The Double Derivative Poem

Double Derivative Poem

The poem above serves as an example of what I am calling a double derivative poem. In the study of mathematics a derivative is the rate of change of one thing as measured by the change in another. The double derivative poem addresses the first and second derivatives of a “phantom function”. The “mathematical function” that I am speaking of is to be experienced with ones intuition as opposed to being explicitly described as a single curve on a Cartesian coordinate system.

The idea for this poetic structure occurred to me while reflecting on the equations from physics that describe the relationship between position velocity and acceleration. Its similar triangles structure dawned on me because physics teaches the position of a moving object is to velocity as velocity is to acceleration.

In the study of physics, calculus tells us that the first derivative of position is velocity and the second derivative of position is acceleration. Furthermore, it just so happens that this ‘ratio form’ is the same structure used for a similar triangles poem. (You need to be familiar with the similar triangles poem and mathematical differentiation for this to make sense)
Shown below are visual aids to understand the derivative.

The derivative:

Animation showing that when delta x approaches zero the secant line becomes tangent. (click on the image to see the animation)

Each mathematical term “a” “b” “d” or “e”(see similar triangles poem) is a word or phrase. In the derivative poem each mathematical term is a metaphor relating to the derivative paradigm which is an expression relating the first derivative to the second derivative. (the change and the change in the change)

The first word is mapped into the source domain for the first metaphor in our paradigm serving the target metaphor of ‘position’.

Liking IS “position” (I use George Lakoff’s nomenclature for metaphor see "parts of a metaphor" at this link)

The second word is mapped into the source domain for the second metaphor in our paradigm serving the target metaphor of ‘velocity’.

Caring IS “velocity”

Lastly, the third phrase is mapped into the source domain for the third metaphor in our paradigm serving the target metaphor of ‘acceleration’.
Dailey rituals of love IS “acceleration”

Here is the poem shown in the similar triangles form

Here is the poem solved for “Liking”


I find the poem more interesting if solved for the word “Caring”

Visualizing the exact mathematical function of “Caring as a function of time” would be impossible with the small amount of information given however; a single point on that function is present in the poem even if it is nebulous in form. Furthermore, other poems could be written to describe other points along the phantom curve. I find it very interesting to ponder the shape of the "phantom curve"

The challenge in making a successful derivative poem is in the ability of the poet to express the proper metaphors to fit the paradigm of first and second derivatives. That is to say that the poem expresses a change relative to an idea and then a change in the change relative to that same idea. If all of these requirements are met then one may be able to visualize a point and part of the nebulous function graphically in their mind.

Now to take this idea a little further lets think about this. As I had mentioned before; a derivative is just the rate of change of one thing as measured by the change in another. Furthermore you can have a third derivative, a fourth derivative etc. So in effect we could create a mathematical poem that has its structure as a ‘string or sequence’ of derivatives expressed as an expanded similar triangles poem. Now that sounds like an interesting challenge! Who is going to be the first to do it and send it to me?



also see this

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.

Mathpo Eclipsed By Fire

This is the only thing on my mind tonight ... This is a photo shot from space of southern California. I am between the first and second fire from the bottom of the picture. (San Diego)

A Math Art Moment #8

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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To see more math art delineations click here

Indexed

I stole this mathematical poetry image from a fun mathematical/life inspired blog called "Indexed" check it out ... some really fun stuff including Venn diagrams and other mathpo visuals.

Mathematical Poetry

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

Friedrich Schlegel

This page is to collect the two post which discuss German philosopher Friedrich Schlegels's mathematical poem. This poem was written around 1800 and is the first mathematical poem that I know of.

The Introduction ... Earliest Mathematical Poem?

The Translation

The Good Path

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

Do The Math: Lies Secrets and Algebra

I ran across a website that lead me to Wendy Lichtman. Wendy is a writer that happens to have a mathematics degree. Furthermore she has put it to use in her new book, “Do The Math: Lies Secrets and Algebra. Check it out on her website.

I snatched a ratio she had given at a lecture published at this website and turned it into a similar triangles poem.

