Kaz Maslanka's interests in the 1980s began to move from using art to transform aural experiences into a visual language to transforming a visual experience into a mathematical language. Maslanka has placed his thoughts on visual perception directly inside Newtonian kinematics to create metaphors that point where space, time and perception meet. He was curious of the psychophysical implications of his work but was more interested and motivated by the aesthetic process. Kaz's main focus was blending the aesthetics of Math and Physics with that of conceptual Art. He has also used similar principles to create. Mathematical Poetry
Visual Kinematics and Psychovectors is a series of conceptual art works concerning itself with recontextualizing verbal thoughts on the mechanics of visual perception into a physics paradigm.
This document is a primer to understanding
visual kinematics and the psychovector series, which are eight
conceptual-like art pieces. (1981 through 1988) The document is
intended for people with basic math, physics, and art backgrounds.
If we sweep our hand through the water in a swimming pool Figure 1 . and have the hand positioned so that the greatest area of our hand (the palm) is facing parallel to the direction of movement we feel resistance through the water. This resistance is less than the resistance we experience when having the greatest area of our hand facing normal or perpendicular to the movement. Figure 2 . If the same amount of force is used we notice a greater speed of water when the palm is parallel to the movement. Seeing this experience as well as feeling it is an example of how the information from each of the senses is merged into the meaning of the experience. Later when we experience information from one sense we can recall the meaning or can implicitly experience information about the other senses because of our past experiences with similar situations.
If we look at the two triangular images figure 3... Equal momentum study of isoceles images ... seven times diference in velocity 1981 36" x 48" oil paint on canvas the question arises: which image is implying the greater velocity. Let's limit our viewing context to one direction (the direction toward the top of the picture) and view it as a flat two dimensional image.
Almost everyone will agree the narrow image
on the left looks faster, but why? Because the slope of the lines
coming from the vertex is
greater on the left image one has the illusion of greater velocity. The lines rise toward the top of the picture faster than they run across
toward the side of the picture. If we want to describe this mathematically, we can create a ratio and count the units the line rises
and divide it by the number of units it runs. Thus: slope=rise/run. figure 4. The line rises seven units as it runs one unit. Thus:
rise/run=7/1=7. The slope of figure 5. is one because the line rises one unit as it runs one unit. We can now describe the visual velocity
mathematically. As we look back at figure 3. we can see the left image has seven times the velocity as the right image...it looks as though it
is traveling seven times faster.
Let's ask another question...which image is the more massive?...why?... the image on the right, because it covers a greater area appears more massive.
In Physics momentum (p) is defined as the mass multiplied by velocity, or p=mv. Let's imagine we have two marbles that are made of different materials. One is made of wood and the other of steel. If we throw these two marbles at someone's chest with the same velocity (or speed) which will hurt more when it hits? figure 6. Of course the one made of steel hurts more. It has more momentum. The velocity of the marbles is the same but the steel has more mass thus giving it more momentum (mass times velocity) . Given the same velocity, more mass means more momentum.
We have described the velocity of the triangular images as the slope of the lines relative to the base of the picture and we have determined the mass to be the area . figure 3.Given this we can describe the visual momentum (pv) as the slope times the area. pv = slope(area)
At the risk of being confusing I would like to substitute the term slope with a new synonymous trigonometric term, cotangent of 1/2 the vertex angle (cot (a/2)). figure 7. Also, we will call the area of a triangle 'K'. Thus K is a variable representing area or visual mass. Now the equation for visual momentum is pv = cot(a/2)K
Now we can describe the visual momentum in
both triangular shapes figure
3. as having the same momentum; but the image
on the left has seven times more velocity. It turns out that any isosceles (triangles with two sides of the same length) images of the
same height will have the same momentum. That is the mass of one makes up for the velocity of the other and vice versa.
figure 8... Equal momentum study of isoceles and scalene images ... three times diference in velocity 1981 36" x 48" oil paint on canvas shows an example of equal momentum in images other than isosceles. The isosceles image on the left has three times the velocity of the scalene (triangles having unequal sides) on the right and both have equal momentum.
