Factorial By Scott Glassman

i
am a
quotient of the

sun
i am
a quotient of

the
moon i
am a quotient

of
the one
i am a

quotient
of the
two i am

a
quotient of
the burn i

am
a quotient
of the dew


2.

i
am a
multiple of the

earth
i am
a multiple of

the
sea i
am a multiple

of
the birth
i am a

multiple
of the
tree i am

a
multiple of
the word i

am
a multiple
of the air


3.

i
subtract myself
from you for

luck
i add
myself to you

for
love i
subtract myself from

you
for luck
i add myself

to
you for
love i subtract

myself
from you
for luck i

add
myself to
you for love


4.

i
am zero
over you +

1
i am
zero over you

+
2 minus
0 over you

+
1 minus
0 over you

plus
2 minus
you over me

+
0 minus
1 over you

The poem above is a poem by Scott Glassman called factorial taken from his blog.

I find this poem of Scott Glassman very interesting in that I can see it as an example of mathematical poetry buried inside mathematics poetry. (Click here for the difference between mathematical poetry, mathematics poetry and mathematical visual poetry) The first section of Scott’s poem I have transformed into a piece of mathematical visual poetry. (above) This mathematical visual poem shows four separate mathematical poems that are contained within section one of his mathematics poem.



The verses in the second section have different meanings dependent on whether the poem is lineated or written without lineation. However, both ideas are present in the poem. You can feel the tension between differing statements and the shift in context between the statements due to reading it lineated and then reading it not lineated. I have written out all the mathematical poems/verses I could find contained within this section and displayed them in the image shown above.



The third section functions much the same as the second as far as tension between lineation and reading it without the lineation. However this section has only two statements repeated three times. The interesting part in this section is that the lineation creates two more mathematical poems which are shown in black (above).



The fourth section is a bit more difficult to map out. Therefore I shot a photo of my deductions from the poem. (above) You can see the brackets point to three mathematical poems that are delineated by the brackets inside the mathematics poem. The third one of the three I used algebra to simplify the expression into a compact form/context. Watch the meaning change in this poem through all the metamorphoses.

Geof Huth Mathematical Poetry Links

This page is reserved for Geof Huth's Mathematical Poems and related material

Algebraic Poem #1

Algebraic Poem #2

Algebraic Poem #3

Algebraic Poem #4

Mathematical Graffiti

art@IIT Upcoming Show

Anonouncing the upcoming show art@IIT currated by my friend Robert Krawczyk

Introduction To ‘Visual Mathematical Poetry’

"Americana Mathematics" (above)

-Details Views (below)-

Introduction to ‘Visual Mathematical Poetry’:
I would like to introduce another category for mathematical poetry related nomenclature. This delineation I would like to call visual mathematical poetry. This is a mathematical poem where the elements in that poem are visual objects. The difference between mathematical poetry and visual mathematical poetry is that the former uses words and the later uses images. Visual mathematical poetry is more similar to mathematical poetry than it is to mathematical visual poetry. However, one could create a poem that has aspects of all three of these types. There are plenty examples of math type poems out there that use elements of visual mathematical poetry however, I have seen none that are done with the intent of having a didactic element within them and most if not all are too abstract to show the mechanics of visual mathematical poetry. Furthermore, I have not seen any that are ‘purely visual mathematical poetry to serve as clear example.
Verification of logic:
I have tested the logic in this piece on a group of aerospace engineers to see if the artistic aesthetic interfered with the logic. All of them clearly saw the logic and understood the mechanics of the piece however, a couple asked, in perfect stereotypical engineering demeanor, why would I bother.
I also presented this to the mathematician Paul Gailiunas who replied below:
"It goes further - there are special numbers if we do multiplication (the primes), but none in addition. Number theory follows. We can set up other systems that work like this, but the elements need not be numbers. They are called rings. Division is a further complication. Sometimes it works, and we have a "division ring", sometimes it doesn't. The integers do not form a division ring because things like 2/3 are not integers."
The mechanics of this piece:
What motivated this piece was some conversations with a few people who have trouble visualizing mathematical poetry in general and the difference between addition and multiplication in particular. I decided to create this piece to possibly help those people approach this nebulous concept. For if we look at addition we see 2 concepts put together in such away that the original concept is easy to remove from the other and both concepts are easy to identify retain their original identity. I think most people do not have much of a problem comprehending this idea. However, multiplication is much trickier to embrace. Using the operation of multiplication augments the result by integrating the identity of both elements being multiplied. That is in the example of 4 x 5 = 20. ‘Twenty’ can be seen to have been augmented by both 4 and 5 and one can see this by dividing up 20 by cutting out 5 pieces of 4 or 4 pieces of 5. What is important is that we recognize that 20 is a higher magnitude relative to both 4 and 5 but has the ‘identity’ of both 4 and 5. “Americana mathematics” operates the same way for in addition one can easily recognize and conceptually separate both identities. Furthermore, the multiplication operation has a result that is an augmentation of both separate identities but obviously is more powerful than the original ideas, has its own identity however; it retains the original identities of both.

