Why does this balloon have -1 holes?

[@standupmaths]

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]

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]

I jest.

[@derekkuldinow5790]

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

[@Usualexpertise]

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]

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

[@johnbeauvais3159]

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

[@KrackerUncle]

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

[@jmr]

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

[@jmr]

@@KrackerUncle Your response could have been a second line

[@olliephelan]

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

[@ainidirieiais]

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

[@collin4555]

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

[@simono.899]

🤣🤣🤣🤣🤣

[@zeus1962]

Good one.

[@timwest788]

Boom

[@archivist17]

Badoom tish!

[@archivist17]

That's a bit of a stretch!

[@T0B1A5_06]

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

[@K1lostream]

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

[@T0B1A5_06]

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

[@fractional_factorial1539]

As a hole*

[@texabot]

Me smirking at the thought of visual aids :)

[@T0B1A5_06]

@@dot1298 thats what im sayin

[@Xalies]

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

[@dandynoble2875]

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]

*his

[@Lampe2020]

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

[@theentertaner]

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

[@DrTrefor]

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]

I got a BS in math and learned none of this

[@Necrotoxin44]

@@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]

probably because it’s totally useless outside math

[@jajssblue]

Completely agreed!

[@zacharym7000]

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.

[@BlankPicketSign]

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]

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

[@arrowed_sparrow1506]

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

[@datpudding5338]

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

[@gildopesce]

AHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAH

[@mihailmilev9909]

@@LAK_770 where is the rest of it lol

[@kitludd465]

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

[@OriginalPiMan]

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

[@rhamph]

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

[@andrewsparkes8829]

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

[@vigilantcosmicpenguin8721]

Just wearing my favorite punctured torus.

[@OriginalPiMan]

@@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.

[@DeathlyTired]

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]

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

[@MrAlRats]

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]

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).

[@themightymcb7310]

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!

[@joshyoung1440]

Then you were applying that thought in the wrong place, no offense. Thickness doesn't matter here.

[@firestormdb]

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

[@darksoles1305]

Or a math word problem

[@jorgepeterbarton]

Or a fetish

[@danielled8665]

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

[@sweetpot8a]

Underated comment

[@dak_black]

Doofenschmirtz

[@MmKayUltra1]

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

[@theBestInvertebrate]

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

[@H2SO4pyro]

@@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]

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

[@FineOtter]

Maybe they were jeggings the whole Time?

[@mydemon]

Its a mathematical pair of pants.

[@GiatrasKon]

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

[@mr.johnson3844]

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]

taurus balloons

[@wcbq]

taurus balloons

[@user-pr6ed3ri2k]

@@wcbq i agree

[@omegonchris]

@@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]

@@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

[@pyglik2296]

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

[@oldcowbb]

i literally screamed NOOOOO

[@deyesed]

Squeak squeak

[@tremkl]

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

[@anuragjuyal7614]

@@bland9876 damn! 😂😂

[@guepardiez]

Not to mention ruining a pair of perfectly good trousers.

[@frankhooper7871]

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]

Yes I was the same.

[@MrEscape314]

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

[@gw6667]

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

[@danieldaugherty918]

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

[@spicyoreos74]

Me too

[@ahorribleperson3302]

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

[@jeremiahevans4175]

Oh no...

[@brandon.duffany]

I laughed so hard

[@embers_falling]

A hole lot worse

[@subnatural5341]

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]

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

[@badlydrawnturtle8484]

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

[@skyjoe55]

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

[@FireStormOOO_]

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

[@dielaughing73]

@@skyjoe55 that'd be an annulus

[@mattomanx77]

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

[@mokopa]

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]

Yeah Matt really tore him a new hole.

[@DrakiniteOfficial]

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]

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

[@twt2718]

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.

[@twt2718]

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

[@zlac]

@@twt2718 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]

@@twt2718 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.)

[@JollyGreenWizard]

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

[@Aaaaaaarrrpirate]

including two pairs of trousers for some reason

[@leorussellmoore3329]

"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]

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

[@photelegy]

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]

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

[@petemagnuson7357]

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]

Patron*, not patrion.

[@brendanh8193]

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]

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

[@mbyard356]

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

[@tuffcat8572]

True story? He ruined so many plans with that.

[@GwynPerry]

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]

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

[@ar_xiv]

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

[@BrainyBrunetteBarbie]

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

[@johnchessant3012]

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]

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

[@krzysztofwysocki76]

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]

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]

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.

[@craigstephenson7676]

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 KZbin videos explaining this in further detail

[@MarieKaltoft]

Bumping this in hopes he sees it!

[@vladimirlenin843]

It's alright No one is gonna use it

[@cretinousmartyr3522]

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]

@@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]

@@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.

[@SendyTheEndless]

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

[@standupmaths]

- Matt Parker, 2021

[@michaelhutson6758]

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

[@EphraimP]

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

[@ManjotSingh-sf2ri]

@@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]

@@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.

[@valentincorman1578]

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

[@CRASDFGH]

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

[@standupmaths]

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

[@sven_lu_]

@@standupmaths *clothed

[@EebstertheGreat]

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

[@p0gr]

@@EebstertheGreat you mean simply connected.

