2025 – This wave sculpture has three cables attached to a tiny sphere.
At first glance it seems that a single moving point is entirely unsatisfying. The point is a 1.5-inch stainless ball bearing. It traces a 3d path known as a trefoil knot, repeating itself every 8 seconds. You would think that our minds would be able to discern this shape, but instead we see the ball as series of isolated moments. Surprisingly, we simply lack the power to combine these moments into a persistent path. Our vision is too quick. Our memory too poor.
One way to slow down vision and see the path is to take an 8-second exposure. This video contains 1507 8-second exposures taken 9 seconds apart. The trefoil looks the same in each image. There appears to be no movement. The little rotating arms that pull on the cables have turned into static discs. Under the sculpture there is a large rotating arm that takes about four hours to go around. Since the video is made of images that are 9 seconds apart, played back at 24 images per second, the arm appears to be moving 216 times faster than it is. At the end of the arm there is another camera. This camera is also taking 8 second exposures.
This is the view from the camera at the end of the arm which is rotating one revolution every 4 hours. It is a sequence of 1507 8-second exposures that reveal the 3d shape of the trefoil. It is revealing a shape that is right in front of our eyes yet invisible to us. It is revealing a shape that exists in a different time than our own.
While an 8-second exposure appears to stop the sculpture, a 2-second exposure gives us a partial curved segment along the trefoil. To make these next videos I took about 4000 2-second exposures that were somewhat randomly distributed across the trefoil path. I then ordered them so that the head of the squiggle advanced along the trefoil. The order in which the images were taken is irrelevant. An image in this video might be preceded by an image taken hours before, or hours later. The important part is that the adjacent images caught the sphere as it traced slightly advancing sections of the trefoil. The relevant time is position along the trefoil, not the time when the image was recorded.
This is another angle of the trefoil created by weaving temporally discontinuous 2-second exposures.
Just a little about the math. There are two common parametric equations that describe trefoils. They are topographically equivalent, but one expression is based on torus knots, and the other has a hypotrochoid as the XY projection. The latter is prettier. Also, by means of trig identities and a change of basis rotation I was able to make the hypotrochoid version precisely using my analog wave techniques. By changing the sprockets in my mechanism higher level knots can be formed.
The view from the end of the rotating arm. This is cataloged as knot 15n41185 with 15 crossings.
To show this sculpture I would install it along with the rotating camera arm. After lighting the venue, I would make new videos to be presented alongside the sculpture. The sculpture is incomprehensible on its own. It gathers form as we step away from our own measure of time.