Connection 2: Elastic muscle magic

Alright, it's business time. If you've ever wanted to understand dance connection - I mean really get to the bottom of it - this might just be the post for you. Recall the following definition from the last post: Connection is achieved when the motion of one partner's centre of mass is influenced by - and influences - the motion of the other partner's centre of mass, in a predictable way. A stronger way to state this is that when two dance partners achieve continuous connection, any observer (including the dancers themselves) who has knowledge of the motion of just one partner's centre of mass (COM) can in principle predict the motion of the other partner's centre of mass. Given all the possible complexities in the motion of two human bodies, this is quite a feat. It is natural ask, how is this possible?! In this post, we will introduce a system of muscle control, which can be followed by each dancer in a partnership in order to achieve this predictable mutual influence simply. In a word, this system is elasticity. But that familiar word means many things to many different people. We will make it our business here to come to a clear understanding of its fundamental meaning and how that applies practically, in dancing.

Haptic communication

First though, we will return to the idea introduced earlier, that the physics obeyed by each partner's body is a slave to the need for cooperation between partners. We don't use a system of elastic connection just because; we use it because it allows each partner to feel how the other's COM is moving, and to influence that in a controlled way which is predictable to both partners. It's pretty magic, really. Ok, consider this: Experienced dancers can dance well with their eyes shut; both follower and leader (ignoring the obvious problems associated with crowded dance floors). I love leading with my eyes shut but it only works with experienced (though not necessarily familiar) followers with whom I am able to move and connect in such a way that my brain receives enough clear information just from the mechanical, tactile connection between us that I am able to predict my follower's motion and interactively control it. The inverse is also true - a follower can only rely on the signals from touch alone if her leader is able to move and connect in such a way that she gets enough information to feel and predict how he is moving (Note: As discussed earlier, there is nothing wrong with a follower predicting how her leaders is moving - if fact, it is useful to do so - so long as she's still truly following and not 'correcting' her motion based on her assumptions about what he might be trying to lead. There are no choices about what to do while following purely; there are only choices about how to be - how to hold oneself and control the elasticity of one's muscles - as we shall see). The technical term for this kind of touch-based communication and control is haptic. Connection allows dancers to achieve haptic communication and shared control.

Listening within yourself to hear your partner

Now, for an interesting question: How can it be that one dancer can predict the motion of the other dancer's COM from haptic signals alone when (s)he is receiving no sensory cues directly from that place? There are no nerves which connect a follower's COM to her leader's brain. The only part of the follower's body with which the leader's nerves are in direct contact is the small area of skin or clothing that (s)he happens to be touching at any given moment - hand-to-hand or hand-on-back contact, say. And the information available from this point of contact (texture, temperature, pressure) is limited in its usefulness for telling much about the follower's motion. So, how does the leader ('he'/'his' from now on, for simplicity) do it? He might not know the details of what his follower's ('she'/'her', from now on) body is doing, but he is privy to a wealth of sensory information coming from within his own body. So, what the leader is doing is monitoring what's going on inside his own body and on the basis of that information is able to reliably infer what his partner is doing. Or, put another way, a leader is able to tell what his follower's centre is doing just from all the information that his brain receives about his own muscles and limbs. And vice versa for a follower. It's amazing!

How is this possible? We will eventually see that it's because both leader and follower have learned to hold a particular kind of relationship - and elastic relationship - between the shapes in their 'frames' and how hard they are pushing or pulling on their partner. We will have to build up the story gradually before this is obvious, however, so let's get started. Every skeletal muscle in your body has little sensory organs attached to it, which continuously sense essential information about it, and tell your brain what it's doing. One organ, called the 'muscle spindle', tells your brain how long/stretched your muscle is and how quickly that stretch is growing or shrinking. If someone grabs your hand unexpectedly and pulls hard on it, the muscle spindles in your arm muscles tell your brain that those muscles are getting longer, quickly. At the same time the 'golgi tendon organ', which is integrated into the tendon that connects each muscle to a bone, measures the tension force in the tendon (and therefore, the muscle). So, in the example, if your arm is being pulled on, if you have a limp arm and don't create any tension by resisting, the golgi organ will tell your brain there's no tension in the tendon/muscle, even if the muscle spindle is saying that the muscle is stretching and stretching quickly. It turns out that together, all of your body's muscle spindles and tendon organs provide your brain with all the information it needs to put together a complete picture of how all the parts of your body are moving, and make predictions about how to control that by activating various muscles (Ok, so in reality there is more information required from other organs as well for a truly complete picture, but for the purposes of our discussion, we can make do with the above). So, if you did decide to firm up your arm to resist the person pulling on it, your brain would quickly figure out that the pull might put you off balance and it might need to make one of your legs take a step in order to prevent you from falling over. This, of course, is exactly what happens in a follower's brain when she is led by a pull on the arm.