For a web page version click here

Perelman and Me

Here is a timely mathematics poem by JoAnne Growny:



Perelman and Me

On Tuesday, August 22, 2006 Russian mathematician Grigory Perelman declined the Fields Medal for his contribution to the proof of a well-known and difficult conjecture first posed by Henri Poincare in 1904. I applaud Perelman’s seclusion.


The gravity of the universe
requires dark matter.
Choosing one thought
prevents another.

Little girls learn social graces
to make others feel at ease.
But friendly greetings
are never mathematics.

Difficult thoughts
are born in isolation :
genius slips away if socialized—
and so he must refuse the prize.

JoAnne Growney
25 August 2006

Why I Don’t Want To Teach (Math Joke#4)

Grumman on Schlegel

Bob Grumman has just posted Marko Niemi’s translation of Friedrich Schlegel’s equation for poetry and God on his blog at this URL: click here

Bob has made the following comments:

“This is a translation by Marko Niemi of the 19th-Century German philosopher Friedrich Schlegel’s formula for poetry. Kaz thinks it may be the world's first mathematical poem. I'm not sure. It seems mostly informrature to me--i.e., intended to inform rather than provide beauty, as literature is intended to do (in my poetics). It is a way of mathematically defining something philosophical as e equals mc squared mathematically defines energy, rather than creating a poetic experience. It is entirely asensual--at least for one like me, who has no notion what material feature "God" has. Mathematically, it is a little silly, too--for if "shit" were substituted for "FSM," the equation would be in no way altered. On the other hand, it is a marvelously step toward what Kaz and I and Geof and Karl are doing, perhaps a pivotal one (although I don't know of anyone who was inspired to create mathematical poetry by it).”

I would like to address a few things from his comments.

Bob says, “Kaz thinks it may be the world's first mathematical poem. I'm not sure.”

I would like to note that I doubt that this poem was the first mathematical poem ever written. It is however the earliest mathematical poem that I have seen. I have seen earlier mathematical visual poems but no mathematical poems this early. For an understanding of the difference between mathematical poem and mathematical visual poem, please check my terminology at this link: click here

Bob says, “It seems mostly informrature to me--i.e., intended to inform rather than provide beauty, as literature is intended to do (in my poetics).”

I see this as expressive rather than informative. The question to ask is, “Was Schlegel’s equation meant to be denotative or connotative. It is hard if not impossible to be denotative when you are dividing by zero. Concerning aesthetics, Bob has a very different idea of beauty than I and his views of mythology are very different from mine as well. Bob is certainly entitled to his opinion. Although I also would have to say that Schlegel’s view of God is about as different to my view as mine is to Bob’s. I think the main aesthetical point to Schlegel’s poem is tying “The Transcendent” to an expression of infinity … not just once but six times. There are many things beautiful to mathematicians and infinity is definitely one of them if not the greatest idea of beauty. On the other hand, those who believe in “God” would also believe that the idea of God is the greatest beauty. However, I am certain that my idea of God is heretical to those same believers, for I do not believe in using lower case letters for the ‘G’ in God. All Gods are metaphors to The Transcendent.

Bob says, It is a way of mathematically defining something philosophical as e equals mc squared mathematically defines energy, rather than creating a poetic experience.

Here Bob equates philosophy with science … That was certainly true in 300 BC. However, there is nothing scientific about this equation for a scientist in Schlegel's time would never divide by zero (it is undefined for scientific use but perfect for poetry in fact it is the crux of metaphor)
Here is Schlegel’s view:
“Schlegel argued that poetry should be at once philosophical and mythological, ironic and religious. As a literary critic Schlegel sought not to reveal objective truths, but to write criticism so that the usual discursive prose becomes a work of art itself.” **

Bob says, It is entirely asensual--at least for one like me, who has no notion what material feature "God" has.

I am confused … I do not know where ‘anything’ physical was stated or implied.

Bob says, Mathematically, it is a little silly, too--for if "shit" were substituted for "FSM," the equation would be in no way altered.

