publications
sensing geometry
Sensing Geometry explores some of the surprising connections found among mathematics, science, and art. While abstract mathematical objects, progressively built from self-contained systems, might be said to exist only in the mind, this interdisciplinary study shows how mathematical and scientific concepts have also been adapted into various forms of artistic expression - architecture, poetry, painting, and sculpture - as examples of hybrid thinking and creative process.
excerpt from the introduction:
"In mathematics, as with art, the deeper truths are often the most compelling ones because they speak a universal language - inherent structures that were already present before us and will remain long after. Because there is debate, even among mathematicians, if certain concepts have been invented or discovered, the field itself might also be considered an idealization - an esoteric science perpetuated by self-made rules - and thus it can also present a pure philosophy. And yet, in spite of its inherent abstractions, somehow the model still conforms to our world. If there is the intention of truth-making in the work, whether artistic or mathematical, that will be both its origin and validation when tested and held to be true."
Sensing Geometry
published by Rock's Mills Press, 2019
Available through publisher and major booksellers
cover image: Sam Oppenheim, Ancient Ice
sea change: reason, revolution, and creativity
Although much has been written about historical developments in the nineteenth century, Sea Change is focused on shared characteristics found in both mathematics and the fine arts as evidence not only of their similarities, but also of individual contributions that eventually led to new paradigms. Traditionally, these disciplines have their own symbolic language, levels of abstraction, expression, and representation, all of which are usually intended to somehow correspond with nature in a meaningful way. Taken together, they ultimately seek a high level of synthesis as active mixtures of logic and imagination, analysis and intuition. With these considerations, the confluence of complex events at this time firmly established a foothold for the next century through mathematical and artistic inquiry, discovery, and reform, aspects that we would later identify as indicators of “Modernism.”
Sea Change is a forthcoming project to be published in 2024
by Rock's Mills Press
image, left: Caspar David Friedrich, Der Wanderer über dem Nebelmeer
(The Wanderer Above the Sea of Fog), 1818, Hamburger Kunsthalle.
re:Andromeda
Originally, the intention of re:Andromeda was to be a descriptive companion to another work, Andromeda, a landscape painting made near Narrowsburg, New York, but while writing, like the organic features of an actual landscape, the manuscript also evolved and became something more. Eventually, both works merged into a unified compound, not merely referring to each other, but symbolically becoming indistinguishable as identical twins, carrying the same message, the same sign called “landscape.”
This book, then, idealistically represents the painting’s double, not as a replacement,
but an equivalent.
re:Andromeda (landscape, text, and transformation) is an ongoing project comprising textual documentation of a series of related landscape paintings capturing nature in the most direct sense.
connecting the tangent function to cardinality
Popular ideas about infinity include asking questions about what the "largest number" might be, and what is the nature of limits, such as the speed of light. In the nineteenth century, Georg Cantor provided simple demonstrations of set theory, which included the possibility of dividing infinity into infinitely many types, such as those that are "countable" and "uncountable."
Deihl and Markinson present a novel method of introducing such notions to high school students when they are studying trigonometry. In particular, this research compares the tangent function as it approaches 90 degrees to that same type of boundary spaceships will encounter as they approach the speed of light. Furthermore, all of the values for tangent from 0 to 45 degrees are found on the interval from 0 to 1, while every other value from 1 to infinity are found in the remaining quadrant, from 45 degrees to 90. This striking comparison is detailed in the Columbia Journal here.
co-authored paper:
Steve Deihl and Mara P. Markinson, in Journal of Mathematics Education (JMETC),
volume 10, issue 2, (Fall 2019), Columbia University.
image: Georg Cantor (1845-1918)
constants of art and nature: "the rainbow project"
Published in the MIT Journal, Leonardo, The Rainbow Project was first presented in the SETI Institute's 2002 Paris Conference, whose theme was "The Art and Science of Interstellar Message Composition" - an interface of art, science and technology in interstellar message design.
How best to frame information that is universally accessible?
A select group of artists, musicians, astronomers, and mathematicians met on 18 March at the home of Roger Malina to discuss the types of messages that can be potentially transmissible to other intelligent life forms. Through this work, and others, it has come to be realized that, although interstellar messages have not typically been construed as works of art in themselves, those art forms may still be transmissible as valuable content in themselves, which is not purely aesthetic.
Such was the suggestion in The Rainbow Project:
that the information contained in a terrestrial rainbow - refracted light that is separated into constituent wavelengths corresponding to "color" - could be both aesthetic, and obviously, convey information about the water, atmosphere, and the physics of light spectra on our planet, Earth.
A "picture" of a rainbow could be transmitted across interstellar space over the course of 7 terrestrial days. The message would be generated using the broadcast frequency as the reference for the rest of the message, essentially using frequency to describe itself. This standard would provide the baseline for translating each color, creating a rainbow pattern according to its specific frequency corresponding to our unique optical notions of "color." The frequency used would have to be universally accessible and recognizable as an essential unit of Nature, such as the signature of cold interstellar hydrogen, the most abundant element in the universe, equal to ~ 1420.405 MHz,
a wavelength of 21cm.
Steve Deihl, "Constants of Art and Nature: The Rainbow Project
Leonardo, volume 37, number 1, 2004
MIT Publication: Journal of the International Society for the Arts, Sciences, and Technology
image: Steve Deihl, Between Worlds: Golden Sections
graphite on paper, 22" x 18", 2004