Thursday, July 19, 2007

The Orthogonal Space Poem

The orthogonal space poem is one of the simplest mathematical structures one can use for mathematical poetry. The structure can be seen in numerous contexts in the discipline of the sciences. Examples in physics would include Newton’s second law “F = ma”, Ohms Law “E = IR”, the kinematical properties of “d = vt”, “p=mv” and E = Fd. Please notice all of the equations are in the form of ‘a’ equals ‘b’ multiplied by ‘c’ or “a = (b)(c)”. This wonderful equation states that the value of one particular concept is equal to the product of two values held by two other concepts. When this equation is depicted in a Cartesian coordinate system you can see that the latter two concepts exist in an orthogonal or perpendicular space.

Before I explain the “orthogonal space poem’s” use in mathematical poetry, let us look at this same mathematical structure in the context of science. Furthermore, before we look at a scientific example let is review a little mathematics. Let us first review the Cartesian coordinate system and its nomenclature.

When we look at the two-dimensional axis of a Cartesian coordinate system, we can see that by randomly picking a point somewhere on the Cartesian plane, then we see there exists is a relationship between this ‘chosen’ point and the point defining the origin of the coordinate system. This relationship is understood by the nomenclature of the coordinate pair (x,y) where x and y are distances along each axis from the origin. Furthermore, if we draw lines from a newly created point, orthogonally (perpendicular) to both the x-axis and the y-axis and taking into consideration the axis system in the background then we will make a rectangle.

The area of a rectangle is product of the lengths of its sides furthermore, in the upcoming example, it is the product of the values for the x and y coordinates of this “chosen” point. I assigned one corner of the rectangle at the origin point to make our example easier to see. Example: Let us pick a point defined by the x-y coordinates of (11,13) and draw lines perpendicular to the axes to illuminate the concept that I just stated. The area of any rectangle is equal to its height multiplied by its base (The product of the lengths of its sides). We have a green rectangle delineated on our axis system. (See figure. 1) The height of our rectangle is 13 units and its base is 11 units. The area of our rectangle is 143 square units … or 13 X 11 = 143 This later example is one of pure mathematics. However if we want to use math as a language then we will have to apply concepts or words to our axis system.

Let us look at a typical physics problem of distance, velocity and time displayed on a two dimensional axis system. Let us assign the y-axis to be levels of velocity in units of miles per hour and the x-axis to be amounts of time in units of hours. Furthermore, let us look at an example using the concept of the “distance an object has traveled is equal to the velocity of that object multiplied by the time the object has traveled.” or “d = vt” In this example let us look at the Cartesian coordinate system as well as its orthogonal construction.

We will use the same pure mathematical example as before but by our contextualizing the axis and assigning the y-axis to represent velocity and the x-axis to represent time, our original point from the last example (11,13) has a new meaning. To reiterate … the point before was in the realm of pure mathematics but now the point represents a moment in time of a speeding object. The object is traveling 13 miles per hour and has been traveling for 11 hours. So to calculate, (d = vt), the distance the object has traveled we must multiply the velocity by the time or 13 miles per hour times 11 hours which equals 143 miles.

In essence, what we have done has been to assign a concept by using words (velocity and time) to our axis system. Moving our attention up or down on the y-axis displays different values of velocity. Moving left and right on, the x-axis displays different amounts of duration or time. Physical experimentation can easily verify the veracity of this equation. In addition, the same experimentation verifies the verbal concepts and their relationship to each other that we have assigned to our axis system. We can see the relationship between the concepts of distance, velocity and time spread out on a two-dimensional plane via our axis system. It is important to note that these concepts occupy orthogonal spaces as well as all equations in the form of a = (b)(c).

The orthogonal space poem possesses the exact same form as our scientific equations however, our intention is poetic as opposed to science.

For our example lets look at the following orthogonal space poem which is titled “Prometheus’s Epistle To Job”

In this poem Prometheus expresses to Job that the suffering of pious people is equal to the arrogance of their God divided by the level of ostentatious generosity imparted by their God.

Lets see how this poem relates to an orthogonal space using a Cartesian coordinate system. We can see how it follows the same structure as the previous physics example.

Another important aspect of creating a orthogonal space poem is to examine all the syntactically different synonymous permutations. Let me reiterate, the structure for an orthogonal poem is a = b c which means that we can solve the equation three different ways. a = b c, b = a/c and c = a/b. When creating an orthogonal space poem you would want to solve and analyze your poem all three different ways to make sure that the poem makes ‘aesthetic sense’ in each different form. Lets look at the latter poem as an example.

The suffering of pious people = The arrogance of their God “divided by” The ostentatious generosity of their God

This poem should also make sense in its two other syntactically different however, synonymous structures.

The arrogance of their God = The suffering of pious people “multiplied by” The ostentatious generosity of their God


The ostentatious generosity of their God = The arrogance of their God "divided by" The suffering of pious people


Anonymous said...


This is such an amazing idea. First of all, I love the idea of juxtaposing the characters of Prometheus and Job, because they're so similar, and so emblematic of the basic elements of raw humanity.

What I love about your mathematical ideas is that they actually make sense. I don't think it's a problem at all to codify the reasons why we write/read a poem, and mathematics is a decent language to select for that process. And while mathematics has a certain stigma about it that connotes a lack of feeling, your writing about mathematics is very rich and imaginative.

I'm looking for other poets to give me feedback on my new web site. When you get the chance, please visit and tell me if there's anything you think I should change.

Keep on writing.

Kaz Maslanka said...

Thank you so much for your kind words. I really appreciate you stopping by. I will check out your site.

Thanks again!

Anonymous said...

Dear Kaz,
The simplicity of your explanation is stunning. Once a mathematical idea has been simplified, it can be translated into words. I differ with you over the term, value to account for the orthogonal equation. I would say an equation states that the function of one particular concept is equal to the product of two functions held by two other concepts in a given argument. The argument of the poem gives the value. To me this allows for the reader to deduce a possible third function. Your orthogonal vision is also brilliant. I want to create a web of words within the argument space generated by a set of simple rules. If you like I can send you an example. Best wishes

Kaz Maslanka said...

Dear Duncan,
Thank you for kindness and I would love to see anything you or anyone creates in the realm of mathematical poetry.


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