Ok, so we now have an idea of how a person's brain is able to monitor the dynamics within his/her own body. But how does this allow him/her to infer reliably, where a connected dance partner's centre is? Answering this question is a bit more involved and we will have to build up to the answer, one step at a time.

Chain, not frame

To begin, I'd like to introduce the concept of what I call the 'muscle chain'. By this, I mean the sequence of muscles which spans the distance from one dancer's centre/COM to his/her partner's centre. It now becomes convenient to identify the centre with the hips (as is often done by teachers, and it's a reasonable approximation), since the centre itself is only an abstract thing and has no muscles attached to it. So, we can think of the muscle chain as beginning with the 'core' muscles attached to the leader's hips and running up his torso. Next come the leader's chest, upper back and shoulder muscles, and then his upper arm and forearm muscles. Progressing to the follower's half of the muscle chain, we begin with her forearm muscles and proceed all the way to her hips through the same sequence of muscles as for the leader, but in reverse. The muscle chain is a mechanical communication device between partners. Each half of the muscle chain is commonly referred to as each partner's 'frame'. I prefer not to use this term because I think it places the focus on shape, and shapes by themselves are of little consequence to good connection (If I had a dollar for every time I've seen a world-class dancer 'break frame' by letting their elbow drift away from/behind their hip, as I was told as a beginner never to do, I would be a rich man. It has been a long time since I've felt that 'frame vs. breaking frame' is a concept useful to anyone but beginners.) What is important, as we shall see, are relationships between shapes and forces. So, we will stick with the term 'muscle chain' and avoid 'frame'. In order for the leader's centre to lead the follower's centre, energy must be transported through the muscle chain. There are many, many ways in which this can happen and most of them are not conducive to good (by our definition) dancing . In order to understand why not, and more importantly, which ways are conducive to good dancing, we must take a step back for a moment and take a look at how muscles work.

Subtle muscles

One can think of a muscle as being made up of lots of little fibers which interlace like the fingers of two hands pointing in opposite directions. And, like those fingers, the fibers can slide over each other as their far ends move further away or closer together (as happens if the arms attached to the hands are pulled apart or pushed together). When a muscle contracts, chemical energy from food and oxygen is used by molecules at the surfaces of the muscle fibers to force those surfaces to slide over each other such that the overall muscle gets shorter. This is the usual process we associate with a muscle doing work. But there is another way the muscle can do work, and that's by extending. Imagine you're standing up, holding onto a shopping bag with one hand, and you've lifted the bag quite high off the ground (by contracting muscles). Now, you want to gently lower the bag to the ground to protect the contents from the damage they would suffer if you simply dropped the bag. So, instead of dropping it, you slowly lower your hand, lengthening your arm - and its muscles - in the process. Your muscles are doing work - giving energy - by preventing the bag from falling suddenly but they are extending while they're doing this work, burning up food and oxygen as they go, in the same way they do for a contraction. We will refer to this kind of behaviour in a muscle as active stretch (The technical term for it is 'eccentric contraction' but this is just a little too confusing, I think!). It is important to note here, that you can choose the rate at which the bag lowers to the ground by choosing the elastic strength in your arm muscles as you lower it. One can think of this as the level of muscle 'flex' or 'tone' which is sustained throughout the movement. If you choose a high level of elasticity/tone, the bag will lower more slowly. If you lower the elasticity/tone - relax the arm more - you will let the bag fall faster. If you relax completely, the bag will fall at the same rate as it would if you just dropped it. We can think of your arm like suspension (as in the springs+shock absorpers attached to car wheels) for the bag's fall.

