From complex to simple 2: 3 thousand moves or 3 degrees of freedom?

Early in 2006, after about five years of regular dancing, classes, workshops, etc, I was feeling frustrated. I had a reasonable repertoire of moves, slides, dips and aerials, which were a lot of fun on the social dance floor and had served me well in performances and contests. But I knew that I was still lacking something major. When I watched the A-list internationals out on the floor, I could see that they had something that was still out of my reach: Whereas my social dancing was just a move salad, they had an element of genuine originality in every dance, creating things in real-time, right before my eyes. I had moves that I could lead on a partner, they had movement that they could share with a partner. Though we weren't sure how to bridge the gap, my dance partner at the time and I decided it was time to focus on getting beyond moves. But how? Like the geeks we were (and resolutely still are), we decided to fight moves with science.

One of the most useful tools in the Swiss army knife of theoretical physics is something called vector decomposition. Forget this jargony name though; the process itself is simple, and I've found it to be a very useful way to think about dancing, and about teaching dancing. The basic idea is this: Any complicated-looking movement can be broken down into a small number of simple movements, which can be learned, led and followed simply, then just added together to re-create the complicated-looking movement. This might not sound very surprising in the context of dance teaching, since all teachers worth their salt will 'break down' moves for their students. But this isn't the kind of breaking down I'm talking about. Whereas it is usual for moves to be broken down in sequence, I'm talking about breaking things down in parallel. That is, rather than telling students to do such-and-such on beat 1, whatever on beat 2, etc, I'm talking about components of a movement, which are happening at the same time. I'm not so interested in what happens on particular beats. I'm more interested in how people are moving through the beats and it's this flowing, ongoing movement which can be broken down simply. Let me explain.

Imagine for a moment, a three-dimensional space which is empty except for a solid ball (or whatever shape you like - check out the figure below, which shows a box rather than a ball but demonstrates the same principles), which is free to bounce around the space any which way. It can move in straight lines, curves, and it can spin. It turns out that there are six fundamental ways in which the ball can move, and all of its possible movements, without exception, can be broken down (decomposed) into those six ways. The six ways are called degrees of freedom (DOF) and for our ball they are: straight line movement up and down, side-to-side and back and forth, and rotation around a vertical axis and around each of the two perpendicular horizontal axes (ie. the up-and-down axis, the side-to-side axis and the back-and-forth axis). So, concisely, we can say that the dynamics of the ball are spanned by six DOF. That is, the movement within those degrees of freedom can together 'reach out and fill' all of the possible movements of the ball. Now imagine that the ball is restricted such that it can no longer move up and down. That is, imagine that it is stuck in a two-dimensional plane. This robs the ball of one of its degrees of freedom, so its movements are now spanned by only 5 DOF, 2 translational ('translation' is the technical term for straight-line movement) and 3 rotational. Now, let's add another restriction and say that the ball can rotate around only the vertical axis. This removes two more DOF, so we are left with just three in total: One rotational DOF and two translational DOF. This system - a mass restricted to translations in a 2D plane and rotations only around the vertical axis is a good analogy for a dancer on a social dance floor.

Yeah, ok, strictly speaking, a dancer has 6 DOF like the unrestricted ball does but not much of consequence happens in 3 of those 6 D's of F, so we can do away with them to simplify how we think about things. Dancers don't move up and down much. Sure, they bounce, jump and dip, but those movements are generally small compared with the horizontal movements in the dance. And, moreover, the up-and-down movements always average to zero quickly because what goes up must come down and vice versa, if the dancers start and finish each move standing on their feet. As for the two rotational DOF we're ignoring, they are only important if the dancers are doing aerials or other tricks which involve rolling movements like backsaults, frontsaults or cartwheels. Those don't happen much. What does happen a lot are translations across the floor, back and forth and side-to-side, as well as rotations around the dancer's vertical axis ('spins').Excepting a few details, pretty much every move done on the social dance floor can be broken down into sideways & back/forth translations, and spins.

Alright, so what? Well, let's see how this kind of thinking simplifies things for both dancers and teachers. Consider a basic Lindy swingout. The conventional way of thinking about this 'move' is as a pre-defined sequence of steps and movements on particular beats within eight counts (a 'dancer's bar') of the music; a recreation of something done historically. This is how I used to think about a swingout: As the leader, I 'rock-step' on 1&2, and while doing this, lead my partner towards me. She steps or swivels in. I get out of her way and we make an effort to keep facing each other ('spotlight' each other) as we pass each other by. I 'collect' her momentum as I catch her and we reach beat 4 facing each other with a nice stretch in our 'frames', ready to be released to create the second half of the move. On '4-and' I lead her back in the direction she came from and either 'lead her out backwards' or 'forwards', depending on my stylisic preference. By the time we get to 8, we have a nice stretch built up again and are ready to repeat the move if we want to.