The latter statement is another aesthetic judgment and again Bob is entitled to any scatological view he desires ;)

Bob says, On the other hand, it is a marvelously step toward what Kaz and I and Geof and Karl are doing, perhaps a pivotal one (although I don't know of anyone who was inspired to create mathematical poetry by it).”

If Schlegel inspired anyone to write mathematical poetry then Marko Niemi may be the closest person to know for he is our source.


**The quote was taken from this web site: click here

Emerson Quote #2

Karl Kempton sent us this Emerson Quote:


Every word was once a poem.

-Ralph Waldo Emerson, writer and philosopher(1803-1882)

Emerson Quote #1:

Language is fossil poetry.

Ralph Waldo Emerson, writer and philosopher (1803-1882)

The Biggest Problem To Overcome With Math-Art

Waterfall by M. C. Escher 1961

The biggest problem to overcome with math-art in general is that it is tied to two mutually exclusive aesthetic ideas. One idea being that pure mathematics pervades all cultures. The second is that Art is the expression of a particular culture. Math being the language of logic shares the same logic in France as it does in China. Art may express an archetype but the ‘expression’ is cultural. I believe these two ideas are true in a broad sense although there is a little room for argument in the finer details.
I feel that using math as a language for art demands that the mathematical expression or structure has to have some relationship to the cultural idea put forward. There is much mathematical art expressed which is beautiful from a mathematical perspective but trivial from an art perspective. Furthermore, the converse of this is true as well. There is mathematical art that artists may find beautiful however, evokes yawns from the mathematics community.
I think the measure of success of any mathematical art lies in how well it is accepted by both communities. This is a very difficult task and there is a plethora of work accepted by one community but not the other. I think the most successful artist that is accepted by both communities is M C Escher. Even though his acceptance is expressed more by the math community than the art community this cannot be helped. Finding the middle ground would be near if not impossible. At the other end of the spectrum, I am going to risk saying that I believe you are delusional if you believe you have made great math art/poetry and you are accepted by only one community no matter how much croaking the one community does.

Why I Don’t Want To Teach (Math Joke#3)

Why I Don’t Want To Teach (Math Joke#2)

Hyper-Dimensional Poetry?

When I was first introduced to hyper-dimensional geometry I was quite fascinated but really didn’t have any clear path to understand it. I had seen two dimensional images of a hypercube (four-dimensional cube) but really understood nothing about what I was looking at. With computer imagery we are able to see things a little better because we can simulate three-dimensions in a video or other moving imagery. The following link will take you to a polytope slicer which allows you to take three-dimensional slices through a four-dimensional object.
Let me expound upon this a little bit. Just about all of us have experienced slicing a near two-dimensional piece of paper with a pair of scissors. When we do this we experience seeing a near one-dimensional line at the edge of the paper where we just cut. Many of us have also experienced slicing a ‘three-dimensional’ orange in half and noticing a two-dimensional surface showing the cells inside the orange. However things get a little trickier when we slice a four-dimensional object. If you notice on our previous examples that the slice is a dimension less than the object we started with. That is a slice of a three dimensional object is two-dimensional and a slice of a two-dimensional object is one dimensional. Therefore, to imagine a slice of a four-dimensional object our result would be something that has three-dimensions. Our polytope slicer does just that! It gives us a three dimensional-section cut of a four-dimensional regular polytope. Your next question may be, “what is a polytope?” A polytopes are to four dimensions as polyhedrons are to three dimensions or what polygons are to two dimensions.

As you vary the parameters in the polytope slicer you will get three-dimensional slices of our four-dimensional polytope. (click here for the polytope slicer).

Now what does this have to do with mathematical poetry? All maths can be used as language for poetry. Use your imagination … I predict that someone will write a poem on a hypercube so that we can read it by projecting it down to the third dimension. This may have already been done but I am not aware of it. After one does it with a hypercube then try doing it on a 120 cell hyperdodecahedron or maybe an epic poem on a 600 cell hypericosahedron

Why I Don't Want To Teach (Math Joke#1)

Here is a math joke sent to me by Aerospace engineers Paul Mossel and Keith Rowley on the subject of why I don’t want to teach.

Geof Huth's Mathematical Poetry # 4

Here is the last of Geof’s Poems from this group. I find it wonderful to see other people making these types of mathematical poems. I especially enjoy this form with a series of poems building a context from which we can stand. Thanks Geof for sharing these with us!

