/sci/ - Science & Math

>>9321541
Can you not have this thread again? You need to define hole rigorously before we can tell you.

>>9321546
>sci doesn't know topology

>>9321541
It's a three dimensional hole. The space occupies a volume.

>>9321541
It's two holes.

Is a hole in the ground only half a hole?

>>9321556
shut up, you idiot

>>9321559
not an argument

>>9321565
It's a three dimensional hole. The space occupies a volume. You're a moron and I bet your face is really ugly

>>9321568
So a hole in the ground is only half a hole then since its merely a straw with a closed bottom?

>>9321568
>The space occupies a volume
that would make it one hole faggot

>>9321568
So if I seal the bottom of a straw would that make it half a hole?

>>9321556
No, a hole in the ground is not a hole because if you simply pulled the ground from all directions around the hole it would flatten.
Likewise, if I have a cup, made of something malleable, I could flatten the edges into a flat disc with no holes by pushing the sides down.

A straw has one home, because no movement without otherwise breaking the object can make it into something with no holes or with two holes. Were I to flatten the edges like I did with the cup, I would have something like a flat donut.

>>9321582
dont listen to that faggot he doesnt know shit and sucks dick

>>9321578
THATS MY ENTIRE FUCKING POINT I HATE YOU WHAT THE FUCK I SAID IT WAS ONLY ONE HOLE FUCK YOU

>>9321582
NO YOU WOULD HAVE A CONTAINER. HOLY SHIT YOU'RE SO STUPID

>>9321582
What are you talking about, you can't have half an A-Press!

>>9321596
haha look someone triggered the autist haha suck my dick bitch

topologically speaking, how many holes does a woman have?

>>9321590
>No, a hole in the ground is not a hole
Ok friend. Then why is it called a hole?

Saw this on facebook. The correct answer isn't even among the propositions.

>>9321598
SUCK MY FUCKING SHLONG. ILL CHOKE YOU OUT WITH YOUR OWN BUTTHOLE YOU BIG DUMB BITCH

>>9321596
>implying containers aren't half holes

>>9321600
Humans are topological donuts, because the 'inside' of your digestive track is in fact on the outside of your body.

>>9321582
you can't have half of a hole you moron. if you cover half of the hole in a bucket full of water its still a hole. theres no such thing as half of a hole

>>9321600
That would be none.

>>9321604
There are 6 holes
1 the collar
2,3 the hand holes
4,5 the weird holes on the center
6 the bottom hole close to your belt

>>9321608
so when you eat food, the food never actually goes inside of you???

>>9321607
lol, I honestly don't know how to respond to that

eat dick for breakfast

>>9321606
try me bitch boy i bet you'd like to see my butthole wouldn't you huh fucking faggot bitch make me cum you whore

>>9321615
Oh fuck yeah, oh shit. Goddamn, oh fuck yeah. That's fucking hot, holy shit. Oh fuck, oh shit. Yes baby, holy FUCK

>>9321612
dumbass, the holes in the middle go through the fabric in the back and front of the shirt, and the neck and waist hole are topologically the same hole.
that means there are seven holes

>>9321619
>>9321615

What the fuck guys

>>9321600
One? The vaggy is closed so that leaves the mouth and shitter making one full hole.
Wait no you have the nostrils connected
So three
And the ears make an independent hole right? Or do the ears stop after a while
Can a science man tell me if the ear holes end or have an opposite hole
Eyes?

Do pores count too fuck

Well we're all made of cells right? So maybe no holes as we're just a collection of no holed cells

>>9321541
this thread is fucking embarrassing you should all be ashamed

the obvious answer is that there is no hole, holes don't exist

>>9321621
True I forgot that, but why are the neck and waist the same hole?

>>9321601
I don't know
Why do people think we only use 10% of our brains?
Why do people gamble when it's mathematically rigged to make you lose over time?

