Shut up and take my upvote!

  • @CrashperM
    @CrashperM 7 років тому +341

    Damn you guys got doc brown to star in one of your videos that's impressive

    • @user-ux2dd9pp8x
      @user-ux2dd9pp8x 7 років тому +42

      More then one

    • @thecrazylovelyboy
      @thecrazylovelyboy 7 років тому +5

      *than

    • @CrashperM
      @CrashperM 7 років тому

      Andrew Korkush no firts he wants more and then he wants 1

    • @thecrazylovelyboy
      @thecrazylovelyboy 7 років тому

      I do not understand...

    • @LeCaNiVideos
      @LeCaNiVideos 7 років тому +16

      Watch all their "Klien bottle"-videos! This guy is so wonderful! He's so excited by maths.

  • @whyuugly
    @whyuugly 6 років тому +16

    first of all, this is beautiful. the simplicity in explanation and the passion this guy has.
    second, imagine how weird out the glassmaker must feel to make all these shapes lol

    • @CraftQueenJr
      @CraftQueenJr 5 років тому +7

      whyuugly he makes them himself.

  • @corncolonel9171
    @corncolonel9171 5 років тому +30

    This is the most beautiful man I've ever seen

    • @leddaudet2350
      @leddaudet2350 4 роки тому

      BoBoMosasaur then u haven’t saw me yet 😉sorry I’m too high a bit of comprehension

  • @ptt619
    @ptt619 7 років тому +173

    This guy must make the coolest bongs ever

  • @calpitruzzello3544
    @calpitruzzello3544 7 років тому +104

    At 5:22 I wish I could get that excited about math

  • @Jaojao_puzzlesolver
    @Jaojao_puzzlesolver 4 роки тому +6

    I love how added some sound effects by his mouth to illustrate like 2:28 😂

    • @asylumarcade
      @asylumarcade 4 роки тому

      王兆成 I love the way he says the phrase "were gonna straighten it out" right afterwards

  • @tparadox88
    @tparadox88 3 роки тому +2

    This video answered a question I had since I was a kid and I saw a traveling topology exhibit at a children's museum.
    Has Numberphile ever covered turning a sphere inside out? I thought I remembered seeing it on this channel, but I couldn't find it. Might not be as impressive as the legendary Outside In, but also wouldn't be as creepy.

  • @martiddy
    @martiddy 7 років тому +162

    I wish my math professor teach me that lessons with that enthusiasm and energy.

    • @zenny3859
      @zenny3859 6 років тому

      Vapor Wave - sama taught*

  • @atklobas
    @atklobas 7 років тому +292

    Topologist: someone who can't tell the difference between a donut and a coffee cup.

    • @KleinGrass
      @KleinGrass 7 років тому +13

      I remember my teacher making that joke on my first year as an undergrad student Hahahaha

    • @josevillegas2721
      @josevillegas2721 7 років тому +5

      The newest one now is : a topologist is a person who can't tell a three handled mug from a hole in a hole in hole.

    • @dojix96
      @dojix96 7 років тому +8

      If I'm honest, I can't either before 10am

    • @L4Vo5
      @L4Vo5 7 років тому +2

      If a 3-hole donut translates to a 3-handle cup, a normal donut translates to a normal cup!

    • @SlimThrull
      @SlimThrull 7 років тому +2

      Buy does a hyper-donut translate to a hyper-cup?
      (I asked in jest, but upon thinking about it, I really have no idea. Does anyone know?)

  • @duckmeister5385
    @duckmeister5385 4 роки тому +5

    "But why?"
    --The Glassblower

  • @hammond1994
    @hammond1994 5 років тому +2

    I would love to see a video of these things being constructed. The glass blower must be a Grand Master of his craft.

  • @firelow
    @firelow 7 років тому +410

    I wonder what that three handled mug sounds like when you hit with a spoon everywhere

    • @starofcctv94
      @starofcctv94 7 років тому +1

      a 6-fold symmetry I would guess? he should definitely try it

    • @iota-09
      @iota-09 7 років тому +1

      yeah, but the handles have holes in them, wouldn't that change things? at least musically speaking.

    • @starofcctv94
      @starofcctv94 7 років тому +3

      It would change the pitch but I don't think much else

    • @fossilfighters101
      @fossilfighters101 7 років тому

      +

    • @siddharth_desai
      @siddharth_desai 7 років тому

      +

  • @lirothen
    @lirothen 7 років тому +648

    You DIDNT get him to tap it with a spoon in 12 spots?! But... but.... 3 handles!!!

    • @NemosChannel
      @NemosChannel 7 років тому +4

      RIGHT?!