Geof Huth's Mathematical Poetry # 3

I would classifiy the poem above as a pure mathematical poem except for one small element that I would classify as mathematical visual poetry ... can you find it?

Geof Huth's Mathematical Poetry # 2

Here is number two of Geof Huth’s mathematical poems.

Geof Huth's Mathematical Poetry # 1

I would like to share a series of mathematical poems by the Visual Poet Geof Huth. The next four days will be dedicated to this series. What I find interesting is that they are almost totally pure mathematical poems and not visual mathematical poems as such. This may surprise some because Geof is such a strong force in the visual poetry movement. These poems are so rich mathematically that making them work as mathematical visual poems would be extremely difficult. Geof tells me he plans to add visual poetic elements to these pieces so it will be interesting to see what he produces.

Golden Fear at Multiple Universes

Golden Fear has been accepted into the Multiple Universes show at the Poway Center for Performing arts in Poway California. The address is: 15498 Espola Road Poway, California -- tel (858) 748-0505

The show opens Sept 30, 2006 and closes Oct 30, 2006 the reception is Sunday afternoon at 2:00 PM Oct 8, 2006

Ancient Mathematical Visual Poem

JoAnne Growney has provided us with an ancient mathematical visual poem and its translation. A copy of the original manuscript can be seen above and at this URL here (click here). (Courtesy of ubuweb's early visual poetry page) The poem's explanation was difficult to find--but friend and colleague Sarah Glaz (Mathematics--University of Connecticut) tracked it down in Petrarch and the English Sonnet Sequence, by Thomas Roche, a book appearing in the bibliography of UBU's site of the Lok's poem. Oh ... and check out the square poems on JoAnnes website!

The translation is below:



Here we have a text interpretation of the manuscript photo, on page 166 of Petrarch and the English Sonnet Sequences by Thomas P. Roche, Jr. New York: AMS Press, 1989). In an Appendix on page 549, Roche also provides the text of two Latin mottos that surround the square. I have placed these at the top and at the bottom. Roche’s Appendix G goes on to point out the complexity of the structure within the square. For example, five lines The actual structure of this square poem is quite a bit more complex than the square itself.
For example, the columns down from E and F read:
God makes kings rule for heaue[n]s; your state hold blest
And still stand will their shields; fear yields best rest. [Roche, p. 550]
Embedded in the poem also are other poems, found by tracing the patterns of other squares (for example the sequence 1, 2, 3, 4, 5) and also crosses (using the letters, A, B, C, D, E, and F as reference points—A, B, E, and F, designate columns, as shown below and C, D designate the 5th and 6th rows.

Friedrich Schlegel’s Mask of God

Marko Niemi has translated Friedrich Schlegel’s mathematical poem for us. Marko also poses the question what happens if you divide the God by zero one more time.
I would love to hear Paul Gailiunas expound on that question. I think he would shy away from the idea of exploring the idea of God divided by zero but he may give us an answer to what happens when you divide infinity by zero.

Earliest Mathematical Poem?

Marko Niemi just sent me this link: (click here) …It looks very interesting! ... unfortunately I can not read German. Maybe someone will translate this for us. Marko tells us it was written by the German philosopher Friedrich Schlegel in the 19th century. Even though I can not translate it, I do know the beauty of dividing by zero. Although mathematically dividing by zero is undefined, the limit as you reach zero approaches infinity. In other words if you graph 1/x you can see the asymptote blow up in your face right at zero and it is a wonderful sight!

It is also interesting to see how artists gravitate toward dividing by zero. An example of this beauty can be seen in the taoist poem above by Karl Kempton.

Here is another thought on dividing by zero

Marko just sent me a translation of Schlegel's poem I will show it in the next blog entry

Here is a link to the translation: click here

Miscellaneous Mathematical Visual Poetry Links

Stratigraphy and Significance in the Fibonacci Sequence

click on the word algebraic

Mathematical Poetry Visual and Verbal

MNMLST POETRY: Unacclaimed but Flourishing

Bridges 2006 Abstracts

Bridges Conference on Mathematical Connections in Art, Music and Science starts Aug 2 2006 --- Click Here to list the Abstracts for the 2006 proceedings.

Bernar Venet

I had mentioned that Bernar Venet influenced me in the late 1970's. I have always enjoyed his work. I found a very nice essay about Venet by the Mathematician Karl Heinrich Hofmann. What I liked the most about this essay is its illumination of the fact that Venet does not present math as art but math as it is. However, the context in which Venet displays his work is in an art gallery or museum.

