Why does this balloon have -1 holes?

Рет қаралды 1,300,703

2 жыл бұрын

Thank you to BetterHelp for sponsoring this video! To get 10% off your first month of therapy, go to betterhelp.com/standupmaths to sign up today.
If you are need of urgent mental health support please check for crisis help lines available in your country.
USA: www.mentalhealth.gov/get-help...
UK: www.nhs.uk/mental-health/advi...
Do check out Jordan Ellenberg's book Shape. This video was inspired by Chapter 2.
www.nytimes.com/2021/06/21/bo...
www.jordanellenberg.com/book/...
Support me on Patreon and I will post you a free torus balloon. I hope I don't regret this. / standupmaths
Here is Sam Hartburn's geogebra file: www.geogebra.org/m/yjtjxr2n
Trouser animations thanks to:
Bentley Davis BentleyDavis.com
Em Raymond / techcavy
Kalina Panteleeva kalinadoesc...
Thanks to Visual Topology & Geometry for "Punctured torus homeomorphism". • Punctured torus homeom...
Me cutting two joined cylinders in half way back in 2015. Good times. (At 29:29.) • Four Dimensional Maths...
CORRECTIONS:
- When talking about the Euler Characteristic of the torus at 16:29 I say the value of zero is "only on our friend the torus" which is technically wrong. In the moment I was just talking about the sphere and the torus but loads of other shapes have an Euler Characteristic of zero. Like the cylinder.
- I'm undecided if the string method of thinking about holes at 17:04 was helpful. I could have talked about the dimension of the boundary manifold, but that felt like I was repeating the previous bit too much and wanted a different way to think about it. Not sure if this counts as a 'correction' per se, but I just needed to talk to someone about it. Thanks for listening.
- Let me know if you spot any other mistakes!
Filming and trouser sewing by Alex Genn-Bash
Editing by Michelle Martin
Graphics by Sam Hartburn
Doughnuts later eaten by Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/products/5b9f...
Nerdy maths toys: mathsgear.co.uk/

Пікірлер: 3 500

@standupmaths 2 жыл бұрын

It's true. I have the world's supply of torus balloons and I'm posting them free to all of my Patreon supporters. Sign up before 7 August and get a balloon full of holes! patreon.com/standupmaths

@theBestInvertebrate 2 жыл бұрын

I see what you're up to, buying up the supply of torus balloons so that the only way to topologicaly indulge is to go through you, nefarious.

@theBestInvertebrate 2 жыл бұрын

I jest.

@derekkuldinow5790 2 жыл бұрын

Where'd you get that shirt, Matt?? Is it something particularly interesting or just a nice design?

@mikeblank8034 2 жыл бұрын

I'm curious because you label the toroid loop as both a 2d hole and a 1d hole, is that correct? If that is the case then does the straw have both a 1d and 2d hole also? Love your videos! 😊

@feliciabarker9210 2 жыл бұрын

Controlling the world's supply of toroidal balloons is the next step in your descent to maths supervillainy.

@collin4555 2 жыл бұрын

"Topology is a very big area of mathematics" Yeah, but it's continuously deformable into a small area

@simono.899 2 жыл бұрын

🤣🤣🤣🤣🤣

@zeus1962 2 жыл бұрын

Good one.

@timwest788 2 жыл бұрын

Boom

@archivist17 2 жыл бұрын

Badoom tish!

@archivist17 2 жыл бұрын

That's a bit of a stretch!

@johnbeauvais3159 2 жыл бұрын

“The jam inside this donut is not mathematically relevant” this might be my favorite line ever

@KrackerUncle 2 жыл бұрын

Because we cant answer if there is any. Its schrodingers jam.

@jmr 2 жыл бұрын

That could have been a line from an episode of "The Big bang Theory".

@jmr 2 жыл бұрын

@@KrackerUncle Your response could have been a second line

@olliephelan 2 жыл бұрын

The jam fills a hole though. Or at least it should

@ainidirieiais 2 жыл бұрын

@@KrackerUncle in this case, it is mathematically relevant :)

@BlankPicketSign 2 жыл бұрын

Captain: "HOW MANY HOLES DO WE HAVE IN OUR AIRSHIP?!" Me: "Well first let us explore the Euler Characteristics of the..." Also Me: *Gets thrown off to my death

@LAK_770 2 жыл бұрын

I’m liking this steampunk novel so far, keep it up

@arrowed_sparrow1506 2 жыл бұрын

@@LAK_770 unfortunately it becomes very one dimensional later on.

@datpudding5338 2 жыл бұрын

@@arrowed_sparrow1506 at least the flight path has double the dimensions xD

@gildopesce Жыл бұрын

AHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAH

@mihailmilev9909 Жыл бұрын

@@LAK_770 where is the rest of it lol

@grug57 Жыл бұрын

The jokes, the maths, the visual aids - I just love this video as a whole.

@K1lostream Жыл бұрын

You missed the opportunity to say the ways you love this video are many-fold.

@grug57 Жыл бұрын

@@K1lostream the math in this video is so great - you couldn't poke any holes in it

$@fractional_factorial1539$

@fractional_factorial1539 Жыл бұрын

As a hole*

@E-AnyaForger Жыл бұрын

Me smirking at the thought of visual aids :)

@grug57 8 ай бұрын

@@dot1298 thats what im sayin

@kitludd465 2 жыл бұрын

dont apologise for confusing trousers and pants, after all topologically they're the same

@OriginalPiMan 2 жыл бұрын

I was thinking the same. I'm glad I scrolled far enough to find someone with the same idea.

@rhamph 2 жыл бұрын

Don't forget the g-string! Trousers is pants is g-string.

