\chapter{Calling to Dancers in the Center}
\label{chap:centers}

\section{The Allemande Spot}

Before we delve deeply into the theory of mental image calling, let's
see how the system works in the simplest case.  Have the heads go into
the center and \call{square thru 4}.  Mentally (or visually, if you
have a live square) follow the number one man as he does the
\call{square thru 4}.  He is the ``designee.''\footnote{The system
works just as well with a female designee.  We will just use a male
designee for this initial explanation.}  The miraculous thing about
the mental image system is that {\em he is the only person you must
follow\/}.  You have to keep track of some other information, called
the ``allemande spot,'' but the only person you need to track is the
designee.  In our diagrams, we will show the designee with a dot
inside him.

\displaytwo
{ \bdancer e & \gdancer s & \bdancer s & \gdancer w \\
  \gdancer e & \dbdancer n & \gdancer n & \bdancer w }
{\call{heads into the middle}}
{ \bdancer e & \gdancer w & \bdancer e & \gdancer w \\
  \gdancer e & \dbdancer w & \gdancer e & \bdancer w }
{and \call{square thru 4}}

As we know, we can call an \call{allemande left} from here.  We say
that he is ``standing on his allemande spot.''  There are four
possible allemande spots, all in the row of people closest to the
caller.

\note{Somewhere we need to discuss how this relates to Beck's MI
system - 8 allemande spots.}

We will show the allemande spot in our diagrams with something like
this:

\begin{center}
\allemandeaO
\end{center}

\noindent in front of the square.  The symbol will be an \x\ or an \o.
Later we will explain how to move the allemande spot around, while
keeping track of it on the fingers of the non-microphone hand.  For
now, the allemande spot is \o2, that is, it is this position:

\displayone
{ \bdancer e & \gdancer w & \bdancer e & \gdancer w \\
  \gdancer e & \bdancern{\o}w & \gdancer e & \bdancer w }
{}

Since the designee is standing on it after a \call{heads square thru
4}, we can call an \call{allemande left}.  We can derive an hypothesis
from this first example: if we dance the heads around until the
designee is on that spot, we can call an \call{allemande left}.  Let's
try a few other sequences and see how well we do:

\begin{sequence}
heads square thru 2\\
partner trade\\
pass thru\\
allemande left
\end{sequence}

\begin{sequence}
heads star thru\\
partner trade\\
allemande left
\end{sequence}

\begin{sequence}
heads star thru\\
right and left thru\\
pass thru\\
allemande left
\end{sequence}

\begin{sequence}
heads fan the top\\
recycle\\
pass thru\\
allemande left
\end{sequence}

Here is one that can't possibly work:

\begin{sequence}
heads right and left thru\\
roll away\\
touch 1/4
\end{sequence}

What is the problem?  The head women aren't facing the sides, that is,
the setup is not an 8-chain.  What this points out is that {\em you
are responsible for formation management\/}.  You may only call an
\call{allemande left} from a suitable setup (in this case an 8-chain)
with the designee on his spot.

The designee is the
only person that you must specifically follow, but you also have
to be aware of the entire 8-person formation and arrangement.
Of course, you must do this to call successfully in any case.

So, given that the sides are normal couples facing in, we know that we
must manipulate the heads until they are in a setup like this:

\displayone
{ \bdancer e & \gdancer w & \bdancer e & \gdancer w \\
  \gdancer e & \dbdancer w & \gdancer e & \bdancer w }
{}

\noindent so that the overall setup is a normal 8-chain.

Is it always true that, if we dance the heads around until the
designee is on his spot, we can call \call{allemande left}?  Not
quite.  It is true that the number 1 man is in the correct position.
By symmetry, the number 3 man is also correct.  But the women are not
known to be correct.  We have either:

\displaytwo
{ \bdancern 4e & \gdancern 3w & \bdancern 3e & \gdancern 2w \\
  \gdancern 4e & \dbdancern 1w & \gdancern 1e & \bdancern 2w }
{this\ldots}
{ \bdancern 4e & \gdancern 1w & \bdancern 3e & \gdancern 2w \\
  \gdancern 4e & \dbdancern 1w & \gdancern 3e & \bdancern 2w }
{\ldots or this}

