Intro to Topology - Turning a Mug Into a Doughnut

[@SorryBones]

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

[@universlion]

100% relatable

[@Fkthisshitimout-f4i]

😂

[@ShaunakDe]

These animations are amazing!

[@pupfer]

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

[@kjrey9878]

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!

[@zaidyounas1602]

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

[@drewscampfire]

Thanks, will do!

[@c7hu1hu]

@@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]

@@drewscampfire I am also like him

[@ITX635]

@@c7hu1hu he lied he quit youtube

[@ShanBojack]

​@@ITX635 how can u say that

[@sankojuprithvi]

These animations are Marvellous and Majestic on Mathematics branch Topology

[@symbolspangaea]

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

[@flyzo1977]

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

[@carsonmcnamer5321]

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]

Appreciate it!

[@IAMASTICKSTUPIDPERSON]

@@drewscampfire yea try to post more

[@hampusbrokmann8249]

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

[@hampusbrokmann8249]

​@@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 KZbin, easy to understand and clear pic of what you are talking about. Sorry for the dyslexia hope you understand 😂😂😂👏🇩🇰😇

[@Alexander-xo5ho]

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

[@xplodingmojo2087]

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

[@nataliaserhiienko9333]

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

[@nrml76]

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

[@epalios]

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

[@aithrasherboi]

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.

[@geokou7645]

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

[@BIackhole]

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!

[@bumblebee9426]

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

[@midohatem57]

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

[@Life_42]

Beautiful video!

[@igxniisan6996]

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

[@tedfritzart]

Just discovered this channel. Really wish to see more!

[@huvarda]

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

[@peterpelle8982]

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

[@RealZynexx]

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

[@jordanblack2250]

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 🙏🤘🙌

[@SM-qw9tp]

Interesting way to expand your mind.

[@chill_orange8374]

This adds more depth to my existential crisis.

[@Glen_Mali]

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

[@yashsoni3835]

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

[@souvikmandal2637]

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

[@ManDancingMoji]

Okay that solution was so cool.

[@WaleedHassanAwan]

This video was so good ☺️ I loved it so much

[@sagarpuri7838]

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

[@jameerlawrencebondoc8162]

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

[@Dhruva_P_Gowda]

Nice Visualizations!!!

[@d-e-p8473]

What an AMAZING channel holy phokin sheesh

[@braziliangentleman5148]

wait, it's all donuts? officer: "always has been"

[@cherylchui4510]

Please do more

[@johnchessant3012]

very nice

[@alfredhitchcock45]

Mind boggling

[@ayushjha3716]

We want more videos!!!

[@aditi28oct]

We need more, keep up the good work

[@myworld4818]

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 😭😭😭😭😭😭😭😭😭

[@raeplaysval]

in my opinion, the moment when the hole is longer than a finger is when it becomes two holes to a human

[@bartekszachu7110]

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

[@Qlust]

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

[@endlesslovingmovement]

This is so well done! Amazing!

[@pasijutaulietuviuesas9174]

Sometimes we forget that topological holes are not the same holes we talk about in everyday speech. To a topologist, a hole in the earth is not a hole at all, but it is a hole by the definition of "hole" that came much earlier than topology as a science existed. Topology created a different definition of a hole. The way we define a traditional, non-topological hole is a locally hollow area on a solid surface. If a dog digs a hollow area, the dog made a hole, despite the fact that the dog only repressed the surface of the Earth topologically. You don't need to consider the entire Earth, you only need to consider the local area for that dog's hole. Likewise, if an object is large or long enough, there could be a single topological hole connecting two opposite ends, but that could be considered as two conventional holes because the object is large or long enough so that the two ends are no longer local to each other. A donut has a single conventional hole, but a long straw, while having a single topological hole, it has two conventional holes, the top hole and the bottom hole. The two ends are not local to each other.

[@Faunadude]

I misread this and thought you said the word butthole what is wrong with me

[@Leo-if5tn]

Awesome video

[@AchrafTheGeek]

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

[@liviemillie6455]

Idk why this was recommended to me, but hey, I tremendously suck at math and 3D quantitative thinking so it was cool

[@maydimutawa8874]

That is absolutely awesome 👌🏻 👏

[@partybrawl1764]

Bro what the hell? 10k views? This is so underrated anyone kill me

[@TrigonometryX]

Just by 2 videos I’ve learned more than my entire career of school until my current grade (5th)

[@vxvnw]

you give senku ishigami vibes

[@thalrosen]

you're the greatest

[@RSLT]

Interesting. Great video!