@andrewsparkes8829 2 жыл бұрын

@@rhamph Ah, but that depends on how lacy the g-string is.

@vigilantcosmicpenguin8721 2 жыл бұрын

Just wearing my favorite punctured torus.

@OriginalPiMan 2 жыл бұрын

@@andrewsparkes8829 Well if you're getting into those kinds of specifics, then jeans have belt loops that are holes, and then pants and trousers are not necessarily topologically synonymous.

@firestormdb 2 жыл бұрын

"I have bought the world's supply of toroidal balloons" sounds like the world's daftest supervillain plot

@darksoles1305 2 жыл бұрын

Or a math word problem

@jorgepeterbarton 2 жыл бұрын

Or a fetish

@danielled8665 2 жыл бұрын

@@jorgepeterbarton that was literally in a show about weird fetishes. Ah, balloon guy…

@sweetpot8a 2 жыл бұрын

Underated comment

@dak_black 2 жыл бұрын

Doofenschmirtz

@frankhooper7871 2 жыл бұрын

It took me a while to realise that you were using the balloon as a model of a sphere - my first thought was that the balloon was in essence a disc as I was considering that it could be flattened topologically once you untied the place where you blew it up.

@RobertShippey Жыл бұрын

Yes I was the same.

@MrEscape314 Жыл бұрын

Yea I agree. The balloon was a disc to begin with.

@gw6667 Жыл бұрын

Yup, he started cutting a hole and I was like, "hey, wait, what? Oh, sphere."

@danieldaugherty918 Жыл бұрын

right I was like "no the balloon is a disc and now it has 1 hole"

@spicyoreos74 Жыл бұрын

Me too

@JollyGreenWizard Жыл бұрын

What this video really teaches us is how to turn the decorations and snacks for a small party into a tax write-off

@subnatural5341 2 жыл бұрын

Topologist jokes before: "Topologists can't tell a doughnut and a mug apart." Topologist jokes now: "Topologists can't tell jeans and g-strings apart."

@vigilantcosmicpenguin8721 2 жыл бұрын

Topologists are never going to see anyone in a g-string anyway.

@badlydrawnturtle8484 2 жыл бұрын

@@vigilantcosmicpenguin8721 That's just it, though; they see EVERYONE in a g-string.

@skyjoe55 2 жыл бұрын

@@badlydrawnturtle8484 if there wearing a skirt wouldn't that be the same as wearing a mug?

@FireStormOOO_ 2 жыл бұрын

@@skyjoe55 I can see the animation in my head now. Send help

@dielaughing73 2 жыл бұрын

@@skyjoe55 that'd be an annulus

@pyglik2296 2 жыл бұрын

The worst thing about topology is drawing with markers on doughnuts.

@oldcowbb 2 жыл бұрын

i literally screamed NOOOOO

@deyesed 2 жыл бұрын

Squeak squeak

@tremkl 2 жыл бұрын

I was terrified he was going to do that, but he only drew on a bagel, which is slightly less bad.

@anuragjuyal7614 2 жыл бұрын

@@bland9876 damn! 😂😂

@guepardo.1 2 жыл бұрын

Not to mention ruining a pair of perfectly good trousers.

@mbyard356 2 жыл бұрын

Well, now I know why I wasn’t able to find any “donut balloons” for my kid’s birthday party. Gee, thanks Matt! 😂

@tuffcat8572 2 жыл бұрын

True story? He ruined so many plans with that.

@mattomanx77 Жыл бұрын

He knew EXACTLY what he was doing bringing in a torus balloon and saying "Things are gonna get a lot worse" Things always get worse when you start bringing those in

@Xalies 2 жыл бұрын

I think he's ability to break a bagel perfectly on the line is underrated

@dandynoble2875 2 жыл бұрын

I think that speaks more to the low quality of the bagel than his ability. Pretty easy to break the yoga mats they call bagels you find at the grocery store.

@necaton 2 жыл бұрын

*his

@Lampe2020 2 жыл бұрын

I also wondered how he got that perfectly flat breaking surface!

@theentertaner 2 жыл бұрын

I read this before i watched the video and was waiting for him to split a bagel down the middle but as a normal person would if they were to eat it

@SquareWaveHeaven 2 жыл бұрын

"When you put a hole in something, the number of holes goes up"

@standupmaths 2 жыл бұрын

- Matt Parker, 2021

@michaelhutson6758 2 жыл бұрын

Unless... there's such as thing as a NEGATIVE hole...

@EphraimP 2 жыл бұрын

Unles you add a hole to a net then you have less holes

@ManjotSingh-sf2ri 2 жыл бұрын

@@EphraimP well u can still have more holes if you drill a super narrow hole with a needle into the threads so that they dont break

@Smitology 2 жыл бұрын

@@michaelhutson6758 There is. If you add a "cavity" in something, kinda like a cyst, that's not exposed to the surface, that's a negative hole.

@GiatrasKon 8 ай бұрын

Man, Swiss cheese must be the bane of topologists' existence

@themightymcb7310 2 жыл бұрын

Whenever the "holes" type questions came up, my first critical thought on the question was immediately to consider that straws and clothing are 3D objects, which immediately complicates things for me in such a way that I'm honestly just out of my depth. This video helped me work out some of the more abstract ideas around topology. Good stuff!

@ahorribleperson3302 2 жыл бұрын

"Things are gonna get a lot worse" *Ominously brings out a second balloon*

@jeremiahevans4175 2 жыл бұрын

Oh no...

@brandon.duffany 2 жыл бұрын

I laughed so hard

@embers_falling 2 жыл бұрын

A hole lot worse

@MmKayUltra1 2 жыл бұрын

You keep asking about the pair of trousers but never told us the number of belt loops which I feel are important.

