Re: Dirac String Trick

[Michael Bowen <fizzbowen@MINDSPRING.COM>]

Hugh Haskell wrote:
> I've been doing that trick for some time, but it's hard to describe.
> You really need to see someone do it. The first rotation (under your
> elbow) leaves your hand kind of "upside down" when you finish, and
> its a bit uncomfortable. But if you always keep you palm as near
> upright as you can, and continue the rotation in the same sense, but
> this time bringing your palm over your head, you will end up with
> your hand in the same position it was at the beginning. I don't
> recommend doing it with a full glass the first few times you try. In
> fact, you can get the idea if you leave your hand empty, but open
> with palm up throughout.

OK, I think I have it figured out. If you're still working on it, stop
reading here! Not having a cup handy, I used my trusty TI-85
calculator for the object (the large screen gives a nice visible
landmark for orientation that is visible even when my arm is in a
weird position). I concentrated on keeping its keyboard facing in the
general direction of the ceiling. (I'm sure that the manufacturer
never intended for it to be used this way.)

I held it in my outstretched right palm in the conventional position,
keyboard up and oriented about 45 degrees relative to both my personal
x- and y-axes (assuming here that z is the "cylindrical" axis of my
body). As seen from above, I started to rotate it counterclockwise
(clockwise if it was in my left palm; see, I really did try it both
ways) with the wrist and elbow joints, so it passed directly below the
elbow that was attached to the same hand that was holding it. As it
passed below the elbow (about pi radians so far), the keyboard was
"upside down" (it still faced the ceiling, but the key text was
inverted from my viewpoint). I continued with this motion until the
keyboard was again in the readable orientation, although at this point
the convex side of my elbow joint was facing upward in the awkward
manner that Hugh described, so actually reading the keyboard at this
point was a bit problematic.

Having accomplished the first 2-pi radians, I fully outstretched the
arm to my side (the same side of my body as the arm that held the
calculator). Using the shoulder as the pivot, I swung the entire arm
(still straight) in front of me through almost another pi radians, so
my elbow was basically right in front of my forehead, with arm now
outstretched toward the side of my body opposite it. From this
position, which was pretty close to 3-pi, I allowed the arm to pass
over the top of my head, bending the elbow slightly as needed to
maintain mobility. Once behind the head, it required only a fairly
natural motion to return the calculator to its starting position. I
looked up to watch the calculator passing overhead to make sure there
was no cheating with the orientation during that passage (it can feel
like you're rotating it around a different axis if you're not watching
it).

With practice, of course, some of the exaggerated movements can be
toned down. Now I want to see if I can do it in reverse.

What an interesting exercise! Thanks, John D., for pointing it out,
and to everyone else who helped with the logistics. I apologize for
the painfully explicit description, but maybe it will help anyone else
that is as congenitally clumsy as I am.

--MB