Movement 2: Communication through predictability, fun through unpredictability

I remember feeling that my understanding of 'dance mechanics' made a leap when I realised that the physics of each partner's body is a slave to the need for communication with the other partner. The partnership comes first; individual freedom within it, second. Understanding the communication then, is essential to understanding the physics obeyed by each partner in order to make that communication possible. When two people dance as a partnership, they are constantly sending and receiving information between them through vision, hearing and touch. Each partner (in most cases) can see, hear and feel what the other is doing and on the basis of all that information, can predict the trajectory of the partner's dance into the near future (on the order of a fraction of a second to a few seconds, depending on parameters like tempo) and make plans about how to cooperate with it. This post will begin with a simple introduction to the ways in which the human nervous system deals with sensory signals - how it notices things, uses what it notices to make predictions about what new things might come next, and ultimately 'gets bored' when those predictions are consistently easy to make. I must stress up front that this introduction will be pseudoscientific, making specualtions based on a few basic facts taken from real perceptual science. (I will pitch things at this level because to attempt a rigorous account would require vastly more research on my part and also because I don't think that going into all that detail is useful for our practically-focused purposes. Nonetheless, if you know that something I've written is at odds with the established science, please let me know so that I can correct it.) After their introduction, these ideas will be applied to a discussion of dance movement. The emphasis at this stage will be only on visual communciation between partners; tactile communication ('connection') will be covered later. Three physical principles of good dance movement will be presented, one which applies when following, one which applies when leading and one which applies in both cases, ie. all the time. Ultimately, it will be argued that good dancing maintains a tension between predictability at one level, and unpredictability at another, though it is the need for predictability on short time scales that governs what has come be taught as good dance movement.

The human nervous system is sensitive to change, not constants. Have you ever had the following experience?

You're about to go out for the day and you slip the usual things, like keys and wallet, into your pockets. It's been too long since you cleaned out your wallet and when you sit down on it - to drive somewhere, say - it's a downright uncomfortable, bulky lump. But within a couple of minutes your attention is elsewhere, you've stopped noticing the lump and can sit comfortably. Then, as you approach your destination and have long since forgotten about absent-mindedly grabbing your stuff on the way out the door, or the discomfort of the lump in your pocket when you sat down, you are suddenly hit by a worry that you might have forgotten to bring your wallet with you. In an attempt to check, you bring your attention to the delicate meats of your hind quarters to see if you can feel a wallet between them and the seat below. Nope, nothing. 'But I thought I grabbed my wallet on the way out!' You then reach down with your hand to double check and voila, there's your wallet!

Or how about other experiences like these: You walk into a restaurant and are struck by the smells of a menu-full of dishes all around you but after a couple of minutes, you don't notice them anymore. You have no trouble sleeping in the same room as an appliance with constantly-lit light on it but a flashing light of similar brightness makes it harder to get to sleep. You are able to concentrate on your work with a loud fan or air conditioner humming away in the background but the unpredictable (and not particularly loud) banging of a distant hammer by your renovating neighbours distracts you persistently.

All of these experiences are consistent with the finding that almost any persistent, unchanging stimulus (ie. signal from one or more of your senses) will gradually become less and less noticable. The gradual decrease in perception of a constant stimulus is known as habituation. Stimuli that change over time - like a flashing light - resist habituation for longer than constant ones, which is why we notice them for longer (the next time you're walking down a street with lots of neon signs, notice that some flash and some don't. The flashing ones are better at grabbing and holding attention.)

The details of the way in which a stimulus varies affect how long it takes a perceiver to habituate. For example, you will stop noticing the regular ticking of a wall clock long before you stop noticing the irregular hammer-banging of rennovating neighbours. This means that your brain, in processing information from your senses, is sensitive not just to changes in that information but changes in the changes. ie. A constant hum does not change. A ticking clock changes, varying from sound to silence at a constant interval with each tick, but this pattern of change is constant (the ticking interval does not change). Random hammering changes from sound to silence with each bang and this change is changing randomly; sometimes the hammering will be frequent, sometimes there will be long silences. In this latter case, because the signal (the sound from the hammer) is assumed to be (perfectly) random, it is impossible to predict, by definition. When you hear one bang, you cannot know when the next one will be heard; it may come soon, maybe not. By contrast, if we assume that the clock's batteries will never run out, then the clock's signal is perfectly predictable because its ticking is constant (the changes in the sound are not changing). You can predict when the next tick will happen based on when the last tick - and all the other ticks before that - happened. The random signal of the hammering is subjectively more interesting than the constant hum and the ticking clock because one can never know what's coming next, sound or silence. It 'keeps us guessing'. There is, however, a sense in which even this unpredictability is predictable; once the signal is established as random, it is also established that one will never be able to predict it, so the act of trying to predict it gets boring too. Eventually, one will habituate even to a random stimulus. If your rennovating neighbours keep at their random hammering for long enough, you will stop noticing.