@theBestInvertebrate 2 жыл бұрын

I mean he kinda did, as you can see from the animations and it's euler's characteristic it has no belt loops.

@H2SO4pyro 2 жыл бұрын

@@theBestInvertebrate Then you'd have to wear them with suspenders, which add 2 additionnal holes. So they'd be equivalent to 2 trousers glued back to back, or a 4 legged trousers

@ericbsmith42 2 жыл бұрын

Also, almost every pair of trousers has at least one button hole.

@FineOtter 2 жыл бұрын

Maybe they were jeggings the whole Time?

@mydemon 2 жыл бұрын

Its a mathematical pair of pants.

@reaganduggins5279 2 жыл бұрын

This is easily one of the best, most intuitive explanations of any topological concept that I have seen.

@krzysztofwysocki76 2 жыл бұрын

Hi, regarding 2-d holes mentioned at 18:00, how about explaining this as "how many gases you can fill in the spaces created by manifold without mixing them together?" for instance you can have oxygen inside the sphere and nitrogen outside, which defines the number of 2d holes of sphere as 2.

@blackmber Жыл бұрын

You might have to subtract 1 because the sphere and the torus each have 1 two-dimensional hole and can separate 2 gases.

@angelmendez-rivera351 6 ай бұрын

This is mathematically inaccurate. As demonstrated in the video, the number of 2D holes of a sphere is 1, not 2. The Euler characteristic of a sphere is 2, but this is because spheres include 1 0D hole. 3D space can always be filled by 1 gas without mixing, in the absence of higher dimensional holes. Introducing one 2D hole allows 2 gases, but it can get complicated once you also introduce holes of other dimensionalities.

@mr.johnson3844 2 жыл бұрын

I can't believe he established a temporary monopoly on the distribution of *torus* balloons in order to make being his Patreon supporter more desirable. This is peak economics.

@user-pr6ed3ri2k Жыл бұрын

taurus balloons

@wcbq Жыл бұрын

taurus balloons

@user-pr6ed3ri2k Жыл бұрын

@@wcbq i agree

@omegonchris Жыл бұрын

@@user-pr6ed3ri2k the shape is called a torus. Taurus is a zodiac sign and constellation derived from the Latin word for a bull.

@user-pr6ed3ri2k Жыл бұрын

@@omegonchris ur late to the convo he said taurus balloons before probably hinted by the fact that the comment was edited and the word torus is bolded out

@DrTrefor 2 жыл бұрын

This is such a fun intro to the Euler Characteristic! I think it's kinda sad that so often we don't expose students to these accessible ideas from topology until late in an undergrad program, but there is no reason it can't be explored way way earlier.

@MuttFitness 2 жыл бұрын

I got a BS in math and learned none of this

@Necrotoxin44 2 жыл бұрын

@@MuttFitness As it turns out, mathematics is full of a lot of different disciplines, haha. I also got a BS in math, but at my university I concentrated in 'pure math', and so I did learn this stuff. It would depend on your concentration, but I could also well imagine a more general and spread out math curriculum might miss some of this stuff.

@MikehMike01 2 жыл бұрын

probably because it’s totally useless outside math

@jajssblue 2 жыл бұрын

Completely agreed!

@zacharym7000 2 жыл бұрын

I've always found maths sorta dry but stuff like this makes me genuinely interested. I love seeing people take complex subjects and break them down for the laymen like me.

@dinoeebastian Жыл бұрын

I'm astonished at how he's able to hold a doughnut in his hand without eating it

@jaisenroa4219 Жыл бұрын

you could tell that he wanted it when he was holding it

@valentincorman1578 2 жыл бұрын

Now I wonder how the machine to make the toroidal ballons looks like. Great video, super interesting content, as always. Thank you!

@DeathlyTired 2 жыл бұрын

If the barrier to entry to a subject is that you've got to be as smart as Poincaré , Riemann, Betti & Noether, I think, at that point, it's acceptable to simplify things a bit.

@jako7286 2 жыл бұрын

Yeah, people like me, who don't know their asymptote from a hole in a graph need to keep things simple.

@MrAlRats 2 жыл бұрын

Most people believe that P is not equal to NP. Which means, in essence, that the ability to verify the solution to a problem is trivial compared to actually coming up with the solution in the first place. Developing the mathematical framework for studying a class of problems is considerably more difficult than merely understanding it after it has been fully developed. More or less, what one person can understand any other can as well. The only barrier to entry to any subject are having access to content created by those who understand the subject and self-motivation.

@angelmendez-rivera351 6 ай бұрын

The entry barrier does not require you to be as smart as Poincaré, Riemann, Betti, and Neother, just as how the entry barrier to using a computer does not require you to be as smart as Claude Shannon (there are plenty of idiots who know how to use a computer).

@mokopa 2 жыл бұрын

11:51 Matt apologises to blue balloon for being mean to it about calling its homology class horrible 13:18 Matt continues insulting balloon's homology class right in its face

@Scootfairy 2 жыл бұрын

Yeah Matt really tore him a new hole.

@Martin_Huetter 5 ай бұрын

as a 3D artist working with 3d objects and surfaces every day and "morphing" them into flat 'sweing patterns' (UVspace) this is in a very weird way super fascinating. Explains really well how you would map a flat texture (a plane) onto a torus.

@pauldubois0 4 ай бұрын

This is my problem with the jeans animations. The original jeans can be uv mapped with no seams, which I guess is another way of saying they can be embedded in the 2d plane. The sewn-legs jeans cannot. So, if they are modeled as surfaces rather than volumes, they must be different shapes.

