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