Introducing Verbogeometry

Life has been real busy lately so unfortunately I haven’t made a blog entry for a while. One of the things that have been demanding my time has been my paper on verbogeometry. My plan has been to deliver the paper next summer in London at the Bridges conference on mathematical connections in art music and science. I have been excited about finishing the paper for it’s the most important thing I have written to date on mathematical poetry related matters. I have created a link to an expanded version of the paper on my website. I believe this paper really allows one to understand how words and their meanings can be viewed in space as well as how to approach mathematical poetry in general. Some people don’t know how to approach visualizing mathematical operations on words and their meanings. I believe this paper will give one new tools needed to enjoy mathematical poetry and hopefully inspire new poets. I have hardly scratched the surface of this genre. I imagine many who will fly past me discovering large treasures of aesthetic joy. I feel I am part of a beautiful vista while standing in my tiny garden pitched on a mountain side looking at colorful fields of mathpo expanding out to a horizon of mathematical mountains that I know I will never be able to reach much less enjoy.

Verbogeometry link click here

Although verbogeometry has existed in my work since 1981 I have never tried to explain the mechanics of how it works. I was hoping people would find their way into it. however, that never really happened proving either I am delusional about its importance coupled with the fact that it is a cumbersome task that delivers far too little aesthetic value for the work required to understand it.

or...

it is a worthwhile endeavor
blending languages
which will induce poetic winds
clearing obscured connections
the spiritual world has
to the physical
bringing a new rationality to art
firmly grounding one end of metaphor
while the other is steadfast
to the infinite.

I am certainly not excluding the former and acknowledging that I may be delusional. However we must also recognize that if we artists were not delusional we would never create anything new which strains the norm. For we would never have the energy required to make art in our aesthetic exile. The avante guard never dies but its endless warriors pay dearly, many sacrificing love and fortunes only to melt into the insignificant gloryless noise quantifying a lonely instant in the spectrum of time.


K

Sentence Structure in Mathematical Poetry

Here is a detail of the equation from above

Today I would like to share part of a conversation I had with Gregory Vincent St. Thomasino dated December 2, 2005 …

Gregory Vincent St. Thomasino said:

You have to find the analogy between math and the grammar of the sentence, and make your "math" work within that grammar.

Kaz Maslanka said:

I am not sure if I understand exactly what you are saying but I find grammatical similarities in physics equations all the time. For example F = ma ---- force is equal to mass times acceleration. “ma” could easily be seen as a clause where mass is the subject and acceleration is the predicate. Many of my polyaesthetic pieces rely on physics equations to supply a sub-context for the piece. Lets look at the piece from “Karmic influences on the double helix” First we must talk a bit about physics. This piece utilizes the physics equation for Energy. E = Fd Energy is equal to force multiplied by distance. In other words the Energy expended on an object is equal to force applied to that object continually spread over a distance. The latter sentence obviously has grammatical qualities and is synonymous with the equation. We also know that F = ma. Now lets break force into its components of mass and acceleration and substitute (ma) for ‘F’ it in our equation that defines energy.

E = (ma)d or E = mad

In other words the Energy expended on an object is equal to the accelerated mass of that object applied continuously over a distance. (Notice again that we are using words to be synonymous with the actual equation)


Even the equation can easily be mapped with sentence structure. The energy in question is equated to Fd or (ma)d where ‘m’ is the subject ‘ad’ is the predicate and d is the object of the verb ‘to accelerate’ To reiterate the mass is the subject and ‘acceleration over a distance’ is the predicate where ‘over the distance’ is the object of the verb ‘accelerate’

Before we look at the poem lets take a look at the distance formula (in two dimensions) used in analytical geometry. In a nutshell the distance formula is the Pythagorean theorem mapped onto a Cartesian coordinate system. e.g. the hypotenuse of a right triangle is the distance we wish to solve and we can do so by using the difference in the y values as one leg of the triangle and the difference in the x values as the other leg of the triangle. This whole mess is a lot easier to see visually. Click here

Now let us look at the poem.


