Small Goals is a series of paintings, each roughly 16 x 20 mm and 1.8mm thick. I refer to them as “micro-paintings.” Micro is the metric prefix for one millionth (10-6 or 1E-6 in scientific notation, and symbolized by the Greek letter μ [mu]). A microsecond is one millionth of a second; a micrometer is one millionth of a meter; a micro-painting is not one millionth of any particular unit or object, nor is it one millionth of a painting. The Small Goals are made with a range of media—wax-based colored pencil, graphite, permanent ink, inkjet printing, acrylic paint and acrylic medium applied to thermo-sensitive polystyrene plastic sheets (commercially available in The Netherlands as Krimpie Magic Plastic). Completed compositions are heated at 160°C and shrink to between 1/3 and 1/4 of their original size; the type and combination of media applied affects the shrinking in different ways.[1]

One micro-painting has a volume of 0.576 cm3. The Earth has a volume of 1,083,210,000,000 km3. Therefore, a Small Goal is 1.8805729 x 1027 (1,880,572,900,000,000,000,000,000,000) or one octillion, eight hundred eighty septillion, five hundred seventy-two sextillion, nine hundred quintillion, times smaller than planet Earth.

Selection from the series Small Goals, 2015
Colored pencil and graphite on thermo-sensitive polystyrene
20 x 16 mm

The concept of a fifth dimension, extra to the four we perceive—up/down, forward/backward left/right, time—was first introduced by the German physicist and mathematician Theordor Kaluza in 1919. He wrote a letter to Albert Einstein proposing an extra dimension as a potential solution in the attempt to unify the forces of gravity and electro-magnetism in one theory. His hypothesis was published in 1921 in a paper called “On the Problem of Unity in Physics” (“Zum Unitätsproblem der Physik”). In 1926, Swedish mathematician Oskar Klein offered a quantum interpretation, suggesting that this fifth dimension might be tiny, circular and found everywhere at each point in space. With the work of several independent research groups, the Kaluza-Klein Theory was completed by the 1940's. In this theory, tiny is undetectably small: 1.6162(97) x 10-33 cm. This measurement—chosen by Klein—is known as the Planck Length, named after physicist Max Planck. It is approximately one thousandth of a millionth of a trillionth of a centimeter (Randall, 2005, p.34). Therefore the Kaluza-Klein “curled up” fifth dimension is roughly one trillionth of a trillionth (septillionth) the size of an atom and three hundred fifty-six nonillion, three hundred ninety-one octillion, five hundred forty septillion (3.5639154 x 1032) times smaller than a Small Goal painting. That is exceedingly small. In terms of a ratio, the Planck length is still over one hundred thousand times smaller than a micro-painting is smaller than planet Earth.

Contemporary versions of String Theory call for five more extra-dimensions at this scale. The six nearly infinitesimal dimensions are tangled up in a shape known as the Calabi-Yau manifold, named after Eugenio Calabi, an Italian American mathematician who conjectured the geometric shapes, and Shing-Tung Yau, a Chinese American mathematician who proved them.

Simulation of a Calabi-Yau Manifold, source: the Internet.

[1] In 2008 Anthony Grimes, David N. Brslauer, Maureen long, Jonathan Pegan, Luke P. Lee and Michelle Khine published a paper in the “Lab on a Chip” section of The Royal Society of Chemistry scientific journal titled, “Shrinky-Dink Microfluidics: Rapid Generation of Deep and Rounded Patterns”. Microfluidics is the manipulation and engineering of fluids on a sub-millimeter scale and is used in physics, chemistry, biochemistry, nanotechnology, biotechnology (think DNA testing), etc. In this article the group presents their method of using bi-axially oriented polystyrene thermoplastic sheets (commercially available as Shrinky-Dinks' in the United States) and a laser-jet printer to create microfluidic pattern templates from which they form functional devices. "We printed features onto this thermoplastic, and found that after heating for 3–5 min at 163°C, printed features shrink isotropically in plane by approximately 63% from the original printed line width and length. There is an additional corresponding increase in height of the features by over 500%. We subsequently used these shrunken features as a rigid mold for soft lithography." (2008, p.170) This is also the material support used in the Small Goals series.

Table of Contents

Vanishing Exercise
Through a Double Slit
No Dreams, No Logic
Erotics of Art and Science