Eddingtons Anti-Sonnet

Here is a mathematical visual poem done by the Australian visual poet pi.o. to see his explanation check it out on Geof Huth’s blog here

A Math Art moment #7

Delineation#7
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The goal of art is to go beyond language. Mathematics is a language to describe what is beyond us.

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To see more math art delineations click here

Congruent Apology

One of the best aspects of the internet as well as the worst (most embarrassing) is the fact that if you make a mistake it is permanent and you cannot go back and erase it. I have discovered an error in my mathematical terminology and need to correct it. What I have been calling "congruent triangles" are not congruent triangles they are “similar triangles.” "Congruent triangles" are referring to two triangles that are the same size. Similar triangles have the same shape but different sizes. Obviously, my memory is not good as it needs to be. If conveying this error has caused any embarrassment to anyone one, I am sorry.

--However--

The good thing is that it does not affect the meaning, mechanics or the importance of this poetic form. However, I must clean up the mess and continue. What you have known to be the "Congruent Triangles Poem" is now correctly re-identified as a "Similar Triangles Poem". Furthermore, if you notice a mistake on my blog or website please challenge it. I appreciate all help.

Art and Science Forum Presents Kaz Maslanka

THE ART & SCIENCE FORUM

Presents: Kaz Maslanka "Polyaesthetics and Mathematical Poetry "
Thursday,October 4, 2007 6:30 PMThe Salk Institute - The Trustees Room

10010 North Torrey Pines Road

La Jolla, CA 92037

Polyaesthetics is a term Kaz Maslanka has used in connection with his artwork, as it embraces three different aesthetics; the aesthetics of verbal language, the aesthetics of visual language, and the aesthetics of mathematical language. Kaz’s artwork can be regarded as a blend of ‘visual poetry’ and ‘mathematical poetry’.
Kaz Maslanka’s definition of ‘mathematical poetry’ is that it is an artistic expression arising from performing mathematical operations on words or images as if they were numbers. One may find this baffling at first because it appears as though mathematical poets are confused about knowing the difference of the states of quality versus quantity. However, it is through the fusion of this dichotomy that mathematical metaphor is spawned.
Although there have been a few people write mathematical poems before Kaz Maslanka, it is arguable that none have pushed the genre’s boundaries farther. Kaz has lectured and published numerous papers on topics involving the aesthetics as well as the mechanics of Polyaesthetics and mathematical poetry. His polyaesthetic work has been shown internationally as well as across the United States. Furthermore, he continues to write about his mathematical poetic explorations as well as that of others on his blog at http://mathematicalpoetry.blogspot.com/ His polyaesthetic works can also be viewed at his website http://www.kazmaslanka.com/
Kaz states, "I infuse ideas into physics equations in ways that transform an equation into a metaphor, which helps in studying how we construct language and its cultural relationship between the physical and conceptual. I am also interested in exploring archetypes in a contemporary context by expressing my own mythology in relation to my struggle to comprehend my path, in nature's system, which directs and guides my life's moral and ethical decisions."
As usual, following this presentation there will be ample opportunity for lively discussion.

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Ron Newby
ronnewby@san.rr.com

The Collaborative Substitution Poem

This post is one of the most important (if not the most important) post I have ever written to this blog and I have been wanting and waiting to write it for a couple of years I just needed the right time.

The most important aspect of mathematical poetry in my ‘humble’ opinion is collaborative substitution poems. Collaborative substitution poems can evolve eternally and infinitely like no other form of poetry. Even non-poets can make mathematical poems using existing mathematical poems. I get very excited whenever I think about how these poems could evolve. The mathematical poem is very special in the sense that its structure lends itself very easily to substitution of terms/variables.



Just like in the equation from physics which states that force = mass multiplied by acceleration. F = ma. (image above) Since acceleration can be defined as the change in velocity per time we can substitute delta v divided by delta t into the equation to yield F = mass multiplied by delta v divided by delta t or F= mass delta(v)/delta(t)

What this means for mathematical poetry is that all variables are capable of being substituted by another poem. This gives a poem infinite flexibility in that future poets can substitute the variables within it in ways that could turn a small poem into a giant rhizome of ideas with roots that extends itself into many directions similar in shape to the black dotted arms spreading across the tabletop of the domino game. Today we are making the first step (that I know of) in this process.

