Originally Printed in Zip Coder Magazine, April 1989
In a recent article (Zip Coder, February 1989), Bill Heimann did an excellent job of delineating the difference between high quality and high level dancing. I would like to take the liberty of summarizing the main points of Bill's article (or at least what I perceived to be the main points) so that I can use them as a springboard for my own remarks. Bill made the following points:
In reading Bill's article, the first thing that struck me was that Bill's list of good dancer criteria actually consisted of a single point, with a number of supporting elements. Most of Bill's criteria were in fact specific instances of his first point - better dancers make fewer mistakes. I think that better dancers make fewer mistakes because they have a good grasp of fundamentals, are adaptable, can deal with distorted setups, are precise, recognize errors, and know how to recover. Further, dancers who make few mistakes tend to be confident and are more liable to be able to help others. Therefore, I think that Bill's list actually boils down to a single point: better dancers make fewer mistakes.
While I do not wish to argue that a low error rate represents the only virtue a good dancer need possess, it seems clear that the level of error exhibited by dancers must represent the single most important criterion in evaluating how well they dance. This being so, I think it might be instructive to examine dancer performance from this point of view. How many mistakes is it reasonable for a competent dancer to make in the course of an evening? How many sequences out of a tip is it reasonable to expect a square to execute successfully?
First, we need to define what we mean by mistake. I'm not talking about momentary hesitations or false starts. I'm referring to those killer mistakes that cause squares to crumble. I call these fatal errors. I define a fatal error as follows:
An incorrect action (or inaction) which:
In pondering this, it quickly became evident to me that there is no easy answer. It is easy to say 2. or 17. or 89, but without a supporting rationale, the number itself has no meaning. The underlying premise in our concern with dancing errors is the fact that mistakes contribute directly to broken squares and broken squares result in dancers being transformed into spectators who watch the other squares dance. Our problem is that we consider the proportion of time spent spectating to be growing to unacceptable levels. This line of thought splits my original question into two:
Since we are concerned with the number of mistakes dancers make, it is useful to quantify that as an error rate using the number of sequences danced as a base. For instance, if a dancer makes fatal errors at the rate of 1 error every 5 sequences, it follows that he or she dances faultlessly 4 out of 5 sequences. In other words, you could say that the dancer executes without error 80% of the sequences called. This value can also serve to express the probability of that dancer executing any given sequence successfully. Henceforth, I will refer to such a dancer as an 80% dancer.
Now let's examine how well dancers with various probabilities for dancing error-free might be expected to do. Let's suppose that each of the dancers in the square dance 90% of the sequences without fatal error. A mark of 90% is usually considered pretty good in school. In dancing terms that means that you blow one sequence in ten. We are interested in is the probability of 8 dancers, each with a 90% probability of dancing error-free, making it through a sequence without any one of them making an error. Statistics tells us that the formula for this calculation is to take the product of all the probabilities. Therefore, a square composed entirely of 90% dancers could expect to make:
.9 x .9 x .9 x .9 x .9 x .9 x .9 x.9 = .43 = 43%
LESS THAN HALF of the sequences
Or in other words, they would be standing around more than half of the time. I do not think many would be prepared to argue that spectating for more than half of the time is satisfactory. Let's look at this from another angle. Suppose we apply our 90% number to the entire square instead of the individual dancers? How well do the dancers have to dance in order for a square to make 90% of the sequences? We need a number n such that:
n x n x n x n x n x n x n x n = 0.9
If you work it out, it turns out that n = 0.987 or 98.7%. In order for the entire square to make 90%, each individual needs to be dancing at 98.7%.
This seems like a very high performance level. After all, in school only genius level students get 98.7%. When you consider that the average 2-1/2 hour dance comprises 7 or 8 tips each containing 10 or 12 sequences, 98.7% represents, at most, one mistake per night. Perhaps attempting to achieve a 90% level of success for the square is shooting too high. However, we have already seen that 90% dancers will stand for more than half their time on the floor, so it is clear that whatever value we use will have to be higher than that. By now many of you will be saying to yourselves, But that doesn't make sense. I've danced in squares with totally incompetent dancers, and we still got most of the sequences. These numbers can't be right. And, of course, they are not. What the above calculations overlook is the fact that many, if not most, mistakes are corrected before the square dissolves. In fact, when dancers know one another well, many mistakes are anticipated and prevented before they are made. That is, there are dancers in the square who not only dance their own parts flawlessly, they also correct at least some of the mistakes of others.
Another way of looking at this is to say that dancers who correct others are, in effect, dancing higher than 100%. They are dancing 100% of their own parts, plus some parts that should be executed by other dancers. For instance, let's assume we had a square composed of six dancers dancing 100% and a seventh dancing 80%. If the eighth dancer merely dances 100%, then the square gets 80% of the sequences. But if the eighth dancer can dance all of his or her own part, plus fix half of the seventh dancer's mistakes, the square could attain 90% success. Thus, it can be argued that the eighth dancer is performing at 110%; 100% on his or her own behalf, plus 10% of the seventh dancer's responsibilities. If one of the other dancers could also manage this feat, then the square could theoretically attain a 100% success ratio despite the presence of an 80% dancer.
This phenomenon is an integral part of the dancing process. More often than not, when one dancer makes a mistake, another dancer is able to correct it and avoid damage to the square. This process is essential to a healthy square and is a normal part of good dancing. Where it becomes pathological, however, is when the help always flows in a single direction. Instead of a bi-directional interplay, we have one person who always helps and another always on the receiving end. I believe that this last point goes straight to the heart of the quality-of-dance issue. If we were to survey the dancer population at any given level, the skills of the dancers could be grouped into three categories:
So we cannot just dump these phase 1. dancers - they are the future. Since they require help, however, they must be balanced by an appropriate number of phase 3 dancers. In a perfect world, any given level would always be populated with dancers from all three phases in balanced proportions - for instance 20% in phase 1, 60% in phase 2, and 20% in phase 3. But the world isn't perfect and therein lies the crux of our problem. Because of the pressure to advance from level to level, many people are short-cutting the three phases. They progress from phase 1 to phase 2 and then move up to the next level (where, of course they are phase 1 again). As this becomes more prevalent the proportion of phase 3 dancers at all levels starts to erode which diminishes the help that is available to the new dancers. With less help available, phase 1 dancers progress to phase 2 less rapidly - or not at all.
Now comes the most insidious part of the process. New dancers arriving at a level find that there are no phase 3 dancers available to help them become competent. Nobody at this level seems to know what they're doing. But, of course, we all know that the better dancers all dance at some level higher than we do, therefore the answer is to memorize the calls on the list for the next level and move on up. This process results in dancers who have yet to master C1 showing up on C3 floors.
As Bill Heimann said towards the end of his article, it is time to clean up our act. We need to acknowledge that when we present ourselves on a dance floor at any given level, we have an obligation to the other dancers. That obligation is to dance our fair share of the material. To the extent that we cannot dance our fair share, we represent a burden on the other dancers, one which we imposed upon them unilaterally by arriving in their square. What is our fair share? I believe that it varies with experience at the level:
If you move on without repaying the help you were accorded, you are short-changing the people who follow you into the level. If you move on before you are competent at the level you are currently in, then you are short-changing both the level you leave and the level you move to. But most important of all, you short-change yourself.
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