Introduction: special thanks to Dave Wilson and Vic Ceder for their contribution to this article.

This article is about square breathing. It aims to explain the whole issue and also destroy some myths or repeated falsehoods. The facts listed here are valid across all levels, they are not only Challenge specific. The level-depended effects will be clearly highlighted.

This article provides the set of rules, which are not documented by Callerlab, but are fundamental to our current dance style starting with Basic. The article describes how to breath correctly in every case. It also provides directions of thinking, which must be done during or after the call execution.

Terms

To understand the square breathing is necessarily to understand the meaning of few terms. Dance spot – a spot in a formation is, or may be, occupied by a dancer. For example, the formation “Wave of 4” has four spots. Between the ends of the wave are two spots. Free space (space) - space is any area not occupied by any dancer. This area is not part of the formation and exists only because people need some space around them. Phantom - this term refers to an imaginary dancer who is dancing at some particular place. The phantom is part of the formation and it is needed to take it into account the process of formation adjustment.

Example of a free space

Consider a formation of two parallel waves, which is the formation of 2 x 4.

Image is deliberately drawn to show unnecessary space. Although between the waves is a larger than necessary space, it is still just a vacancy with no phantoms. This space is not counted in the call execution, it is here only for convenience of people. In practice this means that on the call Boys Circulate the trailing boy moves on the spot of the lead boy. In the definition of Circulate there is nothing like “on a Circulate you must go two steps forward”.

What is square breathing

Square breathing is the way formations change shape. The total size of the square doesn't change very much, but it becomes shorter in one direction as it widens in the other, and it becomes taller as it narrows. When seen from above, the square seems to be pulsating.

Why is this happening? Let's look at the example. Consider two parallel ocean waves. The call Spin the Top takes a wave which is 4 spots wide by 1 deep, and turns it 90 degrees, so it's quadrupled in one direction and divided by 4 in the other direction. Parallel Waves are 4 x 2 at the start, but the Tidal Wave after Spin the Top is 1 x 8. The waves "breathe out" away from each other to make a space in the middle.

Breathing also works the other direction. Starting in a Tidal Wave, the call Recycle (in each wave of 4) produces Facing Couples on each side of the square. If dancers didn't adjust, they would be too far apart to hold hands in the center of Facing Lines. The square must "breathe in" to make nice Facing Lines.

The basic principle of square breathing is to add or to remove free space so that dancers still feel comfortable (not too crowded) AND they assume a required formation.

Breathing rules

Rule 1 – breathing is for everybody

Square breathing is not just for active dancers. Sometimes inactive dancers must adjust, even though the call tells them not to move.

Example: from a Squared Set, Heads Swing Thru requires the Sides to adjust slightly backwards, in order to give the Heads sufficient room. In the Chapter “Extended applications” is discussed less obvious cases.

Rule 2 - if the call is directed to certain part of the square (six or fewer people), the call must begin and finish in the same part of the square

From certain point of view, the rule 2 is THE breathing rule. If you follow this rule, you cannot be wrong in the execution of the calls. The best way, how to follow this rule, is to divide the whole set into the imagined rectangular pieces defined by the given call, then each rectangle executes its part of the call (which may be also just staying and nothing more) and finally each rectangle slides so as not to overlap the others nor be far apart from them. The rectangles must border each other.

A well known example: let us have two parallel waves. After the call Fan the Top the formation will change to 1 x 8. If the waves were at the beginning far apart, perhaps there would be no problem. In most cases, however, the dancers must stretch out a bit and make room for emerging Tidal Wave.

Another example. Consider the formation of Lines facing in. After the call Step and Slide, Centers should take a step forward and Ends slide together. Dancers must make sure however, that the Centers did not do such a big step forward, so as not to Pass Thru. The resulting formation would be completely wrong. Proper execution is such that the Centers step forward either very little or not at all. It is important to stay on their half of the set. Then Ends probably retreat a little.

Similar behavior is needed in the execution of the calls like Wheel and Deal, Turn and Deal, Step and Flip and the like.

The rule is applied always and anywhere, even for two persons calls.

Starting formation for Step and Slide		Resulting formation

The same behavior is required also from Tidal Wave setup. Consider the Tidal wave with the Girls as Center 4 and Boys Outsides. The call is: Girls Recycle, Boys Explode and nothing.

Starting formation
Correct resulting formation	Wrong resulting formation

 Space invaders

In square dancing we have a certain small group of calls known as SPACE INVADERS. In order to understand space invaders you must have an elementary understanding of matrices. In square dancing, quite often, when speaking of space invader (SI) calls, we have to assume that we are on a grid; a matrix which is quite often 12 or 16 possible spots on the floor. Even though we physically occupy only 8 of those spots on the floor at one time, we are bound to the confines of the matrix's 16 or 12 spots on the floor. (Occasionally, the matrix grows, but let's limit ourselves and not concentrate on this.)

Picture of parallel ocean waves the dancers are standing on 8 spots of a 16 matrix formation.

Much the opposite of square breathing, in executing SI calls, we neither breathe as the non-active dancer nor breathe as the active dancers after (or during) the execution of the call. In the example below, on the call "Ends Fold", the non-active dancers do nothing and the active dancer assumes one of the positions of the 16 matrix setup.