    • @NemosChannel
      @NemosChannel 7 років тому +7

      RIGHT?!

    • @fofolp1213
      @fofolp1213 7 років тому +5

      RIGHT?

    • @NemosChannel
      @NemosChannel 7 років тому +8

      LEFT?
      (doublepost happened because of a youtube error)

    • @fafetico
      @fafetico 7 років тому +7

      I really hope this is the second part of a trillogy

  • @nakamakai5553
    @nakamakai5553 5 років тому +2

    Having read (and been absorbed / amazed by) The Cuckoo's Egg in my youth, it's been just a blast to discover all the Cliff videos all these many decades later. I never knew what he'd gone on to do, and now I enjoy every minute of his passions on-screen. I was in zoology at the time, with a heavy emphasis on math and theoretical ecology, and I must conclude that his book contributed heavily to the fact that I've now spent 30+ years in IT, nearly all of it in security. What a great inspiration he is.

  • @Lynn-rv4ty
    @Lynn-rv4ty 5 років тому +2

    it is so adorable how excited he is about not only the math but also about his glass creations

  • @carlacamargo4158
    @carlacamargo4158 7 років тому +74

    2011 - Welcome to my new channel, Numberphile, a channel about numbers. The first video will be about the number 11.
    2016 - Let's talk about a hole in a hole in a hole.

  • @AgentMidnight
    @AgentMidnight 7 років тому +20

    The world is seriously lacking more of Cliff. What an energetic guy!

  • @CaptDF97
    @CaptDF97 4 роки тому +3

    I was taking my topology final today and the last proof required me to invoke _that_ one classical theorem, which I couldn’t remember for the love of my life.
    Then suddenly I thought of this video, and at that very moment, my mind went: “Ah yes, a classical theorem of topology states that *blblblbrblbrlrbrlrbrbbbbrrrr* .”
    This video saved my GPA!

  • @xexpaguette
    @xexpaguette 4 роки тому +2

    *Yay! It's Doc from Back to The Future again!*

  • @therealteal620
    @therealteal620 7 років тому +90

    Had no idea what "homeomorphic" meant until he said "This is homeomorphic to *this!*"
    Then the whole video clicked into place.

    • @WeAreGRID
      @WeAreGRID 7 років тому +5

      homeo meaning same, morphic meaning shape, literally its definition is something of the same shape, and in this case, possessing all the same features; three holes.

    • @TosiakiS
      @TosiakiS 7 років тому +3

      Homeomorphic simply means you have a function that is continuous both ways. Continuous functions are something you learn about first thing in calculus.

    • @VAFFANFEDE18
      @VAFFANFEDE18 7 років тому +1

      And the function needs also to be a bijection

    • @TosiakiS
      @TosiakiS 7 років тому

      Federico Mangano A function has no inverse in the first place without being a bijection

  • @mrvolans7862
    @mrvolans7862 7 років тому +98

    I wish i could be as enthusiatsic in school, as this guy is about topology.

    • @oz_jones
      @oz_jones 6 років тому

      About everything, actually.

  • @theoverseer393
    @theoverseer393 4 роки тому +2

    I love the enthusiasm in this.
    That 3 handled mug is awesome

  • @Linkophere
    @Linkophere 6 років тому +2

    When someone teaches with passion you can't help but wanna hear what they have to say. Great work

  • @MarioFanaticXV
    @MarioFanaticXV 7 років тому +329

    I cannot imagine how long it took to make all these examples.

    • @markgriz
      @markgriz 7 років тому +42

      Those are the videos I want to see

    • @Cragnathar
      @Cragnathar 7 років тому +97

      This man has thousands of klein bottles under his house

    • @coolbrotherf127
      @coolbrotherf127 7 років тому

      MarioFanaticXV that's what I'm wondering. It looks like it would take awhile.

    • @MarioFanaticXV
      @MarioFanaticXV 7 років тому +2

      111SPIDERPIG999111
      Yeah, but it's a lot easier to make lots of the same object than a few of many objects thanks to mass production. The whole reason he has so many is because he needed enough that it would be profitable to make them en masse.

    • @NoahWenzel
      @NoahWenzel 7 років тому +2

      so are you suggesting that I might buy one somewhere!?

  • @aircraftcarrier6789
    @aircraftcarrier6789 7 років тому +235

    In the end all mathematicians just want coffee and donuts
    xD
    Great video numberphile

    • @forloop7713
      @forloop7713 6 років тому

      Andy Chamberlain That'a actually a beer glass

    • @peteman1000
      @peteman1000 6 років тому +2

      I think you can only dip 3 holed donuts in it though.

