Tuesday, December 18, 2007

Reza Sarhangi - At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January. The following image is by Reza Sarhangi and Robert Fathauer (see Robert's work)
Reza is one of, if not the most important person in the vismath genre for Reza is the nucleus of the Bridges conference on mathematical connections in art music and science. He is a very special man and I really appreciate everything he has done and continues to do for the genre.

This print was inspired by Abu’l-Wefa Buzjani's (10th Century Persian mathematician) construction of a regular heptagon contained in his treatise, “On Those Parts of Geometry Needed by Craftsmen”. His construction is illustrated by the linework in the center portion of the print. The characters around the perimeter of the design repeat Buzjani’s name in Farsi.

Reza Sarhangi, Professor of Mathematics, Towson University and Robert Fathauer, Small business owner, puzzle designer, and artist, Tessellations Company

Reza Sarhangi is interested in Persian geometric art and its historical methods of construction, which he explores using the computer software Geometer's Sketchpad. Robert Fathauer creates digital artworks on a Macintosh computer, primarily using the commercial programs FreeHand and Photoshop.

Saturday, December 15, 2007

Gary R. Greenfield - At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January. The following image is by Gary Greenfield who also happens to be the chief editor of the Journal of mathematics and the arts. I really enjoy Professor Greenfield no nonsense approach concerning this genre.

Virtual interacting particles are realized as small paint droplets encased in hard shells. Particles move under the influence of artificial gravity. When a particle touches the canvas it adheres, its shell disintegrates, and the particle's footprint becomes visible. Particles stream from fountains located slightly above the canvas. Back scattering and dispersion occur when particles from two or more intersecting streams collide. This series of images was made by sequentially turning on and off 120 pairs of streams where some collision potential existed. Each stream contained 400 particles, all particles in a stream were of the same color, and four colors were available. The resulting "fountain paintings" lie on a spectrum somewhere between simulated Pollock style drip paintings and simulated air brush paintings.Gary R. Greenfield, Associate Professor of Mathematics and Computer Science Mathematics & Computer Science Department, University of Richmond, Richmond, VA 23173

Mathartist Statement:

"Many of my computer generated algorithmic art works are based on visualizations from simulations that are inspired by mathematcal models of physical and biological processes. Examples include cell morphogenesis, swarm behavior, diffusion limited aggregation, and interacting particles. By experimenting with the parameters affecting simulation settings and drawing attributes, I try to focus the viewer's attention on the complexity underlying such processes. "

Friday, December 14, 2007

Michael Field - At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January.

The following Image is by the mathartist Michael Field. Looking at these small jpegs is quite an injustice to these works. If you see them in person, you will be amazed at the complexity of texture. I have loved professor Field’s work since the first time I saw it at Bridges.

Part of a repeating pattern of type pmg. The pattern was generated using a smooth symmetric torus mapping and then lifted to the plane. The colors reflect the density of an associated absolutely continuous invariant measure.
Michael Field, Professor of Mathematics, Department of Mathematics, University of Houston

Mathartist Statement:

"All of my art work is based on ideas rooted in dynamical systems, chaotic dynamics and invariant measures (part of my field of research). I developed all the software, algorithms and coloring used for these images. I also built the computers used to generate the images and printed these images myself.
My interest primarily lies in the ways in which one can achieve certain desired artistic effects using a "mathematical palette" (as opposed to using images toilluminate the mathematics)."

Thursday, December 13, 2007

Robert Fathauer At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January. The following image is an M.C. Escher homage by Robert Fathauer. Also to note that Robert has curated many mathart exhibitions around the world.

"Angels and Devils" is a digital artwork based on a fractal arrangement of circles within circles. Two half-scale circles are placed within the starting circle and rotated by an angle of π/4 in opposite directions. These steps are then repeated in the smaller circles, etc. The motifs pay homage to one of M.C. Escher's most famous prints, "Circle Limit IV", which also contains angel and devil motifs. Escher's print is based on hyperbolic geometry, which distorts the motifs as they get smaller. All of the tiles in "Angels and Devils" are similar in the Euclidean plane.

Robert Fathauer, Small business owner, puzzle designer, and artist, Tessellations Company

Robert Fathauer makes limited-edition prints inspired by tiling, fractals, and knots. He employs mathematics in his art to express his fascination with certain aspects of our world, such as symmetry, complexity, chaos, and infinity. His artworks are created on a Macintosh computer, primarily using the commercial programs FreeHand and Photoshop. More recently, he has been exploring fractal arrangements of polyhedra

Wednesday, December 12, 2007

Anne Burns At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January. The following image is by Anne Burns who is a prominent figure in the vismath world and I continue to find her fractal imagery extremely fascinating.

I use mathematics to invent algorithms and recursive subroutines that model structures found in nature such as clouds, trees and flowers. The program that generated this picture was written in Visual Basic.

Anne Burns, Professor of Mathematics, Long Island University.Mathartist statement:

"Just out of high school I entered Pratt Institute to major in art. For a number of years I painted in oils and water colors. I returned to college in my thirties and found that I loved mathematics. I never realized the connections between math and art until I bought my first computer and began writing computer programs. This enabled me to combine my love of art with my love of mathematics. Another of my interests is identifying wildflowers; this led to writing programs trying to imitate the structure of plants and other forms found in nature. I love programming and I am fascinated by the process of recursion and how it can be used to create pictures of astonishing complexity with very little code."

