Intro to Topology - Turning a Mug Into a Doughnut

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  • Опубліковано 21 січ 2025

КОМЕНТАРІ • 224

  • @SorryBones
    @SorryBones 9 місяців тому +89

    People just can’t wrap their heads around this. I tried explaining this to someone and they told me to get out of their house because they didn’t know who I was. It’s pretty simple if they just watch the video

  • @zaidyounas1602
    @zaidyounas1602 2 роки тому +194

    Hi andrew, i recently bumped into your channel and i must say i wasn't disappointed. Keep em. coming

    • @drewscampfire
      @drewscampfire  2 роки тому +22

      Thanks, will do!

    • @c7hu1hu
      @c7hu1hu 2 роки тому +4

      @@drewscampfire Will you though?🥺 Just saw was quite a gap in your uploads. Which is understandable however considering the beauty of your work, it really is great sir.

    • @partybrawl1764
      @partybrawl1764 2 роки тому

      @@drewscampfire I am also like him

    • @ITX635
      @ITX635 Рік тому +2

      @@c7hu1hu he lied he quit youtube

    • @ShanBojack
      @ShanBojack Рік тому

      ​@@ITX635 how can u say that

  • @kjrey9878
    @kjrey9878 2 роки тому +81

    My dude Andrew, I first saw your 4d klein bottle video and instantly subscribed! You're really smart and good at what you do. Please keep creating and I can't wait to see what you come out with next!

  • @carsonmcnamer5321
    @carsonmcnamer5321 2 роки тому +74

    Keep it up man!! You’ll only get better with time. Sorry I’m a little late to this video, had to move into college. Can’t wait for the next video. You deserve way more views with this amount of effort.

    • @drewscampfire
      @drewscampfire  2 роки тому +15

      Appreciate it!

    • @IAMASTICKSTUPIDPERSON
      @IAMASTICKSTUPIDPERSON 2 роки тому +4

      @@drewscampfire yea try to post more

    • @hampusbrokmann8249
      @hampusbrokmann8249 Рік тому +1

      ​@@IAMASTICKSTUPIDPERSONwell it Cant be that long before there is a new video now 😂😁👏

    • @hampusbrokmann8249
      @hampusbrokmann8249 Рік тому +1

      ​@@drewscampfireyou need to ramp up you video output and you make a ton of money on the side of you normal life. You are way better to show and tell Then most ppl on UA-cam, easy to understand and clear pic of what you are talking about.
      Sorry for the dyslexia hope you understand 😂😂😂👏🇩🇰😇

  • @hishwaar
    @hishwaar 2 роки тому +36

    That handcuff puzzle was pretty cool. The 3D animation really helped with understanding. Great video!

  • @ShaunakDe
    @ShaunakDe 2 роки тому +84

    These animations are amazing!

    • @pupfer
      @pupfer 2 роки тому +4

      Mindblowing! Even if you figure out the answer, it is still so incredible to actually watch the deformation!

  • @flyzo1977
    @flyzo1977 2 роки тому +43

    5:42 wow that gave me chills very intersting continue with your videos they deserves so much more views I wish you success

  • @symbolspangaea
    @symbolspangaea 2 роки тому +8

    Perfect intro to topology. I've used this one to explain to my wife, why I'm so much time in the computer... Thank you! now she still doesn't understand me completely, but she as a sense of why I like math so much

  • @sankojuprithvi
    @sankojuprithvi 6 місяців тому +5

    These animations are Marvellous and Majestic on Mathematics branch Topology

  • @Alexander-xo5ho
    @Alexander-xo5ho 2 роки тому +9

    hands down the most interesting video about coffee mugs and donuts ive watched

  • @RevShifty
    @RevShifty Рік тому +3

    I hope you're still out there somewhere. Your videos are incredible, and I've already shared a this one and the 4D Klein bottle video a couple times.
    In any event, I hope you're well. And thank you for these videos, they're incredible.

  • @xplodingmojo2087
    @xplodingmojo2087 2 роки тому +4

    This is exactly like that one video where those two people turn a sphere inside out. You’ve earned my subscription.

  • @nrml76
    @nrml76 2 роки тому +6

    More videos on topology for non mathematicians please. You did a great job of presenting concepts in a very understandable way.

  • @afsa376
    @afsa376 2 роки тому +1

    I love how I got this into recommendations and I hate how I didn't know about this channel until today

  • @malicksoumare370
    @malicksoumare370 Рік тому +1

    It's exiting how I was glued to the screen even if I didn't learn anything new. Thank you. We are waiting for future videos.

