Our third type of “mathematical poetry” — or, rather, of “mathematical

*poem,*” because within the mathematical poetry

*genre*there exists different types of mathematical poem and our three types are but one family type and this expressly concerned with the analogy between “the grammar” of the mathematical proposition and

*the grammar*of the linguistic statement.

Our third type of mathematical poem is based on the “parallel lines” situation in geometry. Our formal symbol, here, will be two horizontal lines, the one parallel to the other, that make for the “parallel lines” situation; however, as we progress, that formal symbol will change, and the change will represent an actual situation come into being, as distinct from a potential situation or from what is simply

*the place*or

*topos*for a future situation, and we will call this actual situation a “transversal.”

So while we may speak of two formal symbols, we will actually be using only one formal symbol. Why then still speak of a first formal symbol and what does it mean in relation to our poem? To that end, let’s gain some perspective on this

*first*formal symbol (and on formal symbols as such):

In my

*Logoclasody Manifesto*I included a brief addendum entitled “On Mathematical Poetry” and there I put forth a proposition, a challenge of sorts, to myself and to the mathematical poet. Every good student en route to Aquinas via Copleston will have come upon this proposition, which

*in situ*is for the relation between substance and accident, namely those qualities and relations which exist only as qualities and relations of that of which they are predicated. Here is my rendering of that proposition — and in the form of a challenge, of sorts, to myself and to the mathematical poet:

*Write for me the mathematical sentence equivalent of the sentence, “Peter is sitting on the chair.” Write for me the mathematical sentence equivalent of “sitting on” existing as an entity apart from any sitter.*

There is a distinction here, between “Peter is sitting on the chair” and “sitting on”

*per se.*We might speak of “sitting on” as

*a position without magnitude,*or, as

*abstract*as opposed to

*concrete*(and indeed in that you cannot picture it!), or, as

*empty,*or, as without specification, or, as being in the same position as a formal symbol. The formal symbol,

*per se,*is empty; it is without circumstance; it is like a predicate without a subject (thinkable only in the abstract); and in the case of our

*first*formal symbol,

*the parallel lines,*what we have is a situation

*in posse,*a place

*in posse,*a topos

*in posse,*awaiting some action or state of affairs. This state of affairs is brought on by the transversal line, which crosses both parallel lines thus bringing them via their formal relation into an actual relation, or, indeed, into many possible relations, each signaled by the angle and by analogy with the angle the many possible poetic and ideational senses.

Formally, parallel lines are situational, they are the place, the topos, where things come to happen. That happening is the transversal line (and the angles or by analogy the poetic and ideational senses it carries with it). Our poem, then, which we will name “the transversal poem,” requires a formal symbol other than the two horizontal lines that indicate the parallel lines situation; our symbol will have to indicate or show or signal to the reader that here is an actual situation; that here is a poem, and that here we must consent to the intention of the poem; that we must as it were enter into the confidence of the poem. Our formal symbol then will be thus

≠

and will thus be known in this context as the “transversal poem.”

And our poem will take this structure, or, syntax or arrangement:

lines ≠ spirals

particles ≠ waves

constancy ≠ change

permanence ≠ transience

The transversal line, along with the angles it suggests, is then analogous to the many senses brought about by the juxtaposition of our words (of the poetic elements or ideas or images we bring to our formal symbols situation). Those

*angles,*or,

*senses,*or, “transversals,” if you will, exist side-by-side, and as often do complementary, competing and contradictory ideas. Some of these ideas can be said to exist in a state of “perpendicularity” or to be at right angles with each other, which is to be “at odds with each other.” Such as:

multiculturalism ≠ ethnocentricity

government ≠ media

determinism ≠ character and motive

turpitude ≠ enlightenment

a poetics ≠ an attitude

creationism ≠ evolution

god man ≠ monkey man

Some “transversal poems”:

the order of ideas ≠ the order of causes

the causal relation ≠ the relation of logical implication

word ≠ memory

paradox ≠ semantic tension

attractive ≠ repulsive

force ≠ matter

edgèd words ≠ edgeless words (sounds)

milquetoast ≠ white bread

iteration ≠ chromaticism

Our next post will be about “mathematical prose.”

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