Probably because they're all fucking brainlets like you

Wow such scientific/mathmatical answers. Not impressed.

someone please define a hole and give me the correct answer.

>>9321626
Uh oh. We have a conceptual child here folks. YOUR BRAIN IS SO DUMB

>>9321623
>do the ears join in the middle of the head
lmao what the fuck

no, the ears and eyes are just elaborate indentations, like the vagoo and urinary tract

I hadn't actually considered that the nostrils are indeed connected, so i suppose that does make 2 holes.

anything inside the body wouldn't count since we're concerned with just surfaces

>>9321626
if the shirt was entirely elastic, and you could change it however you pleased, you could re-arrange the material such that the neck and waist hole were joined. you couldn't do that with any other hole though

>>9321627
That's not an argument. It didn't convinced me. It just insulted me. Being mad online is not an argument. I consider my point: made.

>>9321541
https://www.merriam-webster.com/dictionary/hole

>>9321590
>a hole in the ground is not a hole

>Take a coke can
>It's closed, no holes
>Punch a hole at the top
>One hole now
>Punch a hole at the bottom
>Still one hole

This is what one-holers actually believe

>>9321636
We can't all be as smart as you anon. Now go do your linear algebra homework, you have an exam soon, don't you?

>>9321637
Thanks! I was worried the weird holes in the middle were making the process you're describing impossible but I see now that I was wrong to worry.

Fuck im autistic

>>9321642
Merriam Webster isn't a scientific dictionary faggot
It gives explanations for brainlets

>>9321619
fucking faggot bitch i knew it haha EXPOSED motherfucker what NOW

>>9321613
Nothing ever goes inside. We are just holes upon holes upon holes. Our cells are just holes that surround the nutrients. Food just passes through our digestive system. One main hole, and all these branching holes. Macroscopic to microscopic holes upon holes.
HOLE SYSTEMS. JUST HOLES ITS ALL HOLES.
THEY ENTER HOLES AND THE LEAVE THROUGH HOLES IN SPACE AND ITS ALL JUST HOLES HOLY FUCK IT ALL MAKES SENSE HOLY FUCK I CAN SEE EVERYTHING

>>9321615
>faggot
why the homophobia

>>9321650
Punch me in the head and throw me in the mud. Call me a boy tonight!

Shave my head in front of my dad, call me a boy tonight!

>>9321651
Holey shit

>>9321643
Mathematically speaking, it isn't.
Of course in English it is a hole, by all means. But an English "hole" isn't a mathematical "hole".

>>9321646
it's a sphere with 8 holes in it. You can take any hole, pull on it, and you get a flat piece of fabric with 7 holes

>>9321660
you're wrong nigger, that's not a flat two-dimensional surface with sharp edges, its a three-dimensional object with depth.

isn't every circle a hole? depending on how you slice this bitch up there's an infinity of holes

>>9321663
Why the racism?

>>9321666
A hole implies volume. A circle is 2 dimensional and without depth.

>>9321666
satanic trips means this is now canonical topology everybody

>>9321675
no it doesn't, shut the fuck up. youre not the authority here. suck my dick

youre the person who is dumb

>>9321645
IF YOU PUNCH A HOLE AT THE TOP IT STILL HAS NO HOLES YOU STUPID FUCK ITS A CONTAINER

>>9321655
what is this faggotry chant make it stop

>>9321651
Are you on LSD?