The energy in question is “Karmic Energy” which is equal to the ‘mass’ being the phrases: “the conscious embryo, rampart, through the viridian passage” multiplied by the ‘acceleration’ which is “misfortunate paranoia” and multiplied by the distance between the concepts of the difference between the concepts of “the discovery of the wheel and extra-dimensional travel” and the difference between the concepts “single cell intelligence and the discovery of the wheel”

You can see that the poem follows the exact sentence structure of the physics equation, Furthermore the physics equation serves as a paradigm or metacontext for the poem to ‘ride’ or ‘be carried ’ in.

Distance and Visual Poetry

The piece, “DISTANCE”, shows how the concepts of velocity and time tessellate a plane in an infinitely woven tapestry of distance.

The piece above “distance” is a little different for me for it is influenced by new information I have learned from the ‘visual poetry’ movement. The piece has elements of visual poetry that I have never used before. It functions in two different ways. One way it functions mathematically as a visual paradigm for a physics tenant of kinematics. Notice a paradigm is not a metaphor it is a simile. The Second way it functions is mathematical vispo because it performs math operations on text. The bottom line is that I would not call it mathematical poetry as such because we are not performing mathematical operations on words as meaning with the intent for connotation. However we are performing math operations on text and I reiterate that I feel this is in the realm of mathematical vispo. Check out Geof Huths amazing blog if you want to understand all the branches of visual poetry.

On a side note here is a visual poem I made for Gregory Vincent St. Thomasino titled “church” It is inspired by and uses his math poem, “change + purse = church”

Four-Dimensionally Centered

This piece was inspired by the beauty in New Mexico and its relationship to the spiritual ideas of its native people. It is a four dimensional point metaphorically pointing at the atonement archetype.
There are four axes in this Cartesian system: the first axis is that of east and west the next axis being north and south the third axis being up and down and the last axis being inward and outward. Mathematically speaking the point described uses the analytic geometric midpoint formula to define the midpoint in each of the four axes. Metaphorically speaking The point described is at the center of everything and nothing.

Joint Mathematics Meeting Report

American Mathematical Society

I just returned from the Joint conference on Mathematics in San Antonio and was extremely pleased with the Art Show. Many of the ‘Bridges’ mathartists participated in the show and some attended the conference. Here is a picture of my good friend Reza Sarhangi the nucleus of the Bridges conference (left) standing with Slavik Jablan an extremely important and interesting figure in the Mathart movements in Europe.

Here is a picture of my friend Paul Hildebrandt (left) and Ivars Peterson dining on good Mexican food. Paul is the president of Zometools and Ivars is extremely important figure in the proliferation of fun filled mathematical ideas and is the creator of “Math Trek” for Science News.

Here is a snapshot of Robert Fathauer standing next to his mathart. Robert is president of Tessellations company and he also is involved in the curation of many mathart shows.

Here is a snapshot of Francisco Lara-Dammer with his beautiful Cayley diagrams



Here is a snapshot of Gwen Fisher who does amazing mathematical beadwork.

Here is a snapshot of Anne Burns and her beautiful mathematical landscape

My apology to to Bradford Hansen-Smith for missing the opportunity to shoot his picture (he also attended the conference)

Remember the Alamo!

Mathpo Beauty?

I snagged this quote off of the new-poetry list, submitted by Jeff Newberry

"Life is doubt, and faith without doubt is nothing but death."
Miguel de Unamuno

When I look at this quote I easily see it also as a mathematical metaphor.

Life = Doubt
Faith - Doubt = Death

What hits me so obviously is how much more beautiful the verbal language is relative to its 'seemingly cold' mathematical counterparts. However, the beauty in mathematical poetry is being able to see within an instant all the mathematically synonymous permutations and synergistically experience them as a whole integrated with the poetic beauty and power of the verbal language.