Let us now consider cases in which a person wants not only to pay attention to a signal, but to somehow cooperate with it. For example, imagine you decide to tap your finger on the desk every time you hear a sound, and further, you'd like to make your tap happen as closely in-time with the sound as possible. In the case of the constant hum, the task is so simple and uninteresting that it hardly makes sense; you only tap your finger once when the sound is first perceived and since it never goes away, no more taps are required. One sound, one tap, game over. With the ticking clock, the task is only slightly harder and only slightly more entertaining. After a few ticks in which the rhythm is established, you find yourself able to keep good time with the ticks and the task becomes monotonous. Game over, almost as soon. With the random hammering, the game is impossibly difficult. It is interesting for a while as you struggle to find a predictable pattern so you'll know when to tap. Eventually, however, you will find no pattern and, if sane, will give up.

Although I have no hard evidence to back up my conviction, I think it can be concluded from these simple examples that the most entertaining tasks in which a person attempts to cooperate with some sensory signal are those in which the signal has some predictable components and other unpredictable components. The predictability makes the task achievable while the unpredictability makes it challenging.

Consider a group of jamming jazz musicians (to any accomplished musician readers, I apologise for whatever musical ignorance I may demonstrate in the following). As the musicians play, they each emit an auditory signal (their own music) and each receive the signals of all the other musicians in the group. Their task is to make their own signal combine with all the signals from everyone else in such a way that their combined total signal (the group's music) is pleasant to listen to. For each musician, certain elements of the task are predictable from the outset; the key and the tempo, for example. These provide 'home base' - a place to start from and come back to - for all the musicians; this helps to make the task achievable. What makes it interesting is the unpredictability in the indivdual musicians' choices about rhythms within the beat, melodies within the key, and all the other interesting variations in other musical parameters the can exist within the frame provided by tempo and key.

Now, let us consider the process of making a change in a property of the music, the predictability of which all the musicians are relying on in order to stay together. For example, let's say the drummer decides to double the tempo by the end of the phrase. Importantly, we have stated both a planned end point (a doubled tempo) and a time interval in which to get there. Strictly speaking, there are an infinite number of ways to make the transition. He/she could simply double the tempo within a single beat, at some randomly chosen point within the phrase. Such a sudden transition would be completely unpredictable and so would be impossible to work with for all the other musicians. How can the transition be made as achievable as possible for the whole group? Anyone who has ever watched a band do this together will know that it must happen gradually (unless there is a pre-made agreement between the musicians that it will be made is such-and-such a quick, fancy way). Over the course of the phrase, the tempo is gradually pushed higher and higher in such a way that all the musicians are able to keep track of each other's tempo. In general, the easist way to make such a transition is to make it as gradual as possible. Indeed, it is not uncommon for a whole band to change its tempo unintentionally over the course of a song because the change happens so gradually as to be imperceptible from moment-to-moment. Another way to describe this kind of change is to say that the rate of change is minimised. This allows for mutual predictability between the musicians in such a way that they are able to work together while still being able to play interesting parts (which have some degree of unpredictability) as individuals.

What can we infer about dancing from all this? There are implications for both movement and connection. We will discuss movement now and connection later. In light of the material presented in the last post, we will simplify things by focusing on the motion of each dancer's centre. Just imagine a tiny marble floating in space, located near each dancer's bellybutton. We will consider the motion of that marble to represent the motion of the dancer.

We will now introduce some basic physical concepts of motion. No matter who you are, you will already be familiar with these through experience, even if you've never really thought about them in this way before. The first concept is simply the position of an object. In order to be meaningful, position must always be stated as a distance from some other object (eg. Q: 'Where do you work?' A: 'Three blocks north, up the street from where I live.'); for our purposes, we can think of a change in an object's position and a change in the distance the object has travelled as the same thing. Now, the rate at which position or distance is changing with time is called speed or velocity. Finally, the rate at which speed is changing is called acceleration. That is, acceleration is the change in the change in position as time passes.

Let's apply these ideas to a simple 'thought experiment' with two dancers dancing a Lindy 'swing out'. Using our simple model (as per the last post), we imagine the little marbles at the dancers' centres of mass. The following description refers to the dynamics of those marbles. At the beginning of the swing out, the dancers are momentarily not moving. That is, their speeds are zero. Their positions are located two semi-outstretched armslengths away from each other. Even though their speeds are zero at this point, their accelerations are nonzero because there is energy being passed from the leader to the follower (the leader is leading). Acceleration is the rate of change of speed, so this means that the dancers are speeding up. The following is an important point; try to remember it because we will refer back to it later:

Whenever a dancer is speeding up, slowing down or changing the direction of his or her movement, he/she is accelerating.

