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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Connection 1: Body language

We have finally arrived at what I think is possibly the most interesting - and most confusing - issue discussed by partner dancers: Connection. We have already flirted with questions of connection in earlier posts but now we will dive into them head first. The discussion will begin by introducing connection as a kind of tactile language; a means of communicating through forces and shapes experienced/observed in two dance partners' bodies. We will then consider an argument that a particular system of such language is more effective than others that are commonly used in facilitating musical, co-creative dancing. It will be argued that this system is more-or-less universal between the various styles of improvisational partnered jazz dancing, being different only in fine-tuning between Lindy, Blues and Bal (and other styles as well, even outside the jazz genre). Finally, this system will be explained in depth. In order for the explanation to be as clear as possible, a simple physical model of connection will be developed and explored. Please don't worry if you've never studied physics; I will attempt to explain things in a way that is accessible to everyone. For those who are interested in the quantitative details of the model, there will be small 'technical supplement' (read as 'shameless geekfest') sections along the way.

It is useful here to state a very brief summary of much of what has been discussed in earlier posts:

• There are many ways to define 'good swing dancing'; we have chosen to define it as musically co-creative connected movement which is innovative within a historical frame.
  
• Both musical auditory processing and sensory-motor control of your body are evolved human capacities and carry the legacy of that evolution.
• Gestural and (later) verbal language provided the survival advantage of efficient communication in cooperative social groups. Current theories of the neural processing of music suggest that it evolved in parallel with language processing. We have speculated that musicality in dance results from the music-verbal language-gestural language links.
• Fast, efficient sensory-motor control of a single human body (ie. the one which houses the brain that controls it) is biologically evolved and therefore intuitive. Control of two connected bodies, shared between two brains, has evolved not biologically but culturally, through trial and error, by many dancers over many years. These systems involve self-imposed restrictions on the movement of each individual partner, which facilitate shared control.
  
• Particular systems of shared body control have emerged as more effective than others. These are the systems used by the most respected dancers. Good teaching consists in distilling these systems into basic principles and communicating those principles accessibly, in entertaining ways, to students.
  
• Individual partners move in a way conducive to good shared control when they move with maximum predictability over time scales short compared with a whole dance (ie. less than a second to a few seconds). Predictability over longer time scales (eg. Dancing the same move or sequence of moves over and over) can make a dance uninteresting, so good dancing combines predictability over short times with originality over longer times. We have speculated that maximum predictability over short time scales is achieved when individual dance partners move in such a way as to minimise the jerk of the motion of their individual centres of mass. This makes the dancers' motion smooth, preventing sudden, difficult-to-work-with changes, each partner helping the other to have the experience, "Ah, I can feel and see what you're doing and where you're going. I can work with that!".
• For the purposes of good shared control, the primary function of steps and footwork is to carry movement; where you put a foot is much less important than how you control the motion of your centre of mass through the space above it.
• The following steps are required for shared control:

1. Partition the control into roles of lead and follow. The roles can be passed back and forth but in general, only one person is leading and the other is following at any given time.
   
2. Restrict individual movement in the ways described for leader and followers in an earlier post.
3. Restrict the connection system to obey a particular set of rules, which is known to both partners, or can be learned through 'tuning in' to each other on the social dance floor.
   
4. Cooperate to create shared movement, which reflects the music.
   

Now, for a very simple functional definition of connection: 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. Let's keep this in mind as we proceed. First, however, we will take a step back and consider connection as a kind of language-based conversation, which will provide a familar analogy against which to frame the later technical discussions.

The various partnered jazz dance styles are primarily social dances, meaning that the primary goal within each is for a dancer to be able to visit a place where (s)he has never danced before, dance with someone (s)he has never met before, to music (s)he has never heard before and still have fun. This extreme flexibility requirement places heavy constraints on the complexity of the movement/connection system which dancers should learn. Strict systems with long lists of specific rules to learn are not likely to facilitate this kind of flexibility. So, if dancers seek to learn lots of specific moves as their end goal, they may find that unfamiliar partners don't know any of the same moves, making it difficult to find common ground on which to share a fun dance. We can make a linguistic analogy here, imagining that two strangers - one English speaker and one Spanish speaker, say - might try to prepare to have a conversation in a new language (eg. Japanese) which is unfamiliar to them both. If they each prepare by learning randomly selected phrases from a phrase book, it is unlikely that their conversation will achieve any depth, if it manages to get off the ground at all. What's required then, are some general rules - preferably as few of them as possible - allowing people to communicate flexibly. In language, these are the rules of grammar, which allow for the building of meaningful, original sentences. Two mutually unfamiliar dancers can have a creative, original dance then, if they just know the same rules of grammar, which is a significally smaller set of things to learn than a long list of pre-cooked sentences.