Click here for the essay

Karl Kempton Links

The Mathematical Visual Poetry of Karl Kempton links:
Revista de Poesia

M is for Mathematica

Runes about Karl's runes by Karl Young

The Root of Pi

Mathematical Poetry links:

Buddhist Mathematics

My Big Mouth

Mouth

Dusk

Six Alone In

Zen Poems

About Karl Kempton:

dbqp

North America's Longest Running Visual Poetry Magazine Edited by Karl Kempton, Harry Polkinhorn, and Karl Young -- Kaldron

Critical writings of Karl Kempton:

VISUAL POETRY: A Brief History of Ancestral Roots and Modern Traditions

CARRYING POETRY INTO THE 21ST CENTURY

Centered in London

My piece “Centered” was accepted in the Bridges Exhibit of Mathematical Art.

There is a lot of very interesting Mathematical Art in the Show Check out the other Art at the following link.

Righteousness

I have always found Mytho-spiritual aphorisms to be beautiful and every time I discover a new one if feel my life has new depth. They seem to me to be the archetypical fabric in all mythologies / religions as I have found them to be translatable and transmutable between the myths. I have also found that translating them into the language of math to be aesthetically rewarding. The piece righteousness above is one such aphorism which basically states that the more you display righteousness the less you really have. Of course this aphorism can be said for many disciplines for it seems we have all experienced the braggart who is more interested in covering his insecurities than setting an example for us to follow.

The equation is 'D' is proportional to 1/r ... or in otherwords 'D' is inversely proportional to r

New/Old Math Humor

I don't know where this came from but it reminds me of the logic used by a mathematical poet I know.

click here for the video

Early Karl Kempton visual poetry (plotter poems)

Here we have some interesting early visual poetry from Karl Kempton which used mathematical programing to plot these poems the link takes you to a page on Dan Wabers wonderful minimalist concrete poetry site. Here is the main page: minimalist concrete poetry

Mobius Poem by Endwar

Here is a link to a wonderful Mobius Poem by Endwar. Very Nice!
Click here for the Mobius Poem

Prometheus Epistle to Job

Do the muses scatter ancient fragments of thought or do they just perpetuate them. How is it that the ancient Greek Titans can still speak?

also see Orthogonal Space Poem

The Virtuous Sphere (part two)

The Virtuous Sphere (part two)
This blog entry is a continuation of “The Virtuous Sphere” please read the last blog entry so that today’s will make sense.

On the last blog entry, we had just finished talking about the equation of a sphere. However, the next question one may ask is, “why are there words in the equations instead of numbers?” To answer this question, you should read my essay on verbogeometry. I am going to republish some of the essay that relates to “The Virtuous Sphere” but if you have not read the essay on verbogeometry then you may not get as much out of this as you would if you were to read it.

Distance Formula and Verbogeometry: As we have seen, to calculate the distance between two points, we need to describe our points by its coordinates using the nomenclature of the coordinate pair. Let me reiterate, describing a point in verbogeometry is no different from numerical coordinates except we use words. Lets look again at the example in figure 15 where we used the midpoint formula to find the exact point between the points: P1(love,praise) and P2(hate,punishment) but instead of putting them in the midpoint formula lets put them in the distance formula. (See below)

Here we have an expression for the distance between the points P1(love,praise) and P2(hate,punishment) in two dimensions. But we can also use verbogeometry in any number of dimensions including hyper-dimensions. But before we look at hyper dimensional verbogeometry lets look at another example which we will express in the third dimension. The following example uses a three dimensional Cartesian coordinates system with 3 simple antonym word-axes. (See below) The first axis is noble / ignoble the second axis is just / unjust and the third axis is loyal / disloyal.
Now lets look at the expression for the distance between the points P1(noble,just,loyal) and P2(ignoble,unjust,disloyal) (see below)
Notice the green line in figure 33 is the visual representation for the mathematical expression above. However, it would be much easier to visualize if we were able to rotate the axis. Figure 33 is an isometric view, which I chose to use because it is best for viewing the axis but unfortunately at the expense of viewing the spatial orientation of the green line.

(The virtuous sphere is written in the language of three dimensions. What I find interesting is that we can write a spherical equation in hyper dimensions. The following shows the distance formula written in a hyperdimension.)

Now let us look at verbogeometry in a hyper-dimension. Let us look at the distance formula used in seven dimensions:Figure 35 shows the mathematical poem 1+1+1+1+1+1+1+1 =1 This is a metaphorical piece that creates a metaphoric path from the concept of confusion, to where seven deities meet. The piece uses the analytic geometry distance formula in a seven dimensional space where each dimension is a gradation from confusion to a point where a deity exists.

