Cedar balls: the kind of balls that you put in the closet to chase away insects.
Now, one positive thing you can say about this experiment is that it smells nice,
and you can't say that about many experiments.
[Brady]: Oh, can I smell? [Professor]: Yes, yes.
[Brady]: (sniffs) Mmm, yeah.
[Professor]: I should probably polish them because I've been using them for a long time.
Here is a soup bowl that I sto... I mean, borrowed from a cafeteria in Cambridge,
and if I put a few balls -- let's say three -- and swirl
you see that the balls circulate in the direction that I'm swirling.
"Of course," you say.
Now when I say "swirl" I mean: do this motion.
I'm not actually rotating the whole thing, I'm just doing this.
So when I swirl, those balls circulate in the direction that I'm swirling;
I'm swirling in this direction and balls circulate in the same direction; that is, counter-clockwise.
But now, let's increase the number of balls; make them more crowded.
When I swirl now
the balls start circulating in the *wrong* direction, opposite direction.
So there was a transition.
With one ball the circulation is the same direction as the swirl.
Two, three we have already seen, they circulate in the same direction.
Four it's still the same direction.
But five there's a lot of hesitation.
Six.
But at seven it's pretty clear that they're circulating in the opposite direction.
And eight and so on.
This is quite remarkable.
And it's a bit like a phase transition -- if you like -- a total phase transition between gas and liquid.
When you have only a few of those balls and I swirl, these balls are independent particles
they don't talk to one another, they are minding their own businesses.
And what happens is that whenever the wall of the soup bowl bangs against one of them,
it just transmits the bang, linear momentum, in the same direction.
So if I'm swirling like that, they are being sent in the same direction;
that's why they are the circulating the same direction that I'm swirling,
because they are not talking to one another, they are independent particles.
In contrast, when you increase the crowdedness,
whatever linear momentum I input into the system
gets scattered among the neighboring contacts because they are very closely touching one another.
But what doesn't get wasted is the rubbing phenomenon.
So. Imagine that you have a ball like this, and then the wall of the soup bowl rubs against this.
Not only does it get pushed away, but it also gets rotated like that.
And this rotation is transmitted because the neighbors are very close to the next one, the next one, the next one.
So this rotation is propagated among all the entire group.
So the linear momentum is being wasted,
but the angular momentum -- that is, a tendency to keep rotating;
that's the quantity that measures how much there is rotation -- gets transmitted.
So you have a transition from the linear momentum dominated regime
to the angular momentum dominated regime.
And what happens is that when you rub it like this it rolls in the direction opposite.
It starts moving globally, drifting in the direction opposite to the way I'm pushing.
That's why there is this take over effect.
And that is really a little bit like -- in some facetious fashion -- like a transition between gas and condensing to liquid.
Because you see in gas, molecules are just flying around minding their own businesses;
they're free and they don't really talk to one another, and they bounce against the wall of vessel, and then they bounce.
But when you are a liquid, you have molecules that are touching against each other;
they can slide against each other, but they interact a lot. So it is really like a transition from gas to liquid.
And the order parameter is increasing the crowdedness, is like lowering the temperature, or increasing the pressure.
And if you keep making them more and more crowded then they eventually freeze solid completely.
So you see this is really like a phase transition.
Ok, now...
One or two perhaps details...
When you have, say, so many,
we've already seen that collectively they circulate in the direction opposite to the direction I'm swirling.
That's true.
Please look at individual balls; for example the middle one is probably easiest see.
I'm going to swirl the whole thing counter-clockwise like this.
You can see that the middle one is also
spinning; going around around in the counter-clockwise fashion.
And it's the same for any of the individual balls. For example look at this one; when I
swirl like that, this one is drawing a trajectory which looks like this.
It's still counter-clockwise but there's a global drift which goes clockwise.
So it's quite interesting that the individually they're still doing the right thing, so to speak,
but together there's a purely collective group behavior that emerges, which does exactly the wrong thing.
So it's really not what's happening to individual particles, individual molecules, that
-- how they are behaving together --
that is the collective phenomenon that emerges.
The way to analyze this is ...
Of course, you know, rotations of three dimensional balls, that's very complicated,
you should do it in two dimension of analog.
So you imagine for example, discs which are sliding on the completely slippery surface like an ice skating rink, but coated in rubber let's say,
so that when they are in contact with one another they can rub against each other. And so is the periphery of this arena.
And when you do that you get exactly the same kind of phenomenon.
[Professor Tokeida, speaking on a previous video]: Each paper clip is linked to the rubber band but not between themselves.
Let's finish with something that is work-in-progress.
So far we have been linking paper clips together, and sometimes we refer to this as addition.