I think it's interesting to spend a moment discussing the language spoken between regular dance partners, particularly in the case of rehearsing/performing choreography. Frequently, such partnerships are able to achieve things in their dancing, which neither partner can achieve while dancing socially with someone else: particularly impressive tricks and aerials; quick, subtle changes of direction, etc. At the same time, the dancers in the partnership might not have as much fun while dancing with each other as they do when dancing with unfamiliar others, because all too often, with each other they are having the same conversation over and over. We might think of this as analogous to a couple of actors playing out the same scene, learned from a script. They have each got their own lines down, complete with emotional nuances, and can predict each other so well that the scene flows smoothly enough to convince an audience. But the internal experience of the actors themselves is not the same as it would be if they were having a real, original conversation. Yes, if they are good actors they are still able to bring some genuine emotion to the script and 'play off' each other but they both know that there is only one way the conversation will go.

Ok, so, point taken, I hope. What does this have to do with connection - the physical mechanism by which dancers achieve movement together? The key point, I believe, is the amount of information which must be pre-learned by the dancers. Choreography still uses connection but it uses very complicated connection. It does this because it can afford to - there's lot of time to learn the rules and rehearse. Choreographed performances might involved sections where two dance partners are able to precisely coordinate their movements without being in physical contact at all. They might use subtle visual signals in order to communicate when it's time to change and do something differently. And as a result of all this complexity, they are able to achieve things which are rarely achieved on the social dance floor. It would be *great* if every dance we ever had looked as good as the best choreographed performances. Indeed, when most of us first come to partner dancing, we dedicate ourselves to learning cool new moves and tricks and love dancing them on the social floor with familiar partners who know the same stuff. But we soon realise that the prospect of having the experience of executing precise choreography with everyone we ever dance with is going to require a godlike memory and a preparatory discussion before every dance. "Hi! Would you like to dance? Great! Do you know such a such a move? Do you know how to get into it from this move? What about this sequence? Ok, well, let's forget the sequence but we can do that move. Great! Let's do it!" Imagine having to go through all that every time you want to have a dance! It might be fun and impressive to pre-learn a script and act out an amusing 'conversation' for an audience but trying to take the system by which that is achieved and imposing it on social dancing doesn't result in much fun. So, what's the alternative? A simple, powerful system of tactile connection; a mechanical grammar which allows two unfamiliar dance partners to achieve amazing things on the social floor without any shared preparation whatsoever. Dancers the world over pay good money to learn from instructors who have mastered this, and students with a passion for excellence spend months and years trying to put the teachings into practice.

I don't think I'm describing anything new here. I think dancers know that they need to learn general rules of movement and connection. I skeptical, however, that there exists a single, well-formulated grammar of dance connection, which is agreed upon by everyone. Different teachers teach different grammars and when their students try to dance together, it is analogous to two people who speak different languages trying to have a conversation. The languages aren't usually all that different; it's not like Mandarin and French coming together. I think it's usually something more like different dialects of the same language. Nonetheless, this can make things difficult. Sometimes the two partners can manage to figure each other's dialects out and have a great dance. Other times though, there is an ongoing clash. One might argue that there simply isn't a singluar 'best' grammar and there's no point trying to find one. I think this is too strong a statement. I think that there are good reasons to argue for a single, optimal system of connection - a single, most effective grammar - which, if learned by everyone, would facilitate 'better' (according to our definition) dancing. Sure, there will always be dialects but perhaps the goal should be to leave them behind, or least be aware of them so that one can choose one's particular, quirky dialect consciously, rather than because it's the only think one knows how to do. I am not arguing here against individual styles; far from it! I'm arguing for a clear system of communication. Two people who speak exactly the same language can certainly have fun, meaningful, creative, exciting conversations!

In what follows, I will attempt to describe what I believe might be the optimal dance connection grammar, which is used by the world's best dancers. I should make a small qualifying point here that Lindy, blues, Bal, etc, are definitely different dialects. But they are NOT different languages from a biophysical standpoint. I cannot emphasise this strongly enough. The systems of muscle control used by Blues dancers are the same as those used by Bal dancers. The two dances differ only in so far as those systems are subject to historical constraints. Bal dancers only 'talk' (ie. have tactile discussions on the dance floor) about the topics which are accepted by the Bal community, and vice versa for blues dancers. But the language they speak when having those topical discussions is the same. The (relevant) nerves attached to your muscles do not know whether you are dancing Bal, Lindy, Blues or Polka. All they are able to tell your brain is how long/stretched each muscle is, and how much load/force it is bearing. Your brain accepts signals of this type from every skeletal muscle in your body constantly, synthesises them, interprets them in the context of whichever dance you are choosing to do, decides what to do next, and then activates the relevant muscles when required. This is not to say that there are not different systems of shared body control out there. There are. But as far as I can tell, the systems used in all of the various improvisational partnered jazz dances are fundamentally the same. The differences between them are less than fundamental.

In the next post we will get down to business and begin describing the simple, fundamental rules of connection, the rules which relate the shapes in dancers' bodies to the forces they are applying on their partners.