>>9321687
Call my mom and tell her I'm dead! CALL ME A BOY TONIGHT

>>9321671
>a hole implies volume
i didn't know that

The "number of holes" is defined as the genus [math]g = \operatorname{dim}H_2(M)[/math], namely the dimension (or the number of generators) of the second homology group. For a space [math]X[/math] that is homeomorphic to a cylinder [math]S^1\times I[/math] such as a straw, it can be homological-invariantly retracted to [math]S^1[/math]. Using [math]U \cong V \cong \mathbb{R}[/math] as subsets of [math]S^1[/math] without the north/south poles, respectively, we can compute the homology group with the Meyer-Vietoris sequence
[eqn]
\dots \rightarrow H_2(U\cap V) \rightarrow H_2(U)\oplus H_2(V) \rightarrow H_2(X) \rightarrow H_1(U\cap V) \rightarrow \dots
[/eqn]
which is equivalent to
[eqn]
0 \rightarrow H_2(X) \rightarrow 0
[/eqn]
which by exactness of the sequence means that [math]H_2(X)[/math] is [math]0[/math], so there are no holes in the straw.

trolling topologists is so easy
you just have to say
>cut it
and they lose their shit
you guys are such fucking nerds lmao

>>9321713
>what is surgery theory
Fucking idiot.

>>9321712
Topology is gay if there's no holes in a straw

>>9321712
>for a space X that is homeomorphic to a cylinder
and just HOW did you reach this conclusion

>>9321719
settle down
>>9321712
i'm too stupid to know if this is true

>>9321722
Just uncrumple the folds lol.

so can we define hole to mean the number of planes you need to give the object an inside?

>>9321729
a hollow cylinder is NOT homeomorphic to a cylinder you cretin

>>9321733
a hollow cylinder is a cylinder

>>9321723
It's not. You can't morph a straw into a cylinder. It's fucking wrong and might I just ask where the fuck did that person get the nerve? I'm a fucking genius.

>>9321733
>he's fucking retarded
do you seriously not know how to visualize [math]S^1\times I[/math]?

>>9321737
>You can't morph a straw into a cylinder
bullshit

I fucked up.
The genus is actually defined as the dimension of the FIRST homology group [math]H_1(X)[/math] and since [math]H_1(X) \cong H_1(S^1) = \mathbb{Z}[/math] there's actually 1 hole in the straw.
>tfw I'm a fucking idiot

>>9321745
>there's actually 1 hole in the straw.
i thought you were trolling. it worked out that way anyway lol.

>>9321699
i know what ill call you tonight ill call you A BITCH

>>9321745
GET DUNKED ON. THERE IS NO ROOM FOR MODESTY OR HUMBLENESS AMONG GENIUSES

>>9321766
did your mommy call you her little genius? because it's nauseating for a legitimate genius to hear you talk about yourself that way

>>9321768
How dare you. Damn. That was very stone cold Steve Austin of you.

>>9321766
I was wrong not for the reason you thought though. You're still a massive retard lol.

>>9321712
The number of holes would rather be the dimension of [math]H_1[/math].

Your sequence becomes [math]0 \to H_1(X) \to H_0(U \cap V) = \mathbb{Z}^2[/math]

>>9321774
See >>9321745.

>>9321772
You couldn't conceptualize your way out of a paper bag. You literally failed to do that. I know exactly what you did wrong, you little shit.

>>9321778
there's a discrepancy between your answers

>>9321779
Whatever you say little boy.
>>9321780
There isn't. The poster >>9321774 is saying that the sequence [math]0 \rightarrow H_1(X)\rightarrow \mathbb{Z}^2[/math] is exact, and I'm saying that this implies [math]H_1(X)=
\mathbb{Z}[/math]. You can also see this from the fact that for path-connected spaces [math]H_k(X)[/math] is the Abelianization of [math]\pi_k(X)[/math], and since [math]\pi_1(S^1) = \mathbb{Z}[/math] and it is itself Abelian, [math]H_1(S^1) = \mathbb{Z}[/math].

>>9321792
forgive me I'm blind and retarded

>>9321792
In English, please

>>9321575
a hole in the ground is topologically equivalent to no hole at all

>>9321792
0->A->Z^2 exact doesn't imply that. stop using so much notation to say dumb things please

the fundamental group reasoning is the only reasonable thing to say and should have been the answer from the get go

>>9321795
It's ok anon I forgive you.
>>9321802
Except that it does in the context of singular homology. The degree-reducing boundary map from the Mayer-Vietoris maps [math]\alpha\in\mathbb{Z}[/math] to [math](\alpha,\alpha)\in\mathbb{Z}^2[/math].

