Internal Peripheries, Unilluminable Room, 2017
57 x 42 x 32 inches
MDF, acrylic, aluminum mirror, water, plumbing, water pump, sawhorses

In 1953, mathematician Roger Penrose showed that there are mirrored “rooms” which can never be completely illuminated by a single-point light source. In this way they have unilluminable, peripheral spaces within their interior. Like much of mathematics, the solution depends on many assumptions that are physically impossible, such as a single-point light source, perfect mirrors, and the absence of diffraction.

Here a mundane faucet perpetually drips into a pool shaped like a Penrose Unilluminable Room. Due to the shape of the pool, the ripples from the dripping faucet are unable to reach the entire surface of the pool. The faucet can swing into two different regions of the pool creating two different ripple patterns, but theoretically the ripples should never cover the entire surface of the pool. The contrast between the Platonic ideal of the Penrose’s solution and the banal dripping faucet with its backed-up drain suggest the failure gap between practice and theory.

The work also speaks to me of Godel’s Incompleteness Theorems which state that for any logically consistent system there will always be truths that are unprovable from within the system and that a given system cannot demonstrate its own consistency. There are thus regions of the system that can only be proven (a.k.a. “illuminated”) by going outside the system. The sad, leaking faucet resting on sawhorses suggests the resignation of an abandoned project while demonstrating the impossibility of completeness itself.