@syriuszb8611 7 ай бұрын

As engineer I often encountered word "manifold", especially in CAD programs. I never could get a solid explanation, and after a while I just assumed "it's just a thing, a shape" but never thought it was actually correct enough to have mathematician agree with that poor definition! But I learned today that it unifies shape name between dimensions.

@craigstephenson7676 2 жыл бұрын

I would recommend you don’t get sponsored by better help again. The organization is very shady and overstates the level of involvement actual experts have. There are plenty of KZfaq videos explaining this in further detail

@MarieKaltoft 2 жыл бұрын

Bumping this in hopes he sees it!

@vladimirlenin843 2 жыл бұрын

It's alright No one is gonna use it

@cretinousmartyr3522 2 жыл бұрын

Yeah just let him collect these paychecks and skip the ad if it bugs you, but since it does matter, I think the message he delivers during the ad read feels more like a "seek counseling in if you feel you need it" more than "go use my better help link" compared to many other ad reads and that's a respectable message I'd say

@Applecraftpro 2 жыл бұрын

@@RobABankWithABagel The problem isn't as bad anymore, if you watch the phillp defranco update he did at one point he says they have majorly improved and have made there marketing clearer so while he still wont be doing sponsorships with them he doesn't think other creators should be discouraged from doing so. If you want more info you can watch his video but basically while they still have a bad rep and honestly I probably wouldn't use their services, they have fixed the issues so there isn't really any moral problems with taking a sponsorship.

@5h4d0w5l1f3 2 жыл бұрын

@@Applecraftpro sure would be great if they put effort into proving that and explaining the changes that they've made rather than continuing ad campaigns totally not acknowledging that. but cool, you go fight for this unknown internet business. they probably need and appreciate it.

@Sicarine 2 жыл бұрын

And then the sequel. "How many holes does a punctured Klein Bottle have?"

@theBestInvertebrate 2 жыл бұрын

I think 0?

@BlueBeBlue 2 жыл бұрын

It's a really good ideia, maybe it has a 3d hole? Idk

@Nerketur 2 жыл бұрын

Given that it's made from connecting two mobius strips of opposite directions, I think two. Puncture and it becomes two joined mobius strips. So from 0 to two

@samuelthecamel 2 жыл бұрын

@@Nerketur You can't put one hole in it and get two more holes! (Or maybe you can. Idk, I'm not a topology expert)

@Noname-67 2 жыл бұрын

2 holes, it'd be 2 mobius strips or an annulus and a mobius strip, it hard to imagine but 2 holes either way

@wombat4191 2 жыл бұрын

30:00 and it becomes even more creepier when you imagine how someone would wear them when treated as the same shape as regular trousers.

@angulinhiduje6093 9 ай бұрын

i do a bit of 3d modeling, i used terms like "non manifolds" without every questioning them. to me it was just the software term for "mistakes" that created holes. very good video

@ThePlacehole 2 жыл бұрын

Patreon exclusive: Matt wears the mathematically "equivalent" trousers.

@dathaniel9403 2 жыл бұрын

He’d be an honorary member of the Ministry of Silly Walks.

@dwagincon4841 2 жыл бұрын

You been the onlymaths exclusive

@MuzikBike 2 жыл бұрын

jesus

@katyungodly 2 жыл бұрын

Someone would be into that 😂

@ashtonhoward5582 2 жыл бұрын

I think you'll find that that's on his OnlyTopologists channel.

@TheTallCurlyOne 2 жыл бұрын

"Ignore the fact that there may or may not be jam inside of this doughnut, that's not mathematically relevant." You say while not confirming the jam status so it's now in some schrodinger's doughnut superposition shenaniganry. Which to be fair is still not mathematically relevant.

@hyperfox0934 2 жыл бұрын

*exasperated physicist sighing*

@grepgrok8735 2 жыл бұрын

Actually, if there IS jam and we consider the doughnut to be exclusively dough, then the jam creates a void (aka 2d hole) which would make the doughnut a sphere instead of a solid ball, which is extremely mathematically relevant. Thus, a doughnut hole (aka a solid bit of dough) is what he should have used to represent a ball.

@brendanh8193 2 жыл бұрын

So, to say this poetically, "is the jello hollow? Such states set said Schroedinger superposition shenanigans sour." Or to quote that great poet, Homer, "Doh!"

@joewilson3393 2 жыл бұрын

I wonder if I can look up any of my old math teachers and get their opinion on the mathematical relevancy of jam? I'm sure that won't be a strange question coming from a student 20 years later....

@ReimerGodt 2 жыл бұрын

#AlfFromMelmac would love Schrödingers cat oven backed, filled with plum jam. I believe.

@Almrond 2 жыл бұрын

This is the content I truly love. Your title made me think, and I continued to do just that throughout watching. Thank you for the thought.

@stephenj9470 2 жыл бұрын

I understood very little from this video. And yet I watched it to the end, because Matt is so mesmerizing.

@leorussellmoore3329 2 жыл бұрын

"Now, from personal experience, it's pretty hard to draw on a doughnut. It's a lot easier to draw on a bagel. Although technically, still a doughnut." - think this has to be my absolute favourite Matt quote now. Had to pause the video cause I was laughing too much.

@nixel1324 2 жыл бұрын

I'm pretty sure I remember the video where he learned that, the one where he turned a bagel into two interlocked rings.

@Devlinator61116 2 жыл бұрын

"Whenever you put a hole in something, the number of holes goes up." *Nets have entered the chat.*

@parodoxis 2 жыл бұрын

You'd have to stick a needle into the rope to split it in two, yes forming another hole. Just tearing the rope in one spot is tearing the net, not really "putting a hole in it" though we say it that way

@TatharNuar 2 жыл бұрын

Fabric is just a really tight net.

