Techniques for Discovering Arrangement

Rich Reel 9 Feb 2007

This article is specifically targeted to the sight caller that calls for groups with mostly mixed-gender couples. If most dancers are not dancing their biological gender position, you may find it difficult at times to know when you may call gender-dependent calls such as Star Thru or Boys Run, usually an essential step before resolving the square. Unless you carefully track the arrangement at all times, you may find yourself occasionally needing to probe to find where the boys and girls are. While it is always ok to occasionally ask: "Where are my boys (or girls)?", this article presents some techniques for finding them more "discretely".

Use Gender Identifiers

A simple strategy is to designate boys or girls to do a call that is legal from all arrangements, then look to see who did the call.

[W] (any wave) Boys(or Girls)-Trade (some callers use this particular one too much!)
[L] (facing lines) Boys(or Girls)-Forward and Back (fun if you use the boys(or girls) in whatever formation they get when they step forward in a follow-up call)
[LO] (lines facing out) Boys-Trade ...pause... Girls-Trade
[LO] (lines facing out) Boys(or Girls)-U-Turn
Mix and match: [LO] (lines facing out) Boys U-Turn while Girls-Trade
[LO] (lines facing out) or [F] (2 face line) Tag The Line; Boys Face In, Girls Face Out

This strategy is common enough that some of experienced dancers will know what you're up to, but if you only use it occasionally, and use maximum variety, you'll maintain your "great caller" reputation.

Use Partner and Corner Pairing Information

It turns out that the rules of symmetry in a square can allow you to deduce a lot of information about gender placement around a formation (any formation) from a single piece of information: some dancer 'A' and another dancer 'B' in known positions are opposite gender.

If you don't remember any specific dancer's gender, you should at least know some partner pairing information in order to resolve the square.

You should know...

Partners in a memorized key couple. These dancers are opposite gender.

You may know...

Corners between your memorized key couples. The two corners are opposite gender.

The simple knowledge that one set of opposite gender dancers can be in a position to interact with each other for a two dancer call (facing or side-by-side for example) can be used to say mathematically that ALL such interacting dancers in the formation must also be opposite gender. This means you can confidently set up and call a gender-specific call that requires EVERY interacting pair of dancers in the square be opposite gender, without knowing ANY specific dancer's gender.

Understanding Gender Positioning

Facing dancers in facing lines

Say you have facing lines. You do not know anyone's gender. You happen to notice that two partners of one (only one) of your key couples are facing each other. These two dancers could Star Thru with each other if were called. Say this is all we know about this formation.

Question: Is it safe to call Star Thru from this setup knowing that Star Thru requires all facing dancers be opposite gender?

Let's look at this logically.

First, our two facing dancers are original partners so they must be opposite gender. Let's call them boy #1 and girl #1.
Boy #1 has a same-gender mirror-opposite: boy #3. Girl #1 has a same-gender mirror-opposite: girl #3.
Formation Symmetry dictates that from any position, we can find the mirror opposite position by starting from the known position, moving in a straight line to the very center of the formation, then continuing on that straight line the same distance beyond the very center of the formation to arrive at the mirror opposite position. Therefore we know exactly where boy #3 and girl #3 are - in the mirror-opposite positions in the formation from boy #1 and girl #1, facing each other.
This leaves two boys and two girls remaining to stand in the four remaining positions in the formation.
We know the remaining boys (boy #2 and boy #4) must be each other's mirror opposites. The same should be true of the two remaining girls (girl #2 and girl #4) - they must be each other's mirror opposites.
In facing lines formation, there are no mirror image positions that face each other.
If we place one boy (say boy #2) into one of the remaining four positions, then the last boy (boy number #2's mirror opposite - boy #4) must stand in the mirror-image position. Since these last two boys can't be facing each other, they must be facing one of the remaining two positions which could only be filled by the remaining girls. In other words, both boy #2 and boy #4 must be facing girls.

Does it matter which positions our known facing dancers were in?

