Has anyone built a macroscopic object that has spinorial behavior but is not tethered to a frame by strings or ropes? (For an example of what I don't mean, see Ethan Bolker's article "The Spinor Spanner".) I envision an egg that emits a hum when it's resting on its base and is in the correct spinorientation. Rotate it 360 degree about any axis: no hum. Rotate it again about any axis: it hums. It's okay with me if the egg's mechanism "tethers" it via electromagnetic waves to an external device that tracks it in 3D and tells it when to hum. It's also okay with me if the egg isn't an egg but a sphere or cube (or a doll resembling P. A. M. Dirac). Jim Propp
On Sun, May 22, 2011 at 9:57 AM, James Propp <jpropp@cs.uml.edu> wrote:
Has anyone built a macroscopic object that has spinorial behavior but is not tethered to a frame by strings or ropes? (For an example of what I don't mean, see Ethan Bolker's article "The Spinor Spanner".)
Your body is such an object! Stand facing a wall, arms straight out in front of you, at a distance where you palms just touch the wall. Now rotate one arm in as large circle as possible in a plane perpendicular to the wall; that is, keeping is straight, bring it down, then away from the wall, then up, then towards the wall again. observe that your palm no longer touches the wall. Now repeat the process with a second circle, and observe that your hand now touches the wall. It's not a perfect example, because you don't have the freedom of movement to rotate your arm through 360 degrees in any but that one direction. And it's tethered to the rest of your body (though not by string or ropes, unless you count tendons and ligaments). But it's still cool. Andy andy.latto@pobox.com
One standard demonstration of this phenomenon goes by the name "the soup-plate trick" --- moving only one arm, without moving the feet or changing the grip on the dish, the (full) dish may be returned to its initial position after rotation through any even number of full turns --- but NOT odd. A sadistic demonstrator will invite his victim to perform the trick with a full beer mug instead: the natural approach of seizing the handle of the mug may lead to grisly contortions followed by beer on floor, performer, and audience. I can't find a demo on you-tube. How about putting one up, somebody? WFL WFL On 5/22/11, Andy Latto <andy.latto@pobox.com> wrote:
On Sun, May 22, 2011 at 9:57 AM, James Propp <jpropp@cs.uml.edu> wrote:
Has anyone built a macroscopic object that has spinorial behavior but is not tethered to a frame by strings or ropes? (For an example of what I don't mean, see Ethan Bolker's article "The Spinor Spanner".)
Your body is such an object!
Stand facing a wall, arms straight out in front of you, at a distance where you palms just touch the wall. Now rotate one arm in as large circle as possible in a plane perpendicular to the wall; that is, keeping is straight, bring it down, then away from the wall, then up, then towards the wall again. observe that your palm no longer touches the wall. Now repeat the process with a second circle, and observe that your hand now touches the wall.
It's not a perfect example, because you don't have the freedom of movement to rotate your arm through 360 degrees in any but that one direction. And it's tethered to the rest of your body (though not by string or ropes, unless you count tendons and ligaments). But it's still cool.
Andy andy.latto@pobox.com
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I couldn't find it on YouTube either, and I couldn't persuade my son to do it, so I became the actor http://www.youtube.com/watch?v=Rzt_byhgujg On Sun, May 22, 2011 at 8:59 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
One standard demonstration of this phenomenon goes by the name "the soup-plate trick" --- moving only one arm, without moving the feet or changing the grip on the dish, the (full) dish may be returned to its initial position after rotation through any even number of full turns --- but NOT odd.
A sadistic demonstrator will invite his victim to perform the trick with a full beer mug instead: the natural approach of seizing the handle of the mug may lead to grisly contortions followed by beer on floor, performer, and audience.
I can't find a demo on you-tube. How about putting one up, somebody? WFL
WFL
On 5/22/11, Andy Latto <andy.latto@pobox.com> wrote:
On Sun, May 22, 2011 at 9:57 AM, James Propp <jpropp@cs.uml.edu> wrote:
Has anyone built a macroscopic object that has spinorial behavior but is not tethered to a frame by strings or ropes? (For an example of what I don't mean, see Ethan Bolker's article "The Spinor Spanner".)
Your body is such an object!
Stand facing a wall, arms straight out in front of you, at a distance where you palms just touch the wall. Now rotate one arm in as large circle as possible in a plane perpendicular to the wall; that is, keeping is straight, bring it down, then away from the wall, then up, then towards the wall again. observe that your palm no longer touches the wall. Now repeat the process with a second circle, and observe that your hand now touches the wall.
