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Home > Columns > Ross Robertson > March, 2004 - Vitruvian Man Meets Da Vinci Girl
by Ross Robertson

Vitruvian Man Meets Da Vinci Girl by Ross Robertson

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Aikido training involves learning to better perceive what is real. We seek an understanding and relationship with that which is true (makoto, or "fundamental truth"). Whatever is true, as far as practical application is concerned, should be both discoverable and demonstrable. Architects and engineers speak of a square or line as "true," and have tools both for measuring and for creating something which is functionally true. It does not matter whether these forms are Platonically pure or perfect in the abstract sense, only that the building or device stands or functions well.

Interestingly, in addition to whatever is manifest, the real also involves unseen and non-physical components. The center of mass of a horseshoe and the parabolic arc of a projectile are instances of phenomena that are very real, but completely non-physical. Proper study of aikido should foster a keener intuitive vision of this type of unseen reality. Human geometry has its obvious physicality which must not be ignored, so much of our art is directed toward a deeper understanding of gross anatomy. But within and around the wonderful human form is a rich terrain of vectors, spheres of influence, and potentialities.

Leonardo da Vinci's famous drawing Vitruvian Man appears to be primarily concerned with the harmony and proportion of the ideal human (male, in this case). Indeed, the accompanying text is a commentary on Vitruvius' treatise on proportion in sacred architecture. In it, the figure of a man with arms outstretched and legs in a wide stance appears inside a circle and a square. These two primitive geometric figures suggest the basis for implied triangles and numerically consonant, harmonious other forms generated by these, and extrapolated from the proportion of the human form. Students of aikido will immediately recognize the conjunction of circle, triangle, and square as the same as that which fascinated O-Sensei.

Image 1: Leonardo da Vinci's Vitruvian Man

Although a static image, Vitruvian Man suggests a certain dynamism. The duplication of limbs and their placement within the circle shows the arc of the range of motion. In aikido, we must learn to see not just the position of the body and its parts, but where they can be, and where they can be the most stable and the most weak. We need to see the central axis of the body and its relationship with the gravitational vector. We need to look at the position of the body and the trajectory that put it there, and from that visualize the momentum of the future path. We need to perceive if the partner presents a square or triangular base. We learn to understand that each of the attack forms has its own shape which unfolds in space and time. Like physicists who describe the structure of the atom by the shape of electron valences, we should perceive the body and its limbs as surrounded by shells or spheres of potentiality and energy states.

In other words, da Vinci's Vitruvian Man only offers the barest of hints about the possibilities, and invites us to look deeper for ourselves to see what can be discovered. Luckily for us, we have a number of technological tools available to us to assist in extending da Vinci's vision, and to render images useful to beginners those things that adepts have learned to see through experience. For example, stroboscopic photography allows us to see an object as it moves through time, and the resultant shape that develops.

Image 2: 3D render which simulates a stroboscopic
photograph of the movement of the arms
(Click to view full-sized image)

But as mentioned earlier, in aikido we need to look at where bodies may go in addition to seeing where they've been. For that, I have found it useful to visualize the full range of motion of the articulate body as a set of spheres overlapping one another. In particular, it is helpful to learn to see the limbs and the arcs that they are capable of creating as they move within their respective spheres. Thus, there is a sphere created by the extended arm with the shoulder as its center; another one with a radius of the elbow to the shoulder; and yet another sphere with the forearm as its radius. Likewise with the legs and knees.

Using 3D rendering tools, we can derive this more modern interpretation of da Vinci's drawing. It looks like this:

Image3: Da Vinci Girl
(Click to view full-sized image)

Just as da Vinci was clearly influenced by the work of another and named his drawing accordingly, I have chosen to give Leonardo credit for his influence on us. And so I refer to the image above as the Da Vinci Girl.

The colors of the spheres are mainly arbitrary. Transparency mapping allows us to see the original model, but also the overlapping nature of the spheres. We could further refine the image by changing the intensity of the colors to show where the limb is strongest or where it may move the most freely, and a portion of the sphere would be completely invisible where the limb is unable to move (as in the case of the limits of extension of the forearm). However, variances in flexibility from person to person make this impossible to map precisely, and therefore we will content ourselves for the time being with idealized spheres of range of motion.

