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
etaison@stillpointaikido.com
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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