[@好吧-h6k]

How does this only have 2k views

[@vishva8kumara]

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

[@HAG47]

Amazing reall, keep up the good work

[@urkanchha]

I saw you transformed same handcuff 5:44 to the same 6:46😂 (but you challenged converting one hole trapped into two hole trapped one) no one complaining of that😂

[@noobatredstone3001]

… 6:14

[@papope_i]

acabo de encontrar este canal y me duele ver que haya dejado la actividad

[@spencerdumlao1654]

5:37 sliding them

[@Hyscull]

Everything is a donut... NOW IM HUNGERY!

[@lesbrooklyn]

0:30 th-that’s pretty average

[@clarenscourtois8927]

Made my day 🤓!

[@mathscapsule979]

You are a great teacher

[@matrixtech6917]

A very interesting video

[@EugeneHKrabs-ie1lc]

Is it possible to learn this power

[@Nick-Bel]

0:35 it's at this point the straw stops having 2 holes and starts having one Anyone that wants to dispute this is welcome to reply

[@xfa_f]

Love your vid man keep it up

[@hkayakh]

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

[@Uchiha____Sasuke]

Hey Andrew we know good quality stuff lacks quantity . It's the same way thete are very few people who like and understand your videos. Thas why you have less views. But please make new videos. It's better to have 1 good viewer than 1000 bad ones.

[@pritamroy3766]

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 .

[@HeWhoProclaims]

Great video but I think that describing why this is would help a lot of people. Whereas what's shown in the video only explains that it's the case but not why. Is that because no one knows yet? Why is the Euler formula important and who's to say deforming isn't the same as cutting like who decided all this and where did the problem first pop up for someone to be so specific about something that's so vague in usefulness. There's a lot of compliments in the comments but people don't realize that a deeper and more understandable explanation is needed for this kind of subject imo.

[@B121AN1]

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

[@adrenaline647]

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

[@alfredhitchcock45]

Now I won't look at coffee and donuts the same way again

[@mhffseriouslythisistaken]

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

[@hede638]

so good

[@bystander85]

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

[@kingcrafteroderderfahradtu7331]

A straw has infinite holes stacked on top of each other

[@kingcrafteroderderfahradtu7331]

It gains the others once it’s no longer curved like a donut and has a „flat“ line between the two edge curves that’s larger than one rotation inside the straw (I think that’s called the circumference). Basically once the path from the top hole to the bottom hole is longer than the edge of the hole would be if it where opened into a line. A Petri dish without a bottom would only have one hole but those amusement park rides have infinite holes

[@casssaph2287]

cool video, but i dont really understand the purpose of the camera focusing effect? its distracting and im not sure if it has some meaning to it or not im also not sure if this answers the question "why topology?" it is very cool to see geometry and topology be bridged though even though I don't feel like it answered the question "why topology?", it was a cool video regardless. i think a video more accurately detailing the question "why topology?" would probably be something explaining the history of topology or its practical uses

[@drewscampfire]

Thanks for the feedback! This video was kinda rushed so I tried to mask some of the inconsistencies/breaks/mistakes with blurs/focusing effects. Band-aid fixes, essentially.😄 I totally understand how this could be distracting and thanks for pointing it out! Regarding the title, I agree. I'll surely consider other titles that fit the video better.

[@equestenebris4055]

1:24 can I have that naofumi-sama?

[@Faunadude]

My brain hurts but I love it

[@sagarpuri7838]

7:05 for more info

[@ITHrealXD]

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

[@Dante_The_Great]

Theres another way to do that last puzzle.

[@souraday1133]

Why is this counterintuitive ? Because it breaks and unbreaks symmetry.

[@rubirox5691]

Its prismo from adventure time yall! : ' )

[@partybrawl1764]

3:00 here comes the pi (unknown value. Ie we can't split 100 in 3

[@kate8276]

Great videos!!!!))))

[@ExcitedBakedBread-ho9bq]

I see it.

[@ExcitedBakedBread-ho9bq]

INFINITY♾️ IS NOT A NUMBER.

[@user-db2fb1db1m]

Earth is a 4th dimension polyhedron- same - flay 🌍

[@stackgator]

Doesn't the mug have two holes? The handle and the cup

[@uykatik]

The cup is not the hole, it's deepening. You can't see through it

[@stackgator]

@@uykatik makes sense! Thanks!

[@uykatik]

@@stackgator no problem!

[@flint6000]

HAIRY BALL THEOREM

[@BlakeGibbons]

Or E-F-V. Same thing.

[@BlakeGibbons]

Also alphabetical and easier to remember.

[@mihaleben6051]

A cup has 2 holes

[@BahramMortazavi4048]

Let's just say that our human minds can't understand 4D.