Here is a detail:

Lets look at the coordinate pairs for these two points P1(confusion, confusion, confusion, confusion, confusion, confusion, confusion) and P2(Allah,Buddha,Jesus,Spider woman,Vishnu,Yahweh,Zeus)

The Virtuous Sphere (part one)

The Virtuous Sphere (part one)

I thought it would be a nice idea to post "The Virtuous Sphere" and talk some about it. First of all I would like to say that I believe there are many ways to define virtue, this is only an artist rendition of one way. Please do not get bound up here in the idea of some absolute truth… remember the Hindu saying: “All wars are Just on both sides” When this piece was originally mediated to me my intentions were not so much interested in an answer of denotation but in the aesthetic inherit with the structure of a mathematical sphere and the coloration and distortion of that sphere by the personal ideas of integrity, justice, nobility and of course virtue.

Today's blog entry will talk about the analytic geometry involved in the piece and the next blog entry will discuss the verbogeometrical ideas needed to approach this piece.

Let me talk a little about the mechanics of this piece. This piece is a standard verbogeometry piece so obviously I will be borrowing sections from my essay on verbogeometry to help open this up for you that are not familiar.

We all should be able to recognize a sphere, but did you know that a sphere has a relationship to the Pythagorean Theorem? To see this relationship we first should talk about the relationship between the distance formula and the Pythagorean Theorem. Then we will look at the relationship between the distance formula and a circle and after that the sphere. The distance formula uses the Pythagorean Theorem to calculate distances on the Cartesian coordinate system. The Pythagorean Theorem says that the square of the hypotenuse of a right triangle is equal to the sum of the square of it sides.

Solve for c and we get the following:


Let us look at little closer at how the Pythagorean Theorem works in a Cartesian coordinate system. Here is an example: Plot two points on a two-dimensional axis system P1(-9,10) and P2(4,3) and If we draw a lines between the points and lines parallel to the axes we can obtain a right triangle.

To solve the length of the hypotenuse we first find the difference between the x values and the y values to create the sides of the triangle then we plug the values into the Pythagorean Theorem. The x value is 9 - 4 = 5 and the y value is 10 - 3 = 7Now we plug it to the equation and we get the expression in the following figure:

The distance or length of the hypotenuse would be the square root of 74 or approximately 8.602

The distance formula in two dimensions is thus -- Given two points (x1,y1) and (x2,y2):

To reiterate -- you will notice that the distance formula is nothing more than Pythagorean Theorem placed on a Cartesian coordinate system! The x1-x2 in our equation actually shifts the line horizontally and the y1-y2 shifts the line vertically. In effect if we start at the origin for our point (x1,y1) then we can simplify the equation as shown below:

Let us look at the equation for a circle: (below) --- Doesn’t it also look remarkably like the Pythagorean Theorem? In essence it is the Pythagorean Theorem! Notice that the radius of the circle corresponds to the hypotenuse of the right triangle. What we do is sort of ‘nail down’ one end of our right triangle at the hypotenuse and spin it around so that the other end of the hypotenuse follows the form of a circle.
All of the equations that we have been looking so far function in two dimensions but what if we wanted to use the Pythagorean Theorem in three dimensions? To use the Pythagorean Theorem or the distance formula in three dimensions we append another term at the end of the equation so it looks like the one below.

The Pythagorean Theorem in three dimensions is the same as it was in two dimensions except that we add another term at the end to give us the extra dimension.

Let us look at the equation for a sphere (below):

Notice that it looks just like the Pythagorean Theorem in three dimensions? It follows the same thought that we did in two dimensions. Where we ‘nail down’ one end of the triangle and spin it around in a circle but since we are in three dimensions, we also spin the circle around an axis and so it goes that the end of the triangle we started with now follows the form of a sphere.

This concludes discussing the analytic geometrical aspects of “The Virtuous Sphere” You can see that I used the equation for a sphere as my mathematical language for this piece. The only thing we haven’t discussed is the verbogeometric properties of the piece. The next entry in my blog will discuss some of the mechanics of verbogeometry that are needed to approach this piece.

