This is a great visualization that just keeps getting better and better all the way through. The way the demonstration progressively expands your ability to perceive what is happening is fascinating.
Posted by: Carlos | Nov 7, 2007 10:34:05 AM
Thanks for that. Hypnotic and enlightening, it's enhanced my understanding of stuff in general, too.
Posted by: Doug l | Nov 7, 2007 11:10:34 AM
My question is why, if one surface can freely pass through another, you can't pull out a kink? But then this is way over my head -- can you imagine how many brain cells it takes to imagine a problem like this?
Posted by: Luke Lea | Nov 8, 2007 10:11:51 PM
At the risk of sounding greedy; I'd love to see the "wireframe" (the stage/view of a 3D animation showing only the vertices of the object-sans the skin)of the inside to outside transformation. I'm not sure if it would really clarify anything but it would be a fascinating sequence on its own. Thanks Abbas; this use of 3D animation does something truly expansive for one's imagination. When was the last time I could say that about a piece of CGI?
Posted by: Pete Chapman | Nov 8, 2007 10:49:22 PM
Luke, I think pulling out the kinks would equal to breaking the topology. If you allow that, then you can convert any curve (or surface) to any other curve (or surface), and the game is not interesting.
It is the rule of smooth transitions, no tearing and no kinks, that define topology, or classes of surfaces or curves that are not all part of the same mess, and are therefore a worthwhile subject for mathematicians.
Posted by: Janne Sinkkonen | Nov 24, 2007 2:49:06 AM
""My question is why, if one surface can freely pass through another, you can't pull out a kink?""
Well, the material is elastic too so a bend of unlimited magnitude like a kink would put an infinite amounth of tensure on the belt detroying it.
Posted by: Johan | Dec 22, 2007 4:40:56 AM
I suspect that in the actual math behind it, allowing creases means the transformation function isn't infinitely differentiable, so it is a less powerful result.
Posted by: Duncan | Dec 23, 2007 4:04:10 AM
This has got to be one of the stupidest videos labeled as "scientific" I have ever seen. There is no mystery in turning a sphere or a circle inside out. The mystery is why obtuse mathematicians would create ridiculously random rules such as "no sharp edges or creases." Get rid of the stupid rule and you no longer have a problem. Now you are free to turn your mental faculties towards something more worthwhile.
Posted by: Orolokarr | Dec 23, 2007 9:17:34 AM
I disagree with Orolokarr - I think Scientific American has done a fantastic job explaining a very complex and powerful concept. Thanks for sharing it!
Very interesting demonstration. The rule about allowing sides to pass through each other seems like a contrivance, though, when looking at a sphere. It does not seem like that would have a physical application, except maybe in magnetic fields.
Posted by: Ernie Oporto | Dec 23, 2007 11:34:17 AM
Orolokarr: just because your understanding of the world we live in is stunted, doesn't mean the world we live in is simple.
The reason for this excercise is not about moving spheres in space. This is just an intuitive representation of a mathematical problem which exists whether you like it or not: that is to be able to maintain differentiability over a domain. It is important because it allows for things like Quantum Physics to be understood and manipulated. And for you to be able to sit at your computer and make assinine comments like this, some people somewhere had to understand Quantum Physics deeply to create transistors.
Anyways, does anyone know how many corrugations are necessary? is it always 8? can it not be 3, 4, 5, 6? What's so special about 8?
Posted by: Marc | Dec 23, 2007 2:37:53 PM
To all those complaining about the "crease" condition or the lack of physical realism: This is *not* a physics problem, it's a math problem--and in the realm it comes from the problem is actually pretty natural.
Here's an analogy... imagine you're studying curves drawn by someone moving their pen swiftly over a piece of paper. In that case self-intersections of a doodle would be fine--why shouldn't a doodled line cross itself? At the same time, sharp corners or points (a 1-D "crease") would be unnatural, since the pen would have to stop or change direction infinitely fast.
Don't know if this is helpful, but hopefully it gives some sense of why the conditions of the problem don't seem contrived to mathematicians.
Posted by: anon. | Dec 23, 2007 4:00:03 PM
I like The Optiverse version, which looks more "natural" as it has minimal bending energy and the fewest "catastrophes" (surfaces pushing through each other).
Posted by: Sagredo | Dec 23, 2007 5:38:38 PM
I think I must be on LSD. And thank god for that.
Posted by: biff | Dec 29, 2007 4:33:03 AM
It is precisely this schism that Johanna Drucker's collective work addresses itself to, in the process constituting one of the most striking oeuvres in late twentieth century aesthetics. Drucker, who holds a Ph.D. from Berkeley, is currently Associate Professor of Art History at Yale University. For twenty-five years she has been writing, printing, and binding artists' books, many of them under the imprint of her own Druckwerk press, using both letterpress and offset production techniques.
-------------
johnsmith
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this superb site."—Steven
Pinker, Johnstone Professor of Psychology, Harvard University.
"I have placed 3 Quarks Daily at the head of my list of web bookmarks."—Richard
Dawkins, Charles Simonyi Professor of the Public Understanding of Science at Oxford University.
"Just wanted you to know I’m one of many who reads and enjoys 3 Quarks....almost daily."—David Byrne, musician, former lead-singer of the Talking Heads, artist, intellectual.