  • @inujosha
    @inujosha 5 років тому +3

    I wish I could have had this man as a professor for anything in college.

  • @RaindropsBleeding
    @RaindropsBleeding 6 років тому +4

    I love your videos. Your fascination with glass work and pushing the boundaries of three dimensional topology is intoxicating.

  • @trevorhunt
    @trevorhunt 7 років тому +252

    Tadashi this guy's got your cup!

  • @PsychologyStud
    @PsychologyStud 7 років тому +211

    He looks like a mad scientist.

  • @srenhaandbk7904
    @srenhaandbk7904 Рік тому +1

    The absolute burning passion for maths that made this guy blow several dozen intricate glass tubes and spheres

  • @martinmonath9541
    @martinmonath9541 Рік тому +1

    My alltime favourite professor in numberphile. Like his explanations so much.

  • @ortipianinho
    @ortipianinho 7 років тому +153

    I want to be just like him when I grow up

    • @JackSwatman
      @JackSwatman 7 років тому +11

      you're going to grow up? brave, i'm not

    • @fofolp1213
      @fofolp1213 7 років тому

      dito

    • @SpeedyRK
      @SpeedyRK 7 років тому +5

      I highly recommend his book, The Cuckoo's Egg. It's fantastic and a really great insight into Cliff Stoll's life. Never know where life will take you. ;)

    • @henrikkoberstein
      @henrikkoberstein 7 років тому

      One of the best books I've ever read. You can't stop reading, you just have to know what happens next.

  • @doggonemess1
    @doggonemess1 7 років тому +13

    I'm always amazing that this guy isn't surrounded by broken glass and covered in cuts. Gotta love him. :)

  • @Otoma
    @Otoma 6 років тому +6

    Cliff is a legend.

  • @michaelpowers6632
    @michaelpowers6632 4 роки тому +1

    This is Sikowitz’s father from Victorious: free spirited and a little unpredictable and easy to love at work! Awesome video!!!

  • @XamRei
    @XamRei 7 років тому +90

    That, my friends, is a very expensive proof. oO

    • @zaephou2843
      @zaephou2843 7 років тому +26

      I mean, he works in a glass shop lol

    • @The_Blog
      @The_Blog 7 років тому +5

      It's not THAT expensive. He (or atleast one of his friends) works in a glas shop so they got enough glas around to basicly produce 2 handfull or glas balls.

  • @kimberlychin1996
    @kimberlychin1996 7 років тому +203

    This man is really cool! I love that he talks so excitedly about topography. And all that glass shapes!

    • @ferikeem
      @ferikeem 7 років тому +6

      *topology, topography is something else

    • @kimberlychin1996
      @kimberlychin1996 7 років тому +4

      omg I'm so embarrassed. ^^yeah

    • @kubkub7156
      @kubkub7156 7 років тому +2

      Pro tip: You can edit comments

  • @taith2
    @taith2 4 роки тому +1

    That is like super long and exciting ad for a math merch, perfect gift for mathematician

  • @jamspoon
    @jamspoon 5 місяців тому +1

    A wonderful demonstration of glass blowing and topology

  • @zackferguson1661
    @zackferguson1661 7 років тому +226

    jeez, how big is this guy's glass collection? xD

    • @bigmike8586
      @bigmike8586 7 років тому +106

      Why do you think he's so happy all the time?

    • @Heligoland360
      @Heligoland360 7 років тому +20

      He has a robot to sort his thousands of glass models.

    • @bootblacking
      @bootblacking 7 років тому +24

      I want a Klein bottle bong so I can get fourth-dimensionally high.

    • @Aletaire
      @Aletaire 7 років тому +39

      He has 1000 Klein Bottles on his basement. There's a video about it.

    • @davidhansson7041
      @davidhansson7041 7 років тому +12

      If I would think, his house is probably one of those kienbottle-houses they showed. Möbius buildings I think they're called

  • @adaharrisonn
    @adaharrisonn 7 років тому +21

    5:21 is unquestionably the best part

    • @UCyYuGkOkjrLqRgKh-_j1oNA
      @UCyYuGkOkjrLqRgKh-_j1oNA 5 років тому +1

      Read the comment yesterday and came back just to see if it's still there and to click on the time-stamp again.

  • @thegaminpianistccc3580
    @thegaminpianistccc3580 3 роки тому +1

    The fact that this guy has the patience to make all these models out of glass, HAND-BLOWN glass, deserves some respect in itself.

  • @hikaru-live
    @hikaru-live 6 років тому +2

    Should have ended up with a nice glass of drink in that mug. (And it being double layered means it can have fantastic thermal insulation, perfect for both chilled and heated drinks to be kept for longer.)