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Steps: The biggest myth in dancing

Sometimes when I'm somewhere where there's music and people are moving to it, I'll ask a friend who I know/suspect might have never had any dance lessons whether she'd like to dance (not *because* she's untrained; because it's fun to dance with a friend!). Understandably perhaps, friends who know that I've been dancing for some years are hesitant because they feel pressure to perform. Even if I reassure them that there's no need for any of that, that it's ok to just move to the music however feels natural and just have fun, I am still sometimes refused because she 'doesn't know any steps' (or at least that's why I'm *told* I'm being refused :->). People often identify dancing with 'dance steps'. Whether or not it's intended, this association places the focus of a dance on what the feet and legs are doing. To 'get the dance right', one only needs to put one's feet in the right places in the right sequence. Whatever the rest of the body is doing is a mere detail. Some readers may have seen the old printed dance instructions where footsteps are drawn on a page, connected with dashed lines and numbered to indicate the order in which one should put one's feet in different places in order to do the dance. This post will discuss this kind of 'step-centric' approach to dancing and propose that a more functional view might be quite the opposite; to put movement first and steps second.

It is common to teach 'moves' in Lindy, Bal, etc, using language that focuses on steps. "Ok, leaders, start with a rock-step, triple-step as you lead the follower towards you. Then, step behind with your right foot as you catch her and send her back in the other direction...." I believe that this kind of language serves to 'discretise' (break up into chunks) peoples thinking about how they move through a 'move'. The process becomes a sequence of small, intermediate goals, which need only be achieved one after another in order to get through the move successfully. So, a dancer learning a move might think, "Ok, step here on 1, then step there on 2, lead over here then step down on 3, hold 4, ......" Combined with this thinking might be a sequence of shapes, which the dancer aims to make as (s)he progresses through the step sequence. So, there might be a notion of the general shape that one should make with one's body when taking a particular step in the sequence. Overall, this way of thinking about a dance seems analogous to the way that a movie is made up of a fast-switching sequence of still images. Dancers are taught all the still images and then are largely left to figure out how best to dynamically connect them. This kind of thinking (and the kind of teaching that encourages it) is very effective at making long sequences of complex movements amenable to memory. It is less effective, I believe, at helping people to progress from 'doing moves' to actually dancing, since good dancing consists primarily in particular ways of generally moving and less in the fine details of the location, orientation and timing of a particular step. I'm not saying those things aren't important; I'm saying they are of secondary importance. Steps are only important in so far as they carry movement (with the exception of deliberately showy footwork - 'steps for steps' sake' - but this too is less important to solid, co-creative partnered dancing than is good movement).

By focusing on the steps to be taken on various beats, a dancer's attention is drawn to only a small fraction of the time for which they are actually moving. An 8-beat move inhabits the full time interval between 8 and 8 and there is a lot of time between the moments we identify as beats. Many good teachers speak of the importance of dancing in the 'spaces' between the beats. I agree with this philosophy. I think that a good way to promote it is to place less emphasis on the beats themselves in the first place. I'm not encouraging arhthymic dancing; I'm encouraging an emphasis on movement, rather than steps. Or, rather, I'm proposing that steps be thought of differently, as tools for the control of movement, instead of as an end in themselves. 'Stepping behind on 4' is not a goal that encourages good dancing. 'Moving your body in such-and-such a way between 3 and 5, and supporting the movement but putting your foot down behind you on 4' is.

Ok, so, it's all very well for me to complain about the the focus on steps, but what are the details of what I'm proposing instead? How, exactly, do steps 'carry movement'? Is there a 'best' way to step? If it's not about position and timing, what *is* it about? Recall the theme of the last post: good communication between partners is facilitated when each partner controls his/her movement in such a way as to minimise the *jerk* of the movement of his/her centre of mass (COM). The remainder of this post will attempt to explain the mechanical details of jerk minimisation through well controlled stepping.

Good dance movement would in many ways be easier if people had somehow evolved to have wheels instead of legs. If we could roll around the floor smoothly instead of having to take steps, it might be easier to deal with the requirement for minimum jerk. But we don't have wheels; we have two fancy, multi-jointed support-sticks that we call legs and we have to learn how to use them in certain ways for good dancing. I think that a useful way to summarise good step control is to say that one needs to learn how to use steps to move one's COM around the floor as if it were on wheels, gliding smoothly through space. This ignores the issue of the rhythmic pulse that shows up in all swing dances but we'll get back to that later. For now, I'd like to ask you to let yourself believe that the basic tools of good dance movement can be learned entirely without rhythm (as indeed, I promise you they can!). We will demonstrate that this is the case by taking a conceptual tour through the detailed process of what we mean by 'taking a 'step'.