Physics can define force (F) as the change
in momentum per unit time. What does this mean? Take for example
the egg toss game where a two person team competes with one person
tossing a chicken egg to the other person. Each completion requires
increasing the distance the egg is thrown-stepping backwards one
step. The team who can toss and catch the egg the greatest distance
without it breaking is the winner. In essence the object of the
game is to change the momentum of the egg from maximum (when the
egg is flying in the air) to minimum (when the egg is caught)
over the greatest amount of time. figure
9. This can be done by slowing the egg gradually as
it is caught; as opposed to catching the egg quickly in a short
period of time, applying a greater
force usually breaking the egg. To reiterate: the change of momentum per time is force... if the egg is slowed quickly over a short period of
time it creates more force; if the egg is slowed over a long period of time it creates less force.
Let's talk about visual force. We know howto
define visual momentum so we can talk about the change in momentum
which is initially zero and is finally at maximum. We see this
in the images of figure
3. but we don't know how much time has elapsed. However
we can see a distance of travel implied figure
10. and we know from physics that the distance an
object travels is equal to the velocity it traveled, multiplied
by the duration of time elapsed during its course of travel. d=vt
We know the distance implied figure
10. and we know the velocity. With that in mind we
can solve the equation for
average time. This turns out to be half the base of the triangular image.figure 10. This makes sense: velocity =distance divided by time (physics)
and velocity=rise over run (visual kinematics). What we have defined is the average time (the final time plus the initial time divided by two) .
What we are seeking is the definition of final time which is equal to twice the average time or 2t. Using this we can describe visual force
Fv =(Kcot(a/2))/2t (the change in visual momentum per unit time). Physics also describes energy as force times distance or E=Fd. Thus
visual energy is Ev =d(Kcot(a/2))/2t.
figure 11. Equal force study of isoceles images 4 times the difference in momentum 1984 36" x 48" oil paint on canvas is an example of visual force: the left image has 4 times the momentum of the one on the right and they both have equal force.
So far, we have limited our context to discussing
visual movement in one direction. A triangle actually moves in
three directions. figure 12. Before we talk about pandirectional movement we need
to introduce the concept of vectors. The definition of a vector
is any thing with magnitude and direction. If we throw a baseball
north at 30 miles per hour then it is a vector; 30 miles per hour
is the magnitude and north is the direction. A weight of 230 lb.
can be considered a vector, with the direction being down and
the 230 lb. being the magnitude. So each of the three individual
movements in a triangle can be considered a vector. figure 12. A vector sum is the
addition of the individual components of two or more vectors.
Let's try to illustrate. Consider three people holding ropes tied
to a ring which is positioned between them. figure
13. Each of the people has created a force vector,
that is they each pull with a certain force (magnitude) and a
direction (toward themselves). Let's instruct the two people with
the blue shirts to pull harder than the one with the red.
Which direction will the ring move? It won't move toward either of the people in blue who are pulling harder, it will move between the two. It
can be said that the vector sum of the three people pulling on the rope has a certain magnitude and is in a direction between the two people
with the blue shirts. We can add the individual vectors together to see which way the object moves. The final magnitude and direction of the
object is called the resultant vector ... basically the result.
Coming back to the triangle, we see that we have three visual momentum vectors or visual force vectors. figure 12. We can add the visual vectors together to see which way the vector sum points or which way the triangle visually moves. figure 14 ... Equal momentum vector sums 1984 36" x 48" oil paint on canvas is visually tricky because we may read the left triangle to be moving down and to the right, but if we think about the movement coming from the inside or center of the triangle then we can see the vector sum would indicate it to be moving up and to the left. figure 15 The right triangle is much easier to read. Actually both triangles are moving the same direction with the same visual momentum magnitude. figure 16 ... Equal force vector sums 1984 36" x 48" oil paint on canvas is the same study as figure 14. focusing attention on visual force.
The next three works in this series involve momentum and force vector sumations and a visual energy sumation of an entire field of triangles. Because there are no units for this type of study, I gave the unit chron for visual time, Kandinskys for visual force, Apollinaires per meter chron for visual momentum and Mattas for visual energy. The resultant vectors are noted under the triangle field in each piece.
figure 17 Psychovectors no.1 1988 36" x 48" oil paint on canvas.
figure 18 Psychovectors no.2 1988 36" x 48" oil paint on canvas.
19 Psychovectors no.3 1988 36" x 48" oil paint on canvas.
Another piece concerning itself with proprioception is Quantum Leap 2 (1980- photos and text 24" x 30" ) which is 4 photos that are taken inside 4 different Wendys restaurants. The camera now is actually facing the different directions that are stated under the pictures.