The Alexander Sphere

[teckforce37]

Just like eigenvalues and eigenvectors, this is pointless...

[RyanKaufman]

Looks like one heavy kettle bell.

[osheaad]

THAT IS AN IMPOSSIBLE SHAPE, YOU CANNOT SHOW WHAT THE FINISHED PIECE LOOKS LIKE, YOU ONLY MAKE-BELIEVE THERE IS AN INFINITUM ITERATION. YOU CANNOT PROVE THE INFINITUM EXISTS, or can you?

[Aeleita1]

FRACTAL!!!

[Nulono]

What's the point of that thing?

[97kevinhuanle]

Copyright can eat an inside out square! >:(

[tigershark132]

My name's Alexander! XD

[bothmer]

There used to be sound to these videos, but we had to erase them due to copy-right problems. 

[Broax]

in the credits, what do they mean with "soundman"?

[juggalohomiez9]

sphere with arms.

[weldon0m]

what is this?.....we the people from xuioxxe must be informed of its use should it be a threat to our race !...there wii be reprisals for any indiscreation toward our people on this planet you call Earth!

[wrylie188]

AHHHH MY BRAIN!!!

[Zandrokatsu]

And it goes on and on and oooon and it goes on and on and oooon I throw my hands up in the air sometimes...

Yea this describes this frigggin awesome sphere

[awke01]

it's like a taurus xD

[dengphua517]

im jus wondering, wats the point of these shapes? wat does understanding them benefit the world in anyway?

[awke01]

@dengphua517 this ones in particular not much.. it's cool to watch hahaha... it's cool to watch how all that abstract math can be represented in a concrete simple animation

the understanding of topology (that wich is behind this) has lots of applications... to physics, to mention an important one... or economy... so if you understand the world better you can do better staff, obviously... =P

[jlk05001]

@dengphua517 exactly. how does something like this apply to our physcial molecular world and the fact that, potentially, subatomic particles are the smallest particles in existence that have been physically collected other than the space particle that can travel through matter that was detected before i was born that i can't remember right now. regardless, i just don't see practical applications for understanding something that cannot be manifested for science and not religious purposes.

[killalmostwise]

@dengphua517 Well, it looks cool and when you're applying for next years grant, you need cool looking stuff.

[kaengogyoubodi]

what does homeomorphic mean?

[bothmer]

A and B are homeomorphic if a continuous bijective map f: A->B exists whose inverse f^-1 is also continous. Less formally it means that the two objects can be deformed into each other without cutting or gluing. In the movie you can see a visualisation of the homeomorphism between the usual sphere and the alexander sphere. The arms grow out of the sphere with no cutting or gluing.

[Transamstance]

@kaengogyoubodi It like when your dad tucks and tapes his dick down and then dresses up in your sisters clothes.

[aNonInteligentGuy]

Booooring

[R4GEAG41NSTTH3M4CH1N]

surely you could just bring the two arms together. why not? explain.

[TheseEyesGod]

Okay, I like the vid. I'm sure the explanation in the description field is okay for people who know more than I do. I'd like to see it simplified a bit more, though... for us 'civilians.'

I thought I'd be resourceful, and look up 'homeomorphism.' Did not like what I found, especially Wikipedia just using other big words to define it. Give us a break, here. We'd like to understand, too.

So, if you've got time - and interest - help us understand this a bit better.

Thank you for the neat vid

[VolkColopatrion]

i take it that this loops infinately?

[Luneth274]

yes

[ltzul2vi7l]

how could it be infinite when it already has a finite size

[kiedog250]

errrrr wtf they dont meet whats all that about

[deoxy999]

@kiedog250 They're not supposed to meet.

[dougie200194]

i dont mean to sound crude or stupid but wat the hell is this!?

[WieFunktioniertMathe]

@dougie200194

It's topology, better said, a problem out of the field of topology.

You could read the description, but probably you won't get out of it as I think that you don't know much about topology, otherwise you wouldn't have asked. :)

[Greeneyeskater93]

i can do that with my fingers

[Sulfurhawk]

cool! you can grow fingers out of your fingers? what a nice ability!!! how gifted! ;-)

[psilocyberspaceman]

boring

[itisme400]

beautiful and obvious!! 5 stars!!!

[biobrainshock]

awsome idea

[atparn]

is this the most unbreakable shit in the universe?

[d3mo0]

I guess so xD

[ricklebalpickle]

the main issue is that theoretically you should both be able to get smaller and smaller, but also have a smallest distance. if you accept the concept of the planck length, then technically you would eventually be unable to tell whether or not they are touching because they would shrink to such a small size that it would be impossible to know if they even exist. there is no real life vs. theory because real life expectations are in themselves purely theoretical.

[pokemonkiller20]

randome

[zigero]

just the same like a mandel brot , another fractal structure, there will be always some space between them, even after billions of splits...