Imagine that you're standing on one foot (or actually do it, if you can still read this at the same time). There is a position for your body, with your COM directly over your foot, which feels most balanced and comfortable. But this is not the only position available to you while supporting your weight on this foot. Your foot is not a sharp point, it is more like a flat plate, extending across the floor far enough to give you the ability to stay standing, even if your COM deviates from its central position over your foot. It is fun and useful (and a great workout for your stabiliser muscles!) to explore your range of balance while standing on one foot. Begin in the balanced, central position and then deliberately lean slightly in different directions, paying attention to the way that your weight shifts from the centre of your foot to one side and then the other, as you change your direction of lean. Notice also that it doesn't take much leaning to get your leg muscles working overtime just to keep you vertical. This 'weight shift' corresponds to the changing position of your COM, which is moving as you lean. Imagine your COM as a small marble floating in space, in your tummy, behind your belly button. As you lean in all the different directions, your marble is 'colouring in' a kind of oval shape in space, which contains all of the possible positions your COM can be in while you're standing balance, at this height, on this foot. If you then also allow yourself to bend your knee and play with your balance at different heights, the oval will be extended into the third dimension, becoming a kind of spherical (ok, so 'roughly ellipsoidal' would be more accurate but we can think of it as a sphere) cloud in space. We will call this the 'control cloud' that corresponds to the step you're standing on. To clarify the definition: the control cloud for a step is the region of space in which your COM can exist while having its motion controlled by the muscles in the the weighted foot.

As you move around from one step to another, whether you are walking or dancing, your COM is floating between the control clouds of different steps. The most important thing for us to realise is that the degree of control available to you is *not the same* everywhere in the cloud. Control is much better when your COM is close to the centre of the cloud and tapers off as it moves ever further away. Accordingly, it becomes more difficult to make sure that you are moving with minimised jerk if, on every step, you allow your centre to stray too far from the centre of the cloud. Of course, eventually control disappears altogether and you will fall over if you lean sufficiently far without taking another step. The art of controlled stepping for good dance movement, which facilitates good communication between partners, requires a dancer to learn how to step in such a way that his/her COM never strays from the region of good control for each step. Two things help with this: The first is simply extending one's region of control through experience and training. There are exercises which one can do to learn how to better control the motion of one's centre through a larger range of movement per step. Simple muscle development also helps. The second thing to learn is step spacing. No matter how controlled you can be with each step, if you want to move across the floor, you will eventually need to replace one step with another. It is common amongst beginner dancers that steps are irratically spaced; sometimes unnecessarily close together, sometimes too far apart. By contrast, experienced dancers know how to space their steps so that they are able to maintain a high level of control over the movement of their COMs. The guiding principle in 'planning' (it is usually done subconsciously by experienced dancers) the right step spacing is to always take as few steps as possible in order to achieve well-controlled movement.

As a simple exercise to demonstrate all of this to yourself, try this: Stand on one foot and keep your other leg underneath you, slightly bent, so that your foot is just off the floor. Now, play with your balance for a moment; move your centre around within the control cloud of the step you're on, noticing that fine control feels ever more difficult, the further you move your COM from the point directly above the centre of your foot. Now, to experience a finely controlled step, try the following: Slowly move your COM in the direction of the leg you're not standing on (ie. if you're standing on your right foot, use your right leg to slowly push your COM towards the left). Keep the unweighted foot *directly under you*, just hanging there, moving with you as you control your motion with your weighted foot. As your COM approaches the limit of the well-controlled region of the current step's control cloud, reach out slightly with your unweighted foot in the direction of your motion, lower it to the floor and transition some weight onto it (but just a little bit! Aim for a 90/10 split between the old step and the new step). [Side note: It is sometimes taught that a dancer should not reach out with a foot to take a new step. This is not true; if the dancer is aiming to move across the floor, there is always some reaching. It's also true, however, that reaching *too far* hinders well-controlled movement. The important quantity to focus on getting right is step spacing.] What you have done by putting the new step on the floor is established a new control cloud for that step, which *overlaps* with the control cloud for the old step. Your COM is now still within the reasonably-well-controlled region of the old step *and also* at the far reaches of the not-very well-controlled region of the new step (hence the 90/10 split between the old and the new). Now, keep your COM smoothly moving towards the well-controlled region of the new step's control cloud. Notice the weight split gradually shift between your two feet as your COM moves: 80/20, 70/30, 60/40. *If you have spaced your steps optimally*, by the time you get to 50/50, your COM will be right at the edge of the well-controlled regions of both steps at the same time, passing from the old and into the new. You can test this by lifting either one of your feet of the floor. You should feel like you're going to fall over but 'only just'. If you have spaced your feet too widely, you will feel like you'll definitely and quickly fall if you lift either of your feet off the floor. If you have spaced your feet too closely (arguably, this is not as problematic as spacing them too far apart, because closely-spaced steps can be easily controlled. Still, they are not without problems, as we shall see), you will feel as though you could lift either foot off the floor and still stay standing by only making a tiny adjustment to the position of your COM (and, you won't have moved very far with your step!) Keep moving your COM gradually until your weight is 100% on the new step (ie. your COM is now directly over the centre of the newly weighted foot). The overall effect of this stepping process has been to provide an unbroken passage of good control between the maximally balanced positions of the two steps, meaning that stepping in this way ensures that the motion of your COM is always well controlled, as required for good dancing.