[@slarzyer]

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

[@whee2390]

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

[@syriuszb8611]

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.

[@aaronbredon2948]

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]

Said inversion is left as an exercise to the reader

[@aaronbredon2948]

@@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]

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]

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]

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

[@reaganduggins5279]

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

[@stephenj9470]

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

[@TheTallCurlyOne]

"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]

*exasperated physicist sighing*

[@grepgrok8735]

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]

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]

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....

[@KarlReimerGodt]

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

[@tsawy6]

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]

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

[@wombat4191]

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.

[@alancash6420]

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]

I love this comment so much 🤣

[@ThePlacehole]

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

[@dathaniel9403]

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

[@dwagincon4841]

You been the onlymaths exclusive

[@MuzikBike]

jesus

[@katyungodly]

Someone would be into that 😂

[@ashtonhoward5582]

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

[@angulinhiduje6093]

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

[@CaptLoquaLacon]

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

[@theBestInvertebrate]

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

[@mestiarcanus]

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]

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

[@fi4re]

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

[@turbofjes2021]

That's not how reusable straws work, thankfully.

[@gordonwiley2006]

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

[@sixstringedthing]

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

[@98danielray]

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

[@Martin_Huetter]

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]

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.

[@rickseiden1]

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

[@nanamacapagal8342]

Cue the illuminati-esque spiritual experience.

[@quacking.duck.3243]

Gloria in x-squaris.

[@nanamacapagal8342]

@@quacking.duck.3243 NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

[@GaryFerrao]

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

[@sankang9425]

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

[@shaunsaggers]

"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.

[@dinoeebastian]

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

[@SoməøneXD]

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

[@Sicarine]

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

[@theBestInvertebrate]

I think 0?

[@BlueBeBlue]

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

[@Nerketur]

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]

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

[@delecti]

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]

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

[@Happy_Abe]

@@MuttFitness odd that you think that way

[@arnauds2222]

0ddly enough, it does.

[@MuttFitness]

@Jacob Coblentz that's odd

[@Happy_Abe]

@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

[@Mr_pumpkin_]

🤣 7:26 "have some fun with the trousers up and down"

[@ANoBaka]

That was a very precise and nice tear of the bagle and I thought I'd take a moment to appreciate it.

[@Devlinator61116]

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

[@parodoxis]

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]

Fabric is just a really tight net.

[@parodoxis]

@@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]

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

[@parodoxis]

@@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.

[@JamesF0790]

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

[@JacksonBockus]

I’m now imagining you setting up a series of shell companies to buy up the stock of torus balloons without driving up the price, like Walt Disney buying up land in central Florida.

[@Quantris]

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

[@columbus8myhw]

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

[@Quantris]

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

[@TechCavy]

Challenge accepted

[@worstuserever]

kzbin.info/www/bejne/j16rnp9rhsylqZI

[@leuenbergemo]

He re-used the hell out of that re-usable straw ... good luck re-using that annulus! :)

[@ReyMysterioX]

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]

can it have one hole?

[@LeeSpork]

@@arididomenico6974 No, that would be a skirt

[@Ditocoaf]

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]

It's 2 right?

[@quin2910]

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

[@DeclanMBrennan]

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

[@slarzyer]

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]

@@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]

@@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_]

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

[@slarzyer]

@@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....

[@samisalama3033]

Thank you for making me obsessed with holes.

[@xanthoconite4904]

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

[@plackt]

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

[@grantnichol4496]

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

[@ANDELE3025]

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

[@henrik.norberg]

@@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]

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

[@ANDELE3025]

@@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).

[@jonpatchmodular]

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

[@Alnakar]

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

[@lightspiritblix1423]

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

[@black-snow]

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

[@JohnnyLeven]

This is a great topology explanation, but it took me up to 18:00 to understand that you're ignoring the tied end of the balloon hole and just calling it a sphere. I love the multi-dimensional hole explanations though.

[@saxbend]

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

[@AlexanderWC]

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

[@flexico64]

My first thought on reading the title: "Oh, if you poke a hole in it, it has zero holes, so mathematically has to have -1 before the zeroth hole is added!" My thoughts after watching the video: *rummages through the medicine cabinet looking for the words, 'headache relief'*

[@Corwin256]

I feel like you are very related to health and mental wellness in what you do. I'm not even joking or exaggerating when I say the 'Parker Square' and the message of 'give it a go' and your willingness to look silly in front of the entire world made me feel more comfortable with myself and more excited to just try things regardless of whether I'm sure I'll get a perfect success. I even mentioned it in a mental health blog that I used to write.

[@scottytremaineplays9461]

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

[@yandoryn]

Been trying to improve my general topology so I can delve further into algebraic. The timing here was perfect for inspiration. Gonna go cut a bagel and dig into Munkres.

[@nooneinparticular3370]

I know how harsh Munkres can get, so good luck mate.

[@MrMctastics]

Yooooooo

[@smithwillnot]

I don't know, that twist looks problematic. I would however settle for calling that "Parker's homeomorphism".