Boy #1 and girl #1 in a different position
Mirror opposite positions must contain boy #3 and girl #3
Remaining positions must have same gender as mirror opposites
or
No way same gender could be facing - opposite dancers must be in opposite positions

So if any ONE pair of dancers is opposite gender in facing lines, all facing dancers in facing lines MUST be opposite gender. And thus it will be safe to call Star Thru or Touch 1/4; Boys-Run or any other calls requiring all facing dancers to be opposite gender.

Study carefully the six (6) possible symmetric arrangements for facing lines. In four (4) of the six (6), all facing dancers are opposite gender.

or or or

Note the other two (2) possible arrangements for facing lines have no opposite gender facing dancers.

Dancers in a quarter of an eight-dancer formation

Say we have any 8-dancer formation than can be symmetrically divided into four quadrants, with two dancers in each quadrant. (A quadrant is the area in one fourth (1/4) of something) Say we do not know anyone's gender but we DO know that two original partners are both in one quadrant.

Let's make this problem more interesting by being somewhat arbitrary in how we might group pairs of dancers into quadrants. Example: Say we have a tidal wave and our key couple happens to be the centers of one side.

Question: Does every quadrant have one boy and one girl?

Let's look at it logically.

First, how might this formation be carved into quadrants?
- We have no choice of the first quadrant, it is where our known-gender dancers are. Otherwise we can't make the original assertion that one quadrant contain two opposite-gender dancers.
- The mirror-image positions would define a second quadrant
- For the last two quadrants, I see two choices: Very End with Near Center -and- Very End with Far Center
  or
- The very center dancers are mirror opposites and must be the same gender so I'd argue these are functionally the same for the purpose of our discussion.
Now that we have quadrants defined, let's proceed. Note the following logic will apply in general no matter how we had to carve up the formation.
Our original couple are opposite gender: boy #1 and girl #1. They are in one of four quadrants.
Boy #1 has a same-gender mirror-opposite boy #3. Girl #1 has a same-gender mirror-opposite girl #3.
Mirror-opposite dancers should be in mirror opposite quadrants from each other. Boy #3 and girl #3 should be in a quadrant together. Their quadrant should be mirror-image across the square from the quadrant containing boy #1 and girl #1.
The two remaining boys must be each other's mirror opposites and the two remaining girls should be each other's mirror opposites.
If we try to place both remaining boys (or both remaining girls) into the same quadrant, we'll find we can't achieve arrangement symmetry (opposite dancers in opposite positions within the formation). The only possible solution is to have one boy and one girl in each quadrant with their opposites across the square in the mirror-image quadrant.

So if any quadrant contains a boy and a girl, then ALL quadrants must have exactly one boy and one girl. It is somewhat arbitrary how we carve the formation into quadrants, but the carving must obey the rules of symmetry. Looking back at the facing lines example, you can think of it as one particular way to carve facing lines into symmetric quadrants - by facing dancers.

Let's use this understanding to help us use some techniques to return the square to a known-arrangement state even though we know very little (if anything) about individual dancer's genders.

Gender-independent Normalizing Techniques

Assumptions - Using these partner pairing techniques assume the square is symmetric. This will be the case with normal symmetric choreography if the dancers have correctly executed all calls. It is also assumed that the dancers remember what gender part they are dancing and that only you (the sight caller) have lost track of the arrangement.

Original partners together in waves

This is one of the easiest techniques to use (assuming you know both dancers from at least one couple).

Without using gender-dependent calls, get all dancers into parallel Ocean Waves (R-H right handed or L-H left-handed).
Without using gender-dependent calls, keep the dancers in waves and call to bring any two original partners together as wave partners (neighbors) - one as an end holding hands with the other in the adjacent center position.
If R-H Waves: Call Boys Run (right). If L-H Waves: Call Girls Run (left).