Doubt = Life
Doubt = Faith-death

Life = Faith-death

I wonder if Mr. Unamuno put much thought into the following quote:

Doubt is life, and life is faith without death

The Evolution of a Math Poem

Bob Grumman has recently posted another mathpoem worth thinking about. Its history goes back to early March 2005 when Bob was blogging about his version of the Basho haiku which concerns a frog jumping into an ancient pond.

Bobs blog 401

Bobs version:
old pond--abruptly, the sound
of a frog's splash-in

on March 10 2005 Bob reveals that a math poet named El Konde had sent him his interpretation of that same Basho Haiku poem.

Bobs blog 403

Which was:

Old pond / silence = frog splash!

Bob replied, “I like the idea of dividing the pond (arithmetically), but it would be more logical, it seems to me, to divide silence by the frog to get the old pond.” Or:

Silence / frog splash! = Old pond

I would like to analyze these two different syntactical forms of the same Basho poem and see how they relate to Bobs recent poem “Mathemaku for Basho”

First of all we must talk about what takes place when we create and equation in the form:

A = B multiplied by C

When we multiply 2 subjects together those subjects are integrated into a new subject that has its identity is founded in both of the previous subjects.

Lets looks a something we are familiar with If you drive your car 100 miles down the Jersey turnpike from New York to Philly at 50 miles per hour you would get there in about 2 hours (assuming someone doesn’t shoot you for driving too slow)

Distance is equal to velocity multiplied by time. d = v t

The very idea of distance is founded on the ideas of time and velocity at least as far as our equation is concerned. It is also interesting to me that we can use different syntax to make this mathematical expression synonymous in three ways.

d = v t (Distance is equal to velocity multiplied by time.)

v = d/t (velocity is equal to distance divided by time)

t = d/v (time is equal to distance divided by velocity)

Now let’s look at El Konde’s version of the Basho poem:

old pond / silence = frog splash!

Which is mathematically synonymous with:
(silence)(frog splash!) = old pond
and
old pond/frog splash! = silence

What we have done is to integrate the break of silence with the frog splash to define the old pond. Or the (the break of) silence is defined as the old pond divided by frog splash Furthermore we could also read it as the old pond divided by frog splash! Defines (the break of) silence.

I realize that I have added my own interpretation to El Konde’s intention of ‘silence’ in his poem by redefining 'silence' as ‘the break of silence’ but I think it is arguable that Basho was talking about the break in silence as opposed to silence itself. I believe my addition makes El Konde’s version much more clear.

Now let’s look at Bobs change to El Konde’s Poem and its mathematical synonyms:

silence / frog splash! = old pond

silence / old pond = frog splash!

(frog splash!) (old pond) = silence

So what Bob expresses by his change is that the break of silence is defined by the integration of frog splash! and old pond or that the old pond is defined by the break of silence per frog splash and last but not least … frog splash is defined by the break of silence per old pond

Now that we have broke it down, you the reader can make your own decision on what version makes the most sense to you.

Note: (Bob’s intention may have been to think of 'silence' standing as itself, not as 'break in silence', but I doubt it especially since he has ignored it altogether in his new poem)

In conclusion lets look at Bob’s Mathemaku for Basho: http://comprepoetica.com/newblog/blog00691.html


(pond)(frog) = (((((((haiku)))))))

So it shows that Bob is consistent with multiplying pond and frog but he has 'defined haiku' as opposed to defining 'the break in silence'.

By putting parenthesis around the word haiku he has incorporated a vispo technique in his mathematical poem to imply splashing water waves.


So much for evolution,
R Mutt

Math Tricks ... Numeric Vispo?

Apenas uma curiosidade...
Vê o que acontece se multiplicarmos 37 por múltiplos de 3:

3 x 37 = 111
6 x 37 = 222
9 x 37 = 333
12 x 37 = 444
15 x 37 = 555
18 x 37 = 666
21 x 37 = 777
24 x 37 = 888
27 x 37 = 999

Agora vê isto:

111111111 x 111111111 = 12345678987654321

Repara neste trapézio:

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111

E neste outro:

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

E ainda neste:

0 x 9 + 8 = 8
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
987654321 x 9 - 1 = 8888888888
9876543210 x 9 - 2 = 88888888888

I find these little pieces very interesting.

