Substitution in Mathematical Poetry

Substitution in Mathematical Poetry

If you have no understanding of similar triangles poems then please read about it at the following link: “Similar Triangles Poem”

This Blog entry will show an example of substitution in mathematical poetry. Substitution can occur when we have two equations that have a common term. For example let’s look at the two equations which have the same form as two similar triangles poems: A = BD/E and A = HJ/U since both equations have the term ‘A’ in common and consequentially they both happen to be solved for ‘A’ then we can set both equations equal to each other as such:

BD/E = HJ/U

We know that we can solve for any of the variables in our new equation and get a new equation in terms of one variable. Let do so and solve for ‘J’ so we now have: J=UBD/EH

So now let’s apply what we have just witnessed to two similar triangles poems.

First of all we must look at the following two poems.

We know from our earlier example that we can solve a mathematical equation for any term in it. If we take the first poem and solve it for “my memories” we then can present the poem as:

Notice (below) that we have the two poems solved for the same term (my memories).

Now we can set each poem equal to each other because they both have identical terms. (see below)

We also know that we can solve this poetic equation for any of the terms in it. So let us solve this poem in terms of “Delaware River”

Now we can see that the later poem was derived from the two similar triangles poems shown at the top. What is interesting is that all of the logical processes used to create the first two poems are contained in our resultant poem including the subtle differences in the contexts of each initial poem.
Substitution can also be used in poems created by different poets as long as they have a common term. Follow this link to collaborative substitution poems.

The following polyaesthetic piece uses the image of a shipping beacon located at Cedar Swamp on the Delaware side of the Delaware River. The full Delaware River Poem from our example is nestled in the lower left hand corner of the image. The physical size of the digital image is 67” x 31”

Delaware River Correction

I actually made a mistake on my last blog entry. I meant to post the two similar triangles poems (above). If you were on your toes you would have noticed that the last blog entry was actually the same equation (poem) solved for different terms. Today’s entry is two different poems that also share a common term. What is interesting is what we will do with these two poems on the next blog entry. Can you guess what I will do?

The Gift of San Shin 산신 (Polyaesthetic)

Here is the Polyaesthetic version of "The Gift of San Shin" which utilizes a Similar Triangles Poem.

In the vernacular this mathematical poem can be spoken four ways but the two most important ways are: 1.) Wisdom is to Adversity as the Wind is to a Cage  2.) Wisdom is to the Wind as Adversity is to a Cage.  It can also be put into the syntax of an orthogonal space poem.   I like to think of the denominator of  orthogonal space poem as some kind of valve that controls the value on the other side of the equal sign. For example I like to look at the limit of "The Cage" as it approaches zero thereby making "Wisdom" near infinite. 

General Music

Here is another “Similar Triangle Poem” Titled “General Music” Inspired by the differences in their philosophy of battle execution.

산신 의 선물

Here is the Korean version of the Similar Triangle Poem titled “The Gift of San Shin / 산신 의 선물

” shown in the previous post.

The Gift of San Shin 산신

Here is another Similar Triangles Poem inspired by the Korean Mountain spirit San Shin 산신

Ego Pride

Here is a new similar triangles poem titled “Ego Pride”

The Muses

Here is another similar triangles poem

Jennifer Karmin And The Monocular Mistress

During the 2nd Annual Chicago Calling Arts Festival, Chicago-based artist, Jennifer Karmin will be reading Beast Poetry that she has assembled from sources outside of Chicago. One of the poems she will be reading is the similar triangles poem “The Monocular Mistress” shown above.

Death by Thierry Brunet

The mathematical poem above is a similar triangles poem titled "Death" Furthermore it was sent to me by the French Poet Thierry Brunet.

Mathematical Poetry

Here is another "Similar Triangles Poem" titled "Mathematical Poetry"

The Good Path

Here is another "Similar Triangles Poem" titled "The Good Path"

Anthropology

The mathematical poem today is a similar triangles poem inspired by the text below which appeared in the delancyplace blog Tuesday, August 21, 2007

Delanceyplace.com 08/21/07-The Guillotine
In today's excerpt--Dr. Guillotin's invention, the guillotine, which debuted in Paris in 1792 and was still being used for capital punishment in the 1950s. Guillotin's motive was to introduce a more humanitarian form of capital punishment, and his success in that was evident from the very first use of the guillotine when "the crowds, accustomed to bloody bouts with the ax and sword, thundered in disappointment, 'Bring back the block!' " Yet almost immediately, guillotine executions became Paris's favorite form of entertainment, with families bringing picnic lunches and reveling in the carnival atmosphere that surrounded them. During the French Revolution, with a virtual civil war raging in the provinces, "at least half a million people were slaughtered on local guillotines or in battles between opposing forces." Here is a description of France's last public guillotine execution, which occurred in Versailles in 1939 when convicted murderer Eugene Weidmann, a German, was decapitated:
"Weidmann's execution was slated for June 17, and throngs had been pouring in from Paris and elsewhere for days, lending a holiday mood to the town. Permitted to stay open all night, bistros overflowed with customers as elated by the event as fans on the eve of a football match. The guillotine, which had normally done its deed inside the jail, was moved to the street outside, and proprietors of apartments above were cashing in by renting seats in their windows. From his cell Weidmann could hear loudspeakers blaring jazz interspersed with commentaries on his impending demise. ...
"Despite his years of experience, Desfourneaux [the executioner] was slow and jittery. Only after three tries did he manage to squeeze Weidmann's neck into the lunette, and he also fumbled with the lever. The operation lasted twelve seconds--twice the normal time. The crowd, which had been waiting in hushed anticipation, stormed the police barrier as the blade fell. Men shouted anti-German epithets; elegant ladies, avid for souvenirs, rushed to dip their handkerchiefs in the blood; and, for the rest of the day and far into the night, revelers chanted songs and swilled wine. ...
"Perched on rooftops, photographers recorded the tumult, and their pictures quickly appeared in newspapers around the world and became a staple of postcards. The fiasco shocked even the most intransigent proponents of capital punishment, and also cast doubt on the doctrine that public executions deterred crime. Fearing that future outbursts would damage France's image abroad, Premier Edouard Daladier decreed that guillotinings were henceforth to be conducted within prison enclosures."
Stanley Karnow, Paris in the Fifties, Three Rivers Press, Copyright 1997 by Stanley Karnow, pp. 161-162.