A Screening of Super-8 films by Robert C. Morgan

I studied with Robert C. Morgan in the late 1970’s and he is responsible for much of my earlier artistic development. He exposed me to the conceptual art movement in general and Benar Venet in particular. Venet noticed that science had aesthetics as well as art and was bold enough to re-contextualize these scientific aesthetics as Art. It wasn’t until I read the Dancing Wu Li Masters by Gary Zukav that I experienced an epiphany that drove me into mathematics and science. Prior to that event I had no interest in mathematics and some disdain. However, I must say I loved math up until I was seven years old then, as I mentioned, I abandoned it until 1979.
Robert has always been supportive and I always wish the best for him.

Millennium Film Workshop

presents


A Screening of Super-8 films by Robert C. Morgan

Saturday, June 17, 2006, at 8 PM



Although known today primarily as a critic and curator, Robert Morgan
emerged as a "post-conceptual" artist in the mid-seventies. Between 1974 -1989,
Morgan worked in a variety of different media, including an extensive body
of work in Super-8 film. He regards his films as "counter-narrative" in that
they deconstruct both Hollywood and commercial television -- the two primary
forms of visual narrative in the entertainment industry -- by laminating appropriated
footage against a personal and often political narrative. This is a rare opportunity
to see films by one of the formative "appropriation" artists of the seventies.

A reception will precede the screening in the Millennium Gallery at 7 PM

Admission: $8 / $6 (members)


For further information, please contact:

Millennium Film Workshop
66 East 4th Street, NYC 10003
Tel & Fax: (212) 673 - 0090
Email: cinema@millenniumfilm.org

The Transformation of Poison

The image above has been simmering in the background for a few years now and has finally come to fruition. It came about in December 2001 over a cup of coffee while taking a break at the ASCI conference in NYC. At the conference I met a very interesting Poet/Artist Philosopher and NASA scientist named Farzad Mahootian. We had a wonderful conversation between sips of dark java in mid town Manhattan and talked of many things. I shared my ideas on verbogeometry while he shared his ideas on sculptures that purify the environment. In our mutual excitement he thought it would be a good idea to incorporate the two ideas into a piece of Art. The piece above is the result. I decided to make a symbolic wedge from a verbogeometric prism and have it cleaning the air with chrysanthemum power.

Terminology for Mathematical Poetry and Related Endeavors*

‘ Visual Art Aesthetic’ is the aesthetic that concerns itself primarily with the beauty or horror expressed in direct sensory experience, whereas the ‘ Mathematics Aesthetic’ concerns itself with the beauty in the structures of logic and thinking.

‘Mathematic Aesthetic’ is the aesthetic that concerns itself with the beauty in the structures of logic and thinking, whereas the ‘Artistic aesthetic’ is concerned primarily with the beauty expressed in direct sensory experience.

'Mathematical Conceptual Art’ This form of Art focuses on the Math aesthetic and re-contextualizes it as Art personally I feel conceptual art is not art however, it is aesthetic but. That does not necessarily mean that Math is art. The main difference between ‘Mathematical Conceptual Art’ and ‘Visual Mathematics’ is that in the former the artist presents their the work as Math, where as in the later they display the mathematical object as Art. In both types, they display the object in the context of an Artistic space. A good example of “Mathematical Conceptual Art’ would be the work in the late 1960’s of Benar Venet in which he would study Math and Physics and present what he had learned purely for the aesthetic of the topic involved. There are many works of Sol Lewitt that could be considered “Mathematical Conceptual Art’ as well. A contemporary Artist who I would consider a ‘Mathematical Conceptual Artist’ is the British artist Justin Mullins although he does some work that could be considered as ‘Mathematical Visual Poetry’. The main difference between Mathematical Conceptual Art and Mathematical Poetry is that the Conceptual Art movement as a whole was not concerned with the intention of metaphor in any form and Mathematical Poetry relies mostly on metaphor to make its connection to poetry in general

‘Mathematic Constructivism’ Is one of the most popular forms of Mathematically related Art. It is a term I will use to sum up a conceptual thread that started with the Russian constructivists and ended up in the modern movement of visual mathematics. The former started in the political and social upheaval of the 1920’s with the emergence of Artists such as Naum Gabo, Vladimir Tatlin and ended up in the latter movement with mathematicians such as Donald Coxeter who felt their mathematical work is a form of Art. Donald Coxeter imparted much mathematical assistance to M C Escher.
The conceptual idea of Cubism pushed visual Art into a process of abstraction whereby the artist removes unnecessary visual layers of an object in order to point to a metaphysical idea of the object. Art Constructivism moved to push the methodology of abstract Art more and more abstract to the point of the object being something not found in nature -- a “construction”. If we push this idea further we end up in realm of ‘Visual Mathematics’ where the object of Art is pure logic, a reflection of the logical structures of language in our mind. Today ‘Mathematical Constructivist’ work has moved more toward ‘Visual Mathematics’ and can be seen in the work of Max Bill, Helaman Ferguson, Rinus Roelofs, Robert Fathauer, Brent Collins and many others.