[VolkColopatrion]

only theoretically. if we go in the "real world" there will be a point where we hit a bump in that progression... say at around Planck's constant, am i right?

[XQbit]

Yup.

[TheGodfatheroriginal]

think about THAT next time your scratchin your butt!!!

lol

[turningheadfart]

i rlly dun get this at all wuts the point of this video

[superchang847]

i don't see why it's necessary it's a sphere would it not work in other circumstances?

[StrattonW94]

it's just the paradox that if one goes only halfway every time he moves, then he will come very close but never make it to the point in which he was intended to arrive.

[ookookschool]

In theory, that's right, but in reality, it eventually becomes impossible to move that half-distance.

Try shrinking a person in half every time he moves halfway. There's how your paradox REALLY works. That's also how this one works. Notice how the mini-locks keep shrinking?

[ChampDinga]

THats supposed to be a sphere?

Does it have like infinite of those or somthing?

[dragoo994]

i knewed that sooner or later someone will drop a flashbang^^

[VitalSigns1]

So can this object be used as a lock?

[Shonbi]

First, we need the technology to make this even work. Second, the mini-locks could break easily. :/

[LovelyKyoru]

No, because the thing never ends. It's not possible.

[waparker4]

Wow, that is a really cool counterexample to a seemingly intuitive idea. I believe you could be more clear in your video description. It sounds like you're saying that the inside and outside of a simple closed curve are homeomorphic to each other: don't you mean that the inside is homeomorphic to the inside of a circle, and respectively for the outsides as well?

[indigogirraffe]

this is like chaos theory, never ends right?

[helmut345]

yeah moment 22

[nupanick]

I'm not sure what I'm looking at... is it some sort of fractal?

[MestreXian]

Thats a nice locker

[chengtsu]

can someone please illuminate me, so i understand the arms will never meet, not even in infinity, my question is: is there any application of this figure, or is it just another example of never ending, repetitive pattern of fractals?

[bothmer]

It shows that a certain topological Theorem which is true in 2 dimensions is false in three dimensions. Click on the explanations for this video to get a little more detail.

[chengtsu]

aha, thank you very much, now i am understanding a little better.

[Muvlonion]

3d fractals and my brain dont mix too well

[WalterJVeith]

I wish i could edit my posts, but i now know what this looks like more than a sphere... it looks like many spark plugs coming together in unity...

[WalterJVeith]

OR this is probably what Obama calls "CHANGE" ;)

[WalterJVeith]

but yeah... with this sphere... which does not look like a sphere, what is the point of this? Bush may like it and implement it as an energy plan or health plan... oh wait, too late... maybe McCain will implement this "sphere"... ;)

[WalterJVeith]

If you always walk half of the remaining distance you'll never get where you're going. ;)

It's a theoretical imposibility... or is it a theoretical possibility? ;)

[frosty956]

learn some calculus

[anaikahas]

what's the point?

[rauldurand]

what is homoemorphic?

[AlboKid23]

so what if the arms never touch ? what does that prove?

[MimiTheTurtle]

Absolutely nothing

But it's very interesting to think about ;)

[shortyskater524]

i don see the point in this?

[waffle12996]

This is a neverending fractal.(That may sound redundant but it's not;really) Color fractals aren't infinity because eventually you will get down to only 1 color and that's it. For The Alexander Sphere the two "arms" will never touch so it can get smaller and smaller and smaller and smaller until infinity.

[Dragozine]

actually, they will touch...when an arm grows from an arm, it gets closer ad closer to the other side doesnt it?

[waffle12996]

But each time another arm grows it will get smaller and so will the space between them but they still won't touch.

[TQCKyle]

There's an important theroem from analysis, the Archimedean Principle I believe, that says given any two points in R^n (or R^3, 3-d space in this case) you're guaranteed to find a point along the "line" between them. This implies infinite divisions and thus the arms could be made to never touch.

[QuaziGNRLNose]

well, as you approach the atomic level, wont they get close enough to each other to be considered to be actually atomically bonded? atoms have space between each other and eventually you reach a level where the atoms are close enough that they are actually bonded, moreso than even touching each other, you must define "touching", cause this will get closer toghether to itself than you could ever touch your hands toghether in real life.

[llamasownyou]

This is a on a hypothetical level, so the physics of it is irrelevant... I think.

[QuaziGNRLNose]

well hypotheticallity is the only thing that makes infinitism possible in physics

not that i would absoluteley know (im only 14) but i think my assumption that the arms could eventually touch under this fractal structure in the real world is logical, and would probably hold true.

i would like to see if physics were irrelevant in fractacals, it seems they should, as fractals are kindof based off nature and real world phenomena like a logarithmic spiral.

lol i sound smart right now

[MinotauroNog]

no they won't touch, did they touch in this video? No. this pattern repeats forever in exactly the same way, so if they didn't touch in here, they won't touch.