On August 13, 2007 Cherryl Floyd-Miller posted a similar triangles poem titled death. It just so happens that I created a similar triangles poem posted May 17, 2007 also titled death.

Here is another look at Cherryl’s poem “Death”



Here is another look at my poem “Death”



If I solve for the term “death” in my poem (actually it is already solved for “death” in the original posting) and replace the variable “death” from Cherryl’s poem with my poem (solved for death) then we get the following expression. I have kept the color of the words so that they can be easily seen within both contexts shown below.



I have solved the expression above for the term Life and this leaves us with the following poem.



Now that we have seen it together in the later image I present the final image Here is our “collaboration poem”

One of the things I really enjoy about this poem is the conflation of the original contexts. Cherryl’s poem had a context of corporal finality where the context of mine was more about the process of spiritual growth. In this poem both ideas can be seen.

Now the next thing that could happen is that another mathematical poet describes one of the other elements in this poem such as “pulseless” or “heresy”. Then they take their poem and substitute it for “pulseless” or “heresy” and viola we have a new collaborative poem made from three poets. And so on and so on and so on …

Philosophic Cocktails by Thierry Brunet

Here is a mathematical poem by Thierry Brunet which has elements of a similar triangles poem (with a Boolean twist) and a metamorphic mathematical poem.

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.

Dodecaorthogonal Space Poem

A few days ago, Pablo Kagioglu shared a power point presentation that he made in where he had constructed a verbogeometric coordinate system, which displays 12 contiguous orthogonal space poems that share a common axis system. This is important for what I see him having done is creating is a crystal-like dodecaorthogonal space poem! He has shown us another beautiful mathematical poetic structure. Now I must say that his philosophy may be controversial and I have to admit that I find some of the poems a bit problematic. However, I really am not interested in critiquing what he has said. What I find extremely important here is that he has discovered a new mathematical poetic form that we all can use, build upon or do what ever our creative hearts desire. Furthermore, I want to congratulate him on doing so!

As I said, I am not going to analyze his content I am going to post it just as he sent it to me. He has graciously allowed me to post the following for everyone to enjoy.


Planes of Truth and Perception by Pablo Kagioglu

As I have become more interested in what goes on around the world, I have also become somewhat frustrated by the actual lack of true information available; this in a world that is literally flooded with news. Long ago there were only Newspapers, then Radio came along, then Television. Each time adding the medium more immediacy to the availability of information, but not necessarily more relevant content. So, in the age of 24-hour news channels, it is amazing how miss informed most people are about important world events…

I have traveled around Europe and the Americas quite bit, and listened to the opinions of many people, watched their newscasts, read their newspapers. On occasion, I was asked about my own opinions, and as I gave my opinions I slowly came to this realization:

“The futility of formulating an opinion on important events based on what we see on news broadcast alone”

- Our perceptions or opinions are constructed in the same manner as a drawing a picture using dots with numbers
- Different newscasts give us only a partial number of the dots required to come up with the correct picture
- Some of the newscasts number give us properly “located” dots, but numbered with the incorrect sequence
- If you are unfortunate enough to watch an unreliable source, you will get wrong positioned dots altogether.
- Newscasts keep giving us the same dots over and over, instead of additional (new) dots.
- Over time, we never get enough (properly numbered) dots to formulate the complete “true’ picture of what is really happening.

In general, it can be said that “true” information is broadcast all around the world, but no one is likely to get the “whole package” delivered to them from one source, specially only watching local/national news.

If one searches really hard, and looks at all possible “good” sources, you still may only end up with only half the dots anyway (the more controversial the subject, the fewer the dots you are likely to get).

In the end most people sit around and argue because some drew a House while others drew a Pyramid, when it reality it is probably neither.

So, I wondered if Truth and Perception could be plotted in a 3-dimensional space somehow, using various concepts as the 3 axes.

Words pairs that come to mind are: Truth/Lies, Knowledge/Perception, Openness/Deception, Order/Chaos, Guilt/Innocence, Censorship/Approval

What follows is the construct of the various planes of demarcation for Truth or Lies, Knowledge or Perception.