Before rounding up this post I would like to discuss a stepping habit with which many good dancers sabotage their ability to work well with their partners: Taking too many steps. It is natural, especially for an inexperienced dancer, to want to spend as much time as possible within the safely balanced, well-controlled region of each step. One can manage to do more of this while moving around the floor, simply by taking more steps and spacing them more closely. The same speeds and trajectories can be achieved in many cases, but the dancer feels more controlled. The trouble with this strategy is that it removes options for communication between partners. Every step is a commitment to a position on the floor. It can be a lot of fun to flirt with a step without actually committing to it; to move in one direction only to stop before stepping and go back the other way. It is also fun to add rotations/swivels into steps to make trajectories more interesting. Stepping earlier than required can cut off both of these options, which can be very frustrating to a partner who is trying to 'enjoy the spaces between the steps'. Again, the guiding principle should always be to take as few steps as are necessary in order to maintain well-controlled movement that facilitates good leading and following. I like to teach the mantra, "Never hesitate to move. Always hesitate to step."

For several posts now, we have discussed the art of partner dance movement. In the next post, we shall progress to the next chapter: 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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Movement 1: Hairless crash test dummies, simple models of the human body and the magic of its 'centre'

Before proeeding into a nuts-and-bolts explanation of how and why maximum mutual predictability gives rise to good dancing, it is necessary to discuss what is meant by a dancer's 'centre', and why it is important. The goal of this post is to introduce the idea that a complicated physical system, like a pair of people dancing, can be effectively represented by a simple model. This simple model is useful because it is easier to understand than the real system and can be used to gain insight into what makes the complex, real system tick. I will argue that in the case of a dancer partnership, the motion of each partner can be adequately represented by the motion of his/her 'centre', or centre of mass.

In later posts, we will gradually put together a simple model, which I believe effectively represents good partner dancing. If we just launched straight into the model now, it might not be clear where that model came from or why it works, and that might be annoying. So, at this point, it will be useful to first describe the general process of creating an effective simple model for a complicated physical system - like a connected pair of dancing human bodies. We will take a brief step away from dancing and just talk simple physics for a moment to get a feel for the big picture of how we will look at dancing afterwards. Doing this now will help things to make sense as we proceed further down the track. Please don't worry if you've never studied, or even liked, physics. I will do my best to make this as painless as possible. I promise there won't be any equations, at least not yet ;-)

Physics is mostly about describing fundamental relationships in the natural world. The practical process of how this is done usually proceeds something like the following. We will consider a practical example throughout, to help it all make sense. This example - that of using crash test dummies to understand how human bodies move during traffic accidents - might seem a bit gruesome but I have chosen it because it deals essentially with the same question we are facing in trying to model good dancing: How simple can I afford to pretend that a human body is so that I can study its behaviour more easily? Do I need to study a perfectly lifelike model, with all the detailed features of the human body, like hair length, eye colour, etc, or can I get away with studying a simpler model like a 'stick figure', which lacks all these details but still has all the important bits? The process by which we usually answer this question in physics goes like this:

Step 1) Observe something interesting in the world and wonder about how it works - how all the parts relate to each other.

Let's begin our example in an historical context. In the early days of automotive transport, cars were engineered to transport people and stuff, without a lot of consideration for keeping all that stuff safe in the event of an accident. Over time, as more and more people got hurt in car accidents, patterns were identified in the kinds of injuries that resulted. This posed a question - why do these kinds of injuries happen in car accidents, and how can cars be better engineered to prevent them from happening in future?

2) Based on your experience of how things have worked in other parts of nature you're familiar with, identify the essential features of this new system and, for simplicity, temporarily forget about all the stuff you think is probably non-essential.

What are the features of a person's body, which most strongly determine his/her injury risks in a car accident? Based on past experience, you might assume that body mass, size and approximate shape, for example, are more important than hair colour or length of fingernails.

3) Put together a simplified model (often called a 'toy model') in which the system of interest is composed only of the features you have decided are likely to be essential. This is usually done first in one's head and then in diagrams.

I am not familiar with the actual historical process of how car manufacturers went about modelling car accidents and how that progressed over time, but I know that it eventually resulted in sophisticated experimental tests using the iconic (and hairless) crash test dummies that have become familiar to the public. Presumably, things started much simpler than that. The very first crash tests might have just had human-weight bags of sand on the seats, for example. Early theoretical models might have been very simple, just representing a person's body with a simple shape - maybe a sphere or a square-edged box - with the same mass and roughly the same size (so, the same density) as the average human body. It's always easier to start with a very simple model and add in complexity in small steps from once the simple model is understood.

4) Using fundamental laws of nature and mathematics, derive equations that describe the dynamics of your toy model.

