this idea is rather natural

“This Idea Is Rather Natural,” an MFA exhibition by Matthew Teigen, represents the fusion and resolution of two important and long-standing streams of the artist’s work: drawing and sound, synthesized by an animation practice that operates primarily in the formal culture of contemporary art. 

The concept “ethnomathematical visuality” is at the core of this show; it implies an aesthetics – a visual art – that is derived from the culture of done mathematics. That is, the art takes its formal language from what is done by mathematicians, rather than relying on any sort of generative process in which math is used to determine characteristics of a given work.

Matthew Teigen is an emerging artist whose work with sound, animation, and drawing engages in the aesthetics of mathematics and ethnomathematics. Matthew was born in Montreal, and spent several years in the United States where he did his undergraduate work in Imaging and Digital Art at the University of Maryland, Baltimore County. “This Idea is Rather Natural” is the culminating exhibition of Matthew’s MFA at the University of Western Ontario.

Photographs of the exhibit, which ran from June 16-27, 2011, are here. Or, you can go back home.

second bird
pencil and marker on 22" x 30" paper

The bird-human hybrid appears a lot in my work. "Second bird" features what looks like diaristic journal-writing, often plaintive in nature; this came about due to the unforseen degree of effort it took to do so much unrehearsed algebra and arithmetic.

algebraic ring
ballpoint pen and marker on 22" x 30" rag paper

A deliberate decision to fill up an entire page with math. In a sense, this drawing is the most conceptually honest, because it comes the closest to being purely "math-as-art" -- there's (almost) nothing but math on it, even though I wasn't doing the math but only copying it.

differential geometry
photocopier collage and marker on 22" x 30" paper

For a long time (a few weeks or months), this drawing wasn't really a drawing, but consisted of only the photocopied geometric figure pasted onto a blank sheet of paper in what was, I suppose, a minimalist gesture. Eventually a shape was improvised around it, and "differential geometry" became a full-fledged drawing. 

deceptacon
photocopier collage and marker on 22" x 30" rag paper

"Deceptacon" is one of two similar drawings, both consisting of a sea of algebra with an icononic shape-in-a-sun floating above it. God, spirit, or universals -- something that can be present in math depending on one's philosophical position -- is hinted at here.

monolith
photocopier collage and marker on 22" x 30" rag paper

The title "monolith" is a reference to the Arthur C. Clarke novel 2001, which ellaborates visually and narratively on the liminality of spiritual and scientific themes.

kind of a macro-micro, celllular/sci-fi thing
pencil and marker on 22" x 30" paper

As alluded to in the title, this could either be at a very large, planetary scale and harken to science fiction fantasy, or represent a scenario of microbiological interaction.

waterslide
pencil, ballpoint pen, and marker on 22" x 30" paper

red trefoil
pencil, photocopier collage, marker, and ballpoint pen on 22" x 30" paper

The photocopied shape at the centre of this drawing -- in fact, a (blue) trefoil, a subclass of string diagram -- is responsible for as much formal content as the birdman, if not more. I found the shape to be compelling, and used it often.

hockey rink
pencil and marker on 22" x 30" paper

I copied some diagrammatic notation from a graduate math thesis, but did so sloppily. Then, I went over my sloppy lines with deliberate ones in order to warp the subject, and then added colour. I found, in the process of doing these drawings, that a better approach was to build the abstract or purely formal elements around math, as opposed to working the other way around. 

no math at all
cut paper collage, marker, and pencil on 22" x 30" paper

There was math here, but it got cut away. Now, there's nothing in "no math at all" to indicate the conceptual direction of my thesis show, or my drawing project. Nevertheless, "no math at all" touches on the creation of purely abstract forms in my art practice, and in doing so hints at another discourse altogether.

the power rule
pencil and marker on 22" x 30" paper

For the creation of "the power rule," I re-learned some of the calculus that had almost totally escaped my memory and took derivatives on drawing paper (using the power rule of differentiation). The concept and process surrounding "the power rule" are so vital, from my perspective, that it becomes difficult for me to analyze the drawing objectively and formally, and assertain whether or not it's working as a visual object. Even if it were not working, this drawing is immensely important to me and to my project of "the look of math."

unitled
pencil and marker on 22" x 30" paper

Very similar to "red trefoil", and reminiscent of "macro-micro": all three involve outlined charater-shapes with what could be seen as feelers or antennae, interacting in some way with a larger, surrounding environment.

adrastea
digital animation, 00:03:23

"Adrastea" speaks to a celestial mysticism made accessible to an observer via an ordinary category and conduit: Raphidophoridae, also known as the cave cricket.

Nature -- commonplace, terrestrial nature -- is a bridge between an ultimate universal and human consciousness (see: First Nation Shamanism, Celtic Paganism, Shinto, and other nature-based spiritual systems).

Jupiter (or Zeus, in Greek) and his moons (or dubiously free-willed love objects) iconographically commandeer a spirituality that is semeiotically foreign to us; it's something we can't reach with our extant cognitive, conceptual, and technological toolbox.

But with the cricket, an ordinary and Earthly insect that is revealed to be quite beautiful upon mindful examination, we are brought back down to Earth and Earth's natural structure. Ultimately, we're brought back to human self-awareness and self-actualization.

The cricket is a bridge between inaccessible signifying images, which praise an alien, mystical spirituality, and ourselves. We always have the cricket, which returns periodically, to pull us back down to Earth, and via which we can get our bearings between excursions to a mystical place where we are uncertain of the rules or categories.

