A Math Art Moment #3

Delineation#3

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

To see more math art delineations click here

Ed Schenk's World

There are about three people that are almost regular contributors to this blog and Marko Niemi is one of them. Marko has continued to keep me on my toes and has graciously sent me a link to a mathematical poem found on vispoets.com

I would like to dedicate this blog entry to Ed Schenk’s poem that he posted on vispoets.com and I have reposted above.

First of all I would like to say I like Ed’s Pythagorean Theorem Poem with the idea of world being the hypotenuse of a triangle with the adjacent and opposite legs being perception and reality. Ed’s intent is such that he is asking whether the world is equal to these things. You notice that he has ‘???’ in the field of view. My guess is that Ed wanted to avoid the trap that too many people get hung up on concerning mathematical poetry. It seems that many people think that we are trying to create axioms or scientific statements. The latter idea I believe is due to the provenance of mathematics having much momentum since it is the language of science. However, I look at math poetry with a lack of scientific eyes. There could be an entire debate on whether Ed needed to put those question marks on his piece and I could argue both sides. The point I want to make is that mathematical poetry is not science.

I believe one good reason to leave the question marks on his poem are to insure that we avoid a philosophical debate and focus on the beauty of the language while entertaining the ideas presented. When it comes to philosophy and mathematical poetry I feel it is very difficult to be good at both philosophy and art. I feel mathematical poetry is less distractive when inspired by established philosophy and illuminated with a new and expanded life. Although I am sure that I have crossed the boundaries on occasion.

I also wanted to mention a technical delineation, that by putting the question marks underneath the poem it becomes a mathematical visual poem for to become a pure mathematical poem the question marks would be located above the equal sign as shown in the Avrin proposition posted April 22, 2007

I love the form of Ed’s poem however; it is hard for me not to like a Pythagorean Theorem poem. I love everything about the Pythagorean Theorem for it is always a great one to ponder just because it has such a magical quality expressed in such simplicity. ---- Although, I wouldn’t advise it, one could spend their whole life making poems in this form alone.

Of course I will have to mention as soon as I see a mathematical poem in the form of the Pythagorean Theorem, like Ed’s, then my first thought is to take it into analytic geometry and map it on the Cartesian coordinate system.This in effect is taking the Pythagorean Theorem and spinning it around a single point to create the equation of a circle.

So what would Ed’s piece look like expressed on the Cartesian coordinate system? Well, let’s look at it. This is Ed's poem spun around a point with verbogeometric axes of perception and reality.

Another thing that always occurs to me when I look at the Pythagorean Theorem is to ask how many dimensions I need to express what I want. Ed has chosen two for his poem and this is good however, we have the option to pick as many as we want. Since the idea of ‘world’ could bring about a visualization of the earth we could choose three dimensions and use the equation of a sphere. (This is the equation of a circle spun around a line)

The image below is an example where I have added an extra dimension to Ed’s equation to come up with a spherical poem. I decided to use belief as a dimension because it was the first thing that popped into my head. For this paradigm, it is not important so much as to what I am saying for I am really just trying to serve an example of how to add an extra dimension to the equation for a circle to render the equation for a sphere. Thus creating a spherical poem or in other words the Pythagorean Theorem in three dimensions and visualized in the Cartesian coordinate system.

Grumman's Christmas Poem 2007

Grumman's Christmas Poem

I would like to bring to your attention a poem I saw on Bob Grumman’s blog a few months ago. Bob basically has been doing most if not all of his recent mathematical poems in the form of long division. He rarely constructs a pure mathematical poem as almost all that I have seen are mathematical visual poems. The poem below is one such poem. Bob has been described by his friend Geof Huth as a curmudgeon and I have to admit that when I read his non-mathematical poems, his blog or his editorial writings I never find the boy child-like quality that he so beautifully expresses in some of his mathematical poems. Furthermore this poem has that particular boyish quality that can touch any man who allows it to happen. I feel it is one of Bob’s best. Here is a link where you can read Bob’s Blog entry where he talks about this poem.

A Mathematical Love Poem By H. K. Norla

I would like to give recognition to a wonderful mathematical love poem. I found the poem the other day on an abandoned blog by a young man named H K Norla. I tried to contact him but am not able to find an email address for him. His poem titled “Of X’s and Y’s” can be found on his blog here as well as my repost below.

I found his wonderful poem to be a great example of mathematical poetry with a new twist that I haven’t seen before. In between the pure math symbols he has made verbal statements that relate and segue to the adjacent equations. JoAnne Growney and Sarah Glaz are edition a book on mathematical love poems and I wish Mr. Norla was around to submit this piece to the book. (It may be too late anyway however, this is a wonderful poem)

The following is my visualization of Mr. Norla’s poem

Numerical Notation Bibliography

Here is a great source of information in general and a source for “Numerical Notation Bibliography” in particular. This is a link to a bibliography of 1047 academic publications about numerals, numeral systems, numerical notation and numeration. Compiled by Stephen Chrisomalis -- Here is a link to Stephen’s book page.

Thanks to Karl Kempton for pointing this out to us.

The Platonist Dilemma

I don’t see ‘Nature’ as mathematical
I see ‘Nature’ forcing us to be mathematical

Judgment

Quantify Not And Ye Shall Not Be Quantified!

A Math Art Moment #2

Delineation#2

Mathematicians generally agree on what is mathematically correct. Artists generally have no idea what is artistically correct.

To see more math art delineations click here

The Avrin Proposition

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.

Here in the Avrin proposition we are bouncing our understanding of the words and our feeling of the relationships against the resulting number and thus forming a comparison for metaphoric conflation. In another words the source domain of the metaphor is the statements “playing the lottery” divided by “ogling pornography” as well the statements “financial fantasy” divided by “sexual fantasy” and our target domain is the number “1”. Here we have a very good example of an aesthetic feeling involved in metaphor that conflates from number and words.

Thank you Bill Avrin for pointing this out!

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.