  • @sumirunihon
    @sumirunihon Рік тому +2

    congratulations on your first sponsor deal, glad your channel is growing and keep it up!

  • @antoniuskonovalov
    @antoniuskonovalov 2 роки тому +5

    Thank you, downloaded the Brilliant app via your link, worth it.

  • @epalios
    @epalios 2 роки тому +5

    I love this channel! You discuss topics im most interested about! Keep posting pls!!

  • @BIackhole
    @BIackhole 10 місяців тому

    05:10 now way the erik satie's amazing piece, gnossiende no 1 is playing in a video that explains an amazing topic! Two wonderful things together!

  • @midohatem57
    @midohatem57 2 роки тому +2

    High quality work, really liked your klein bottle video, highly underrated, keep going 👍👍

  • @y1729
    @y1729 Рік тому

    Wow. Amazing.

  • @kamranshafiq2597
    @kamranshafiq2597 Рік тому

    Excellent way to explanation. Surely you deserved millions of view

  • @huvarda
    @huvarda Рік тому

    This video is great! Definitely deserves more views than just 50k

  • @RealZynexx
    @RealZynexx Рік тому

    So many good UA-cam channels like this popping up in my recommended section! Keep it up man, your videos are great!

  • @Swoger
    @Swoger 2 роки тому +2

    another really good video from you!

  • @nataliaserhiienko9333
    @nataliaserhiienko9333 Рік тому +2

    It's a pity that there aren't any new videos on this wonderful UA-cam channel😔

  • @jordanblack2250
    @jordanblack2250 Рік тому

    Dude your videos are incredible, psychedelic even.. The animation is over the top awesome and the music is perfect. You MUST, plz, make more of these 🙏🤘🙌

  • @Quanlemon
    @Quanlemon 2 роки тому

    Yoo only 4 videos and feels like you are a professional youtuber, you are a great inspiration❤️

  • @Life_42
    @Life_42 2 роки тому +3

    Beautiful video!

  • @clarenscourtois8927
    @clarenscourtois8927 Рік тому +1

    That was super great, I can understand 3d and some other things related to complex geometry better now. Thank you!

  • @peterpelle8982
    @peterpelle8982 2 роки тому

    watching ur animations bring me calm in this hard times of my metal health. THXS

  • @musuhabadi2534
    @musuhabadi2534 3 місяці тому

    We need more topology stuff from you bro !

  • @opamp7292
    @opamp7292 Рік тому +1

    These videos are awesome!!! I’m so glad to have found them and looking forward seeing more. Thank you so much 😊

  • @bumblebee9426
    @bumblebee9426 10 місяців тому

    This is one of the best videos i’ve ever watched on youtebe

  • @tedfritzart
    @tedfritzart 9 місяців тому

    Just discovered this channel. Really wish to see more!

  • @father47_
    @father47_ Рік тому

    please continue making videos like this, they are super interesting!

  • @goldfink2612
    @goldfink2612 2 роки тому

    omg you have posted again!! i love your channel!

  • @ivusofficial
    @ivusofficial Рік тому

    Most mindblowing video I've ever seen

  • @cherry1leii
    @cherry1leii Рік тому +1

    Damn, Topology is something very different and I kinda begin to love it

  • @olafzijnbuis
    @olafzijnbuis 2 роки тому +16

    Great video!
    What type of software did you use to create it?
    I could do a few of the basic shapes in Povray, but the transformations are stunning!

    • @RacoonAndres
      @RacoonAndres 2 роки тому +5

      probably blender

    • @wannabewyvern
      @wannabewyvern 2 роки тому

      Blender, you can see the blender font in some of their videos

    • @awkarbi4646
      @awkarbi4646 Рік тому +1

      blender probably

  • @jschmid26
    @jschmid26 Рік тому

    These animations are amazing, damn

  • @rasmusvanwerkhoven1962
    @rasmusvanwerkhoven1962 2 роки тому +7

    So in theory, we could have an object with a negative number of holes, giving it an Euler characteristic greater than 2!- I wonder what that would look like, if it’s even plausible to make. And what about fractions; how would objects appear with a fractional number of holes?
    Also btw, I loved your video and the neat knowledge it brought!

  • @yashsoni3835
    @yashsoni3835 Рік тому +1

    At 5:59 the first part slides over the second part and creates a hole, which changes the topology.

  • @nativeantarctican3325
    @nativeantarctican3325 2 роки тому +6

    What software do you use to make your amazing videos?