@parodoxis 2 жыл бұрын

@@TatharNuar by a loose definition, yes, and in that sense the fabric of reality is nets all the way down. But if we don't stop somewhere and just call it a "surface", none of the stuff in this video applies.

@karl810 2 жыл бұрын

@@parodoxis fish net tights get holes all the time, I cant think of any other way of explaining it, they're definitely holes.

@parodoxis 2 жыл бұрын

@@karl810 if you consider the fishnet to be one fabric, sure. But if you see the net as a bunch of holes, then no, you have not created a hole, you've actually joined two or more holes. Thus the number of holes goes down, thus you're losing holes not adding them.

@komicalican 2 жыл бұрын

That is just amazing. Great work!

@ar_xiv 7 ай бұрын

I like that the hand drawn animation actually got it the most correct by showing the transition to the figure 8 “cord”

@rickseiden1 2 жыл бұрын

"So it's like they're all the members of the same one terrible homology class." "There is only one true parabola!"

@nanamacapagal8342 2 жыл бұрын

Cue the illuminati-esque spiritual experience.

@quacking.duck.3243 2 жыл бұрын

Gloria in x-squaris.

@nanamacapagal8342 2 жыл бұрын

@@quacking.duck.3243 NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

@GaryFerrao 2 жыл бұрын

😂 that was his best video ever. his beginnings of video editing. look where he is now 😎

@sankang9425 2 жыл бұрын

@@GaryFerrao lol. He basically shoved in every sound and video effects that he could use

@CRASDFGH 2 жыл бұрын

I remember when this video was titled "How many holes do things have" It was a simpler time.

@standupmaths 2 жыл бұрын

It was a more simple time when everything was smooth and closed.

@sven_lu_ 2 жыл бұрын

@@standupmaths *clothed

@EebstertheGreat 2 жыл бұрын

It was a more path-connected time when every loop could be contracted to a point.

@p0gr 2 жыл бұрын

@@EebstertheGreat you mean simply connected.

@slarzyer 2 жыл бұрын

there is no wholes in 2d ....a pair of pants has 3 holes one for each leg and the hole around it

@WindyNight114 2 жыл бұрын

I’m loving this channel!

@JamesF0790 2 жыл бұрын

Aw, I missed out on a toroidal balloon :( Still, such is life. Thanks for the mind bending holes talk Matt!

@johnchessant3012 2 жыл бұрын

Fun fact about Jordan Ellenberg: He has one of the lowest Erdos-Bacon numbers, having cameoed as a math professor in the film 'Gifted'.

@matthewevans7703 2 жыл бұрын

I remember seeing that cameo, he seemed like he was genuinely excited about the math that he wasn’t even teaching to a class

@photelegy 2 жыл бұрын

PLEASE: Let there be an astronaut currently on the ISS, which is a patreon ... I want a video of Matt explaining how he had to manage to get a balloon on to the ISS 😂

@garychap8384 2 жыл бұрын

I want Matt to explain what he was doing with a childs pants. Where's the child??? This video is deeply disturbing.

@petemagnuson7357 2 жыл бұрын

He could probably back out by saying that aren't "anywhere in the world", but I don't doubt he would find a way

@stevenutter3614 2 жыл бұрын

Patron*, not patrion.

@brendanh8193 2 жыл бұрын

Don't worry, he can easily change his question into how many holes in a saxophone. See the Olympic closing ceremony for proof. While we are at it, what shape can be made from the Olympic rings?

@GummieI 2 жыл бұрын

Easy fill it with helium and just send it away at the right moment, and they will be able to catch it at the ISS

@black-snow Жыл бұрын

Waiting for the children's book "How many holes does it have?'

@placeboantwerp4312 2 жыл бұрын

Great work Matt. Love this one.

@Quantris 2 жыл бұрын

you need to animate that deformation with someone wearing the pants the whole time

@columbus8myhw 2 жыл бұрын

Wearing pants normally corresponds to having one leg through the sewn-together pantlegs and the other through the space between the pantlegs

@Quantris 2 жыл бұрын

@@columbus8myhw indeed, but I want to see the inbetween states in their full glory maybe it would lead to a fashion revolution

@TechCavy 2 жыл бұрын

Challenge accepted

@worstuserever 2 жыл бұрын

kzfaq.info/get/bejne/j5N4oM9mts3Wo2Q.html

@alancash6420 2 жыл бұрын

I hired Matt to do balloon animals at my kid's birthday party. Reception was mixed, but they liked the n-dimensional hyper-sausage dog

@miriamrosemary9110 2 жыл бұрын

I love this comment so much 🤣

@chuckghaly 2 жыл бұрын

Loved the animation 👌 great presentation

@Greyorange_ Жыл бұрын

Best Blender tutorial I've seen so far

@DrakiniteOfficial 2 жыл бұрын

I appreciate the explanation of the differences between torus and doughnut, ball and sphere, and circle and disk. I didn't really consider that there was such a rigid difference between the definitions of each two.

@zlac 2 жыл бұрын

So, when you deform a square, do you get a circle or a disc?

@twt1524 2 жыл бұрын

It’s about dimension ex 1d, 2d, 3d. Circle 1d. Disk 2d. Torus 2d(only has surface area). Donuts since they’re solid objects are 3d. A sphere is the 2d surface of a 3d ball.

@twt1524 2 жыл бұрын

“Flatten” a square you get a circle . The 2d surface of a cube can be “flattened” into a 2d disk

@zlac 2 жыл бұрын

@@twt1524 So square is just a perimeter - just like the perimeter of a disk is called a circle, right? How is a surface surrounded by a square called?

