..  _lets-dance:

Let's Dance
###########

In our last lecture, we introduced the notion that there are a bunch of
electrons zinging around the atoms that make up some material. If that material
cooperates, we can get electrons to move, and we call the material a conductor.
We make wires out of these kinds of materials, so we can send signals from one
place to another. 

But if each atom is just sitting there minding its own business, how does this
electricity stuff make things move. 

Let's find out.

I was after pondering about how to get this idea into your heads better one
night, and I came up with something (at 3am!) we can do in class. We will dance
in class!

Don't worry, you do not need to move (much).

This dance is going to be a bit strange. It will not matter if you cannot dance
a lick!

Setting up to Dance
*******************

I will ask all of the humans in the room (including your instructor) to stand
in a circle with something like a desk between each of you. That desk is going
to be a spot where a stack of cards can be placed. 

As you stand in this circle, your world is focused on the cards to your left,
and the cards to your right. You will not move your feet at all in this dance.

(Sheesh, not much of a dance, if you ask me. I heard you muttering that!)

All the action will involve those cards on either side of you.

..  note::

    Obviously, each stack of cards is "shared", meaning they "belong" to a pair
    of students, who will fight over them (well, not really!)


Your Role in the Dance
**********************

Do you see those two piles of cards to your left and your right? If the number
of cards on each side of you is not the same, you are not a happy dancer. You
are so unhappy, that you simply must balance the number of cards to be happy.

That means you must pick up the two piles of cards on both sides of you, then
split that big pile up into two stacks with as close to the same number of
cards in each pile as you can get, then put them back down.

However, there are a couple of rules covering how you do that!

..  note::

    There are two silly rules in this dance:
    
    The first rule should be obvious. You cannot cut any card in half!

    The second rule is not so obvious. The cards absolutely want to move to
    create a balance. If there is only one card on one side, and none on the
    other, it will move to the spot with no card. 

    Hey, I am inventing this dance here!

Now, that rule is applied by each "dancer" when it is their turn to dance.

What, we have to take turns dancing? This is really not the dancing I know!

Dance Version 1
***************

There will not be a drum in this dance, pounding away. However, your friendly
instructor will start things off. The action will start when I place a stack of
cards on my right table.

Initially, all the tables will be clean, there are no cards in sight. Everyone
is happy!

However, as soon as I place that pile of cards on the first table, the student
on my right is suddenly very unhappy.  That student will pick up the two piles
(OK, so there is only one) and try to balance them on both sides. As soon as
that student is done, the one on her/his right, will be unhappy, and do the
same thing. We will continue this process until everyone is happy!

If it is your turn, and you are happy, just tell the student on your right that
you are happy! You are done, and that next student has a turn.

..  note::

    I wonder how long this will take! We will see! I also wonder if we will
    reach a situation where everyone is happy as can be, and nothing really
    happens. Hmmm!

    You need to think about how this will go. I lay in bed that night, thinking
    about this, until I came up with this plan on how we will do the dance. It
    will do what I want it to do!

The Instructors Role
====================

In our first version of this dance, I will not participate in the dance, other
than injecting that first pile of cards onto that first table. If cards appear
on either side of me, they will just sit there. As you should see, we take
turns trying to get happy, and sweep around the circle from left to right. As
soon as it is my turn to get happy, I will simply do nothing, and pass the turn
to the student on the right, to again try to get happy.

Dance Version 2
***************

In version two of this dance, everything will stay the same, except for one
minor twist.

Your role as a student will not change, However, your instructor's role will
change. 

Insted of plopping all the cards in my initial pile on that first table, I will
place only one card on my right table when it is my turn. The dance will
continue until it is my turn again.  At that point, I will remove any card
found on my left table and keep it in a second (hidden) stack. I will take
another card from the first stack and place it on my right table again. The
student on my right will then take a turn once more, and the dance continues

I will stop placing new cards on the table when I have as many cards in my left
(hidden) pile as I have on my right (the pile I use to add new
cards into the dance). At that point the dance is done.

..  note::

    Again, I wonder how long this will take!

Dance Version 3
***************

We might do this in class. Otherwise, you just get to think about it.

What would happen is we all just started doing our "dance" at the same time. We
might get into small fighting matches, where two players fight over the stack of
cards between them. One will want to steal a card, while the other might want
to put another on. Maybe both will want to so the same thing. Who knows? The
players are going to work a lot harder to get this dance done.

But, after the smoke clears, what will have happened? We will have to see. I
suspect, after a suitable amount of time, and a few small fights, we might see
similar results.

Interesting!

Final Note
**********

Your first real lab project for this course will be to write a C++ 
program that simulates version 1 of this dance. I will provide
some starter code for this after we do the dance in class. That will make sure
you understand the rules of the dance well enough to write the code.

I will let you work in teams of three/four students, to discuss the design of
this simulation. I still want each of you to write your own version, but you
can share ideas. (See the lab assignment for more details)

I hope you read this before class. Otherwise, it will take more time to explain
the rules.