Similar Triangles Poems

Similar Triangles Poems / Proportional Poems

I would like to map out the structure and show examples of what I call "Similar Triangles Poems"or "Proportional Poems". Let me use the example of Similar Triangles to help visualize the proportional relationship in this mathematical structure.

Let us first look at two similar triangles with sides labeled ‘a’ ‘b’ ‘c’ and the second with sides labeled ‘d’ ‘e’ and ‘f’ Notice the laws of geometry state that a/b is equal to d/e as shown below. I am going to call this latter equation "The Similar Triangles Relationship".

Also let us note that we can solve for any or all of the variables. This will give us four synonymous variations of the similar triangles relationship in terms of one variable – examples shown in the next slide:

Now let us look at the logical structure of the following comparison: Apples are to apple butter as peanuts are to peanut butter. Furthermore, let us also look at how we can map the latter statement into the similar triangles relationship.
The following slide shows us a good example of how metaphor can be applied to the relationship of similar triangles.

Now let us substitute the terms of our logical comparison into the all of the similar variations to create four similar triangles poems.

We now have four poems that are logically equivalent but syntactically different. Each poem says the same thing only with a different flavor much like playing a piece of music in four different keys.

The pedagogical example above uses rather mundane subject matter. To see more poetic examples, please click on the lablel for "Similar Triangles Poems" (below)

Frank Sauce

This blog entry is a response to some comments made at my blog entry displaying the similar triangles poem titled “The Lotto”

Frank,
I appreciate you stopping by and I enjoy engaging your comments in some discussion even though you didn’t really leave much behind. I took the liberty to stop by your blog to try to understand your point of view in order to decipher your comments. I am going to assume from your blog entry, concurrent with your comments on my blog, that you are frustrated with the attention given to Ron Silliman’s idea of torque in poetry as well as being annoyed with my blog posting of a way to look at 'torque in poetry'. (Please notice I said 'a' way not 'the' way) Furthermore it seems that Ron's blog brought you to mine.

Your first comment was, “mathematics is objective”

I now ask you to notice the analytic geometrical equation for a circle “x squared plus y squared equals the radius squared.”

This is a mathematical description of a circle which is pure, and clear furthermore, it is as accurate as the human mind can fathom. There is no object in the universe that exists that matches this equation. There are plenty that very roughly approximate it, but none that match it. Even if you are not familiar with the analytic geometric equation above, you probably are aware that the ratio of a circle’s diameter to its circumference is equal to the irrational number pi. I would also guess you are aware that pi is not an object. Mathematics is a language not an object. You can not find pure math in nature any more than you can find the word ‘tree’. The tree is the object not the word. Pure mathematics is not objective.

I think where you and many others may be having trouble is that you have never seen applied mathematics used for connotation. Therefore it does not exist. I ask you to slow down for a moment and ask why not? I find this argument to be the same as someone who believes that a child should always stay inside the lines while coloring in a coloring book. Thinking that a mathematical equation must be used only for denotation is a paradigm that mathematical poets want to shatter. The equation is merely a logical structure that can be used for anything including metaphor.

After reading your blog entry I think I see another problem that you may have. It seems that when you see mathematics you automatically think “science”, “definitions”, and “laws”. I think it is safe to say that ‘mathematical poets’ have no more use for these terms than traditional language poets. (No less use as well) My work in particular may express something within a logical framework and it may even be philosophical however; it is not and was never intended to be science. I will say it again, “mathematics is merely a language.”


Your next comment was, “this poem is subjective”

Yes however, as I pointed out Pure math is subjective as well.

Your next comment was, “the symbols are obvious and cliché “

You really haven’t given me much to work with so I have decided to address this in two ways. My first response will assume that you fully understand the logic and the aesthetics in the mathematical structure of the poem. My second response will assume that you do not understand the logic nor the aesthetics employed in the structure.

My first response:
You have actually illuminated one of the difficulties when choosing the descriptive elements in a mathematical poem. The more literal the words used in the poem then the more clear and readable the intention becomes, yet one always runs the risk of being cliché. Of course this can be said in traditional poetry as well for you can become so narrow in your attempt at being descriptive that you become cliché. Because mathematical poetry is so new to many I have decided in many cases to focus on the beauty in the mathematical relationships between the elements as opposed to the verbal expressions within that structure. Many times I place a pedagogical spin to a poem in hope of spawning interest. However, here is a case where it may have backfired.

My second response:
Since you don’t understand the mathematical language it is really difficult to take your response to heart. It is much like listening to a person passing judgment on French poetry while not knowing the French language.