>>9321810
you're just throwing tons of unnecessary, hand wavy shit around. the actual reason is you didn't put the next term, H_0 which is Z. it's 0->H_1(X)->Z^2->Z and from there it's clear

>>9321817
>unnecesary
Wrong.

>>9321821
whatever mate, just do all of us a favor and stop importing homology notation from wikipedia or wherever to argue dumb shit on 4chan

it's unbelievable that someone who claims to know homology can think that the number of holes is encoded in H_2. it's not an honest mistake and makes it really hard to believe you know any of this.

>>9321827
Would someone like that admit to having made that mistake? Aren't you the one who jumped the gun and responded without even reading 2 posts down where I've fixed the mistake? Just how recently did you learn this sweetie?

Okay, so for the people who can automatically tell that a straw has one hole, who exactly are people doing the mathematical proofs trying to impress?

So far, I've seen one person actually slip up and say there were zero holes because they did their proof wrong. The defended that proof by asking someone else to conceptualize it.

Are these proof-tards betraying their actual conceptual intelligence or just plain sloppy while trying to impress strangers online?

>>9321835
I'll repeat myself since you can't read. I really, really don't believe it's an honest mistake. I might be wrong, but I don't think so. So, just cut the shit.

>>9321836
I think they're trying to impress strangers online by trying to copy paste shit they don't understand well

>>9321845
>I really, really don't believe it's an honest mistake.
You're wrong again, but believe whatever you want to believe, undergrad.

>>9321851
ohhhhhhHHHHHHHOOOOOOHHHHHHHHHHHHHHHHHHHHHHHHHHH FLGURHGURHARGAREGGFGHAHF UNDERGRAD HAHAHAH BURNEDDDDDDDDDD OH SHIT

>>9321851
you're someone who uses shit like
>Wrong.
>[...] sweetie.
goes around calling people undergrads, and throws heaps of useless notation and name dropping to be authoritatively wrong about obvious things

I don't know what to tell you. You're a pretty disgusting poster honestly

>>9321857
>ohhhhhhHHHHHHHOOOOOOHHHHHHHHHHHHHHHHHHHHHHHHHHH FLGURHGURHARGAREGGFGHAHF UNDERGRAD HAHAHAH BURNEDDDDDDDDDD OH SHIT

two holes cmon dont be a prude ill keep it in the front but if i shove a thumb or a sharpie or a farm vegetable up there while im goin at it you know ull love it

>>9321792
This is ridiculously incorrect I cannot believe you're even trying to fool others. Wait till you get to the doctorate level like me you pleb.

>>9321860
>be authoritatively wrong
Which was fixed and the mistake admitted. Someone who's just trying to impress internet strangers wouldn't do this now would they, dear? Try not to be this autistic next time.

>>9321867
you admit your mistake by throwing even more heaps of notation and more wrong reasons, to try to arrive at what everyone noticed was the right answer and save face. then you call people names, and use inflammatory reddit tier shit like "sweetie", "Wrong.", calling people undergrads, and "dear" when called out.

what are you even doing? your posts are terrible in general.

>>9321867
You're trying so hard to save face, but the fact remains that you before you corrected your mistake you defended the conceptual implications of your "no holes" bullshit to a person who clearly understood the concept on a deeper level than you ever did.

>>9321874
>you admit your mistake by throwing even more heaps of notation
That's wrong though. In the post where I admitted my mistake I straight up just said the answer. There wasn't any unnecessary notation at all. Try learning how to read sometime.
>>9321876
>You're trying so hard to save face
Then I would've just left the thread. Jesus Christ how detached from reality are you?

>>9321881
This is the definition of cringe.

>>9321886
>hurr cringe
Good post.