These have been floating around on the web lately and were emailed to me twice by different people. I have no idea how old they are or who originally discovered them. I would imagine that more than one person contributed to this group. I would not call them mathematical poetry but they may be considered some form of numeric Vispo.

They remind me a little bit of magic squares.
http://mathforum.org/alejandre/magic.square.html

If odd math expressions are your thing you may want to check the following:
http://curiousmath.com/

Happy Holidays

Golden Fear

GOLDEN FEAR 

This aesthetic distillation was inspired by the concept of being told to to fear something that is associated with the golden rule. 

The American Mathematical Society has accepted “Golden Fear” in their upcoming show in San Antonio, Texas Here is a link to the other Mathematical Artworks accepted in the show.

http://myweb.cwpost.liu.edu/aburns/jmm06/jmm06.htm

“Golden Fear” uses one of the equations for the golden ratio or phi, which is the most irrational number compared with all irrational numbers. Out of all the equations for phi “Golden Fear” uses the equation, which is in the form of a continued fraction. However, the word ‘fear’ is substituted for the number '1' in the original equation

Here is more information on the Golden Ratio.

http://mathworld.wolfram.com/GoldenRatio.html

Power of Confidence

Bob Grumman reviewed a couple of pieces of mine on his blog and I would like to share my comments to him.
http://comprepoetica.com/newblog/blog00676.html



Bob,
I appreciate the posting and would like to comment.


Bob said,” To be frank, I'm not sure why he seems to provides a range of values for his delta time,”

My answer is:

Delta means the “change in” see the link below for they explain it quite well. In a nutshell, when delta is present one must put things in terms of what it changes to from what state it originally had. So it goes that the change in x would be between two different states of x. In equation form it follows that (x1-x2) or basically the change from the existing state of x1 to the change of the new state, which is x2. That is why we had two different states in the poem … one being temporal neutrality and the other being the state of eureka

what are deltas?


Concerning the relationship of the Images to the math, I view the relationship of the images to the math poem the same as one would view the music in relation to the lyrics of a song … As to the task of putting my work in terms of Vispo … I guess my work would fit under the category of emblem poems with math poems instead ‘text only’.


Your Blog entry has inspired me to go into detail about how this piece works. The physics equation for Power states that power is equal to energy expended per duration of time. That’s all there is to it … That is the definition of power. (The term work and energy are synonymous)

Understanding the equation for power

However, there is much to what energy means. So now let us look at what physics says about energy.

Different faces of energy

In my piece Energy is the amount of force exerted over a distance. Let’s talk about distance. Distance is basically the Pythagorean Theorem mapped out on a Cartesian coordinate system. What we have is a change in position in one axis relative to a change in position in another perpendicular axis. (The following link explains it quite well)

http://www.purplemath.com/modules/distform.htm


Because there is a relationship between Energy and force lets look at what physics says about force. Force is mass multiplied by acceleration and acceleration is the change in velocity per time. (Delta t) So lets put the puzzle altogether and see how it reads.(in two dimensions) Power is a mass multiplied by a change in velocity per time multiplied by a change in position in one axis relative to a change in position in another axis and all of the previous verbiage is divided by a change between two positions in time.

Now let’s put the equation for power in context with my piece “The power of confidence”

Let me introduce a term … “virtual object” can be an emotional or psychological object present in my mathematical poetry that utilizes physics equations as a paradigm “to carry” the poem. The virtual object is a substitute for the physical object that is normally the subject of a physics equation.

The mass is of our virtual object is “Your diamond strength crystal bravery, a faceted fortress tempered by your self love”

The change in velocity 'delta v' of our virtual object = “From the cold insecurity of night to the sun shaking your hand each morning while your heart drums life's confirmation song”
The change in time that affects the virtual object 'delta t' = “From temporal neutrality to that split instant your intuition knows . . . eureka!”