[ijmaxwell]

They won't touch, but there is no *minimal* distance apart: for any distance greater than zero, they will eventually be closer together than that.

[danedaworld]

though in real life, they would not touch, however "theoretically" they will touch

[fender920521]

itd be the other way around.

in real life they may touch, but theoretically they will never touch

[llamasownyou]

Well, my point is, if it were in real life they would have to touch because once it got to the atomic level, the lines couldn't get any smaller.

But, because it's hypothetical, it's not made of particles, and therefore could be infinitely small. So again, they COULD touch if it were real. But the physics of subatomic particles IS irrelavent in fractals, because there aren't any.

[Cr4ckerjake]

Ah, but things get infinitely smaller than the atomic level, you have the subatomic level, the 'quark' level, the 'string' level, etc.

[sneewsp]

this fabric would be virtually impossible to make let alone try to shape since it can go through other materials, so it isnt even necessary to go into real life hypotheticals

[llamasownyou]

Hmm... say you start with one dollar. Than the next day you get 50 cents, the next day 25 cents, and so on. You'll never get 2 dollars, even in you get infinitely close, because no matter what the distance between the number you have and 2, you'll only get half that much.

This works on the same principle.

[OMGLOLOLOLOLOLOLOLOL]

Color fractals are still "infinite" fractals, limitations of computer processings should not strike you as direct output, such an offending opinion, color fractals are still fractals! there will always be a hole left to generate upon!

[saha1994]

at risk of sounding dumb, i dont get the significance of this figure

what makes it special?

i read the info, but I dont get it.

[insult0master]

every arm gets closer to each other, but they will never touch

[saha1994]

aaaa ok thanks i see.

But you waited three months to answer me!

[ijmaxwell]

If you draw a closed non-self-intersecting loop in a plane (a topological "circle"), it will have a well-defined, separated inside and outside, and any path from one to the other will have to cross this loop somewhere. This has been proved.

One would probably guess that the same thing holds for topological "spheres" in a 3D space: that they always separate the space in two. However, this turns out to be false: a sufficiently weird "sphere" (such as this one) will *not* separate the space.

[PurpleLightsaberAlex]

Wow, if you bend them apart, will it break?

[DividedAkhiloth]

It doesn't actually have to be a circle.. You could just use 2 tubes or a torus. And also, that's a one sweet fractal.

[32121452145225255658]

that would be a 3d fractal (-the circle part

[Max11551]

Does infinity exist? (Ontologically speaking.)

[DavidtheDuke]

If you think about it, it would take forever to truly know that ;)

[jms2055]

Is the Alexander Sphere a fractal? (as i could see in tag, i suppose yea)

[DaConstruct]

this totally looks like a fractal

[moonraven86]

yes after the sphere, the hooks are a fractal

[LookMaNoBrains]

does this mean the end of coffee and breakfast?

[notscooter952]

...wait, no more breakfast?

[DaDaDumDaDa]

so why arent the inside and outside homeomorphic?

[bothmer]

As far as I understand it, it is not possible to contract a loop around the handles without making it infinitely long when moving through the fractal shaped area depicted in this film. Loops inside the spere can be contracted without dificulty.

[lapk78]

finite volume, with infinite surface area? I don't understand the implications of what you've just said, but its very intriguing.

[wenaolong]

@bothmer Something fundamental about dimensionality, the same way that fractal mathematics is, having to do with the need to understand that interactions between elements are open to further interpretations. It seems to reveal that dimensionality itself is a sort of mathematical equivalent to Godel's idea that no logical system is truly closed. If I try to close it I must do so "from outside". To close these loops together, I would have to force them into a new space where it could be done.

[hbrtqazwsx93]

the ends dont meet in infinity, the ends just reach an atmic level until they cant get any smaller

[goldencako]

atomic level??? this is topology bro

[Bonzenpunk]

do the ends meet in infinity ?

[domakulic]

I don't think so.

[madhatter689]

watching you your videos makes me feel stupid, i don't understand this

[OtakuRonin]

yeah, it gives me a headache trying to understand this

[TQCKyle]

Unless you're a graduate mathematics student, you're not supposed to!

[lapk78]

I'm a greduate mathematics student currently taking a topology course. We haven't looked at anything like this, and the semester is almost finished. I wish that we did investigate things like this. Only point-set.

[MaisPraLaQuePraCa]

Do I see fractals here?

[bothmer]

Yes!

[zerotensor]

(not equal), that is.

[zerotensor]

inside = outside {in 3d}

gee whiz.........

[mattlax8]

wow thats really complex

[yuwnttnwuy]

coolers =P

[otusqueeky1]

oh my god O_O

[CrescentStudios]

Pretty good, eigh?