Everyone should now be in standard arrangement couples. You'll get one of the following:

[0L] - standard arrangement Facing Lines
[0LO] - standard arrangement Lines Facing Out
[0F] - standard arrangement R-H 2-Face Lines
[L.0F] - standard arrangement L-H 2-Face Lines

It's tempting for the newer caller to call Bend The Line after Boys Run, because the result is convenient standard arrangement facing lines. True. However, you only have 1 chance in 4 that the flow will be good for everyone. There's no one (Mainstream) call you can call automatically and guarantee nice flow for ALL four possible resulting formations. Plan on a brief pause to evaluate which formation you get, then choose your next call.

If any boy is facing any girl (if any original partners are facing each other)

If all eight dancers are facing someone directly, no dancer is facing their mirror-opposite and any two facing dancers are opposite gender, then all facing dancers must be opposite gender. (See either "Facing dancers in facing lines" or "Dancers in a quarter of an eight-dancer formation" above)

From [L] or [B], if you see a boy facing a girl, you can confidently call Star Thru or Slide Thru to get everyone into standard arrangement couples. Note that's standard arrangement only, not necessarily facing lines! In fact, exactly 4 formations are possible.

From [L] + Star Thru, possible results are: [0P] [0B] [0T] or [0M].
From [B] + Star Thru, possible results are: [0L] [0LO] [0F] or [L.0F].

For help understanding these formation abbreviations, click here

To use this as an arrangement-normalizing strategy, call to bring the partners of one of your memorized couples together facing each other (avoiding all gender dependent calls) then call Star Thru. Have a flowing follow-up call in mind for all four cases so you can quickly call it the instant you identify which formation you get.

Consider a Star Thru equivalent...
--SldTh --T1/4 G-UTurn --LT1/4 B-UTurn --PasTh G-FaceL, B-FaceR
...or any of the following to get standard arrangement couples...
--T1/4 B-RunR --LT1/4 G-RunL

If you don't have a clue about anyone's gender...

(Good luck resolving the square!)

If you have either [B] or [L] and have no idea where boys and girls are and call Slide Thru, (assuming symmetry) you'll get one of 6 possible outcomes in each of the 2 boxes in the formation (2x4 or 4x2 has two 2x2 boxes)...

Facing Out Tandem Special Magic Box

A Special Magic Box

A "Magic Box" is half of a "Magic Column" formation (on the C1 list). It is a 4 dancer box formation where 2 dancers are facing each other and the other 2 dancers are back-to-back. There is one right-handhold and one left handhold.

The "Special" Magic Box has a very helpful arrangement state when using the calls above. If you get a Magic Box at all (1 chance out of 3) it will always be the best 1 of 6 possible arrangements states. The Boys will always be holding right hands and Girls will always be holding left hands. From the Special Magic Box, if the 2 dancers who are facing each other Pass Thru, the dancers will always end in standard arrangement couples (back to back in the box).

Take a moment to verify that the Special Magic Box indeed ends with standard arrangement couples facing out if Facing Dancers Pass Thru.

Using the Special Magic Box

Get facing lines [L] - arrangement unknown
"Slide Thru" (Note Star Thru is not legal from 2 of the 6 possible arrangements)
"(In each box of 4) - Those dancers that can - Pass Thru"

This will always give you standard arrangement Trade By formation [0T].

What might be more useful is look to see what you get after step 2 above. If you get the Magic Boxes case (called a magic column), call Those facing directly Pass Thru (no need to say "in each box of 4") to end in standard arrangement Trade-By formation [0T]. If you don't get the Magic Boxes case, look for one of these 4 formations...

[0B] - standard arrangement 8-Chain Thru formation
[0T] - standard arrangement Trade-By formation
[0P] - standard arrangement (beginning) Double Pass Thru formation
[0M] - standard arrangement Completed Double Pass Thru formation

If you are ready to recognize what you have and quickly call a flowing follow-up call, the dancers will never know you lost track of the arrangement.

You might want to use inflection in your voice on the Slide Thru to prepare the dancers to possibly expect something strange.

Waves U-Turn Back method - more versatile way of using the Special Magic Box

Get parallel R-H waves [W] - arrangement unknown
"Single Hinge and the Girls Turn Back"
"If you can, Pass Thru"
"Bend The Line"

This will get you to standard arrangement facing lines [0L] from any of the 6 possible starting arrangements. You may skip step 3 if you see that no one can Pass Thru. Of course if everyone can Pass Thru at step 3, you already have facing lines so you could optionally end there.