The model has certain advantages. For those possessing the appropriate hardware and software, it can be viewed from any angle at any scale or proximity. The spheres can be turned on or off to examine specific elements. Their colors can be user-defined, and their transparency adjusted. The spheres are parented to their respective elements. Therefore, when the pose of the model is altered, the spheres are adjusted with it automatically. The scene can be animated, so we can have a better suggestion of the range of influence as a person walks, strikes, kicks, and tumbles. The software that I used to make the image is called Poser. It also includes some other useful features which can be toggled on and off, such as joint parameters, shoulder/hip alignments, ground plane, and vanishing lines.

Image 4: Da Vinci Girl Strikes

Image 5: Da Vinci Girl Kicks

Image 6: Da Vinci Girl on a Roll

All of us grow up with an awareness of body space. Different cultures have different sensitivities for what is appropriate intimacy in body space. In aikido, we should train to become even more aware of where we are with respect to our own body space and that of our surroundings. Da Vinci Girl is a more precise portrayal of where the physical limits of this space are. The tips of the fingers represent a fairly exact limit of a person's reach, but within the radius from fingertip to shoulder is a large field of potential.

To be sure, that potential is always in flux. When one possibility is actualized, the field of potential is changed from one state to another. An arm fully extended is likely to retreat. An arm fully retracted may equally deploy a hand or an elbow depending on the relative position of the players. A more sophisticated program would register these changes automatically. When all the weight is on one leg, that leg's potentiality sphere would disappear until the weight shifts again. Spheres would be mapped gradationally to show areas of highest and lowest potentials, and these would also change as the figure changes. Add another figure into the picture, and filters could be added to show only the potentials that involve the interaction of the figures.

R. Kobayashi Sensei, the founder of Seidokan Aikido, frequently spoke of the principle of "range of effectiveness." He constantly urged his students to "stay outside an opponent's range of effectiveness, and well within your own." To be outside the opponent's range of effectiveness does not necessarily mean to be outside their reach. Indeed, it is possible to be intimately engaged with your partner, but positioned such that they may not use their strength or balance against you. In this regard, Da Vinci Girl is no more than a graphic portrayal of the principle of "range of effectiveness."

The benefit of obtaining a truer perception is that it may allow us to interact more realistically with our world. We seek not just to perceive, but to influence and direct toward wise outcomes. For self-defense situations, we can learn to be more keenly aware of the precise limits of range of effectiveness. When we study the Da Vinci Girl, it's easy to understand that a limb moved toward the outside of its sphere will affect the rest of the body. The action of inverse kinematics means that a body part moved far enough will cause displacement throughout the chain of connections, from extremity to trunk.

To unbalance a body, we must displace its axis out of the line of gravity, and off of its base. We may do that directly if we can get close enough, or we can do it indirectly by working with the extremities. If we do not pay attention to the spheres represented by the Da Vinci Girl, we can still achieve adequate results through training. But we are likely to do more than is necessary. If we can learn where the very precise threshold of an element is, we can then move that element just beyond its limit and no more, and still be confident that the balance will be taken. This fosters greater subtlety and efficiency. Conversely, knowing our own limits allows us to better maintain our stability and effective mobility.

I suspect that O-Sensei could do the things he did because he saw things that you and I do not. He certainly described his experience in mystical terms, and indeed, I don't doubt that something like a functional hallucinatory state may have been at his disposal. If some musicians can see sounds as colors, I don't see why a genius of movement may not have similar faculties. On the other hand, what O-Sensei saw may have been nothing more than simple truth.... lines and angles and rotational vectors and fulcrum points. I hope for the latter, because that means the rest of us may do as well or better. Even a dog, for all its limited intelligence, when chasing a Frisbee expresses a calculus of stunning beauty.

I like to imagine that Vitruvian Man and Da Vinci Girl may consort a bit with one another, if such would not be too incestuous. Perhaps a child born of that union would appear in our hearts and minds and lead us further down the path to truth. And should we discover that aspects of that road are neither visible nor physical, let us remember that they are no less real for it.

Ross Robertson
Still Point Aikido Center
Austin, Texas, USA

Original text and images © 2004 R.A. Robertson

"Vitruvian Man" by Leonardo da Vinci
Gallerie dell'Accademia, Venice, Italy

For an interesting article on da Vinci's Vitruvian Man, see http://www.aiwaz.net/Leonardo/vitruvianman/index.html which explores the proportionality, numeration, and hidden geometries contained or implied in the drawing.

For more information on Poser, see http://www.curiouslabs.com/

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