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Turning a sphere inside out
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veganclimber


Sep 9, 2011, 9:27 AM
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Turning a sphere inside out
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Just in case you're wondering how it is done.

http://www.youtube.com/...BVVfs4zKrgk&NR=1


saint_john


Sep 9, 2011, 10:08 AM
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Re: [veganclimber] Turning a sphere inside out [In reply to]
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I usually geek-out for stuff like that.
that was too geeky for me, though. could only get through 4 minutes.


blondgecko
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Sep 9, 2011, 8:07 PM
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Re: [saint_john] Turning a sphere inside out [In reply to]
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I laughed. I cried. Then I cried some more when it abruptly finished at 8 minutes while still not having gotten to the point.


jakedatc


Sep 9, 2011, 9:35 PM
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Re: [blondgecko] Turning a sphere inside out [In reply to]
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blondgecko wrote:
I laughed. I cried. Then I cried some more when it abruptly finished at 8 minutes while still not having gotten to the point.

yea... part 2! brain hurts quite a bit actually..


veganclimber


Sep 9, 2011, 9:50 PM
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You have to watch part 2 for that.

http://www.youtube.com/...&feature=related


dan2see


Sep 9, 2011, 11:29 PM
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Re: [veganclimber] Turning a sphere inside out [In reply to]
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I endured only half-way through the second video. I don't believe the inversion will work, and I don't believe the waves add anything. I'd allow that 3 dimensions might offer another degree of freedom. But still I could not understand what was the impact of all the different ways of counting the curve number.

But mostly, I don't believe the procedure will work, so I don't have to watch the entire video.

On the other hand, I had fun browsing the chemistry demonstrations.


veganclimber


Sep 10, 2011, 12:38 AM
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Re: [dan2see] Turning a sphere inside out [In reply to]
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You think the video was bad? Try making your way through the proof.

http://math.brown.edu/~thobel/smale.pdf


dan2see


Sep 10, 2011, 6:02 AM
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Re: [veganclimber] Turning a sphere inside out [In reply to]
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Ain't math grand?

No I did not pay the $24.00 to see the text, so I did not go any further.

Maybe the idea of inverting everting the sphere is simple, and maybe the article actually describes the procedure. But the abstract is a standard example of how "Math is a language". That means two things:
1. The symbology and syntax in the discussion is not obvious. You must read that stuff with the same structural ideas that the author intended.
2. You can learn the language by reading and practice, in the field where it is used. The cost of acquiring this language is considerable. You should expect to study in the math classes of some university for at least a year, possibly more.

But it's too late for me!

Sometime around 1965, Scientific American Magazine published an article on how to invert the sphere. The description was straightforward, and the diagrams were clear and easy to see. I was able to follow every step of the procedure, but I was troubled by the feeling that I was missing something. It felt a little like some math problems where you accidently divide something by zero, and fail to notice.

Well the following month, in the "Letters to the Editor", somebody wrote to congratulate the author on the excellent presentation in the "April" edition, along with DaVinci's helicopter and Thomas Crapper's flush toilet.

So you see, my mind is already made up. It's too late to present any kind of proof to me!


(This post was edited by dan2see on Sep 10, 2011, 8:47 AM)


dan2see


Sep 10, 2011, 9:23 AM
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Re: [veganclimber] Turning a sphere inside out [In reply to]
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Here's another description of the problem, and what some solutions look like:

"The Optiverse" and Other Sphere Eversions by John M. Sullivan, 1999

The text and pictures show more clearly what is happening.

---o---o---

I understand why you must not crease or tear a surface, and why it's OK for a surface to intersect itself.

But I am bothered by the indirect approach to the theory. How does embedding a surface give it extra properties that it didn't already have?

Also, in the discussion I've linked above, he proposes that a surface has an inner side and an outer side, and that these two things can be somehow have their own identities.


(This post was edited by dan2see on Sep 10, 2011, 9:24 AM)


veganclimber


Sep 10, 2011, 11:54 AM
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Re: [dan2see] Turning a sphere inside out [In reply to]
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dan2see wrote:
Ain't math grand?