It's not a perfect example, because you don't have the freedom of movement to rotate your arm through 360 degrees in any but that one direction. And it's tethered to the rest of your body (though not by string or ropes, unless you count tendons and ligaments). But it's still cool.
Andy andy.latto@pobox.com
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-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
Fast work, TP --- but how much coffee did you have in the cup? WFL On 5/22/11, Thane Plambeck <tplambeck@gmail.com> wrote:
I couldn't find it on YouTube either, and I couldn't persuade my son to do it, so I became the actor
http://www.youtube.com/watch?v=Rzt_byhgujg
On Sun, May 22, 2011 at 8:59 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
One standard demonstration of this phenomenon goes by the name "the soup-plate trick" --- moving only one arm, without moving the feet or changing the grip on the dish, the (full) dish may be returned to its initial position after rotation through any even number of full turns --- but NOT odd.
A sadistic demonstrator will invite his victim to perform the trick with a full beer mug instead: the natural approach of seizing the handle of the mug may lead to grisly contortions followed by beer on floor, performer, and audience.
I can't find a demo on you-tube. How about putting one up, somebody? WFL
WFL
On 5/22/11, Andy Latto <andy.latto@pobox.com> wrote:
On Sun, May 22, 2011 at 9:57 AM, James Propp <jpropp@cs.uml.edu> wrote:
Has anyone built a macroscopic object that has spinorial behavior but is not tethered to a frame by strings or ropes? (For an example of what I don't mean, see Ethan Bolker's article "The Spinor Spanner".)
Your body is such an object!
Stand facing a wall, arms straight out in front of you, at a distance where you palms just touch the wall. Now rotate one arm in as large circle as possible in a plane perpendicular to the wall; that is, keeping is straight, bring it down, then away from the wall, then up, then towards the wall again. observe that your palm no longer touches the wall. Now repeat the process with a second circle, and observe that your hand now touches the wall.
It's not a perfect example, because you don't have the freedom of movement to rotate your arm through 360 degrees in any but that one direction. And it's tethered to the rest of your body (though not by string or ropes, unless you count tendons and ligaments). But it's still cool.
Andy andy.latto@pobox.com
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-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
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="Thane Plambeck" <tplambeck@gmail.com> I couldn't find it on YouTube either, and I couldn't persuade my son to do it, so I became the actor
Bravo! "No beer was harmed in the making of this video."
Barry Hayes points out that I'm upstaged by Dick van Dyke at about 1min, 15 seconds into this video from "Chitty-Chitty Bang-Bang" http://www.youtube.com/watch?v=_D1ZCvmVsFY On Sun, May 22, 2011 at 12:10 PM, Marc LeBrun <mlb@well.com> wrote:
="Thane Plambeck" <tplambeck@gmail.com> I couldn't find it on YouTube either, and I couldn't persuade my son to do it, so I became the actor
Bravo! "No beer was harmed in the making of this video."
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-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
Obviously it *could* be done. I imagine that it wouldn't be hard for an iphone developer to write an iphone app that would do this, since I'm pretty sure there's enough access to sensors in the iPhone to keep track of a path in SO(3) from which it is trivial to lift it to Spin(3). Probably for lots of android phones, as well. I'd like to mention that when we (in particular, my son Nathaniel) were making the "Outside In" video at the geometry center, we found it extremely convenient to specify camera orientation in Spin(3) i.e. unit quaternions, rather than SO(3). This makes interpolation between camera positions much easier, since any two points in $S^3$ except an antipodal pair is connected by a unique shortest geodesic. In SO(3) = RP(3), there is a large cut locus (for each point, the cut locus is an RP(2)), and it's much harder to program interpolation to avoid unwanted jumps in camera position when you, unless you pin down by hand a sequence of camera positions that is fairly close together, to be interpolated. Bill On May 22, 2011, at 9:57 AM, James Propp wrote:
Has anyone built a macroscopic object that has spinorial behavior but is not tethered to a frame by strings or ropes? (For an example of what I don't mean, see Ethan Bolker's article "The Spinor Spanner".)
I envision an egg that emits a hum when it's resting on its base and is in the correct spinorientation. Rotate it 360 degree about any axis: no hum. Rotate it again about any axis: it hums.
It's okay with me if the egg's mechanism "tethers" it via electromagnetic waves to an external device that tracks it in 3D and tells it when to hum.
It's also okay with me if the egg isn't an egg but a sphere or cube (or a doll resembling P. A. M. Dirac).
Jim Propp
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participants (6)
-
Andy Latto -
Bill Thurston -
Fred lunnon -
James Propp -
Marc LeBrun -
Thane Plambeck