Comments
This is a great visualization that just keeps getting better and better all the way through. The way the demonstration progressively expands your ability to perceive what is happening is fascinating.
Posted by: Carlos | Nov 7, 2007 10:34:05 AM
Thanks for that. Hypnotic and enlightening, it's enhanced my understanding of stuff in general, too.
Posted by: Doug l | Nov 7, 2007 11:10:34 AM
My question is why, if one surface can freely pass through another, you can't pull out a kink? But then this is way over my head -- can you imagine how many brain cells it takes to imagine a problem like this?
Posted by: Luke Lea | Nov 8, 2007 10:11:51 PM
At the risk of sounding greedy; I'd love to see the "wireframe" (the stage/view of a 3D animation showing only the vertices of the object-sans the skin)of the inside to outside transformation. I'm not sure if it would really clarify anything but it would be a fascinating sequence on its own. Thanks Abbas; this use of 3D animation does something truly expansive for one's imagination. When was the last time I could say that about a piece of CGI?
Posted by: Pete Chapman | Nov 8, 2007 10:49:22 PM
Luke, I think pulling out the kinks would equal to breaking the topology. If you allow that, then you can convert any curve (or surface) to any other curve (or surface), and the game is not interesting.
It is the rule of smooth transitions, no tearing and no kinks, that define topology, or classes of surfaces or curves that are not all part of the same mess, and are therefore a worthwhile subject for mathematicians.
Posted by: Janne Sinkkonen | Nov 24, 2007 2:49:06 AM
""My question is why, if one surface can freely pass through another, you can't pull out a kink?""
Well, the material is elastic too so a bend of unlimited magnitude like a kink would put an infinite amounth of tensure on the belt detroying it.
Posted by: Johan | Dec 22, 2007 4:40:56 AM
I suspect that in the actual math behind it, allowing creases means the transformation function isn't infinitely differentiable, so it is a less powerful result.
Posted by: Duncan | Dec 23, 2007 4:04:10 AM
This has got to be one of the stupidest videos labeled as "scientific" I have ever seen. There is no mystery in turning a sphere or a circle inside out. The mystery is why obtuse mathematicians would create ridiculously random rules such as "no sharp edges or creases." Get rid of the stupid rule and you no longer have a problem. Now you are free to turn your mental faculties towards something more worthwhile.
Posted by: Orolokarr | Dec 23, 2007 9:17:34 AM
I disagree with Orolokarr - I think Scientific American has done a fantastic job explaining a very complex and powerful concept. Thanks for sharing it!
Posted by: Rio | Dec 23, 2007 10:56:59 AM
Very interesting demonstration. The rule about allowing sides to pass through each other seems like a contrivance, though, when looking at a sphere. It does not seem like that would have a physical application, except maybe in magnetic fields.
Posted by: Ernie Oporto | Dec 23, 2007 11:34:17 AM
Orolokarr: just because your understanding of the world we live in is stunted, doesn't mean the world we live in is simple.
The reason for this excercise is not about moving spheres in space. This is just an intuitive representation of a mathematical problem which exists whether you like it or not: that is to be able to maintain differentiability over a domain. It is important because it allows for things like Quantum Physics to be understood and manipulated. And for you to be able to sit at your computer and make assinine comments like this, some people somewhere had to understand Quantum Physics deeply to create transistors.
Anyways, does anyone know how many corrugations are necessary? is it always 8? can it not be 3, 4, 5, 6? What's so special about 8?
Posted by: Marc | Dec 23, 2007 2:37:53 PM
To all those complaining about the "crease" condition or the lack of physical realism: This is *not* a physics problem, it's a math problem--and in the realm it comes from the problem is actually pretty natural.
Here's an analogy... imagine you're studying curves drawn by someone moving their pen swiftly over a piece of paper. In that case self-intersections of a doodle would be fine--why shouldn't a doodled line cross itself? At the same time, sharp corners or points (a 1-D "crease") would be unnatural, since the pen would have to stop or change direction infinitely fast.
Don't know if this is helpful, but hopefully it gives some sense of why the conditions of the problem don't seem contrived to mathematicians.
Posted by: anon. | Dec 23, 2007 4:00:03 PM
I like The Optiverse version, which looks more "natural" as it has minimal bending energy and the fewest "catastrophes" (surfaces pushing through each other).
Posted by: Sagredo | Dec 23, 2007 5:38:38 PM
I think I must be on LSD. And thank god for that.
Posted by: biff | Dec 29, 2007 4:33:03 AM
It is precisely this schism that Johanna Drucker's collective work addresses itself to, in the process constituting one of the most striking oeuvres in late twentieth century aesthetics. Drucker, who holds a Ph.D. from Berkeley, is currently Associate Professor of Art History at Yale University. For twenty-five years she has been writing, printing, and binding artists' books, many of them under the imprint of her own Druckwerk press, using both letterpress and offset production techniques.
-------------
johnsmith
Wide Circles
Posted by: johnsmith | Jul 29, 2008 3:22:37 AM
I find it hard to believe that a women can be smarter than a man.
Posted by: Laiptai | Jul 30, 2010 2:44:50 PM
I think that for mens is hard to belive... :)
Posted by: Stilingi laiptai | Apr 16, 2011 8:07:28 AM
OMG BEST VIDEO EVAR
Posted by: JONBOI | Jan 19, 2012 6:29:29 AM
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