@iain_nakada 2 жыл бұрын

@@twt1524 I'm not sure you do. The 2d surface of a cube has a 2d hole in it, a 2d disc has no holes in it. (If we're talking topology and holes still.)

@gordonwiley2006 2 жыл бұрын

Topology is my favorite part of math that I constantly feel like I *almost* get.

@sixstringedthing 2 жыл бұрын

Back in highschool I felt that way about quadratic equations, now I'm not even close. 🤔

@98danielray 2 жыл бұрын

that may as well be the case forever if the only exposure to it is random youtube pop-sci-esque videos.

@erikswanenberg8719 Жыл бұрын

great channel really enjoying

@DevynPlaysGames 2 жыл бұрын

I forgot the joy these videos bring

@GwynPerry 2 жыл бұрын

14:00 Matt tears a perfect slice across the bagel with his bare hands. I couldn't make a cut that clean with a bread knife.

@youtubersingingmoments4402 2 жыл бұрын

You have successfully semantically satiated the word "hole" for me. Thanks.

@kennethmitchell1960 2 жыл бұрын

I cannot describe the levels of discomfort each time that marker touches that poor precious bagel

@AlexanderWC Жыл бұрын

Just burst out laughing at 4am because of that damn balloon noise with no warning

@lightspiritblix1423 2 жыл бұрын

"From personal experience, it's pretty hard to draw on a donut. It's a lot easier to draw on a bagel."

@shaunsaggers 2 жыл бұрын

"Ignore the fact that there may or may not be jam inside this doughnut, that's not mathematically relevant" One of my favourite statements ever.

@rogercline5377 2 жыл бұрын

I think part of the issue is this: A hole in a two-dimensional surface is not the same thing as a hole in the three-dimensional solid of which that two-dimensional surface is a skin.

@tichu7 2 жыл бұрын

I can't believe I had to scroll so far down to find someone who articulated this. If you describe a hole in a straw as something a liquid can pass through, the straw has one hole no matter how squashed the straw is. If you describe it as two holes, with one end being where the liquid enters, and the other end being where it exits, it still has two holes, as long as we're talking about a 3 dimensional straw.

@rogercline5377 2 жыл бұрын

@@tichu7 Going by this logic...and counting a hole in a two-dimensional surface as one hole...then we can view a straw as a hollow cylinder with two holes. OR we can view a straw as a plane curved into a cylindrical shape with zero holes...just space surrounded by that cylindrical plane.

@tichu7 2 жыл бұрын

@@rogercline5377 Exactly what I'm thinking. What we call a hole is dependent upon how big the hole is compared to the 2-dim shape. But geometrically speaking, anything outside that shape is a hole...that just happens to be bigger than that shape. Even a disc with no apparent hole could be reframed as having one hole (technically of infinite size) that's bigger than the disc.

@gerrykavanagh Жыл бұрын

Wonderful synergy between this video and a recent Mathologer video on hypercubes

@ReyMysterioX 2 жыл бұрын

Oh yes, topology, the best meme-able field of mathematics. Seeing people argue wether a pair of trousers has 2 or 3 holes is literally one of the funniest things ever because you can clearly see how it breaks their minds…

@arididomenico6974 2 жыл бұрын

can it have one hole?

@LeeSpork 2 жыл бұрын

@@arididomenico6974 No, that would be a skirt

@Ditocoaf 2 жыл бұрын

Problem is that the definition of "hole" used in topology isn't the only definition. If you dig a classic "hole in the ground", topologically that isn't any hole at all. To most people in casual situations, a hole is a break in the *visible outer surface* of something. Like most endless internet discussions, it would go away if there was a separate word for every imaginable concept, but alas that is impossible.

@40watt53 2 жыл бұрын

It's 2 right?

@quin2910 2 жыл бұрын

Why are there 2 arguments? My first thought is to mould it into a double torus for 2 holes. But google says 3 holes sphere

@plackt 2 жыл бұрын

I didn’t “flatten” the straw to get “one hole”, I just started with a solid cylinder and drilled… one hole.

@grantnichol4496 2 жыл бұрын

Or cut two holes in the balloon and stretch. -1 + 2

@ANDELE3025 2 жыл бұрын

So you bore in a entrance hole and a exit hole.

@henrik.norberg 2 жыл бұрын

@@ANDELE3025 So by your definition you can't bore one hole i a wall or anything with a thickness? You always get one entrance and one exit hole. How do bore one hole then? A pit has to be a hole then? By you definition a hole can not exist, only two holes.

@plackt 2 жыл бұрын

@@ANDELE3025 No, I bore a hole which has two entrances and two exits, neither of which are, in and of themselves, holes.

@ANDELE3025 2 жыл бұрын

@@henrik.norberg A hole by (functional) definition a lack of material on a section of a object. This is relative to the context of the type of object. Surface topology doesnt account for that because in pure algebraic topology you only care about the relation of manifolds to declare something a hole. However even that is a field specialized definition as really any manifold border to nothing is in practice a hole. The relation to context of the object is the crucial part as its why a cylinder in which you bore a relatively wide hole from whatever side you decided to be a top, you can also no longer define it as a cylinder but as a cup. But that cup has technically no hole then as a cup with a hole would leak. Similarly a ring is technically just a hole. And a pit isnt a hole in the planet earth but it is in the ground when you walk next to it (you know, why holes in the ground on the street tend to get repaired). Its why we set axioms and why the entire section on defining number of holes by counting odd and even ones was relevant as it can have -3, -1, 0, 1, 2 or 3 holes depending on how funky you wanna get (tho i believe most people would say 0 or 1 when we are talking about it in practice).