The distance our virtual object will traverse:
The difference between x1 and x2 in our first dimension:

x1 = “Celebrating your demonic victories, the transformation to deity”
x2 = “Lying in your crib, frightened of your mothers sneeze”

Furthermore, the difference between y1 and y2 in our second dimension:

y1 = “Forged impenetrable through triumph”
y2 = “Soft as your baby butt”


The Poem in words:
So you can see that our mass of “Your diamond strength crystal bravery, a faceted fortress tempered by your self love” is being accelerated between the concepts of “the cold insecurity of night” to the concept of “the sun shaking your hand each morning while your heart drums life's confirmation song” and this is happening between the moments of “temporal neutrality” to the moment of “that split instant your intuition knows . . . eureka!” and all of this is moving over the distance between the difference of the concepts of “Celebrating your demonic victories, the transformation to deity” and “Lying in your crib, frightened of your mothers sneeze” and moving in a second dimension over the distance between the difference of the concepts of “Forged impenetrable through triumph” and “Soft as your baby butt” Furthermore all of this is occurring between the moments of “temporal neutrality” to the moment of “ that split instant your intuition knows . . . eureka!”

Beginner's Mind ~ Denotation / Connotation

There are numerous meanings throughout Asian philosophical history for the term “Beginners Mind”. That said, I will repeat one of my favorite stories illuminating the term in support of this blog post.

There was once known a famous Zen monk who advised numerous younger monks on the path to enlightenment. One day a younger monk came to sit with him, have some tea, and profess all the great deeds that the young monk had been participating in. The wise old monk was serving the two of them some tea as he sat and absorbed the boasts of the young monk.  While the old monk was pouring the younger monk’s tea, the young monk was startled to find that the older monk would not stop pouring tea into his cup. The tea filled it up and ran over the top onto the table and into the lap of the younger monk. The surprised young monk asked the old wise monk what was this purpose?  The older monk quietly stopped pouring the tea and said, “Your mind is like this cup – it is already full and I cannot help you with your quest. You must always remember to have the beginner’s mind to perfect your wisdom.”  

In the mathematical visual poem entitled “beginners mind” two forms of perfection are expressed. The first one is the Buddhist calligraphic circle called Enso in practiced in Japan or Ilwonsang practiced in Korea. The painting of this circle is created over and over as the monks practice the meditation of staying in the present moment. While in the present moment the “emptiness of self” can be experienced, thus substantiating this image as a symbol of emptiness.  To us it is a perfect example of circular perfection expressed as connotation … and layered on top of that, we have a perfect example of circular perfection expressed as denotation in none other than the analytic geometrical equation for a circle:

x^2 + y^2 = r^2

While using this equation to plot points creating a circle on a two-dimensional Cartesian coordinate system one becomes aware of the awe-inspiring infinite precision of not only this equation but by conceptual extension into all mathematical equations.

The 49 Chinese characters in the background are the calligraphic Chinese expression of “Beginner’s mind”

Link to Enso: https://en.wikipedia.org/wiki/Ens%C5%8D
Link to the equation of a circle: (my example h and k are valued at zero) http://www.analyzemath.com/CircleEq/Tutorials.html 

 A moment of silence for John Lennon ...

AMS American Mathematical Society Conference

I plan on attending this conference ... It should be a good time.

check out their web site.