Mathematically Defined Phantom Words

The mathematical structure that we use when making similar triangles poems provides an interesting result when used in conjunction with the creation of verbogeometric prisms. It appears that we can mathematically define a point in a verbogeometric space whereby we know the meaning of the word in that location however; there is no word in the dictionary for it. It seems to be some kind of phantom word that exists by a set of rules however, no spelling for it.
Let us look at the image above. We can see the points X1 and X2 in the image and notice there are no words in the dictionary to cover their meanings however, we know that it is a direct negation of the words sterile and Barren. These words could be described as "unsterile" and "unbarren" however it may be more fun to flavor them poetically as shown in the examples below.









Alternatively, even more fun … we can really emphasize the flavoring of X1 by using the expanded similar triangles form and including all of the antonyms and synonyms.

Pablo Kagioglu Mathematical Poetry Links

This page is reserved for all of Pablo Kagioglu Mathematical Poems

Dodecaorthogonal Space Poems

Electronic Paradigm Poems by Pablo Kagioglu

Pablo Kagioglu's Love

Pablo Kagioglu's Passion

Pablo Kagioglu's creation

Poincaré's House

The expression above is an expanded similar triangles poem. Inspired by the musings of Henri Poincaré

Flavor one h = (b(d+g)/a) - e

A Math Art Moment #6

Delineation#6

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

To see more math art delineations click here

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.

Pablo Kagioglu's creation

Here is another "Electronic Paradigm Poem" done with the "Orthogonal Space Poem" structurePlease see Pablo's introduction to have a better understanding of his process.

Pablo Kagioglu's Passion

Here is another "Electronic Paradigm Poem" done with the "Orthogonal Space Poem" structure
Please see Pablo's introduction to have a better understanding of his process.

Pablo Kagioglu's Love

Here is a "Electronic Paradigm Poem" done with the "Orthogonal Space Poem" structure

Please see Pablo's introduction to have a better understanding of his process.

Electronic Paradigm Poems by Pablo Kagioglu

I just received an email from Pablo Kagioglu who has been doing some very interesting experimentation with ‘electronic paradigm poems’. The following is an excerpt from his email, which I would like to share. Over the next few days, I will post some of Pablo’s ‘electronic paradigm poems’ which will refer back to this blog post. In all actuality one could make hundreds of ‘electronic paradigm poems’ from the lists that Pablo has provided us with. Thanks Pablo!


"The formula I am using is Ohm’s Law and mainly its relationship to power and potential, not so much the concept of resistance and flow (which to me are acting more like the glue to the whole thing)

Ohm’s Law

I = V/R

Also

Power = voltage multiplied by current
P = V*I

Thus
P = (V*V)/R
P = R * (I*I)

V = P/I

So I just found synonyms of the different variables, sometimes a couple of layers deep, and just started playing with the word combinations and formulas to see what “stuck to the wall” so to say.

“Resistance and Current are acting as opposing ideas”

R = Resistance: opposition, blocking, defiance, protecting, refusal, struggle, antagonism, animosity, antipathy, hatred, hostility, rancor, rivalry, avoidance, abstention, prevention, recession, recoil, restraint, retreat, interruption, indecision, delay, hindrance, procrastination.

I = Current: flow, effusion, emanation, flood, flux, gush, juice, plenty, plethora, river, stream, tide, appear, begin, commence, crop up, derive, emanate, emerge, ensue, follow, happen, head, issue, occur, originate, proceed, result, rise, set in, spring, start, stem, creation

“Power is the realization of the Voltage”

V = Voltage: potential, energy, conceivable, imaginable, doable, plausible, possible, quiescent, thinkable, ability, aptitude, capability, capacity, vitality

P = Power: dynamism, effectiveness, faculty, function, influence, skill, force, locomotion, motility, propulsion, authority, will, decision, longing, passion, pleasure, purpose, resolve, yearning, love, adoration, affection, ardor, desire, excitement, lust.

The word equations (concepts) seem to work better and make more sense to me when defined in terms of Power and Voltage rather than Current and Resistance."