These are the only two possibilities.  The first of them is correct,
the second is not.  Here is where the mental image system comes to the
rescue.  It keeps track of the two possibilities and tells you when
the correct one has occurred.  The way the mental image system keeps
track of whether the head women got switched is through the
characterization of four-person calls as \x\ calls or \o\ calls.  Some
\o\ and \x\ calls are listed in Table~\ref{tab:oxshortlist}.

\begin{table}
\begin{center}
\[\begin{array}[t]{ll}
\mbox{\begin{tabular}{l}
\o\ calls: \\
\call{explode the wave} \\
\call{half sashay} \\
\call{partner hinge} (from a couple) \\
\call{pass the ocean} \\
\call{pass thru} \\
\call{quarter in/out} \\
\call{right and left thru} \\
\call{scoot back} \\
\call{square thru $\langle n\rangle$} \\
\call{star thru} \\
\call{step thru} \\
\call{step to a wave} \\
\call{trade} \\
\call{turn thru} \\
\call{u-turn back} \\
\call{veer left/right} \\
\call{walk and dodge} \\
\call{wheel and deal} (from 2-faced line)
\end{tabular}
}
&
\mbox{
\begin{tabular}{l}
\x\ calls: \\
\call{bend the line} (from 2-faced line) \\
\call{box circulate} \\
\call{centers} (of a wave or line) \call{trade} \\
\call{centers} (of a wave or line) \call{run} \\
\call{fan the top} \\
\call{(reverse) flutter wheel} \\
\call{quarter right/left} \\
\call{recycle} \\
\call{single hinge} (from a miniwave) \\
\call{spin the top} \\
\call{sweep 1/4} \\
\call{swing thru} \\
\call{touch 1/4}
\end{tabular}
}
\end{array}\]
\end{center}
\caption{Characterization of some common calls as \x\ or \o.}
\label{tab:oxshortlist}
\end{table}

The fact that a large number of common ``staple'' calls are \o\ calls
is no coincidence - the mental image system was designed that way.  We
will give more complete call lists in Appendix~\ref{app:lists}.

When we call two calls in succession, the combination is effectively
an \o\ if both calls were \o{}s or both were \x{}s.  The
combination is effectively an \x\ if one call was an \x\ and one
was an \o.  Thus the only important thing about a sequence of calls
is whether the number of \x\ calls is even or odd.

Now the rule for calling to a correct \call{allemande left} is simple:
dance the heads around, with an even number of \x\ calls, until the
designee is on his allemande spot.  Any number of \o\ calls may be
used; the only requirement is that the number of \x\ calls be even.
You can think of an \x\ call as e\x{}changing the head women.  You
must exchange them back in order to get them to the right place.  What
constitutes ``exchanging'' is somewhat esoteric.  Don't worry about
it.  Just keep track of \x\ calls and let the mental image system do
the rest.

Most of the sequences given above, such as:

\begin{sequence}
heads star thru\\
right and left thru\\
pass thru\\
allemande left
\end{sequence}

\noindent were made entirely from \o\ calls.  This one:

\begin{sequence}
heads fan the top (\x)\\
recycle (\x)\\
pass thru\\
allemande left
\end{sequence}

\noindent had two \x\ calls which cancelled out.  This one:

\begin{sequence}
heads pass the ocean\\
recycle (\x)\\
pass thru\\
allemande left?
\end{sequence}

\noindent does {\em not\/} work.  It has a single \x\ call.  Although
the designee is on his spot, it leaves the head women switched from
where they need to be:

\displayone
{ \bdancern 4e & \gdancern 1w & \bdancern 3e & \gdancern 2w \\
  \gdancern 4e & \dbdancern 1w & \gdancern 3e & \bdancern 2w }
{}

\section{Use of a Female Designee}

The mental image method will work equally well with a male or female
designee.  The female designee is the number 1 woman, and her allemande
spot starts out as \o3: \allemandecO.

When we dance the heads around until the setup is an 8-chain and she
is on her spot, and an even number of \x\ calls are used, the sequence
will be resolved.  In this case, the count of \x\ calls keeps track of
the head men, while you keep track of the head women.  To see this,
try the sequence:

\begin{sequence}
heads touch 1/4 (\x)\\
walk and dodge\\
allemande left?
\end{sequence}

The designee is where she belongs, but there was a single \x\ call.
The setup is:

\displayone
{ \bdancern 4e & \gdancern 3w & \bdancern 1e & \gdancern 2w \\
  \gdancern 4e & \bdancern 3w & \dgdancern 1e & \bdancern 2w }
{}

The head men are incorrectly placed.