>>9321881
it's like you're unable to post without being terrible for some reason. and it just keeps coming.

>>9321881
Look I don't know the names of every fallacy, but I do know that you're acting faux indignant because you don't fit your own hypothetical model of what a person I'm responding to acts like.

>>9321902
What? I'm not a psych major dude you'll have to save the armchair diagnoses for yourself.

>>9321904
You can't tell me what you would have done if I were correct that you were trying to save face and have that be your argument without coming across as a complete dipshit.

what are these people even arguing about anymore

>>9321914
I'm making a point because I think that's the anime math poster usually being a general asshole and it's about time someone called him out

>>9321920
i can't tell who's calling out who when you're both being equally incomprehensible. Just say your piece and move on.

Speaking of moving on, instead of calling each other out lets argue about the topology of other objects, like this Dr. Seuss thing

>>9321920
If that person is avatar fagging, then surely they are very much invested in keeping up appearances.

>>9321541
It is topologically equivalent to a torus, anything further is nomenclature

>>9321989
So many idiots on this board, this is [math]I\times S^1[/math], homotopy equivalent to a circle, the first homology is the abelianization of the fundamental group which is [math]\mathbb{Z}[/math], there is exactly one hole

>>9321604
it's not 6?

>>9321604
8, the middle holes must penetrate through both sides of the shirt to see the background

>>9321608
what about the nose,
the Eustachian tube in your ear,
your dingus/vagene,
your every pore,

stupid human

>>9322257
it's actually 7. You don't count holes like the holes on a sphere, you have to morph 1 hole out to make a flat sheet

>>9322209
>he thinks straws have no thickness
Retard.

>>9322239
>>9322257
it's at least seven, there could just be one large hole behind the two holes in the front

>>9321596
>Getting this mad over straw theory

lol

>the absolute state of /sci/

>>9322493
>he thinks the annulus isn't homotopy equivalent to the circle
Weeeeeew.

>>9321601
Because holes were named like this before topology

>>9321601
My fucking sides. I love you anon, you literally made my day just there! I called my girlfriend to tell her about what you wrote. I'm in tears, why is this so funny!

>>9321604
pic related

>>9321621
>topologically
off with your autism, a shirt is not a mathematical object and a question from some normie FB page won't expect you to represent it as one.

>>9321604
the bottom and top aren't holes because they are sewn shut

>>9321600
>>9321608
>>9321613
>>9322489
>>9321613

I am manifold, therefore I am.

>>9321601
Because back when they made the axioms of English, they thought that every 'hole' in the ground had an exit in China, thus making it a hole. You can still see this in old cartoons. Now we of course know a 'hole' in the ground is actually an indentation.

>>9321614
>eat dick for breakfast
Good rebuttal bud.

>>9321604
5 is the only answer that makes sense. We could speculate endlessly about how many holes are on its back. It makes sense to say they drew the holes black so its easier to see them, so we just ignore the back side.

>>9321621
Wrong, 7 is not among the answers. The only way to solve this is to assume that there is just 1 bigger hole on the back of the shirt, and it's the same you see through both of the front holes. Which makes, topologically-speaking, 6 holes.

t. enormous IQ

>>9323167

> t. Sweatboy

>>9321645
>Punch a hole at the top
>One hole now
Niggers out.

>retard answer: 2 holes
>intelligent answer: 1 hole
>correct answer: 0 holes

>>9323540
Why is the intelligent answer not the correct one?

>>9323569
There are 0 holes. The straw is just an enclosed space.

>>9321645
Does a cup cup have one hole? A bowl? A plate? A flat disk with one small speck of dust on it?