I will be posting the poems in the next few days -- K

The Paradigm Poem

The Paradigm Poem

Unlike a simple mathematical structure as in the “Similar Triangles Poem”, the “Paradigm Poem” is a mathematical poetry technique that borrows its structure from an existing equation from applied mathematics of scientific or cultural significance. The “Paradigm Poem has many sub-categories which are as numerous as there are categories for applied mathematics. Examples that we could consider would be: “Physics Paradigm Poem”, “Chemistry Paradigm Poem”, “Business Accounting Paradigm Poem”, “ Psychophysiological Paradigm Poem” etc.
If we think in terms of metaphor using the cognitive scientific language of George Lakoff then we would classify the language of the variables “inside the equation structure” as the ‘target domain’ and the context or traditional meaning of the equation as the “source domain’
Let me show an example of a “Physics Paradigm Poem” using Newton’s second law. For this example I am going to use an excerpt from my essay on “Polyaesthetics and Mathematical Poetry” Journal of Mathematics and the Arts, Volume 1, Issue 1 March 2007 , pages 35 - 40 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954

“My personal view is that almost all mathematic applications rely on using equations with the intent similar to simile. The variables in the equation are compared explicitly with the result for uses in denotation. For example, in the case of an application of
Newton’s second law F = ma, or Force equals Mass times Acceleration, we are comparing the variables m (Mass) and a (Acceleration) explicitly to F (Force).
I can now make a mathematical poem based on the latter example by expressing the Force of ‘yesterday’s freedom’ as being equal to ‘a lush clover patch’
multiplied by ‘the swelling sweet summer breeze traversing the morning’. We can then put this in the form of a mathematical equation as; Yesterday’s freedom = (a lush clover patch) (the swelling sweet summer breeze traversing the morning). In other words, I set the Force to ‘Yesterday’s freedom’, the mass to ‘a lush clover patch’, and I accelerated the mass by ‘the swelling sweet summer breeze traversing the morning’. All of these
phrases relate back to the original equation from physics F = ma. I want to emphasize that I was very careful when I made my choice for acceleration so that the phrase is evocative of the mathematical description of acceleration as defined by physics. Acceleration is the
change in velocity of an object per unit of elapsed time during that acceleration. Here, the change in velocity is implied by ‘swelling’ and the change in time is implied by ‘traversing’.”

In the above example we are using the words “Yesterday’s freedom; a lush clover patch; the swelling sweet summer breeze traversing the morning” as the variables of the equations which supply us with the target domain and then we are using the equation from physics F = ma, its scientific meaning and historical significance as the source domain.

The bottom line concerning the ‘paradigm poem’ is that we borrow an equation from the past which inherently contains historical significance and serves as an paradigm or mathematical model that seems almost “a vessel” to carry the mathematical poem. The paradigm poem always borrows an existing mathematical structure to serve as a source domain in our metaphor.

Paul Klee Quote

To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers. — Paul Klee (1879-1940).

Thierry Brunet Mathematical Poetry Links

This page is reserved for all of Thierry Brunet's Mathematical Poems

No Boundaries

Philosophic Cocktails

Rhesus

Japanese Elvis

Toaster

A Math Art Moment #5

Delineation#5

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

To see more math art delineations click here

RHESUS By Thierry Brunet

Here is another orthogonal space poem via France by Thierry Brunet. Titled “RHESUS”

I have noticed something that I find interesting about Thierry's technique when approaching an orthogonal space poem. It seems he acquires three ideas that can be viewed as being near synonymous. He contextualizes them in an orthogonal space which seems to me to work very well together. If one remembers the prismatic structures in my verbogeometry paper then you may also remember that synonyms are viewed existing on a plane. The arrangement of the synonyms on that plane could easily be viewed orthogonally. Furthermore, I think this is why Thierry’s technique works so well.

L'anxieux

Thierry Brunet has kindly translated “The Insecure” into French. This is an expanded similar triangles poem. Flavor three: h = ((e(a+g))/d)-b

Japanese Elvis by Thierry Brunet

Here is a orthogonal space poem by the French poet Thierry Brunet