It is probably best to use a designee of the same sex as yourself, so
that you will be completely familiar with the calls that you make the
designee execute.  This will improve your ability to move the designee
mentally without mistakes.

\section{Exercises}

\begin{enumerate}

\item Study the following sequences called to the heads in the middle
of the square, and determine for each: 1) if the designee (either head
man or head woman depending on which you prefer) ends up on his/her
allemande spot, and 2) if the number of \x\ calls is even or odd.
Refer to Table~\ref{tab:oxshortlist} as necessary, but try to memory
these staple calls as soon as possible.  In addition, try to follow
the designee in your head rather than using checkers or live dancers.

\begin{sequence}
heads right and left thru \\
star thru \\
pass thru \\
allemande left?
\end{sequence}

\begin{sequence}
heads touch 1/4 \\
walk and dodge \\
partner trade \\
pass thru\\
allemande left?
\end{sequence}

\begin{sequence} 
heads pass the ocean \\
explode the wave \\
partner trade \\
touch 1/4 \\
box circulate \\
boys run \\
pass thru \\
allemande left?
\end{sequence}

\begin{sequence}
heads fan the top \\
hinge \\
box circulate \\
boys run \\
reverse flutter wheel \\
sweep 1/4 \\
pass thru\\
allemande left?
\end{sequence}

\begin{sequence}
heads pass thru \\
partner hinge \\
swing thru \\
boys run \\
bend the line \\
slide thru \\
pass thru\\
allemande left?
\end{sequence}

\item Write some of your own opening sequences using the heads in the
middle of the square that correctly resolve to an \call{allemande
left}.  After writing them in your head, verify that they work using
checkers or live dancers.

\end{enumerate}

\section{Counting on Your Fingers}

We keep track of how many \x\ calls we have used by letting the
allemande spot have two kinds (\x\ and \o) as well as 4 positions (1,
2, 3, and 4).

Thus the allemande spot is always one of these:

\begin{center}
\noindent \o1: \allemandeaO \o2: \allemandebO \o3: \allemandecO \o4: 
\allemandedO \\
\x1: \allemandeaX \x2: \allemandebX \x3: \allemandecX \x4: \allemandedX
\end{center}

Whenever we call an \x\ call while we are dancing the heads around in
the middle, we change the allemande spot's kind without changing its
position.  We change \o\ to \x\ and \x\ to \o.  We start out with \o2
for a male designee and \o3 for a female.  The resolution rule is that
the designee must be standing on his or her spot {\em and the spot
must be an \o.}

So far, we have never moved the spot from the position (2 or 3) that
it started on.  In chapter \ref{chap:something} we will start moving
it around.  So we need a way to keep track of 2 kinds and 4 positions
easily.  Ideally we want to keep track of them in a way that does not
require a lot of thought, since calling takes up quite enough brain
power as it is.  Fortunately, the thumb and fingers of the
non-microphone hand serve this purpose nicely.  Hold the hand with the
palm down in front of you.  The four fingertips, from left to right,
represent the four \o\ spots.  When in an \o, hold the thumb in
contact with the corresponding fingertip.  For an \x\ spot, curl the
finger and hold the thumb against the fingernail of the corresponding
finger.

For example, if you hold the microphone in your left hand and use a
male designee, start each sequence with the right thumb against the
third finger.

Whenever you call an \x\ call to the heads in the middle, the spot
must change between an \o\ and an \x.  Just rock the finger between
having the fingertip in contact with the thumb and having the
fingernail in contact with the thumb.  You can only call an
\call{allemande left} when the designee is on the spot corresponding
to the selected finger, and the thumb is in contact with that
fingertip.

Of course, you don't need to hold the hand out in front of you.  You
can let it hang unobtrusively by your side.