‘Mathematical Poetry’ – Mathematical Poetry is a umbrella term that covers any poetic expression involving Mathematics. An initial list of categories is as follows: Equational Poetry, Mathematical Visual Poetry, Visual Mathematical Poetry, Mathematics Poetry and Number Poetry


‘Equational Poetry’ – This is literally performing mathematical operations on concepts whether they are words or images. A good example would be my page at the following link: Mathematical Poetry

'Visual Mathematical Poetry' -- This is a mathematical poem where the elements in that poem are visual objects. The difference between mathematical poetry and visual mathematical poetry is that the former uses words and the later uses images. Visual mathematical poetry is more similar to mathematical poetry than it is to mathematical visual poetry. However, one could create a poem that has aspects of all three of these types. For an example check out "Americana Mathematics"
‘Mathematical Visual Poetry’ – This is more difficult to define because of the vast areas and the many competing definitions of visual poetry. However, I consider mathematical operations on text as well as mathematical textual information composed for aesthetic purposes to be ‘Mathematical Visual Poetry’ Also words, text or textual elements mixed with mathematical symbols or formulae that are not performing mathematical operations on the word meanings. Although Karl Kempton has worked in many categories, I feel the following is a good example of ‘Mathematical visual poetry’: Another good example is Marko Niemi’s fractal poem described in the following link: Midwinter nights dream Scott Helmes was one of the first visual poets that moved into mathematical motifs. Bob Gruman has probably been the most prolific in this catagory.

‘Mathematics Poetry’ -- This poetry is what I would call traditional language poetry about or inspired by or uses mathematical imagery. I also would consider this catagory to include language poetry that has an interaction of numbers with words. There are numerous examples all over the web but the most popular from google's perspective seems to be Marion Cohen: other sources would be JoAnne Growney and Katherine Stange:

'Polyaesthetics' is a word used in relation to aesthetic works which incorporate many diverse aesthetics. This is not limited to but includes the aesthetics of Mathematics, Art, Music, Science, Religion etc.

'Visual Mathematics' Is one of the most popular forms of mathematically related art. It sometimes has been called “Concrete Art” This is a form of Art that focuses on the Math aesthetic and re-contextualizes it as Art. The main difference between ‘Mathematical Conceptual Art’ and ‘Visual Mathematics’ is that in the former the artist presents his/her personal/emotional relationship with the aesthetic of Mathematics where as in the later the display is less personal and more cerebral. In both types the object of that presentation is displayed as a form of Art. The hero of visual mathematics is M C Escher whose work is so strong anything that resembles it looks cliché. Fortunately there are other arenas in Visual mathematics. A good example of contemporary Visual Mathematics is found in the work of George Hart, Paul Gailiunas, Carlo Sequin, Robert Krawczyk, Michael Sussna and many others. This type of work is primary interested in visualizing mathematic structures. These structures could be anything from computer algorithms not limited to fractal Art or polytopes to hand drawings, plastic sculpture or origami.


*Disclaimer: These are the views of Kaz Maslanka and are a rough attempt at trying to put mathematical poetry in context with most of the mathematical influences in visual Art of the last 100 years

Polyaesthetic example

Boeing 747 Landing gear in the process of being manufactured

Walt Gillette of Everett, the lead engineer on the 787 program and a man Business Week recently called a "plane genius," announced his retirement from the Boeing Co. on Wednesday.

You may ask what does this event have to do with mathematical poetry? … Not much however, the following quote of his is a perfect example of polyaesthetics whereby aesthetics comes in many forms even in engineering and technology.

Walt Gillette says,
"One of the most incredible experiences is to go out ... and stand in the middle of full landing gear of a Boeing 747," he said. "To stand there, right there under that big, fat, huge machine, and you think this thing goes 625 miles an hour and a little-bitty human brain ... tells it exactly what to do and where to go, and it follows just like a docile family pet."

There are many forms of beauty in concepts and some say that if the concept is beautiful then it must be considered as a form of Art. I personally don’t find beauty and Art to be synonymous but I will admit that it is a nebulous concept and very difficult to nail down. Art for some reason seems to be a ‘catch all’ for anything anyone wants to call Art. I wish there was a better ‘catch all’ term other than Art. If you can think of one then I invite you to comment.