Active stretch: the key to advanced connection

Ok, so far so good, I hope. Now, we need to push - no, I should probably say stretch - this concept of active stretch a little further. This is important, so stick with me here! An arm actively stretching can be used not only to slow something down, but also to speed something up. Let's take the above bag example in reverse. Imagine now that you want to pick up a heavy bag off the floor and lift it onto a shelf. There are many ways to do this. The most intuitive/familiar way is to grab the handle and pull it upwards by contracting your arm/shoulder muscles. Once the bag has reached the desired height, you 'lock' your muscles, keeping them at a constant length, and walk to/lean over the shelf before switching your muscles into active stretch and lowering the bag as described above. Now, I'd like you to consider a less intuitive way to lift the bag onto the shelf. This way is not really practical/necessary for lifting bags but it essential for good dance connection, so humour me. In this way of lifting the bag, you hold all your upper body muscles - your muscle chain between your and the bag's COM - at a comfortable, relaxed length (instead of straightening your arm to reach down for the bag) . In order to get your hand down the height required to grab the handle, you bend your legs as far as necessary, keeping you muscle chain at a relaxed length. Now, once you've grabbed the handle, you take a look at the path of motion required to get the bag from where it is to where you want it to go and you estimate how much energy you will have to give it in order to get it there in one smooth motion (without any muscle 'locking'). This estimate might not be easy to make the first time but with practice it becomes easier. The key parameter to estimate is how much elastic strength you will need to hold in your muscle chain. Having made your estimate, you contract your leg muscles, pushing your hips upwards and towards the shelf, sending a pulse of energy up through your centre and through the muscle chain, to the bag's COM. All the while, the muscle chain is only stretching. That is, the muscles between your centre and the bag's centre are only getting longer throughout the entire process of moving/giving energy to the bag. Eventually, after your legs have pushed and your muscle chain has stretched enough, the bag will be moving fast enough to get where you want it to go, all by itself. It will cruise through the air and land on the shelf. Of course, the landing will be hard if you don't move yourself along with it and use some more active stretch at the end to slow its landing. Even in this lifting-through-active-stretch case. we can again think of your arm as acting like suspension, buffering the acceleration of the bag off the floor from the rapid acceleration of your hips as they are pushed by your legs. You muscle chain passively conveys energy by actively stretching. This contrasts with actively adding energy with your arm muscles by contracting them.

Just before we leave behind this gory exploration of active stretch, I'd like for us to step out of the leader's shoes and into the follower's. Here's another non-dance example that illustrates how active stretch works, but for a follower. Imagine you are a particularly acrobatic follower who is partial to climbing trees. While you are climbing one day, you decide you will drop down off one branch and catch yourself by grabbing onto a lower branch with your hands as you are falling past that branch. How will you hold your arms as your first grip the branch, and how will you use your muscles to buffer what might otherwise be a clunking halt? Anyone who has ever done something like this knows that you don't grab onto the branch with dead straight arms. Instead, you have your arms at a comforable bend, leaving plenty of room for them to actively stretch and slow your stop. How fast you are falling when your hands first grip the branch will determine how much elastic strength you will need to carry in your muscles in order to slow yourself to a stop over the course of their stretch. What you are most certainly not doing is trying to contract your muscles at any point between gripping the branch and stopping at a comfortable hang; you will have a hard enough time just letting them stretch in a safe, controlled way! The branch here is playing the role of the leader, changing the direction of the follower's motion (from downwards to stationary; this requires an upward force). What the follower is doing (inadvertently in this case) is continuing to move in the direction opposite to the force being applied by the leader, while she uses her muscle chain to actively buffer that force so that it gradually changes the motion of her centre in as controlled a way as possible. 'Bad following' or 'anticipating' in this example, would be like trying to contract your arm muscles to actively pull yourself upwards as soon as you have a grip on the branch. Shoulder dislocation, anyone?