If we assume, as speculated above, that a simple model of a human body might be a spherical blob with the same mass as the average human body, then for this step of the process, we would use the laws of Newtonian mechanics (originally formulated by Sir Isaac Newton in the 17th century and still used today for describing how physical objects behave on the everyday size and time scales familiar to humans; ie. not very small like atoms or very big like galaxies, but in between like people in cars) to write down equations describing the behaviour a spherical person in a car accident. These equations are usually then used to generate graphs or computer simulations, which allow for the visualisation of how the toy model is behaving.

5) Compare the behaviour of your toy model to the behaviour of the real system you are trying to describe and note how different they are.

Our spherical person model would probably do a good job of describing the behaviour of a person's body overall but would tell us nothing about the detailed movements of limbs.

6) Revise the toy model, adding in some complexity.

We might add some sticks to our sphere so that the toy model now looks roughly like a body with simplified arms and legs.

7) Repeat 4-6 until the model's dynamics are deemed to be sufficiently like the dynamics of the real system.

We can speculate that over time, this gradual iterative process resulted in the crash test dummies that we have today, which are clearly a lot more like real people than is a spherical blob. However, importantly, these dummies still don't have hair, eyes, individual fingers or toes, or other such details, presumably because it has been decided along the way that including these details complicate things without helping to answer any imporant questions about car safety. Eventually, a point of diminishing returns is always reached at which adding more details to the model makes the science a lot harder without significantly adding to the descriptive power of the model.

Ok, strict physics talk over for now. Phew! Let's get back to talking about dancing! The question I'd like to address in this blog is, 'Is it possible to come up with a simple model, which describes the essential features of good, musical, improvisational partnered dancing, and can the nuts and bolts of that model be used to develop practical tools for improving people's dancing?' I think the answer is yes and I will attempt to show how and why.

In our crash test dummy example above, the very simple model we started out with for a person's body was a spherical blob that weighed as much as the average person. It turns out that we could have started with an even simpler model. Before representing the person with a 3D spherical blob, we could started with a 1D blob, called a 'point mass'. We would prented that all the person's mass were concentrated at a point in space and we would locate that point at the real person's centre of mass (COM). So, we would be replacing the person with a microscopic (actually, infinitely small) marble, hovering in space at the centre of where the real person used to be. Despite being tiny, this marble would weigh the same as the person. This is arguably the simplest possible way to represent a 3D object. I will argue that for modelling dancing, this very simplest of models is adequate for practical purposes. We won't even have to make things as 'complicated' as to pretend that a person is a spherical blob. Instead, we will be able to imagine that a person is simply a single point in space, like a tiny marble that weighs as much as the person it represents.

In my experience, most people have some concept of what their COM is but we need to make sure we're clear here, so let's talk for a moment about what, exactly, we mean by COM. Your COM is the average position of all the mass in your body. Your COM changes as you make different shapes with your body, and it can even be outside of your body. For example, if you're standing up and you bend over to touch your toes, your body (seen from the side) is making a kind of triangle shape and your COM will be somewhere inside that triangle. Since your torso is probably heavier than your arms and legs, your COM will be closer to your torso than your feet. Nonetheless, it is probably outside of your torso, hovering in space just below your ribcage somewhere. When you stand back up again, as your body comes to form a vertical line, your COM will sneak back inside your torso, probably just behind your bellybutton. It is important to understand here that your COM is not a physical object, it is just a number calculated from the positions and masses of all the real parts of your body.

Even though the average position of all the mass in your body is just a number, not a real object, it is very useful because it is the fairest way to answer the question, "Where is my body?" with just a single point in space. If someone wanted to know where you are located in a dark room, giving them the coordinates of your little toe does not very fairly represent the position of your body, because most of your body is located to one side of that point. But reporting the position of your belly button gives a much more useful piece of information because (assuming you are standing straight), it is close to the average position of all of the mass in your body; your mass is located all around it so anyone aiming for that point is likely to find you even if they miss in any direction.

I'd now like to demonstrate the usefulness of the COM in tracking a dancer's movement. Imagine that you are given three videos of a dancer dancing in a dark room. In the first video, the dancer wears a glow-in-the-dark dot on one of her hands and all you are able to see in the video is the motion of the dot, which darts all over the place. In the second video, a similar dot has been attached over the dancer's belly button. This dot moves more smoothly and covers less distance than did the dot in the first video. The last video was shot with a 'night vision' camera, so you are able to see the dancer's whole body. You notice that the overall quality of the dance, when the whole body is considered together, is more like the motion of the belly button dot than the hand dot. This is because the dancer's COM will never be far from her belly button and the dynamics of her COM are the best single-point representation of her whole body's dynamics. Her hand, by comparison, will spend most of its time far away from the dancer's COM and so moves in a way that is unrepresentative of her whole body's motion.