http://www.ams.org/amsmtgs/2095_exhibits.html

Mathematical Simile Mathematical Metaphor

Mathematical simile is the function of virtually all applied math equations for which the public is familiar (usually scientific). For example physics equations are paradigms used to correlate experience. Mathematical models can be made for anything rationally understood and are descriptive of the relationships between the elements described.
A simile is a paradigm. One can see this expressed in the physics equation distance is equal to velocity multiplied by time. When you apply this equation to a situation you realize that this is an approximation even for all practical purposes it accomplishes the task at hand. The bottom line is that it is an approximation even though the equation expresses it as exact. The math equation is exact the application is not. Therefore it is simile ‘our experience of distance is like velocity multiplied by time.’ One may argue that the physics equation is metaphor precisely for the same reason e.g. we are saying that distance is exactly equal to velocity multiplied by time and it is not. Therefore we have a logical tension that creates the metaphor. The next step is to look at the intention of the equation, whether it is intended for connotation or denotation. Clearly physics equations are intended for denotation. Therefore what is really important for us is the intention of the equation. This also illuminates the idea that there are a lot of shades of gray between simile and metaphor yet we don’t usually think in this manner. I know a lot of people that think simile and metaphor are really the same. I believe at some point there is a nonsense threshold that one crosses and you can take it no other way except metaphor. Unfortunately that threshold line can be anywhere on a number line between the concept of simile and metaphor. Personally I see that threshold very close to simile. That is as soon as it starts getting nonsensical I consider it metaphor.

The visual image presented takes the following simile and expresses it as metaphor.

Although it may or may not be universally true I find that a man’s intelligence is inversely proportional to the levels of alcohol and testosterone in his system. I gave a lecture last week to a group of art students from Santa Ana Art Institute (Thank you Professor Ben Miles) and when I proposed this statement I got a bunch of laughs and a lot of nodding heads. Consequentially I believe there is some truth in there.

Humor

Tim Repp sent me this little mathpo related humor

Synecdochical Physics

I was inspired by conversations with The Mathematician Paul Gailiunas and a blog entry of Visual Poet Geof Huth to produce some synecdoche physics equations.


syn·ec·do·che n. Listen:
A figure of speech in which a part is used for the whole (as hand for sailor), the whole for a part (as the law for police officer), the specific for the general (as cutthroat for assassin), the general for the specific (as thief for pickpocket), or the material for the thing made from it (as steel for sword).

Whereas in all of the equations the variables, for the physics equations, have been replaced with a synecdoche counter part not all of the equations as a whole could be considered synecdochical. All of them but one created a synecdochical equation.

Newton’s equation on gravity is actually a metaphor. That is due to the fact that the force variable (replaced by attraction) in the mathpoem does not pertain to gravity but is in reference to the attraction caused by hunger. If it were pertaining to gravity then the equation would be synecdochical however anything else makes the equation a metaphor.

http://dbqp.blogspot.com/2005/10/synechdoche-explained.html

A picture is worth a thousand words

Math Poets

I have been delinquent in making entries into the blog but finally I have put some links into the link section. Besides myself I have added a link to a couple of Bob Grumman's pages and one to a Page of Scott Helms. Of all of Bobs Work my favorite is the one above. Bob and I seem to be the only people in the English speaking world who continue to focus on Mathematical Poetry or Math-Po If there are others please let me know. There are others who have done work in Visual Poetry and call their work Mathematical Poetry Karl Kempton is one who has done some very interesting Visual Poetry Using Mathematical operations on text. I would guess that the authority on how Math has been used in Visual Poetry would be Bob Grumman or Possibly Geof Huth. Geof is my focal point on the world of Visual Poetry. The depth of information Geof covers is astounding.
While I am on the subject of Visual Poetry I would like to mention I really like the selected poems by Michael P. Garofalo

What is mathematical poetry

Mathematical poetry is an artistic expression created by performing mathematical operations on words or images as if they were numbers. One may find this baffling because it seems we are being confused about the states of quality versus quantity. But it is through the fusion of this dichotomy that mathematical metaphor is spawned. Historically speaking we believe that math has never been intended for metaphor. We intend to change that. By blending the wondrous aesthetics of mathematics with enigmatic aesthetics of art we intend to bridge the gap between the infinite and the concrete.

The purpose of this blog is to promote interest in mathematical poetry.

If you are interested in mathematical poetry and know others who are mathematical poets please turn us on to them. I would like to invite all to comment on anything pertaining to mathematical poetry.