I don’t see ‘Nature’ as mathematical
I see ‘Nature’ forcing us to be mathematical
The Avrin Proposition
Please familiarize yourself with the similar triangles poems to help with the following.
The physicist William Avrin has restructured the similar triangles poem to form a new proposition to ponder. He uses a edited example of the similar triangles poem titled “The Lottery” that was posted Friday March 9, 2007 (below)
From the poem above to the examples below.
Here we have the "The Avrin Proposition" shown in the simile version
Here we have the "The Avrin Proposition" shown in the metaphor version
The idea of us solving the question, whether the statements equal 1 or any number for that matter, would require some rigorous control of the contexts in question and furthermore, they (the contexts) would need to be limited greatly to have any meaningful value. I personally am not that interested in finding the perfect number that is entirely too scientific for me. However, I wish to say that I believe mathematical poetry is more about the ‘aesthetic feeling’ of the mathematical relationships within the equation as opposed to the quest to solve it for hard numbers. However there is a very interesting twist to this idea of number in mathematical poetry.
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.
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.”
Every country has freedom of speech; it is just the consequences for that freedom varies.
KM
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.