    • @drewscampfire
      @drewscampfire  2 роки тому +2

      I use Blender and Manim! (both are free and open-source)

  • @zone07
    @zone07 2 роки тому

    @6:09 not sure how the shape crossed the bar without breaking through.

  • @WaleedHassanAwan
    @WaleedHassanAwan Рік тому +1

    This video was so good ☺️
    I loved it so much

  • @antoniojpan
    @antoniojpan Рік тому

    Spectacular. Incredible amount of work to create this video. It is really a piece of art. Can you share the explicit formula for the deformation of the mug into the torus? I want to recreate it in mathematica, maple,...

  • @f7ib
    @f7ib 2 роки тому +1

    Nice Visualizations!!!

  • @gregxu5142
    @gregxu5142 2 роки тому +1

    What's the music at 5:10? It sounds so familiar

    • @NikoDood
      @NikoDood 3 місяці тому

      It is Gnossienne no.1 by Erik Satie

  • @aditi28oct
    @aditi28oct 2 роки тому

    We need more, keep up the good work

  • @mhffseriouslythisistaken
    @mhffseriouslythisistaken 2 роки тому

    What's the song in the background around 5:20-5:35? Piano opera.

  • @sparshgongale1943
    @sparshgongale1943 Рік тому

    5:44 that was some cinematic art

  • @endlesslovingmovement
    @endlesslovingmovement Рік тому

    This is so well done! Amazing!

  • @souvikmandal2637
    @souvikmandal2637 Рік тому

    Awesome ❤. Keep it up. Btw how you made these amazing animation?

  • @sagarpuri7838
    @sagarpuri7838 2 роки тому +1

    This is next level explanations. amazing videos , keep it up.
    please make videos on fluid mechanics and semiconductor.

  • @hkayakh
    @hkayakh Рік тому +2

    0:22 actually it has an infinite amount of infinitely flat holes all stacked on top of each other

  • @geokou7645
    @geokou7645 2 роки тому +4

    A sponsorship of a large website with only 4 videos?!?!? This man is insanely good

  • @Qlust
    @Qlust 2 роки тому

    HI, I just wanna say your vidoes are really great and easy to understand!

  • @Kakashi_Hatake36
    @Kakashi_Hatake36 2 роки тому

    Keep them coming man

  • @xfa_f
    @xfa_f Рік тому

    Love your vid man keep it up

  • @HAG47
    @HAG47 2 роки тому

    Amazing reall, keep up the good work

  • @igxniisan6996
    @igxniisan6996 Рік тому +1

    If u keep going down in this rabbit hole of topology you'll finally come across with those sphere inside out guys

  • @d-e-p8473
    @d-e-p8473 2 роки тому +1

    What an AMAZING channel holy phokin sheesh

  • @srijani332
    @srijani332 Рік тому

    Very very helpful... thanks...

  • @maydimutawa8874
    @maydimutawa8874 Рік тому

    That is absolutely awesome 👌🏻 👏

  • @carpedm9846
    @carpedm9846 9 днів тому

    3:00
    That assumes that infinitely subdividing makes a circle and not a really granular polyhedra, take for example a square with side length 1, and a circle inside with radius 1. If you fold the corners of the square such that they touch the circle it does not change the circumfrence of the square, and if you do so infinitely, you get a circle with r=1, and circumfrance of 4, meaning pi=4. Not, because infinitely subdividing a square does not make a circle.
    In a similar fashion, we cant say circles have a euler characteristic of 2 by that method.
    We can still arbitrarily decide that they do because it helps with our logic though as long as everything else is consistent.

  • @Leo-if5tn
    @Leo-if5tn 2 роки тому +2

    Awesome video

  • @RSLT
    @RSLT 2 роки тому

    Interesting. Great video!

  • @ReySilverskin
    @ReySilverskin 11 місяців тому +3

    That "handcuff" puzzle was neat, but could you maybe not keep changing the camera focus in the future? It makes it extremely hard to follow what's going on.

  • @pritamroy3766
    @pritamroy3766 Рік тому

    hi andrew, I have confussion with 1) homeomorphism 2) homomorphism 3) diffeomorphism, my questions regarding are can 1)two manifold be homomorphic as well as homeomorphic 2) two manifold be homomorphic as well as diffeomorphic 3)two manifold be diffeomorphic as well as homeomorphic .

  • @SM-qw9tp
    @SM-qw9tp Рік тому

    Interesting way to expand your mind.