Death by Cherryl Floyd-Miller

My example for the similar triangles poem is admittedly mundane with my only excuse being due to its pedagogical intent. (Peanut butter -- Apple butter -- who cares?)

However, I want to bring attention to a similar triangles poem that I ran across on the internet by Cherryl Floyd-Miller. Mrs. Floyd-Miller recently experienced the loss of her Aunt and somehow wound up in a space in which she was able to share her experience with a mathematical poem. Even though the similar triangles structure is dry and logical, this mathematical poem evokes tears in my eyes as well as calling for a simple spiritual place, nostalgia for life and acceptance of the human condition. This example is truly the way theses structures are supposed to be used.

Physics

Below is another similar triangles poem

The Expanded Similar Triangles Poem

The similar triangles method for constructing mathematical poems easily enables us to manipulate a logical structure for metaphoric expression. What this pedagogical blog entry is trying to accomplish is the introduction and showing of the expanded version of the similar triangles poem. This poetic structure is logically more complex however, still easy to manipulate.

Before you read further, please be familiar with the similar triangles poem. You may read about it here.

The 'regular' similar triangles poem only utilizes two similar triangles and is defined as an expression of two ratios. The expanded similar triangles poem utilizes ‘n’ number of ratios and is able to create very large (infinite) complex mathematical poems and still have a logical structure to act as a source domain for our metaphoric expression.



I am going to create an expanded similar triangle poem made of three similar triangles to serve as our example.
The following image shows three similar triangles with three different sets of relationships:‘a is to b’ as ‘c is to d’ and ‘e is to f’

The trick in the construction of the poem is to add or subtract the numerators of two of the relationships and also add or subtract the two corresponding denominators of the same two relationships. The next image shows us how we construct our three ratios and associated them differently with subtraction and addition to form six flavors. There are actually 12 flavors possible however; I wish to focus on these six, which I consider the best ones to give us a good understanding of what is occurring in this method.

Each flavor yields a group of six equations after the flavor is solved for each variable. The next six images show the six syntactical arrangements for each flavor. There are at least seventy-two different syntactical arrangements however; I wish to focus on what I feel to be the thirty-six most important ones. The next six images show each of the six groups created by each flavor.

FLAVOR ONE YIELDS:
FLAVOR TWO YIELDS:

FLAVOR THREE YIELDS:

FLAVOR FOUR YIELDS:

FLAVOR FIVE YIELDS:

FLAVOR SIX YIELDS:

Lets now create a poem using the following text.

a = Love Lies
b = The Lonely
d = Sugar
e = The Starving
g = Sexual Conquests
h = The Insecure

The structure follows as thus: ‘Love Lies’ is to ‘The Lonely’ as ‘Sugar’ is to ‘The Starving’ as ‘Sexual Conquests’ are to ‘The Insecure’

We then substitute the variables with the poetic phrases to yield thirty-six poems in six groups relating back to the flavors shown above.

I find it interesting to savor each syntactical permutation to get a ‘feel’ for each poetic expression.

GROUP ONE CONSTRUCTED FROM FLAVOR ONE:

GROUP TWO CONSTRUCTED FROM FLAVOR TWO:

GROUP THREE CONSTRUCTED FROM FLAVOR THREE:

GROUP FOUR CONSTRUCTED FROM FLAVOR FOUR:

GROUP FIVE CONSTRUCTED FROM FLAVOR FIVE:

GROUP SIX CONSTRUCTED FROM FLAVOR SIX:


Many of the links below are examples of the expanded similar triangles poem.

Another From Gregory Vincent St. Thomasino

The NYC philosopher/poet Gregory Vincent St. Thomasino would like to see a math poem of his cartoon shown above. The result is a similar triangles poem shown below.

Two Mathematical Poems For Gregory Vincent St. Thomasino

“Profundity” is the title of the first mathematical poem and the second “Logoclasody”.

The drawing above is by Gregory Vincent St. Thomasino

If discourse is a river then what is a lake?
Is not the Philosopher a dam?

Logoclasody


The two mathpoems above are similar triangles poems
Also related is the Avrin proposition

Schopenhauer’s Wax

Here is another Similar Triangles poem titled "Schopenhauer’s Wax"

Also related to this structure is the Avrin proposal

Death

Here is another similar triangles poem Titled “Death”
Also related to this poem is the Avrin Proposal