Swing dancers are often taught to 'move through your centre' and leaders are taught to 'lead with your centre'. The reason for this, I believe, is that a dancer's centre (COM) is, speaking in strict physical terms, the heart of their 'identity' as a physical object. When I am dancing and connecting with my partner, the best way for her to know what I am doing is for me to communicate to her what my centre is doing. The rest is details and those details are easy to lose when the very task of sharing control over the dance partnership is so difficult from the start. The business of movement and connection then, is about doing so in ways that clearly communicate to your partner what your centre is doing. As we will see in more detail in the next post, making your centre's movement predictable for your partner will make it easier for him/her to cooperate with you in co-creating the dance.

One final note should be added to this post. Modeling a dancer as his/her COM is the simplest possible model one can construct and in some circumstances, a slightly more detailed model is useful to consider. One can construct an arbitrarily complex model by combining COM models for components of a dancer's body. The next step up from the basic COM model is a model in which the dancer's body is considered in two halves - upper (from the waist up) and lower (from the waist down). Each of these halves has its own centre of mass; we might call these the 'upper centre' and 'lower centre'. As we will see later, breaking things into two parts like this is particularly useful when considering the connection required to lead and follow turns. From this point, we might take the next step up in complexity and explanatory power by breaking the body into six or seven pieces: the torso (in the six piece model; in the seven-piece, the torso would be split into upper and lower torsos), the four limbs and the head. Note, a three-piece model could also be constructed, and would be the next logical step from a mathematical perspective, but the six-piece model makes more sense from an anatomical perspective. This process can be carried as far as we like, with pieces being broken into ever smaller pieces which are modelled as their centres of mass, until a model is created, which is sufficiently accurate to answer whatever question one might be considering. For most practical questions however - the kinds of questions which might help teachers teach and students learn practically - a basic COM model is adequate.

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Moving and connecting as nature never intended

Most readers will be familiar with Windows Media Player's (WMP) music visualisation programs, which splash weird, eye-catching images across the screen, changing in real time to reflect musical dynamics. These might look pretty but they do a lousy job of representing music. If you watched one with the sound muted, how much could you infer about the music? My guess is, maybe some rhythms at best. Dynamic visual representation of music is not easy.

You can dance better than this.

Now consider this: WMP makes its visualisations using just a single computer. The flow of information is simple:

Music --> Interpretation by a single computer --> Visual ouput, one frame at a time.

This is not all that different from what a solo dancer needs do to be musical. The dancer's visual canvas - his body - is controlled by a single brain. Music is heard and interpreted, musical movements are planned and executed. Obviously this is a simplification of the complex physiology at work but the point is, dancing within one body doesn't ask for anything outside the range of normal human behaviour. Millions of years of evolution and a lifetime of experience have trained your brain to hear music and move your body in all kinds of amazing, finely controllable ways, which are readily adaptable to environmental demands like swingin' tunes.

Why is well-connected, flowing partner dancing so difficult? There are lots of reasons of course, but many of them stem from one fact: a single dynamical system (two human bodies trying to dance together as one) is being controlled by two brains, each with its own ways of interpreting music, and has direct sensory and motor connection to only one half of the system. That is, your brain, via your nerves and muscles, can only directly control the half of the dance partnership that is your own body. And yet somehow, the two parts are supposed to closely cooperate to artistically express, adaptively in real time, some compromise between your two different interpretations of the music. It seems impossible! And yet the best dancers can do it well. How can this be?

Over the years, dancers have evolved - culturally, not biologically - systems of movement and connection, that afford them a high level of shared body control. These systems work by constraining the movement options of each individual partner so as to give the whole partnership more options. Not unlike in most relationships between life partners, each dance partner agrees to not do certain things so that the partnership might be able to do more. Later posts will deal with the mechanical details of these self/shared control systems. The rest of this post will describe the guiding principles behind them.




The first principle is that these systems are primarily functional. They are not the way they are because some authority figure in the past said that people must move and connect in certain ways. Rather, these systems evolved for the same reason that all complex things have evolved: they succeeded where others failed. Many dancers, dancing many dances, for many years, through trial and error have developed efficient systems of movement and connection. These allow for a high level of fun and creativity with the least effort on the social dance floor. Interestingly, it has not been necessary to deeply understand why these systems work; for practical purposes, knowing and teaching the how is enough.

So, on to practical matters! As far as I can tell, the main guiding principle behind effective movement and connection is mutual predictability. Each partner needs to move and connect in ways which make it as easy as possible for the other partner to have the experience, "Ahh, I see and feel what you're doing and where you're going with that. I can work with that!" Of course, too much of anything is a bad thing; if you move too predictably (eg. doing the same 'move' over and over), your partner will get bored. A balance must be struck; it's all about time scale: predictability over a few seconds is good, a few minutes, not so good. Perhaps a better word than 'predictability' is 'trackability'; your partner must be able to track what you're doing. But, for the sake of continuity, let's stick with 'predictability'.