  • @mehmet2247
    @mehmet2247 Рік тому

    Ok, when will you broadcast the next video?

  • @spencerdumlao1654
    @spencerdumlao1654 Рік тому +1

    5:37 sliding them

  • @bystander85
    @bystander85 Рік тому

    What is the definition of a "hole?" It's not clear to me how at 6:01 that is still considered only two holes.

  • @brokeneck
    @brokeneck 3 місяці тому

    Why do you do the camera blur effect at such a crucial time in the transformation????

  • @AchrafTheGeek
    @AchrafTheGeek 2 роки тому

    amazing video, just one complaint, during the puzzle solution, the camera focus effect , the lowed music and the camera movement were very disctracting

  • @mathscapsule979
    @mathscapsule979 Рік тому

    You are a great teacher

  • @myworld4818
    @myworld4818 Рік тому +2

    i had 3 seperate thoughts while watching this video that i didnt want to think too long on and forgot them and they were super super interesting and i probably could've gotten accepted into harvard if i didn't forget 😭😭😭😭😭😭😭😭😭

  • @ITHrealXD
    @ITHrealXD Рік тому

    1:15
    Question: at what point does the donut turn into a pumpkin?

  • @vasil_mullin
    @vasil_mullin Рік тому

    Great video! Thanks! :)

  • @EugeneHKrabs1000
    @EugeneHKrabs1000 2 роки тому +1

    Is it possible to learn this power

  • @aithrasherboi
    @aithrasherboi 9 місяців тому

    I have an easy solution to the straw question at the start of the video, and that's defining what a hole is.
    Imagine a donut, and visually we can see the hole, but we can't just say "if it looks like a hole, it's a hole" because that causes the straw predicament. Imagine a point inside the center of the donut. Now, there is a 2d plane where the point is inside a circle, and it can't escape without using the third dimension. Now, imagine the plane moves perpendicular, so that it moves along the third dimension. We keep track of where it's moved by having the line leave a trail. Once the dot isn't contained inside the circle, we move on the other direction until we reach that same state. Now, the length of that line is how big the hole is, but what we care about is the fact it's all one line, thus meaning there's one hole. Now, if we did this to a straw, we'd reach the same conclusion. We need to stop caring about how far apart two openings are, and figure out if they're connected, because openings and holes aren't fully connected. Thus, a straw has one hole, never two.

  • @bartekszachu7110
    @bartekszachu7110 2 роки тому +2

    Fucking. Masterpiece. Seriously great work m8, keep up the good work, had a great fun watching it!

  • @kingj282
    @kingj282 2 місяці тому

    Great animation! Although I'm still struggling to distinguish topology from metric

  • @ManDancingMoji
    @ManDancingMoji Рік тому

    Okay that solution was so cool.

  • @B121AN1
    @B121AN1 Рік тому

    So how do I turn a sphere outside in without creasing it?

  • @Glen_Mali
    @Glen_Mali 2 роки тому +6

    This is seriously tripping me out. How did it go from 1 hole to 2 holes

  • @thalrosen
    @thalrosen 2 роки тому +1

    you're the greatest

  • @vishva8kumara
    @vishva8kumara 2 роки тому

    3:00 It would be easier if we draw longitudinal lines for the sphere to count edges and surfaces.

  • @jameerlawrencebondoc8162
    @jameerlawrencebondoc8162 Рік тому

    5:15 the color of the "handcuff" seems intimidating

  • @dark_gamer197
    @dark_gamer197 2 роки тому +1

    Pls post more video about topology
    I like ut videos

  • @clarenscourtois8927
    @clarenscourtois8927 Рік тому

    Made my day 🤓!

  • @johnchessant3012
    @johnchessant3012 2 роки тому +1

    very nice

  • @TrigonRL
    @TrigonRL Рік тому

    Do you need four dimensions for -3?

  • @Suds_340
    @Suds_340 2 роки тому

    shoutout kabayan! just saw your video in my recommended section

  • @dp055
    @dp055 7 місяців тому +1

    Bro why did you stop making video 😢

  • @cherylchui4510
    @cherylchui4510 8 місяців тому

    Please do more

  • @adrenaline647
    @adrenaline647 2 роки тому +1

    i do love the hairy balls theorem
    Great video man, the way you explain things makes it much easier to understand 👍

  • @BoyKhongklai
    @BoyKhongklai 9 місяців тому

    My brain hurts. Man I wish you uploaded more 👌👌

  • @ayushjha3716
    @ayushjha3716 2 роки тому

    We want more videos!!!