\section{Exercises}

\begin{enumerate}
\item Go thru the folllowing sequences and keep track of the designee
mentally while tracking the allemande spot on your non-microphone
hand.

\begin{sequence}
heads spin the top \\
boys run \\
bend the line \\
right and left thru \\
pass the ocean \\
recycle \\
pass thru \\
allemande left
\end{sequence}

\begin{sequence}
heads pass thru \\
u-turn back \\
touch 1/4 \\
boys run \\
step to a wave \\
recycle \\
veer left \\
girls trade \\
wheel and deal \\
square thru 3\\
allemande left
\end{sequence}

\begin{sequence}
heads pass the ocean \\
single hinge \\
scoot back \\
boys run \\
star thru \\
swing thru \\
boys trade \\
turn thru\\
allemande left
\end{sequence}

\item Make up your own sequences, in real time, until you can bring
the designee to his or her \o\ allemande spot effortlessly.

\end{enumerate}

\section{Following the Designee Mentally}

We said earlier that you could follow the designee mentally or, if you
have a live square, visually.  Since the designee is a real person,
you might think that you could just watch him until he lands on the
allemande spot that you are keeping track of.  It would not be a good
idea to call this way for three reasons.

First of all, the mental image system requires a good deal of
practice, which can be done in private with no live dancers or other
equipment.  In fact, mental image practice is a good way to make
productive use of time that would otherwise be wasted by business
meetings and similar things.  (Don Beck suggests that the system can
be practiced while driving your car.  We do not recommend this, nor do
we recommend practicing it during important one-on-one meetings such
as performance reviews or job interviews.)

Second, there are a number of ``fictitious moves'' that we will
discuss in later chapters, in which the mental designee does something
other than the corresponding person.  Hence, you can't depend on the
real designee to do your work for you.  You must track the designee
mentally at all times.

Third, and most important, all sight calling, whether with the mental
image system or not, requires that you be ahead of the dancers.  When
you deliver a call, you must figure out what the ending setup will be
before the dancers get there, so that you can give the next call in
time to keep the dancers moving smoothly.  There are two mental tasks
when calling by mental image: figuring out the ending setup, which you
need to do anyway, and figuring out where the designee will go.  You
can easily combine the two tasks in your thinking, thereby reducing
the total amount of effort.  In fact, the ``formation awareness'' part
of your thinking will fall out naturally as a consequence of the act
of mentally tracking the designee.

\section{Categorization of Calls as \x\ and \o}

Here is how calls are categorized as \x\ or \o.  First, we need to
emphasize that the \x\ or \o\ categorization really only applies to
sex-symmetric four-person calls.  Later we will discuss eight-person
calls, and it will be seen that some of them change the nature of the
allemande spot from \o\ to \x\ and vice versa.  That does not mean
that it is correct to refer to such a call as an \x.  All eight-person
calls need to be treated as individual special cases.  Only the
four-person sex-symmetric calls enjoy the simple property that, once you
know whether a call is an \x\ or an \o, there is a single rule that
says how to do it.

Second, we require for now that both the starting and ending setups be
free of any people facing 90 degrees from each other.  This excludes
diamonds and T-bone boxes of the sort that are used at C-1 and higher.
We will fix diamonds presently, but will not handle T-bone boxes.

The classification of a call as an \x\ or \o\ depends only on the
relative starting and ending facing directions of the dancers.  It
does not depend on any other aspect of how the call is done, nor does
it depend on what turning motion was actually executed to reach the
final facing direction.  In any four-person sex-symmetric call, the two
men finish facing in one of four orientations relative to their starting
direction: the same way, 90 degrees clockwise, the opposite way, or 90
degrees counterclockwise.  We can measure that in terms of quadrants
clockwise: 0, 1, 2, or 3.

For example, \call{star thru} turns each man one quadrant clockwise.
\call{quarter left} turns three quadrants clockwise.  The two women
also turn in a way that can be measured in terms of 0 to 3 clockwise
quadrants.

Since we disallow diamonds or T-bone boxes, either both numbers are
even (all dancers start and finish facing head walls, or start and
finish facing side walls) or both numbers are odd (all dancers start
facing head walls and finish facing side walls, or vice versa).  The
sum of the two numbers is therefore always even.  If the sum is a
multiple of 4, the call is an \o.  If it is 2 plus a multiple of 4,
the call is an \x.

It should be emphasized that the formal definition just given is
for explanation only.  {\em You do not need to think about it
when calling\/.}  You only need to be aware of whether the call that
you are using is an \x\ or and \o, which you can memorize from the table.