The poem "The Lotto" where you left your comment has the structure of what I call the similar triangles poem. My next blog entry will be dedicated to illuminating the structure of the similar triangles poem such as the one discussed in this blog entry.

Freedom Of Speech

Every country has freedom of speech; it is just the consequences for that freedom varies.

KM

Polyaesthetics and Mathematical Poetry

I am pleased to announce that the paper I wrote on “Polyaesthetics and Mathematical Poetry” was accepted into the Journal of Mathematics and the Arts. It is now available at the following link :

http://www.informaworld.com/smpp/title~content=t755420531

My Wedding

I feel that my blog has been suffering the past 4 months due to my life being consumed by my wedding and the consequent website that I built to honor the event.

If you are interested you can check it out at
http://www.kazmaslanka.com/wedding_introduction.html

From Ethnic To Creedal

This poem is in the form of a similar triangles poem.

God Doesn't Play Dice

God Does Not Play Dice, God Is Dice

Mandelbrot Rock

JoAnne Growney was kind enough to send me this youtube link to a tune by fellow geek Jonathan Coulton

Torque In Poetry

In response to the blog entry at Ron Silliman’s blog which pointed to this blog entry by K. Silem Mohammad: Lime-Tree (click here)

I would like to contribute to this discussion on ‘torque in poetry’ by giving an example of how one may view the mechanics of torque within a poem. Furthermore, in particular, I will give an example using the Creeley poem previously discussed.

To understand the difference between torque and linear movement in a poem we should understand the difference between the components of the two within the context of a poem. Let me reiterate the interesting ideas that Silem Mohammad has brought forward in the blog entry referenced above.

The concepts in question are pulling, pushing, syncopation, and torque. First of all pushing and pulling are generally thought to be linear forces. (in a straight line) Force can also be used in torque as in pushing or pulling something perpendicular to an axis as in the example of pushing on a swinging door. Pure rhythmic (without glissando or modulation) syncopation seems to me to be a linear force due to the idea that we generally perceive time to be linear at least in an analytical sense. I believe syncopation in music or poetry can express torque with the additional use of pitch such as a talking drum or with synaesthetic visual imagery. I believe you may experience torque in Creeley’s poem due to the visual imagery associated with physical torque as in a car swerving to miss an object in the road:

“drive, he sd, for
christ's sake, look
out where yr going.”


To imply torque in the visual structure of the poem one has to imply force moving perpendicular to an axis. Like the twisting diagram above. So this brings us to the question: What is the axis and what is the force within the structural line-breaks of Creeley’s poem?

One way to visualize the torque within the structure of his poem is to notice that the movement in the line breaks creates a curve that our vision may follow. (See diagram above) It may not follow this exact curve but it must follow a curve if you are experiencing torque. There is an argument that your eyes follow a straight line to the next line. In that case you would experience a linear force not torque.

So let’s look at a curve connecting the lines in the above diagram. The red curve is an enlargement of the black curve in our diagram. Notice that the curve varies in curvature. The radius in the curvature is changing which means the torque is changing also. However, let’s freeze our eye movement for a moment and just look at one radius which is shown in the black circle that lays on the red curve. That radius is represented for a stopped moment in time at a certain place along the curve. This is the point where we can imagine that we can see the radius of curvature that our eyes follow in this poem. This radius is the “r” value in the equation for torque.

Now we must find the force and break it down so that we can see the components of force in the poem.

One of the ways physics describes force is that “force is equal to the change in momentum of an object per the change in time during the objects spatial movement”. (F = delta mv/delta t)


The Egg Toss Game

Many of us have experienced force when playing a particular egg toss game in which the goal is to have your partner throw you an egg and you catch it without breaking it. What you are doing in this game is change the momentum of the egg from its maximum speed when it is flying toward you, to a speed of zero when you slow its fall in the palm of your hand. Furthermore, the objective is to slow its fall over the greatest amount of time possible. Force is the change of momentum per the change in time in other words if you change the momentum of the egg in a short period of time the egg breaks because you created too much force on the egg. You created much more force than if you would have caught the egg over a longer period of time.

So how does all this relate to the poem?
The force involved in at the end of the line break is equivalent to the change in the flow (momentum) in the poem per the change in time as you read it. This idea is the “F” value in the torque equation.

Since force is the change in momentum per the change in time, let’s look at what ideas comprise the momentum at the end of the line break in this poem?