Tuesday, December 11, 2007

Robert Bosch - Outside Ring - At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January.

While we are looking at space filling curves … The following piece is another space filling curve image similar to the last blog entry yet this one has a different premise.

"Outside Ring" is a continuous line drawing constructed from a 3000-city instance of the Traveling Salesman Problem. The line is a simple closed curve drawn with white ink. It divides the plane into two regions: in (drawn with red ink) and out (drawn with black). From afar, the piece looks like an alternating link, a knot formed from two interlaced loops, one red and one black. Robert Bosch, Professor of Mathematics, Robert and Eleanor Biggs Professor of Natural Science, Department of Mathematics, Oberlin College, Founder of http://www.dominoartwork.com/

Mathartist Statement:

"I specialize in "Opt Art", the use of mathematical optimization techniques to create pictures, portraits, and sculpture. I have used integer programming to create portraits out of complete sets of dominoes, linear programming to create pointillistic pieces, and instances of the Traveling Salesman Problem to create continuous line drawings. What all my pieces have in common---aside from how they were constructed---is that they look very different up close than they do from afar. I create my artwork out of a love of optimization---the theory, the algorithms, its numerous applications. I believe that optimization can be applied to virtually every imaginable field, and I believe that my artwork does a good job of helping me make that point!"

Monday, December 10, 2007

Douglas McKenna - Thirteenski - At The AMS Show in San Diego - January

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January.

The following vismath piece is by Douglas McKenna who was kind enough to invite me to visit his studio a couple of years ago. Since then I have been a fan of his 'space filling curves'.

Mathartist statement:
The original Peano and Hilbert Curves represent two out of three techniques for "threading a square". The generalized third technique I recently conceived connects square corners with side centers. "Thirteenski" is an asymmetric, recursive traversal of 13 symmetrically arranged sub-squares that eventually converges as a space-filling curve at different geometric scales according to a Sierpinski Carpet-like pattern. The resulting pattern wonderfully illustrates a struggle between symmetry and asymmetry, arising from the underlying combinatoric constraints governing the solution space.

Sunday, December 09, 2007

Slavik Jablan At The AMS Show in San Diego - January

Graphical work based on links and interlaced structures.

The next few days I am going to diverge from mathematical poetry and display some of the visual mathematics work done by many talented people who have their work admitted to the American Mathematical Society mathart show coming up in January. The beautiful piece below is done by Slavik Jablan

Graphical work based on links and interlaced structures.Slavik Jablan, Professor of Mathematics, The Mathematical Institute, Belgrade, Serbia.
Mathartist Statement:
"For many years I used almost all painting techniques (oil, watercolor...), painting in a color-expressionist manner. Later I transferred to computer graphic and mathematical art, trying to preserve the individuality and originality of math-art works, so my math-art works are not computer-generated. In fact, I am using a computer only as a tool for producing artworks."

Saturday, December 01, 2007

A Math Art Moment #9

Delineation #9

A mathematical theory seems to come in a flash of intuition before the final product is rigorously constructed.

An artistic theory seems to come much after the artwork that has been constructed in a flash of intuition.
To see more math art delineations click here

Sunday, November 25, 2007

Caring Metered

Here is a double derivative poem (above) based on the previous poem (below). I made substitutions in the poem as stated below and the new poem has elements of iambic trimeter. If you are not familiar with the double derivative poem then please click here.

What I have done is substituted the word caring with:

I am stunned in how her
soft spiritual wisdom
confiscated my care
and delivered it in
summer shining prairie
windswept floral baskets
… of love

Liking is substituted with the following:

Cant help but be seduced
by her chocolate locks
and eyes shining a black
night horizon much less
the subtle curve in her
… waist

Lastly daily rituals of love is substituted with:

I breathe my care’s expanse
Cultivating my love
Tilling the space spreading
Compassion’s grace always
Practicing awareness
as she blankets all my
new experiences
teaching me to focus
… care

Saturday, November 10, 2007

개꿈 The American Mathematical Society Has Accepted “DOG DREAM” And “TEMPTATION”

I am grateful and honored that the American Mathematical Society has accepted “DOG DREAM” (above) and “TEMPTATION” (below) to the 2008 art exhibition, which is concurrent with the 2008 AMS conference which takes place in January of 2008.

Both poems are in the form of an orthogonal space poem.

Sunday, October 28, 2007

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’.

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

Saturday, October 27, 2007

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.

Tuesday, October 23, 2007

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)

Sunday, October 21, 2007

A Math Art Moment #8


Artists have an insouciant tendency to get lost in their imagination.
Mathematicians have an attentive tendency to map their imagination.


To see more math art delineations click here

Wednesday, October 17, 2007


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.

Monday, October 15, 2007

Mathematical Poetry

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

Sunday, October 14, 2007

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.

Friday, October 12, 2007

The Good Path

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

Thursday, October 11, 2007

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.

Sunday, October 07, 2007

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

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

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.


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.

Wednesday, September 26, 2007

Art and Science Forum Presents Kaz Maslanka

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.
Ron Newby

Monday, September 10, 2007

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 …

Sunday, September 09, 2007

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.

Saturday, September 08, 2007


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.

Monday, September 03, 2007

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.

Visit the National Gallery of Writing