>>9321712
The straw is a torus (because it has thickness and therefor isn't a cylinder)

>>9321541
its both 1 hole and 2 thanks to quantum superposition objects can have multiple attributes

>>9321608
>humans are topological donuts
This is fantastic stuff

No holes because it's all connected by quantum foam or whatever

>>9324798
that would be energy fields (everything is a amagnet)

>>9323167
>5 is the only answer that makes sense
>head hole
>torso hole
>left arm hole
>right arm hole
>slob hole 1
>slob hole 2

>>9321604
0. There are zero holes in the shirt provided it is made of fabric. The shirt can be topologically reduced to a set of strings

>>9321541
>be waiter at diner
>regular day, a bit warmer than usual
>serve orange juice and pancakes to some old guy
>he looks extremely bored
>stare at him from a distance for a while, think I've seen him before
>It's Ed Witten
>he notices
>"Hey waiter!"
>come up, say I'm sorry
>"No need, I just really need someone to talk to"
>asks me for my name, tell him
>he picks up the straw from his drink
>"Tell me anon, how many holes does this straw have?"
>it's open on both ends, so two
>"Oh anon, everyone knows a straw is homeomorphic to their anus"
>but my anus only has one hole
>"That's a trivial problem"
>he signals the other staff
>one of them bars the doors, the rest hold me down
>Ed takes a plastic knife from his plate
>literally tears me a second asshole
>unimaginable agony, scream at the top of my lungs the whole time
>i lay there, too weak to move any of my limbs
>pic related is the last image i see before i bleed out

>>9325600
>he didn't know that the body is a tube and the corresponding hole to the anus is the mouth
i guess phenotype wasn't all it's cracked up to be

>>9321623

>And the ears make an independent hole right? Or do the ears stop after a while

Medfag here. Depends on whether you consider eardrum to be a topological barrier or not. If not then ear continues on into pharynx and is a genuine topological hole (one for each ear).

https://en.wikipedia.org/wiki/Eustachian_tube

>>9321541
it's a single large(long?) hole

>>9322489
>nose
tracks down to the pharynx, where it splits to the trachea/lungs (topologically closed and thus irrelevant) and to the mouth, thus creating two holes, one for each nostril.
>Eustachian tube
Tracks from the nasopharynx to the middle ear, which in the absence of any grommets or perforations in the eardrum is a closed cavity: no holes.
>Dingus/vagene
Male urethra tracks to dead ends in all directions. Vagene tracks to the uterus, the Fallopian tubes and thus to the infraperitoneal space/retroperitoneal space. Despite the continuous space being extensive, their is no direct connection to any outside surface, in the absence of any fistulas or other anatomical abnormalities.

Thus, people are 3 holes and more akin to pretzels than to donuts, as far as I can see.

>>9321541
if a bendy straw only had one hole, could you imagine what it looked like?

exactly.

it is one tube with two holes. a hole does not stretch, in its theoretical design.

>>9321683
>PUNCH A HOLE AT THE TOP IT STILL HAS NO HOLES
kek

>>9321541
It’s a fucking torus.

>>9323167
You idiot.

>>9327433
it's an annulus

>>9321541
>does not now how many holes in torus

>>9321541
It is one go-through hole. A hole in the ground is a simple hole that also has a bottom. If you would go with a more serious definition, a hole in the ground is a socket because it has a bottom.

>>9321637
nose is connected to your mouth and therefore the rest of your digestive system

>>9321541
It's a torus

>>9321590
> a hole in the ground is not a hole

I think that alot of people who dont get this are not at all familiar with topology. So it’s the strict topological definition that matters here since we are supposed to use mathematical methods.

>>9321575
if the straw is pinched anywhere then it only has two dents

>>9326829
What about tear ducts?

>>9326829
Behold, a man!

>>9321541
It’s two and anyone who thinks I am wrong has some sort of retardation.
Plz debate me. Pro tip you don’t want to.

>>9330116
Actually man is more akin to a pretzel with broad, flat nails.

As many holes as there are real numbers

>>9321764
I fucking love it when /sci/ pretends to be high school students who throw ridiculous insults out like its nobodies buisness.

>>9321637
You could do that with the sleeves or any other pair of holes