[@samuelthecamel]

It's okay if you consider the jeans to have depth, as he said. But, if they are just pure 2D surfaces, then it really is problematic.

[@gernottiefenbrunner172]

@@samuelthecamel even with 2d surfaces, couldn't you morph them into trousers in the middle of some weird walking animation, where the top of the legs is a bit sewn together, and then morph it into regular trousers from there? Either by tearing apart the sewn together surfaces (keeping them connected only on a line), or by reducing the sewn together surface from the other end until it's gone?

[@ZeroPlayerGame]

@@gernottiefenbrunner172 it's easy to prove they are different shapes - normal trousers have 3 different rims, but sewn-together trousers only have one, which makes them topologically distinct.

[@neiljf1089]

I think it is a homotopy equivalence rather than a homeomorphism, because you have to change the dimensionality during that step.

[@fuseteam]

@@ZeroPlayerGame well topological nornal trousers have 2 rims after you've flatten it out, 2 of the leg pipe and the top becoming the outer boundary. while the sewn trouser... also has 2 the top and the one between the legs

[@jakecarpenter1838]

A topologist dips his mug into his doughnut

[@abhishalsharma1628]

Following this process the difference between our initial and then later decision of counting holes is based upon *considering the **_Entrance_** & **_Exit_** parts of the holes*

[@miriamrosemary9110]

Yep

[@Bare_Essence]

"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]

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]

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]

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

[@highpath4776]

@@sixstringedthing I like custard ones

[@satyris410]

I love that I feel Matt is speaking directly to me in his videos. This has nothing to do with my love of donuts. legend

[@gemstonegynoid7475]

14:00 is where I understood. Difference between a torus and donut as the balloon has emptiness, so a line going through the hole of a torus would contain emptiness, and circling the hole would also contain emptiness. But a donut contains matter, and a line through the hole will circle matter. But still contain emptiness as a line around the hole is absent of matter.

[@carlosgomez2305]

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

[@mattglandon3923]

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

[@noahdoss1967]

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

[@00Skyfox]

Going into this I was thinking of the balloon in terms of manifolds and topology (thanks to Cliff over on Numberphile) and figured the answer was 0 holes for the balloon, plus that cutting off the end of the balloon is the same as trimming the outer edge off a disk. BTW, remember that sharpies are certified non-toxic; you can still eat that bagel.

[@luca6819]

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]

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]

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

[@vaclavjebavy5118]

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

[@VivekYadav-ds8oz]

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]

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

[@Almrond]

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.

[@Theraot]

Ah yes, the pointless is just a point. Like the heartless is just a heart. And the nobody is just a body. This all makes sense.

[@allgreatfictions]

What's the Euler characteristic of the jeans when you actually factor in the rest of its holes? There's also the hole you put the button through, and the holes you put your belt through.

[@mbartelsm]

There's also the holes between each thread in the fabric, though I don't know if you can call those wholes because at a small enough scale, a pair of jeans is just a collection of strands, which have no holes (except for 0-d holes).

[@katyungodly]

It depends on the scale you wanna measure by. If you shrink down enough, there are gaps between each atom ;)

[@ashtonhoward5582]

@@katyungodly but at that scale there are no holes because they're not actually one thing.

[@bIeaq]

I forgot the joy these videos bring

[@HebaruSan]

So when someone asks about the "volume of a sphere," I should say zero, because it's only the boundary surface and thus infinitesimally thin?

[@yandoryn]

To give a serious response this is why topologists drop a dimension. A surface doesn't have a volume, can't even be 0. Which would imply that it's a higher dimension sphere. An n-sphere's volume as n approaches infinity is 0, though. Its surface area is too, although the rate at which these approach zero are not the same.

[@zyaicob]

there is an area bounded by it though, so i would still call it volume

[@JacksonBockus]

Only if you want to really irritate people by being technically correct, which I think is why people become mathematicians in the first place.

[@yandoryn]

@@JacksonBockus the counter problem is that layman understanding and misuse and interpretation of math will frustrate you far more often than you get to try to one up someone with technical correctness.

[@Nerketur]

That's actually why some say "the volume bounded by a sphere"

[@Relkond]

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

[@P0nyl0ve]

I love how at least the trouser thing is also relevant in sewing!

[@Lykrast]

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

[@standupmaths]

This is my new favourite take.

[@boynamedcate]

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]

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

[@samuelthecamel]

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

[@menyazavutdavid]

@@vigilantcosmicpenguin8721 balls lol

[@Maninawig]

"The Boundaries of Nothing Pi" sounds like the title of your next book, merging topology with trigonometry.... NGL would buy that book

[@newmerek]

trousers: what about the belt loops; closing the button at the top

[@pyrobryan]

It's hard to draw on a donut. It's easier to draw on a bagel ... though, technically, it's still a donut. That had me rolling.

[@Joe_Payne]

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

[@davidwuhrer6704]

These jokes donut seem funny torus.

[@firstlt2]

Did he really say that topology is a relief?! Awesome!