Starting formation	Resulting formation

The square does not breathe executing a space invader call.

Space invaders are:

The Fold issue

Fold IS a space invader, and as such has the ability to create spots (= change the matrix). The problem is that dancers below C1 have not tools and knowledge to deal with phantoms and unknown matrix.

Consider Lines facing out. While the call Ends Fold is perfectly smooth (the result is a matrix of 2 x 4), Centers Fold causes problem. The resulting formation should be a matrix 4 x 4, but due to inability to work with phantoms most people breath to get a formation 2 x 4. Thus, unfortunately, breathing becomes level-dependent. It is the only exception to the otherwise consistent rules of breathing.

Consequence: in Recycle definition the “centers fold and adjust to a box” is part one. The breathing IS part of the first part of the call.

The Diamonds issue

Between the Points of diamonds are no spots, only free space. Diamond is 3 x 3 formation.

Twin Diamonds formation is as follows:

As is evident from the picture, although between the two end girls are two spots, between the boys is no spot. What does it ultimately mean? The formation may be diamonds, though perhaps not at the first glance. Formation on right picture is (also) diamonds.

Similar situation as with diamonds is with 1/4 and 3/4 Tags. Theoretically, from breathing point of view, Twin Diamonds, 1/4 and 3/4 Tag occupy the same footprints.

	1/4 Tag	After Boys 1/4 Right -> Twin Diamonds	After Boys 1/4 Right -> 3/4 Tag
Before adjustment
After adjustment	---

The Square Set issue (aka Heads Pass Thru issue)

Movements (usually first in sequence) done from Square Set (SS) formation are specially treated. Let's have a look at what Callerlab says. Sentences important for breathing are highlighted.

Why do we speak about this? We inherited Square Set from the traditional country and square dance, which used this formation in 80% of the dance time. Modern square dancing doesn't know how to work with SS precisely. Let's look at the formation closer. Everybody knows this picture:

As we already know, modern square dancing uses matrix not only for description of the formations, but also for execution of the calls. From this point of view, do we have a free space between the dancers, or spots?

	Do we have spots between dancers? Definitely not up to C1 (actually nor any further), because if we had the spots, we couldn't do Heads Pass Thru.
	Do we have free space between dancers? If yes, people are allowed to move to make a compact formation. Picture shows one crazy, but theoretically possible, example. Even from here we cannot do Heads Pass Thru. (By the way, if the dancers breath vertically, result would be the same likewise after Heads move in)
	Do we have some sort of distorted formation(s)? Very presumably yes, even though the kind of formation is depended on the call (details are discussed further).

With the last picture distorted formation was mentioned. This is probably the best answer to the issue, even though this angle of view does not cover whole problem. The reason is that a kind of distorted formation depends of the given call. See the following examples:

Note: unlike the other distorted formation concepts (as “O”, Butterfly and similar), many calls starting from SS finish in normal setup. Therefore SS is not fully distorted formation like we know them from Challenge levels.

Why we don't like Callerlab’s Squared Set Convention

Because it produces different results for equivalents, which should produce the same results – that's why they are called equivalents. Look at these examples:

Consequences of this convention are big, they produce ambiguity, examples see in the table:

How to deal with Callerlab's Squared Set Convention? Square dance is based on definitions and Callerlab is the only institution allowed to maintain them. And because any system is better than no system, we should accept SS convention, but we recommend to stay in the center of the square after each call and back off if necessary.

Special cases

There are special cases excluded off the rules mentioned above. The cases are calls done on the ring or squared set. These calls are:

Extended applications

Dancers usually breath intuitively however, there are cases when dancers must think about breathing by purpose, otherwise they would finish in a wrong formation.

Case 1: Trailers In from 2-faced lines

Consider 2-faced lines and the call "Trailers In".

This combination is difficult; many dancers would not dance it right without prior knowledge. The issue is that people must breath not only vertically, but also horizontally.

Wrong resulting formation	Correct resulting formation

First picture is not correct, because Trailers In is not a space invader.

Case 2: Step and Slide from Tidal Line

First part of Step and Slide is “step forward”, which IS a space invader. Resulting formation are Triple Lines.

Starting formation	Resulting formation

Case 3: From Butterfly Center Box Peel and Trail

Starting formation	Correct resulting formation	Wrong resulting formation

Case 4: From Twin Diamonds Centers Lockit

Starting formation	Correct resulting formation	Wrong resulting formation

Case 5: Beaus Half Run and Roll from 2-faced line

Run is not a space invader, resulting formation is a box. Compare with Beaus Fold.

Starting formation	Resulting formation for Beaus 1/2 Run & Roll	Resulting formation for Beaus Fold

Same logic will be applied for example from normal lines facing out: 1/2 Boys Run and Roll. Resulting formation is 8 Chain Thru, not Triple Columns.

Case 6: Examples of some collisions and fractions

Starting formation	After Exchange the Diamonds 1/4
Starting formation	After Split Circulate
Starting formation	After Split Circulate 1-1/2
Starting formation	After Exchange the Boxes 1/2