No I did not pay the $24.00 to see the text, so I did not go any further.

That's strange. It didn't ask me for money. If you really want to see it, the article is:

Smale, Stephen (1958), "A classification of immersions of the two-sphere", Transactions of the American Mathematical Society 90: 281290, ISSN 0002-9947, MR0104227

I'm sure you can find a free version somewhere.


dan2see


Sep 10, 2011, 12:48 PM
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Re: [veganclimber] Turning a sphere inside out [In reply to]
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veganclimber wrote:
dan2see wrote:
Ain't math grand?

No I did not pay the $24.00 to see the text, so I did not go any further.

That's strange. It didn't ask me for money. If you really want to see it, the article is:

Smale, Stephen (1958), "A classification of immersions of the two-sphere", Transactions of the American Mathematical Society 90: 281290, ISSN 0002-9947, MR0104227

I'm sure you can find a free version somewhere.

Oops! I mis-interpreted the title page, and followed a link where I did not need to.

Well! I was able to follow the odd line here and there in the discussion. But in general, it felt like bushwhacking. Maybe I should admit that the math is 'way over my head? Or eclectic esoteric. But still, it's hard to determine where the discussion came from, and where it leads you.


(This post was edited by dan2see on Sep 10, 2011, 6:34 PM)


veganclimber


Sep 10, 2011, 2:57 PM
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Re: [dan2see] Turning a sphere inside out [In reply to]
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dan2see wrote:
veganclimber wrote:
dan2see wrote:
Ain't math grand?

No I did not pay the $24.00 to see the text, so I did not go any further.

That's strange. It didn't ask me for money. If you really want to see it, the article is:

Smale, Stephen (1958), "A classification of immersions of the two-sphere", Transactions of the American Mathematical Society 90: 281290, ISSN 0002-9947, MR0104227

I'm sure you can find a free version somewhere.

Oops! I mis-interpreted the title page, and followed a link where I did not need to.

Well! I was able to follow the odd line here and there in the discussion. But in general, it felt like bushwhacking. Maybe I should admit that the math is 'way over my head? Or eclectic. But still, it's hard to determine where the discussion came from, and where it leads you.

Yea, I just linked the article to put the video in perspective. A 20 minute video that's sort of hard to follow, compared to a proof that you would need a PhD to follow.


petsfed


Sep 12, 2011, 12:44 PM
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Re: [veganclimber] Turning a sphere inside out [In reply to]
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I'm clearly too high or not high enough to fully understand that video. Considering I'm not high, I can probably rule out the former, but honestly, I'm not sure.


squierbypetzl
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Sep 12, 2011, 4:36 PM
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Re: [veganclimber] Turning a sphere inside out [In reply to]
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What I don't get (in addition to pretty much all of it) is the "rules": you get to use a material that can pass through itself, but not be creased. Seems pretty arbitrary to me.


veganclimber


Sep 12, 2011, 9:17 PM
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Re: [squierbypetzl] Turning a sphere inside out [In reply to]
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squierbypetzl wrote:
What I don't get (in addition to pretty much all of it) is the "rules": you get to use a material that can pass through itself, but not be creased. Seems pretty arbitrary to me.

Surfaces don't have to represent actual materials. Even imaginary surfaces can be very useful. I don't see any applications coming from this sphere thing, but who knows.

The "no creasing" part makes sense too. Here is a picture of a nice smooth surface.



Got it from this article:

http://www.cs.berkeley.edu/...84/TEXT/diffgeom.pdf

You can define a tangent plane and normal (perpendicular) direction. You can't do that if there is a crease in the surface.
Attachments: surface_1.jpg (23.5 KB)


petsfed


Sep 12, 2011, 9:24 PM
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Re: [squierbypetzl] Turning a sphere inside out [In reply to]
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squierbypetzl wrote:
What I don't get (in addition to pretty much all of it) is the "rules": you get to use a material that can pass through itself, but not be creased. Seems pretty arbitrary to me.

Basically, the rule is that the gradient of the surface be well defined, and a crease is a discontinuity in the gradient, so it isn't allowed.


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