@shruggzdastr8-facedclown Жыл бұрын

Something with a torus and a balloon (and a torus balloon), and any other hollow shape for that matter, that needs to be taken into account for is that they have not one, but two, surfaces -- an inner one as well as the outer one that we take for granted bc it's the surface that we can directly observe from our external vantage point

@jakecarpenter1838 Жыл бұрын

A topologist dips his mug into his doughnut

@saxbend 2 жыл бұрын

Euclid: Square the circle? Good luck with that. Topology: Hold my beer!

@BrainyBrunetteBarbie 2 жыл бұрын

Matt saying “that’s a relief” whilst talking about topology made me chuckle.

@eckoschreiber Жыл бұрын

Thx for the explanation and illustration! Love how cutting the Mobius strip (not Marvel related;o) ) results in two separated, two conjoined rings or one large ring depending on the twisting. Higly recommend "The adventures of Archibald Higgins (Die Abenteuer des Anselm Wüsstegern/Les adventures d'Anselme Lanturlu), Comix about topology, IT, gravitation etc., freely available on wiki. And the novel "Flatland" (disregarding the misogony^^). Cheers!

@jonpatchmodular 2 жыл бұрын

44:00 this video is blowing my mind. At first I was annoyed that you said a donut is not a torus, but then you proceed to demonstrate their different amount of holes

@CaptLoquaLacon 2 жыл бұрын

Buys a reusable straw Makes it impossible to re-use Matt, you're a monster!

@theBestInvertebrate 2 жыл бұрын

Indeed far worse for the environment than just using a single use straw.

@mestiarcanus 2 жыл бұрын

No, he just made it possible for multiple people to use simultaneously by making more (shorter) copies! If he'd cut along the length and ended up with a disc, then he'd be a monster.

@notmyname327 2 жыл бұрын

How many holes does a turtle have? How about a turtle with a straw?

@fi4re 2 жыл бұрын

Just use a homeomorphism to stretch the straw fragments back into whole straws!

@turbofjes2021 2 жыл бұрын

That's not how reusable straws work, thankfully.

@DeclanMBrennan 2 жыл бұрын

Said the sphere to the torus: "I don't like your holier-than-thou attitude."

@slarzyer 2 жыл бұрын

a hollow sphere has 1 hole in the center ..this entire math is fake cause it assume there is a hole in a 2d object that has no thickness

@davidwuhrer6704 2 жыл бұрын

@@slarzyer Not all holes are one-dimensional. Matt explained it: The empty volume inside the sphere is actually a two-dimensional hole, and you could thread an area through it in 4D.

@slarzyer 2 жыл бұрын

@@davidwuhrer6704 a balloon is only a deformed disc not a sphere with a hole in it...so once a hole is added it can be reformed into a disc so not a hole just a dimple on the surface... such as the surface of a golf ball where the dimple fills the the entire center... so a solid sphere with a dimple on the surface is not a hole its just a big dimple so to get a hole in a golf ball it must have an exit point giving 2 holes to the surface so to have a "hole in a balloon" it must pierce both sides leaving one hole behind after deformation

@oxey_ 2 жыл бұрын

@@slarzyer I think what you're saying is true in 3 dimensions but not in all dimensions

@slarzyer 2 жыл бұрын

@@oxey_ i was finding it hard to put words to it....and was referring more to the theory of holes not topology...i believe the fault comes with the definition of what a hole is not that a balloon has negative holes....

@nateleavy5189 4 күн бұрын

“The Taurus has two holes: one in the center, and one in the middle” thank you Matt

@nuriocristino2888 2 жыл бұрын

At 22:56 shouldn't it be "square disk" instead of "solid square annulus" since if an annulus is a disk with a hole then without the hole it is simply a disk? Similarly, at 23:05 isn't "punctured annulus" redundant, or depending on interpretation wrong, since it could be refering to a 2-hole-annulus like the trousers? 2-hole-annulus which funnily enough you made at 24:55 to represent said trousers by puncturing the annulus you'd made earlier by puncturing a disk XD Just a little nitpick of something I noticed but didn't see any comments about. Love the videos, keep doing a good job of making them.

@luca6819 2 жыл бұрын

So now when asked how many holes does a straw have, I can fearlessly answer: "There are two holes!". Thank you zero dimensional holes for existing

@gregoryfenn1462 2 жыл бұрын

If you swish and then stretch a straw you can get a disk with one puncture in it easily, so by the opening assumptions in the video that means it has one hole 🕳?

@waterierStone 2 жыл бұрын

It's OK just cover one side you still have a hole. Cuz English or maybe topology who knows

@vaclavjebavy5118 2 жыл бұрын

@@gregoryfenn1462 i think that's the real scientific answer

@VivekYadav-ds8oz 2 жыл бұрын

Then there's not one zero dimensional holes, there's infinite of them. So technically you can always answer infinite. Don't thank me for making topology the easiest branch of mathematics 😎

@lantami1199 2 жыл бұрын

@@gregoryfenn1462 There is one 1-dimensional hole (where the liquid flows through) and one 0-dimensional hole (cause the straw exists)

@carlosgomez2305 2 жыл бұрын

11:35 Matt: *draws a point* Matt: "the pointless"

@mattglandon3923 2 жыл бұрын

"Am I a joke to you!" -the point 2021

@scottytremaineplays9461 2 жыл бұрын

This is the best explanation of Euler characteristics I’ve ever seen - and it’s what my masters was on

@coctailrob Жыл бұрын

Trying to get my head round the trouser topology loop part… when the legs are attached the loop it loses one hole but creates another at the same time. One of the new leg holes is though the inside down what was the left leg, up the right leg and out again and the other is through the ‘donut’ hole created. The difficult part is visualising where the route of the old waistband ends up in the new trousers

@aaronbredon2948 2 жыл бұрын

My father specialized in Sheaf Theory within Algebraic Topology. He had some fun math jokes based on topology (including capturing a lion in the desert by erecting an empty cage then performing an inversion on the desert to put the lion inside the cage, if I remember correctly) Of course I can barely follow the concept, let alone the actual math.