Because these are my cave crickets (I grew up with them hopping around my basement), it becomes my spirituality. I'm using this sample of my own personal experience with nature -- which is something we all have -- to bridge the gap between understanding and the infinite. So, in a sense, this project constitutes my own path to God or an Ultimate Reality.

The non-cricket shapes made from cricket parts are organic, and might resemble some kind of alien creature. In these mysterious shapes there is "The peace of God which passes human understanding," but ultimately they are understandable, because their components -- their semeiotic components -- are familiar. Using a syntax of nature, we can achieve a grammar of God.

trefoil
digital animation, 00:02:36

A series of animated, abstract-yet-narrative vignettes that are very close, formally, to my math drawings. In fact, it might be said that the drawings serve as a sort of concept art for this animation, and that this animation represents the culmination and resolution of that particular project.

p = n^2 - n
digital animation, 00:02:48

Animated musical scoring. 12 pitches were formulaically derived, and their occurrences illustrated in a time-linear way: as the familiar bird-figure marches across the screen, notes play that correspond to the markings on the screen. What follows is an explanation of how, exactly, the pitches were created.

If I want to count from one number (p) to another number in some number of increments (n) which also equals the distance between increments, and I want double the first number to equal the last number, then is there a formula such that if I know one variable I can compute the other?

Yes! It's: p = n^2 - n

Imagine I want to divide up my octave into twelve pitches, each falling 12 hertz apart. We now know n, and can work out p with arithmetic:

p = 12^2 - 12
p = 132

In order to divide our octave into 12 pitches spaced 12 hertz apart, we know our first pitch has to be 132 hertz. Then, we count up by 12, to yield a total of 12 pitches:

132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264

And, indeed, 264 is double 132. so, our equation works.

Of course, you can work backwards if you know a starting pitch.

132 = n^2 - n
n = 12

It's interesting that only one positive integer has properties such that it will yield another number equalling the number of intervals when counting up to double that first positive number, in increments equalling the number of intervals. Can this be proven?

I'm using numbers to work out pitches -- to work out a particular way of splitting up the octave, which is a pitch-distance that is always numerically represented by doubling a number (the fundamental, perhaps measured in hertz) to yield its octave. For instance, a note of 220 Hertz is doubled to 440 Hertz, which sounds an octave higher.

We aren't limited, of course, to using 132 for p and 12 for n. Let's try it with some other quantities:

Solve p = n^2 - n for n = 10:
p = 90
90, 100, 110, 120, 130, 140, 150, 160, 170, 180
180 = 90 * 2 - check!

Solve p = n^2 - n for y = 9:
x = 72
72, 81, 90, 99, 108, 117, 126, 135, 144
144 = 72 * 2 - check!

Solve p = n^2 - n for y = 13:
x = 156
156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312
312 = 156 * 2 - check!

Etc.

Also: it's important to note that counting from one number to another in equal jumps of some other number -- some fixed increment -- is not the same thing as moving in equal jumps of pitch, because the harmonic series is not graphable as a straight line, but rather a curve.

Three Compositions, the Pitches of the First Being Derived From Familiar Mathematical Constants, the Pitches of the Second Being Derived From the Harmonic Series, and the Pitches of the Third Being Derived From Sequential Quarter Tones
sound installation

As the title conveys, this work is a study in pitches derived from numerical manipulation. As such, the pitches (and especially intervals) found in the compositions do not occur in a Western musical context, and therefore sound odd or alien to an ear accustomed to pieces composed in tonal harmony. In all three cases, I generated six sine waves with pitches specified numerically in hertz. Then, I re-tuned an electric guitar to match these six new pitches.

In the first piece, in which the pitches are derived from some familiar mathematical constants (such as pi and the "golden ratio"), I started with the frequency of 82.407 Hz, so-chosen because this is the standard pitch for a low "E" string on the guitar. This was my base value, or "1". Then, to derive an interval based on the value of pi (approximately 3.142), I simply multiplied 82.407 by 3.142, and then tuned the "b" string to the resultant 258.993 Hz. Using the low "E" string as my base pitch, I repeated this process for the remaining 4 pitches, mapping pitch-to-string in a way that is as stress-free as possible to the guitar's strings, which are designed to be tuned to specific pitches.

In the second piece, I derived my pitches from the harmonic series, a term extant in both math in music, which mathematically amounts to 1+ 1/2 + 1/3 + 1/4 + 1/5 + . , and musically amounts to the notes in open-horn tunes like "Taps," "Charge," and "Wake-up Call." Guitar players are also familiar with the harmonic series from laying their finger gently on the string at the 12th, 7th, or 5th fret, plucking it, and noting the pitch.

In the third piece, I derived sequential quarter tones from a base frequency of 175 Hz using the ratio 35/36, which is the way to get an equal-tempered quarter tone (a value equal to 50 cents, or exactly one half a semitone, the smallest interval in Western tonal harmony). For example, to get the pitch after 175 Hz, I multiplied 175 by 36 then divided the answer by 35, resulting in 180 Hz. I did this 5 times to get 6 distinct pitches, each a quarter tone apart.

Each piece consists of 2 or 3 layers of sine waves, and then 1 layer of guitar (tuned to match the pitches of the sine waves, and played unfretted).

The long title is a way of "sneaking in" some didactic, since the piece is conceptual and listeners probably won't get its intent just from listening to the compositions (as in "Oh! Obviously that piece has had its pitches derived from known and used mathematical constants!").