After the acceleration period at the beginning of the swingout, there is a brief 'coasting' period for the follower, in which her/his speed remains constant (actually, we will see later that the best dancers minimise this coasting period, usually removing it altogether by linking the speed-up directly to the slow-down). As the first half of the swingout ends, the leader will lead the follower to accelerate again (it's natural to think of this as deceleration because the follower is slowing down but in strict physical terms, it's an acceleration because it meets the criteria of the above definition) until she again comes to a momentary stop. The second half of the swingout is essentially the same process in the opposite direction. This simple little example was intended to illustrate how dance movement can be thought of in terms of the simple dynamic quantities of position, speed and acceleration, all of which change as the dance proceeds.

We are now finally in a position to introduce the three rules of good dance movement that were mentioned at the beginning of this post. These are rules for movement and mention nothing about connection at this point. They may seem counter-intuitive until considered in conjuction with the rules of connection to be discussed a little down the track. We will simply state the rules first and they will then be discussed in the context of predictability.

1) When following, do not accelerate yourself. Rather, maintain the same speed and direction of movement you have 'left over' from the last lead until this is changed for you with another lead. This applies to both straight line movement (the physical term for a straight line movement is a 'translation') and turning ('rotation').

2) When leading, accelerate yourself (NOT your partner). That is, change the speed and/or direction of your own movement.

3) When following and when leading, minimise the jerk of your movement.

Ok, let's start with 3) as you're probably wondering how jerking got into all this. Believe it or not, 'jerk' is a formal physical term, which refers to the rate of change of acceleration. That is, jerk is the next in the chain that goes

position --(rate of change)--> speed --(rate of change)--> acceleration --(rate of change) --> jerk

The name, 'jerk' has stuck because it has intuitive meaning. Imagine picking up a heavy suitcase. However this is done, the suitcase must be accelerated off the ground. However, if it is done in a 'snappy, jerky' way, the rate of change of the acceleration (the jerk, in the physical sense) is high. If the suitcase is picked up in a 'smooth, flowing' way, the rate of change of acceleration is low. It is well known in biomechanics that people will naturally perform many different motor taks in such a way as to minimise the jerk of the masses being moved. One example is picking up a cup of coffee while taking care not to spill anything.

Note that we encountered the principle of jerk minimisation (in a metaphorical sense) in the above description of how a band can work together while changing tempo. If the drummer were to double the tempo within a single beat, the transition would be far too 'jerky' for the rest of the band to keep up. However, if the drummer has decided on a time frame for the transition, he/she can make sure that it happens as gradually as possible (with minimum jerk) over that time interval. This makes it as easy as possible for everyone to work together during the transition.

Stepping back from the musical metaphor and into the physical world of dancing, let's see how 1), 2) and 3) work together in the process of one dancer giving a lead to another.

Step 1: The leading dancer will decide on a desired consequence for the motion of the partnership and the time frame in which this consequence is to be achieved. For (simple) example, a reversal of direction for both dancers. The leader will begin the process by accelerating him/herself with minimum jerk and with enough energy that in addition to his/her own direction being changed, enough energy will also be available to flow through the connection to the follower. During this time, the follower is thinking only about continuing her movement and is not herself changing that movement in any way, even though she sees and feels the leader move his own body, and feels the energy that he is giving begin to alter her motion. The key point here is that she is neither deliberately resisting the lead nor adding to it. Her motion begins to be altered almost instantaneously (the time delay is due only to the speed of sound through their connection, which is pretty damn fast - Yes, literally the speed of sound, like the speed that jet fighters fly at. This will be explained more later, when we talk about connection) but the alteration takes time to build; it arrives gradually, over the period during which the lead is giving energy (ie. leading).

Step 2: After the leader's self-acceleration has begun, it takes some time for the energy to flow through the connection to the follower. The energy does not all arrive at once but gradually, over an interval of time. During this time, the follower allows the energy to gradually accelerate her. She does not add any extra energy to her motion, above what she is receiving from the leader. She controls her reception of the energy in such a way as to keep her movement 'smooth' (minimise the jerk).

Step 3: With the energy transmission complete, both partners now 'move as followers', conserving their state of movement without adding extra energy. When one partner does choose to add energy, doing so will function as the next lead and the energy will again be passed through the connection so that it is shared between both partners and their motion will be changed again.

In this process, we see both the elements of predictability and unpredictability that make for dancing which is both achievable and entertaining. The dancers control their movement so as to be mutually predictable on the time scale in which leading and following happens (less than a second to a few seconds). This allows them to work together through transitions in their shared movement. However, choices about who will lead what and when are largely unpredictable, keeping the dance interesting.

Before ending this post, a special condition should be mentioned. The above rules apply only when both partners are dancing on balance. Counterbalance - where both dancers are off balance in opposite directions in such a way that their imbalances cancel each other and the partnership as a whole remains balanced - is a different story. This will be discussed properly, much further down the track. First, however, it is time to discuss the practical details of jerk minimisation by focusing on the biggest myth in dancing: the step.

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