Good Morning.  Today is
Thursday, October 3rd, 2013,
and today's topic is 4 pi rotations.
In simplified mathematics, we
often learn that a rotation of 360 degrees
takes you right back to zero.
But that's not always the case in nature,
where there are sometimes strings attached,
and sometimes it takes 720 degrees,
or a "4 pi rotation," in order
to complete the loops that occur.
In science, they usually don't measure
it as "720 degrees"; they usually
call it "4 pi" in radians.
And if Professor Leonard Susskind can 
demonstrate this in his seventies,
at a Princeton University lecture
on Supersymmetry,
then I figure most any able-bodied
YouTuber should be able to do this as well.
Okay... Palm up.
Fingers back.
I'm at zero degrees.
I'll rotate 90,
180,
270... and as I'm getting to 360,
clearly this doesn't feel like I'm back at zero.
My palm is still up, fingers still back,
I continue counter-clockwise,
to 540 and 720, and
NOW I'm back to zero.
Let's add a prop to demonstrate 
this is plam up.
We go one pi,
two pi,
three pi,
and back.
Four pi.
Sometimes nature still has stings attached.
If I go one pi... two pi...
then I can keep this oriented the same direction,
but I cannot untangle what I've started,
without continuing to stay in the same tangle.
Lets go back to our origin.
And I go one pi,
two pi, three pi,
four pi,
And now, I can go back,
keeping the orientation,
and untangle.
Here we have a rigid cylinder,
anchored to the walls of a box.
Let's try this.
We go rolling one, two pi, 
and again, four pi.
We grab it around the front and turn
it around the back...
Likewise, over the front, and 
around the back...
and we've restored it without changing
the orientation of the cylinder.
That's a branch of mathematics known as
twistors [or spinors], 
and it seems to describe not only
the half-spins of electrons,
but even the double spin field
of the gravitational field.
So meanwhile, that's something to chew on.
Hopefully next week, I'll come up with
the Twins Paradox and the
Ladder-in-the-Barn Paradox.
But in the meantime,
this is Joel 'TwistyNye,'
wishing you "Happy Trails."
I will see you next week.
