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is that provern mathematically and what is the purpose of that???

??

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- #1

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is that provern mathematically and what is the purpose of that???

??

- #2

HallsofIvy

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Here's the full video:

http://video.google.com/videoplay?docid=-6626464599825291409 [Broken]

http://video.google.com/videoplay?docid=-6626464599825291409 [Broken]

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Gib Z

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Sorry for the novice-ness, but what realm of mathematics is that? It is topology?

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mathwonk

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horrors, does pure math have a point?

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Before taking an advanced mathematical logic course, I would have said that pure math should be studied for its own sake. Now I'm not so sure.horrors, does pure math have a point?

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http://www.youtube.com/watch?v=dfDIVJXkfCU&feature=related

- #8

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MY QUESTION IS... ok...

they figure out how to turn that sphere inside out...

WHAT IS THE PRACTICAL USE OF THIS...or there isn't any and matematicians are just doing their research for the sake of nothing...

Does that help other sciences to create some assumptions or models for something that can be practical or bring improvements to something not so developed...

i don't get it....

and furthermore...they set conditions to whatever they want to do...

what if that matter can be bended SHARPLY or be creased - and the surface can't go thru itself... what would then happen...... idk..

they prove something that it is impossible in practice and even it is impossible in its abstract version if they do not set the needed conditions and rules in this abstract world :)... why do they do that then?

- #9

Gib Z

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Yes. Modern topology was founded by Poincare and Brouwer in their study of the behavior of solutions of ordinary differential equations. Theorems of topology have unbelievably powerful applications in many areas of pure and applied mathematics. Ie., the Brouwer fixed point theorem, the Poincare index theorem, the generalized Jordan curve theorem/Mazur's theorem, the Hopf fibration, knot theory, the study of cohomology and the discovery of category theory. As in many areas of pure mathematics, the results far outweigh the initial seed of studying ordinary differential equations.Sorry for the novice-ness, but what realm of mathematics is that? It is topology?

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mathwonk

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obviously, this theorem is interesting because it reveals a surprizing aspect of geometry, one that contradicts ordinary intuition. the point is not that one can imagine a sphere turning inside out, but rather that it can be done without ever introducing any wrinkle in the sphere as it passes through itself.

the intuitive operation is to push inward on the sphere at each pole, and continue pushing the sphere through itself and inside out. but this leaves a circular wrinkle at the last stage at the equator. amazingly this can be avoided.

any fact about the geometry of manifolds may or may not have applications in engineering and physics or cosmology.

topologically it was a question of the connectedness of a certain set of deformations of a smooth manifold, and was proved by Smale.

It is also an interesting story of mathematical imagination and communication, since the original expository article in scientific american reports that the chain of explanation from the man who envisaged the transformations to the one who drew the pictures passed through one link of explanation by a blind person, I believe it was bernard morin.

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A concept in pure maths can have a use that is not apparent until several decades after it's been discovered.horrors, does pure math have a point?

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Everything is based on math but math is based and depends purely on one's imagination and intellectual capacity.

The world is so weird... I think I am going crazy when I am trying to understand it or think about the meaning of life ...etc...

Maybe we will never find out why or how the world was created.

Maybe our existence is just a state of our mind.

Maybe we can't find the answers we are looking for because we are a part of them. :P

it's getting late :P

ttyl later people

- #15

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1. Some topics developed by pure math have later been applied to the sciences.

2. Not everything has to be useful.

Of these I would say that (2) is more honest. I think a study should be under taken with respect to (1), since as pure math has flourished in recent times I think (1) is less true than in the past. Never mind anecdotal reports, we need to count how much of the total mathematical content generated in the 19th century is in use today.

As for (2), I often use this line for students and I am tempted to agree with it in general, especially when presented with something like the video in this thread. But getting students to study math is one thing, and paying professionals to dedicate their efforts to it is another. Personally, I don't think (2) is sufficient justification for a lifetime career in pure mathematics. Look at all the scientific efforts that could help the world e.g. better solar panels, recycling methods, fusion power, agriculture, birth control, communications networking, medicine, transportation, etc.

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As far as I know, string theory is based on topology and if it really is the next big breakthrough, then procedures such as inverting this sphere could have real practical applications. In any case, I think this particular method might even be applicable in fluid dynamics or even in electromagnetics. For example, the earths magnetic field is something akin to a sphere, and perhaps this method of inverting the sphere could describe some phenomenon where the magnetic field varies as such. The practical applications of any theoretical concept are only limited by the imagination of the practitioner. Isnt that true?

- #17

morphism

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Does *anything* have a point?

- #18

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the cartesian plane has points?Doesanythinghave a point?

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As for why people care about this one example specifically: eh, it's just something that mathematicians think is cool, unexpected, etc.

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Euclidean geometry has points. Are you calling Euclid aDoesanythinghave a point?

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Points are undefined elements in Euclidean geometry. :tongue: Similar to the direction of this thread.Euclidean geometry has points. Are you calling Euclid aliar?

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In the spirit of an engineer and physicist, the mathematics has to be created before we can apply it. It might now currently have an application but perhaps in the future it could.

MY QUESTION IS... ok...

they figure out how to turn that sphere inside out...

WHAT IS THE PRACTICAL USE OF THIS...or there isn't any and matematicians are just doing their research for the sake of nothing...

Does that help other sciences to create some assumptions or models for something that can be practical or bring improvements to something not so developed...

i don't get it....

and furthermore...they set conditions to whatever they want to do...

what if that matter can be bended SHARPLY or be creased - and the surface can't go thru itself... what would then happen...... idk..

they prove something that it is impossible in practice and even it is impossible in its abstract version if they do not set the needed conditions and rules in this abstract world :)... why do they do that then?

I have a question: How does a sphere pass through itself, if it is supposed to be a solid object?

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- #23

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Simple: the sphere we are talking about is not solidI have a question: How does a sphere pass through itself,if it is supposed to be a solid object?

- #24

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are you serious dude? did you seriously try to steal my joke?Euclidean geometry has points. Are you calling Euclid aliar?

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I bring the human element into your joke. You can thank me when you receive your fields medal.

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