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.

Carl  – (March 25, 2009 at 8:46 PM)  

Fantastic post and explanation. I've often thought of "communicating" my movement to my dance partner by communicating how my COM is moving.

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