Left Hand Variation - Replace steps 1 and 2 above with the following (steps 3 and 4 remain the same)...

Get parallel L-H waves [L.W]
"With the Left Hand Single Hinge and the Boys Turn Back"

8-Chain Variation

Get 8-Chain Thru formation [B]
"Slide Thru" or "Touch 1/4 and the Girls Turn Back" or "Left Touch 1/4 and the Boys Turn Back" (these are all equivalent)

For reference, after step 2 of any of the above, these are the resulting 6 formations depending on starting arrangement...

[0L] - standard arrangement facing lines
[0LO] - standard arrangement lines facing out
[0F] - standard arrangement right hand two face lines
[L.0F] - standard arrangement left hand two face lines
[0I.L] - inverted lines, ends facing in - standard arrangement after Ends Pass Thru
[0O.L] - inverted lines, ends facing out - standard arrangement after Centers Pass Thru

If you get the magic box (inverted lines), a fun follow-up call might be: Those facing start a Right And Left Thru "cue: everybody finish with a Courtesy Turn". This always ends conveniently in [0L] standard arrangement facing lines.

Notes

The Single Hinge is not necessary, but it assures the best flow leading into the U-Turn Back given that we won't know who will be doing it.
For variety at Plus, you could replace U-Turn Back with Boys(or Girls) Roll Twice.

Other Useful Examples

In the following cases, the term "quadrant" specifically refers to the 4 corners (North-East, South-East, South-West, and North-West) in all of the following formations. That means each end dancer of a 2x4 formation would be in his/her own quadrant with his/her adjacent center in the same quadrant with him/her.

In waves, if any wave-partners (neighbors) are opposite gender, then an All 8 Circulate will not change that fact. All wave-partners will still be opposite gender. Why? - If a dancer has his original partner beside him as a wave-partner, then All 8 Circulate will take him to his original partner's mirror opposite which will be the same gender as his original partner.

After All 8 Circulate:

At Advanced, Trade Circulate has a similar effect as All 8 Circulate.

In any formation, if two original partners are not in the same quadrant, but are (one each) in two mirror-image quadrants, then all quadrants must have one boy and one girl. Why? - If our key dancer's original partner is far across the square next to our key dancer's mirror opposite, then our key dancer must be next to his partner's mirror-opposite.

Our key dancer and his original partner's mirror-opposite are opposite gender.
Our key dancer's mirror opposite and our key dancer's original partner are opposite gender.
In waves with the above relationship, All 8 Circulate will put our key dancer next to his original partner and the mirror-opposites (each other's original partner) next to each other.

After All 8 Circulate:

In waves, if original partners are both centers OR both ends of the SAME wave, you may find it hard to get to the wave-partner-pairing we want. At Advanced, the secret call is In Roll Circulate or Out Roll Circulate. At Mainstream, the secret call is Split Circulate.

After Split Circulate:

Just one Split Circulate from either situation above, and you may confidently call Boys-Run!

In waves, if original partners are opposite corners of the same BOX, you may find it hard to get to the wave-partner-pairing we want. The secret call is Centers Trade (or at Advanced Slip) and you may confidently call Boys-Run!

After Centers-Trade:

Note the previous two cases (Split Circulate case and Centers-Trade case) are a Single Hinge or Cast Off 3/4 away from each other. If you know one well and happen to get the other, you may use Single Hinge or Cast Off 3/4 to convert before proceeding. I like to visualize which call (Split Circualte or Centers Trade) would get my two partners into diagonal (mirror-opposite) quadrants to help me choose the correct call to use for the case I have.

At Advanced, in waves, if wave-partners are opposite gender (the goal of all examples above), you may confidently call Explode And Half Breed Thru to get nice standard arrangement facing lines!

See more of ALL8.com! - click here Richard Reel Hayward California USA