For years, I travelled long distances and emptied my poor student's pockets repeatedly to hear lots of different teachers tell me slight variations of the above. Each couple had their own version of the basic, with its mysterious subtleties. Such-and-such started 'leading in' slightly earlier or later than someone else. One awesome leader  had his right foot forward on 4 while this other awesome guy had his left foot forward. This couple put lots of rotation in their basic while this other couple kept it very linear. I constantly had the feeling that if only I could somehow absorb this sublety or that one, I would be able to reach some previously unobtainable level of awesomeness in my dancing. Eventually, I came to realise that this kind of thinking wasn't making me a better dancer, and I was just getting ever more confused about what I should teach. There had to be a simpler way to think about things!

How about this:

In a 'Lindy basic', both partners move back and forth once, roughly equal distances, in a (more or less) straight line, passing by each other, and also rotating through 360 degrees, and this is done with continous connection/communication. That's it. End of story. The movement is within only 2 DOF, one translational, one rotational (excepting a small deviation into the second translational DOF, to get out of each other's way, as you pass by).  For reasons described at length in earlier posts, what, exactly the partners do with their feet along the way is not particularly important, provided it facilitates movement that is not jerky, allowing for mutual trackability. No one cares if you do a rock-step or a kick-ball-change or a hold step, or whatever on this or that beat; that's a personal stylistic choice but it means almost nothing to the partnership. What does matter for the partnership is that the leading and following is done simply, elastically, as described earlier. That's it. Controlled movement and elastic connection. All the rest is details.

At anything but the beginner level, there is just no need for conceptual fluff like 'rock-stepping', 'spotlighting', 'leading in on 2', 'over-rotation', 'leading out backwards/forwards', 'dancing more American style than Swede style', or whatever. Instead, each partner simply moves and connects in accordance with the simple rules we've seen in earlier posts, within 2 degrees of freedom (for a swingout). That is the dance. The dancers are able to choose to move and connect through a shape which happens to be known as a 'Lindy swingout' for historical reasons, and they can add whatever special 'variations' they like but there is nothing special about this 'move'; it's just a shared movement like any other in the ongoing flow of a genuinely connected, co-creative dance. On one of the occassions when I had the pleasure to meet Frankie Manning and hear him speak and answer questions from young dancers, he was asked "How many different styles were danced at the Savoy?" He answered, in that inimitable Frankie way, "Ahhh, we didn't really worry about styles! We just danced!" And, how did they do that? In the most natural ways their bodies knew how to, the ways that allowed for the greatest cooperative expression with the fewest rules, the ways just felt good. I'm yet to hear a world-class dancer get worked up about a 'rock step'.

But enough with the rant, already. I was trying to explain how thinking in terms of degrees of freedom simplifies complicated movement! Having looked at the example of a 'swingout', perhaps the best way I can summarise the merit of thinking in terms of DOF is that, in an important way, it makes every 'move' the same. When a student asks me, "How are you leading that?", my immediate impulse (which I squash because I don't want to seem rude) is to say, "The same way that I (try to) lead everything else." I believe that it really is that simple. Once one learns how to move with smooth control and connect elastically, the answer to every how-do-you-do-that question is just a slight variation on, "Move with smooth control and connect elastically." Then, the dance just happens and endless avenues for expression open up. What's the slight variation? It's simply the number of degrees of freedom you're moving and connecting in! How do you lead a sugar-push? Move smoothly and connect elastically within one degree of freedom - back-and-forth. How do you lead a swingout? Move smoothly and connect elastically within two degrees of freedom - back-and-forth and a vertical-axis rotation. How do you lead a Lindy circle? Move smoothly and connect elastically through three degrees of freedom - back-and-forth, side-to-side and a vertical-axis rotation. How do you create a brand new move, musically, in real time? Move smoothly and connect elastically through as many degrees of freedom as you like, making shapes and a movement trajectory that reflects what you hear in the music. You get the point. This way of thinking can be extended to every single 'move' that is ever done on the dance floor, including aerials, dips, etc, if one adds in the necessary extra degrees of freedom.

The next post will deal with rotational connection. We have discussed straight-line ('translational') connection at length in earlier posts and now this post has introduced the notion that rotational and translational components play equal, complementary parts in any complex dance movement. So, to complete the picture we must grasp the fundamentals of rotational connection. At that point, we will finally have a more-or-less complete picture of on-balance dancing. Hooray! That's not yet the whole story though; a discussion of counterbalance is yet to come!

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