Before moving on though, one other point must be made about this word. Reading the word 'predictability' might be setting off alarm bells for you because teachers often stress, to followers in particular, that prediction/anticipation of leads is a no-no. I agree with this. This is different from the kind of prediction I'm talking about. This kind, the kind to be avoided, is less about prediction your partner's movement and more about assuming that you're capable of reading his/her mind. This is sure to lead to dysfunctional dancing because often, not even the leader knows what he/she is thinking; advanced leaders frequently just let the dance unfold and 'go with the flow', often without strict plans for what will come next. Good followers learn how to keep track of their leader's 'flow' (trajectory) without making any assumptions about what that means for the follower. There is no 'supposed to do' in pure following; there is only letting the dance be done to you. If it is not done to you - if your motion is not physically changed for you by energy provided by your leader, with zero extra energy input from yourself (which is a functional definition of pure following) - then whether or not it was intended doesn't matter. Of course, good followers have a huge amount of input into how they are dancing, but they accept that input as their responsibility; it is not an attempt to guess what the leader might be thinking. In summary then, what I am advocating is promoting each partner's ability to track what their partner is doing within their own body, identify a pattern and see where it is likely to lead, without inferring that some particular response is required (that is the kind of 'anticipation' that should be avoided.) If one can avoid feeling obliged to lead oneself in response to something that one's partner has done with his/her body, then prediction is a useful thing because it provides a reference point for one's own self-directed dancing within the bounds of the partnership.

If you can see that your partner is moving is such and such a way and predict where that will take him/her over the next few seconds then you can plan around that in a way that allows you dance with enough independence to have your own fun while always being ready to pass energy back and forth (lead/follow) with your partner. A simple example of this is a good old footwork variation. A good leader will move and connect in a way that usually allows his/her follower to know when has been given enough 'space' to add in a variation without interupting the flow of the partnership. An inexperienced lead, by contrast, will be harder to track and prone to giving the follower the impression that she/he can never quite know what's coming next so it might be unwise to do anything but strictly follow. Of course, predictions can always be wrong, even between the best dancers. What I am arguing is that in general if partner (A) moves and connects in such a way that partner (B) can be reasonably successful is predicting (A)'s dancing into the near future, then (B) will be in a better position to cooperate with (A). (B) should also try to allow the same kind of predictability for (A). A useful analogy here is a squadron of jets flying together. If the squadron is to stay together without constant radio communication ("Ok guys, we're all about to slowly peel left. You ready?"), then each jet must fly in a way that is predictable to the others. There are certain simple, physical rules (like 'no sudden moves', for example) which allow this to be achieved. We will look at these rules in detail in future posts.

I'd like to finish this post with a brief discussion of lead and follow. Splitting a partnership into lead and follow is, of course, the one big pre-agreement that has to be made between the two brains controlling the two bodies in the dance partnership if anything at all is going to be achieved cooperatively. The agreement is simply this: When one partner is passing energy to the other ('leading'), the second partner will allow that energy to flow naturally into their body and be conserved in the process, meaning that it will usually change the way that they are moving. Note that no mention is made here of one person being the leader and the other, the follower. The best dancers will tell you that both partners are both leading and following throughout most dances. A good dance is a conversation, with two speakers and two listeners, not a monologue with one of each. The only restriction is that, just as in a good conversation, the two partners do not try to talk over the top of each other. When one speaks (leads/gives energy), the other listens (follows/accepts energy). Strictly speaking, I believe it is physically possible to both lead and follow at the same time; it's just extremely difficult and not really necessary for the creation of fun dancing.

I suppose that special mention should be made here of historical exceptions. Blues is probably the most conversational of the usual swing-associated styles. I'd say Lindy hop comes in at second place. Balboa, on the other hand, is more traditional and many people feel strongly that is should be role-based as far as lead and follow are concerned. That is, one person leads for the whole dance, the other person follows. End of story. This is a cultural contraint, however, not a functional one. Speaking in strictly physical terms, lead and follow can be shared back and forth in any partner dance. Doing so will make some things possible, which are not possible if the lead is uni-directional. At the same time, it will make other things harder. Presumably, the Balboa community has decided that the latter is too great a cost to justify the former. For whatever reason, Blues and Lindy have evolved into dances, which allow for lead-sharing whereas Bal, in general, has not. I am not trying to argue that one is better than the other, only that they are different. Cultural constraints aside, the same general physical processes are at work during leading and following in all of these dances. In future posts, I will attempt to explain in detail, the mechanics of pure leading, pure following and lead-sharing.

In this post I have tried to demonstrate that musical, co-creative partner dancing presents a challenging shared control problem. I have argued that systems of movement and connection have evolved, which allow for efficient shared control within a dance partnership, and that this is achieved through mutual predictability between partners. Finally, I have argued that control can be shared in different ways through different systems of leading and following.

In coming posts, I will further explain the notion predictability in movement and give it a clear physical definition. I will then attempt the explain the system of individual movement, which I believe good dancers use to make their motion predictable to their partners, to facilitate good connection.

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