Let’s go back to physics and look at the definition of momentum. Momentum is the mass of an object multiplied by the velocity that the object is traveling.

What is the mass in the poem at the end of the line break?
I see the mass being static concept in the line’s subject. For instance “the darkness” in line five of the poem is the static concept.

What is the velocity?
I see the velocity caused by anticipatory interest we have in finding what the next line says. For example the line ending in the word ‘what’ is not resolved and we experience anticipation to resolve it. Our anticipation is what is moving in our mind until the idea is resolved at the next line. The velocity then slows down as our interest slows down. In other words the more anticipation we experience then the faster our need is to resolve the idea at the next line. Furthermore, the greater the change in the momentum of our interest then the more force we experience. The more force we experience then the more torque we will experience.

In conclusion:
If you want to describe torque in a poem then you must have a force moving on a radius about an axis. If you don’t have those elements present in the poem then you are experiencing linear force not torque.

Extremism

Here is a similar triangle poem concerned with extremism.

The Lotto

Here is a similar triangle poem concerned with playing the lottery.

Marko Niemi Critical Mass

Another animated mathematical visual poem by Marko Niemi

Marko Niemi Divine Intervention

Another animated mathematical visual poem by Marko Niemi

Marko Niemi Eye Of The Beholder

Here is another animated mathematical visual poem by Marko Niemi

Marko Niemi Party-NRJ

Here is a animated mathematical visual poem that Mark Niemi just sent me ... The equation above is the equation from physics describing energy. Marko has animated it to play with the textual meanings relative to its semantic meanings. Check it out

Quote From Samuel Johnson

I am always sorry when any language is lost, because languages are the pedigrees of nations. -Samuel Johnson, lexicographer (1709-1784)

Delineations Between The Aesthetics Of Math And Art

This page is dedicated to collecting ideas that describe the differences in the aesthetics of math and art.*


I would like to invite discourse into the construction of these ideas. Everyone is invited to comment. Making these delineations is not an easy task and I feel the statements may evolve. I will address any comments to these statements.

I feel it is very important to understand the differences in the disciplines of art and math so that we can join them in the most creative, clear and meaningful ways.


Delineation #1:
Mathematical truths are discovered Artistic truths are mediated.

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Delineation#2:
Mathematicians generally agree on what is mathematically correct. Artists generally have no idea what is artistically correct.

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Delineation#3
Math illuminates the supportive skeletal structure of thought whereas Art illuminates the metaphoric wind, which blows through that structure.

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Delineation#4
Science reveals the body of GGod and Art reveals GGod's mind -- or is it the converse?

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Delineation#5
Pure Mathematics has no expression for poetic metaphor however; it does provide us a structure that can be used for it.

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Delineation#6

In general, the mathematician is not interested in finding truths through nonsense as opposed to the artist who is.

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Delineation#7

The goal of art is to go beyond language. Mathematics is a language to describe what is beyond us.

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Delineation#8.
Artists have an insouciant tendency to get lost in their imagination Mathematicians have an attentive tendency to map their imagination

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Delineation #9
A mathematical theory seems to come in a flash of intuition before the final product is rigorously constructed. An artistic theory seems to come much after the artwork that has been constructed in a flash of intuition.

Delineation #10

Mathematical creations are not unique in the sense that they could be discovered by anyone.
Artistic creations are uniquely invented by individuals.

Delineation #11
Mathematics, among other things, is a language.
Art, among other things, uses language.
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Delineation#12
In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it’s the exact opposite. —Paul Dirac
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Delineation #13
Art is the expression of culture.
Pure mathematics is independent of culture therefore, cultureless.



Some of these were published earlier in Bridges proceedings 2002 “Sentences on the Aesthetics of Mathematics and Art” page 256

Unlikely 2.0

Dog Dream

This is my first Korean artwork
Dog Dream = Irrationality / Importance

The poem is in the form of an orthogonal space poem


Check out the lastest Unlikely Stories. My latest two pieces are among some wonderful new art/poetry work.

Temptation At The Asymptote

I have a new piece titled “Temptation” (below)

As you look at the graph of Y=1/x (above) you will notice the values become extremely large as you approach the asymptote where the value of x equals zero. At x = zero the y value becomes infinite (at the asymptote).

We have the same situation when we approach temptation. It gets stronger and stronger as we get closer to the object of our temptation and when you touch your temptation you lose the game. In other words the shorter the distance to your object of temptation the closer you get to the asymptote.

The form of the poem is an orthogonal space poem

Temptation 2006 Kaz Maslanka

Bridges Reminder