\highlight{
The important thing for now is that the \x\ or \o\ property of a call
is:
\begin{enumerate}
\item Independent of the handedness of the setup.
\item Independent of whether men and women exchange roles.
\item Independent of whether you need to step to a wave (e.g.\ \call{swing
thru} from facing couples) or rear back (e.g.\ \call{square thru} from
a wave)
\end{enumerate}
}

So you are almost completely safe in just associating the \x\ or \o\
property with the call name.  There are exceptions for unusual setups.
The call \call{fan the top} is legal from 2-faced lines, but is an \o\
in that setup.  Similarly, \call{box circulate} is an \o\ if it
happens to be a partner trade or a pass thru.  The above list assumes
the ``usual'' types of setups.  It is best simply not to use calls in
unusual setups while doing mental image calling.  The only exception
is \call{hinge}, which is worth learning in both the miniwave form
(\x) and the couple form (\o).

With this definition of \x\ and \o\ calls, we can see how the system
worked when we called to the heads.  Assuming a male designee, when we
got to an 8-chain setup with the designee on his allemande spot, the
head men had turned 3 quadrants clockwise.  Since the sequence was an
\o, the head women must have turned 1 quadrant clockwise in order for
the sum to be a multiple of 4.  The number 1 woman started facing away
from us, so she is now facing to our right.  The only way she can do
that while being in the center of a normal-sex 8-chain is if she is on
the correct spot.  Go back and reread this paragraph until you
understand it!

\section{Exercises}

\begin{enumerate}

\item Decide whether the following calls are \x\ or \o\ based on the
above description.  You can check your answers with
Appendix~\ref{app:lists}.

\begin{sequence}
box the gnat \\
cast off 3/4 \\
chain down the line \\
chase right \\
cross run \\
crossfire \\
dixie style to a wave \\
explode and\ldots \\
follow your neighbor \\
half tag {\rm (from a 2-faced line)} \\
ladies chain \\
lead right/left \\
linear cycle \\
peel the top {\rm (from a box)} \\
single circle to a wave \\
spread {\rm (from a wave)} \\
trade the wave \\
wheel around
\end{sequence}

\item Write some opening sequences using these new calls that resolve
to a correct allemande left.

\end{enumerate}

\section{Starting with the Sides}

As you can probably guess, the system works equally well if you call
to the sides.  You just have to do all of your analysis while
pretending to be standing at one side of the hall instead of on the
stage.

\note{Example from page 50 here}

Notice that, when we start with the sides, our mental notion of how
the setup is divided into two four-person setups is different.  Instead
of one setup on our left and one on our right, there is a near
four-person setup and a far one.

The mental array of allemande spots runs front-to-back instead of
left-to-right.  Since we keep track of allemande spots on our fingers,
it is useful to turn the hand 90 degrees to match the orientation of
the array of spots.  If you hold the microphone in your right hand and
count with your left hand, rotate your left wrist so that the palm is
to your right.

\note{These pictures need work:}

\newcaption{Counting spots on the left hand.}
\displaytworv
{ \bdancer e & \gdancer s & \bdancer s & \gdancer w \\
  \gdancer e & \dbdancer n & \gdancer n & \bdancer w }
{}
{ \ctablebox{\allemandebO \\ \call{heads up to the middle}}}
{ \gdancer s & \bdancer s \\
  \bdancer e & \gdancer w \\
  \gdancer e & \dbdancer w \\
  \bdancer n & \gdancer n }
{\vallemandebO}
{\call{sides up to the middle}}

\newcaption{Counting spots on the right hand.}
\displaytwolv
{ \bdancer e & \gdancer s & \bdancer s & \gdancer w \\
  \gdancer e & \dbdancer n & \gdancer n & \bdancer w }
{}
{ \ctablebox{\allemandebO \\ \call{heads up to the middle}}}
{ \gdancer s & \bdancer s \\
  \dbdancer e & \gdancer w \\
  \gdancer e & \bdancer w \\
  \bdancer n & \gdancer n }
{\vallemandebO}
{ \call{sides up to the middle} }

When starting with the sides, you can let the designee be either \#2
or \#4, so you might as well make the choice that lets your wrist turn
naturally.

When you reorient the setup for calling to the sides, you must
reorient your mind to think of the two four-person setups in different
places.

\note{Picture page 53}

Whichever hand you use, get accustomed to calling and resolving with
side orientation.  Practice.