@fuuryuuSKK 2 жыл бұрын

Said inversion is left as an exercise to the reader

@aaronbredon2948 2 жыл бұрын

@@fuuryuuSKK and technically, you should lock yourself inside the cage so you end up outside after the inversion, rather than inside with the lion.

@eekee6034 2 жыл бұрын

Ooh! I'd forgotten that joke. (It's been a loooong time.) It's a great one if you want weird looks and very confused people. :D

@nikkiofthevalley 2 жыл бұрын

All I can imagine an "inversion" would look like is a mesh (the computer graphics definition) flipping into the shape of the cage. Is that right or is it some wacky BS thst looks like it's travelling into the 4th (spatial) dimension?

@studentjohn Жыл бұрын

@@aaronbredon2948 This is why you have engineers whose job it is to actually apply the maths.

@xanthoconite4904 2 жыл бұрын

wow, I saw the title and was like: ok, I need to see this

@rhandhom1 2 жыл бұрын

That first animation is satisfying to watch. Also, who else expected him to bite into one of the doughnuts?

@PaDelRu 9 ай бұрын

Pants and trousers and interchangeable no matter which country you're in. You've just taught us this. They're the same shape, topologically speaking.

@whee2390 2 жыл бұрын

I didn’t expect stand-up comedy and mathematics to merge so well, but you definitely make it work!

@delecti 2 жыл бұрын

Wait, is there controversy about whether "0" is even? How is that ambiguous, of course it is. It's a bit of a weird case, but it passes all of the tests of evenness, and none the tests of oddness.

@MuttFitness 2 жыл бұрын

I don't know. It seems odd to me.

@Happy_Abe 2 жыл бұрын

@@MuttFitness odd that you think that way

@arnauds2222 2 жыл бұрын

0ddly enough, it does.

@MuttFitness 2 жыл бұрын

@Jacob Coblentz that's odd

@Happy_Abe 2 жыл бұрын

@Jacob Coblentz I don’t think anyone “even” feels it should be odd People probably feel it should be neither and that eveness and oddness only apply to nonzero integers I don’t feel this way just sharing what these maybe think

@noahdoss1967 10 ай бұрын

I’m glad that topology has left me with the ability to know how to put on trousers where the legs have been sewn together

@ogmakefirefiregood 10 ай бұрын

I have explored this question in depth.

@Bare_Essence 2 жыл бұрын

"Ignore the fact there may or may not be jam inside this doughnut, that's not mathematically relevant" lol I'm going to mention that at the doughnut shop when they try to charge me more for that type.

@AlRoderick 2 жыл бұрын

I don't envy the people working in donut and bagel shops near college towns, everyone working in them has definitely heard an unsolicited topology lecture.

@sixstringedthing 2 жыл бұрын

It may not be relevant mathematically, but it's hugely relevant on a personal level (jam/jelly filled is my favourite and now I want one).

@ashtonhoward5582 2 жыл бұрын

There's also a hole that they use to fill the donut with.

@highpath4776 2 жыл бұрын

@@sixstringedthing I like custard ones

@Joe_Payne 2 жыл бұрын

He missed the joke "Its a torus you donut" 😂

@davidwuhrer6704 2 жыл бұрын

These jokes donut seem funny torus.

@scottgriswold384 2 жыл бұрын

I recently bought one of Cliff Stoll's Klein bottles, so I feel topologically significant now.

@schnitzel9003 2 жыл бұрын

*Torus balloon enters the room* Looners: *Heavy Breathing*

@Lykrast 2 жыл бұрын

A straw actually has an infinite number of small holes stacked on top of each other.

@standupmaths 2 жыл бұрын

This is my new favourite take.

@boynamedcate 2 жыл бұрын

Similarly, a balloon is actually just the outer shell of an infinite number of balloon-shaped holes which are nested like Russian nesting dolls.

@vigilantcosmicpenguin8721 2 жыл бұрын

All matter is just an infinite number of quarks, which are topologically balls, I think.

@samuelthecamel 2 жыл бұрын

@@vigilantcosmicpenguin8721 They are not balls, but are instead point-like objects which wouldn't have any holes.

@menyazavutdavid 2 жыл бұрын

@@vigilantcosmicpenguin8721 balls lol

@Relkond 2 жыл бұрын

‘How many holes does a balloon have?” Me, pre video: the one you inflate it with. Me, post video: uh........

@RadicalEdwardStudios 2 жыл бұрын

Could you combine the hole stuff and the knot math? The torus collapsing into connected rings seems like it would relate to knots that cant untangle.

@darianleyer5777 2 жыл бұрын

Regarding the trousers: 2, excluding loops in which to insert the belt.

@cloroxistoxic2077 2 жыл бұрын

and the hole for the button to go through

@Alnakar 2 жыл бұрын

Matt deserves a medal for not taking a bite out of those doughnuts, every time he picked them up!

@tsawy6 2 жыл бұрын

Hey, I appreciate the honesty with the therapy recommendation! Yet another thing to put on the list of "Reasons Matt Parker is a cool dude"! ...it's a long list! Including the fact that he's able to whip out a toroidal balloon, and it's utterly unsurprising.

@thaddeuscosse9527 2 жыл бұрын

Do your research before going to better help. They were just involved with a scandal with the quality of the therapists.