Alright, hopefully we've seen enough about active stretch to have a feel for the concept. Now, let us consider the muscle chain in a dance partnership again. Every one of the muscles in the chain is capable of giving energy by either contracting or stretching. Moreover, it is possible to contract some of the muscles in the chain while letting others stretch at the same time. If more muscles are allowed to stretch and fewer are contracted, then the overall muscle chain will stretch. However, it's not clear exactly how it will stretch. With all the complex ways in which the individual muscles might stretch or contract, it's difficult to predict how the entire muscle chain will behave overall. It is common among inexperienced dancers for there to be inconsistency between the various muscles in the muscle chain. For example, a beginner leader might have a relaxed (stretching) core, a strongly contracting upper arm/shoulder ('arm leading'), and his follower might have a very relaxed (stretching, 'noodle-like') arm and very tense core. The various muscle dynamics combine in a complex way and make it difficult for each partner to get a feel for how the other partner's centre is moving based on touch alone. This is one of the reasons that partner dancing is hard for beginners and why teachers place an early emphasis on the (generally vague) notion of 'frame'. For beginners, perhaps the only way for them to get any kind of idea about how centre-to-centre connection feels, is to have them hold their limbs in the contrived shapes that we might call frame. Anyway...

Elasticity: The whole is the sum of the parts

At this point, a question naturally arises: How should each individual muscle in the muscle chain behave if the whole thing together is to behave in a way that is predictable to both partners? This is where things really get interesting. The answer to the question is 'elastically'. Let's see what this means and why it is the answer.

Elastic is not just the stuff that keeps your pants from falling down. Strictly speaking, 'elastic' describes a relationship between a shape and a force. Imagine you are holding a rubber/elastic band, with one end held in each hand (if you have one nearby, grab it and try this for real). Now, hold one end still while pulling the other end away from it. At first, the band is completely slack. You quickly reach a point known as the 'rest length' of the band, where it pulls taught but is not yet stretching. From there, as the band starts to stretch, the further you pull, the harder the rubber band pulls back on your hand. We can write the relationship between the length of stretch and the force with which the band pulls on your hand, as a simple equation. If you don't like math, don't freak out; it's simple, I promise. Here it is:

Force = - (spring strength) x (length of stretch)

or

F = -k x

for short.

The force is simply how hard the rubber band is pulling on your hands. We can also call this the tension in the band. We can think of the spring strength (called this instead of 'band strength' because the same law applies to springs and is usually presented in that context) as simply the thickness of the rubber band. A thick rubber band is stronger than a thin one, and for the same length of stretch will pull harder on your hands. The length of stretch is how much you've increased the length of the band from its rest length (defined above). The minus sign is there because the force pulls in the opposite direction to the direction of the stretch; as you pull to lengthen the band, it pulls back on you, trying to get shorter again. What we have here is a simple relationship between a shape (length - a 'straight line shape') and a force. Anything which can accurately be described as 'elastic' must obey this relationship.

To see what's so special about muscles that stretch like elastic, we consider just two muscles connected together in a chain and ask the question, 'What kind of force-shape relationship must each muscle display in order for both muscles together to exhibit the same force-shape relationship as each muscle individually?' This question must be answered mathematically. After crunching some algebra, it turns out that there are only two kinds of relationship which will allow this to happen, and one is useless for dance connection for a reason that we need not go into. The remaining answer is, if the pair of muscles is to stretch like elastic, each of the individual muscles must also stretch like elastic. If just one of them stretches elastically and the other does something different, the overall pair will not stretch elastically, but rather in a more complex way that is harder to predict. This reasoning is easily generalised to the entire muscle chain, with its long sequence of many muscles. If the whole muscle chain is to stretch elastically, each muscle within it must stretch elastically.

But why do we want the whole muscle chain to stretch elastically? The key reason once again is that the whole acts like each of the parts. Recall our discussion in the last post, about the need for a simple grammar of dance connection. What each dancer needs is a short list of assumptions, which will allow him/her to step out on the dance floor with a complete stranger and know that "As long as I uphold my half of the bargain and (s)he does the same, this should all work out ok." We can state this with more specific reasoning based on the above discussion. What each partner needs is to be able to monitor and predict the behaviour of the other partner's centre of mass, based only on what he/she can feel to be the case for his/her own muscles. Since this is true for both partners, what is needed is a system of force-shape relationship which will apply to the whole partnership if each partner can make it apply to him/herself individually. As we have seen, the only system which will achieve this is elastic active stretch of each muscle in the muscle chain.

Compressions are stretches

At this point, you might be wondering something: Sure, there's all this stuff about stretch and that's all very well, but what about compression? Good teachers talk about compression all the time, so how can we account for this in our elastic model of connection. The answer to this question has two parts. The first part is simply the acknowledgement that springs don't just stretch, they compress too, and when they do, they obey the same law for the relationship between length and force as they do when stretching. Imagine holding a strudy spring between the palms of your hands. Initial, at its rest length, it does not push back on your hands. As soon as you start to compress the spring - make it shorter - it pushes back on you. And, the shorter you make it (the more compressed it is), the harder it pushes back. Compression in dance connection behaves in the same way. BUT, this leaves one important question open: How can this possibly work when an individual muscle does not - indeed, cannot - resist compression? Muscles can only give energy under tension; under compression, they are just limp pieces of meat. The resolution to this problem is the way that muscles work in pairs with each other, also in cooperation with a stiff skeleton. If you lean against a wall, it is true that you can apply a compression force on that wall because at least some of the musles in your body are under tension and that tension is converted into a compression force by the structure of your skeleton. This is a complicated way of saying that even when you're pushing on something, you're still doing it by contracting a muscle somewhere. When you do a push-up, during the push phase, your tricep contracts; during the lowering phase, your tricep actively stretches. In both cases, it is under a tension force. Compression in dance connection works in the same way. If you want your connection to feel elastic under compression, you still have to learn how to control the stretch of each muscle in your muscle chain so that it behaves elastically.


Tuning, not relaxation

One final point before proceeding to a summary of this post. It is common for teachers to tell their students that in order to achieve good connection, even at fast speeds, they have to relax. This always seemed strange to me, right from my beginner days, and now I realise why; because, if one takes 'relax' literally, it's simply not true. It seems to me that what people are really trying to say when they say 'relax', is to use an elastic connection with a spring constant no larger than is necessary to pass the required amount of energy from one partner to the other while using a comfortable range of stretch lengths in the muscle chain, in order to achieve the desired shared movement. Admittedly, stating it like that is not exactly a pithy gem to have in one's teaching repertoir. But conciseness is, in my opinion, not a worthy trade for truth, and the key point here is that simply relaxing one's frame does not make for good dancing. A 'relaxed frame' - in the literal sense - is a limp, noodle-like frame; exactly what we tell beginners not to have. If I tried to dance at any tempo above maybe 50 bpm with a genuinely relaxed frame, I would risk injuring myself, my follow, and having her tell all her friends afterwards that my dancing is 'flacid'. Point made, I hope. A relaxed frame is not a functional goal. What really separates amazing connection from good connection, I think, is each dancer's ability to fine tune their spring constants to match the energy of the movement being communicated. Tension is definitely required, and it's required in proportion to the energy being passed between partners. A functional goal for dancers aspiring to good connection is to never hold more or less elasticity than is required in order to work smoothly and easily with one's partner, ramping up and down quickly and efficiently when the energy level changes.

Summary

So, time to wrap it all up for this post. What does the above small novel of theoretical mumbo-jumbo mean in practical terms? Here's a summary for practical application. In order to achieve good connection, each partner should make sure that:

- The muscles in his/her half of the muscle chain are only stretching, not contracting, at almost all times (almost because in reality, even the best dancers use contractions in their muscle chains sometimes; we will talk more about this later) no matter what movement is being danced or what pace the music is. This is counterintuitive and needs practice but to do otherwise amounts to the 'arm leading' that teachers warn against, which does not allow for efficient communication/cooperation between partners.

- Energy given by the leader to the follower originates in his leg muscles, which contract to move his centre. The motion of his centre then influences the motion of her centre in a simple, predictable way as energy flows through the elastic muscle chain from one to the other. Both partners must resist the temption to add energy by contracting some of the muscles in the muscle chain. Following purely requires no addition or subtraction of energy by the follower herself. She conserves her momentum and uses her half of the muscle chain simply to buffer and smooth out energetic transitions which find their way to her through the leader's half of the muscle chain. The whole process might not be easy but it is profoundly simple.

- The most important thing to learn how to finely control is the spring constant that you hold in your half of the muscle chain. Fast, powerful communication through the chain (like that used when dancing Lindy hop quickly) requires a high (but no higher than necessary) spring constant. Slow, relaxed communication (like in slow blues) uses lower constants. What really separates amazing connection from good connection is the ability of each partner to dynamically adjust his/her spring constant to match that of the other partner.

The next post will further explore the application of elastic connection in practical dancing. We will see that many aspects of connected dancing, which might initially seem complex and mysterious, become much simpler to understand when they are discussed in light of an elastic model of connection.

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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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