Monday, December 25, 2006

Flaky Pie

This image came from the following link: Flaky Pie

Thursday, December 21, 2006

Merry Christmas

Merry Christmas

Here is my Christmas fractal I constructed for you.

I wish you a Merry Christmas and a Happy New year

Monday, December 18, 2006

Lothar Schmitz

Lothar Schmitz’ sculptures reconfigure and question corporate landscape elements using man-made materials. His topiary-like treatment of landscape alludes to the accelerating pace of ecological change and genetic mutation. He draws experience from both his art and physics background. Schmitz is a past Los Angeles Cultural Affairs COLA Individual Artist Grant recipient and a physicist.


Los Angeles based artists stretch those laws and present some of their own.Mitchell Friedman, Manfred Menz, Lothar Schmitz, Carrie Ungerman and Melinda Smith Altshuler address social, environmental and psychological circumstance in the landscape. Exhibition Dates: December 21, 2006 - January 27, 2007Artist’s Reception: Thursday, December 21, 5:30 pm – 7:30 pm

Sarah Lee Artworks & Projects
2525 Michigan Avenue (Bergamot Station), T1, Santa Monica, CA 90402
Media Contact: Melinda Smith Altshuler, 310 367.5246,
Gallery: 310 829.4938 E-mail,
Gallery hours: Tuesday through Saturday 10:30 am- 5:30 pmPlease direct e-mail inquiries about the exhibition to the gallery’s address (above);

Sunday, November 26, 2006

Celebrate The Tenth Annual Bridges Conference

Celebrate the Tenth Annual Bridges Conference


Mathematics, Music, Art, Architecture, Culture

**** ****

Bridges: Mathematical Connections in Art, Music, and Science
School of Architecture, The University of the Basque Country
San Sebastian (Donostia), Spain

July 24-27, 2007

The conference consists of a 4-day combination of Bridges Conference
activities (July 24, 26, and 27) and an excursion day to Bilbao (July
25). Please visit the Announcement page at the conference website for
a complete announcement.


The Bridges Conferences, running annually since 1998, bring together
practicing mathematicians, scientists, artists, educators, musicians,
writers, computer scientists, sculptors, dancers, weavers, model
builders in a lively atmosphere of exchange and mutual encouragement.

Important components of these conferences, in addition to formal
presentations, include hands-on workshops, gallery displays of visual
art, working sessions with artists who are crossing the
mathematics-arts boundaries, and musical/theatrical events in the


You are invited to submit either a short (two pages) or long (at most
eight pages) paper that presents new work within the scope of the
Bridges conference. Papers must be submitted as Microsoft Word or PDF
to The deadline for paper submission is
Febrary 1, 2007. This deadline is firm! If electronic submission is
impossible, please contact Reza Sarhangi to make other arrangements.
Authors will be notified of acceptance on March 25, 2007, and final
papers will be due on April 23.


There will be several teacher workshops for K-12 teachers and educators
at the 2007 Bridges Conference. If you are interested in making a
presentation in one of these workshops you need to submit either a
short (two page) or long (eight page) paper; The deadlines for
submissions of preliminary and final versions are the same as for the
contributed papers.


At the conference, there will be an exhibition room for 2D and 3D
mathematical art, ranging from computer graphics to quilts to
geometrical sculptures. This art exhibit will be curated by Robert
Fathauer. All submitted artwork will undergo a refereeing process.
There is a limit of five submissions per artist. Images of accepted
artworks will also be published on the conference CD.


There is a registration fee of US $180 that includes a copy of the
Proceedings. Extra proceedings will be available during the conference
with a price of US $50. There is a special discounted rate for
students, artists whose expenses are not otherwise supported, and K-12
teachers. Please visit the Registration page at the conference


Participants have a choice of staying in the campus facilities
(comparable to a three star hotel and within walking distance of the
conference site) or staying in a nearby hotels (a list of hotels is
provided in the Accommodations section of the Bridges website).


You have received this message because you are subscribed to a mailing
list for Bridges-related announcements. If you would like to manage
your subscription, please visit the mailing list web page at

Anyone interested in joining the list may send email to


For any other information not available on the web page please
contact: Reza Sarhangi, Department of Mathematics, Towson University,
8000 York Road, Towson, MD 21252, (410) 704-4922.

Thursday, November 16, 2006

Alligator Cubed

Climax 4 by Mirela Roznoveanu

Presently, Dan Waber has some interesting math-poetry related images on his Blog that I would like to draw to attention. There is an interesting series of works by Mirela Roznoveanu that I would like to note, have verbogeometric properties. Although the pieces are not explicitly mathematical (they do not show equations) they do show graphic ideas in space implicitly related to a Cartesian coordinate system.

Because they are so abstract they can have numerous contexts applied to them pointing to meanings just as numerous. The resultant aesthetic experience is a vector sum of all the contexts applied. Of course this is my personal take on this and I will certainly give you room to express your own viewpoint.

Alligator Cubed by Jeff Crouche

The other piece I want to point out is Jeff Crouche’s “Alligators cubed” This is a perfect example of visual mathematical poem. (a nice one at that)
and thanks to Marko Niemi for keeping me on my toes

Wednesday, November 08, 2006

Applications For Verbogeometry

Shown above is a three-dimensional verbogeometric polyhedral

Applications for Verbogeometry

Neal Goldman, a mathematician has come up with a single verbogeometric polytope to analyze huge amounts of data. Business week online has recently published an article talking about Goldman’s polytope and you can access this article here. I was proposing someone write a polytope poem in my blog entry on August 14, 2006. Goldman’s polytope is not a poem but it can be viewed as a hyper-dimensional verbogeometric structure.

I would like to present an excerpt from the article to arouse your curiosity:

How do you convert written words into math? Goldman says it takes a combination of algebra and geometry. Imagine an object floating in space that has an edge for every known scrap of information. It's called a polytope and it has near-infinite dimensions, almost impossible to conjure up in our earthbound minds. It contains every topic written about in the press. And every article that Inform processes becomes a single line within it. Each line has a series of relationships. A single article on Bordeaux wine, for example, turns up in the polytope near France, agriculture, wine, even alcoholism. In each case, Inform's algorithm calculates the relevance of one article to the next by measuring the angle between the two lines.

Here is the link to the original article from business week online

Sunday, November 05, 2006

Journal of Mathematics and the Arts

I would like to spotlight a new Journal on Mathematics and Art. Edited by Professor Gary R. Greenfield from the University of Richmond in Virginia … I will keep you posted when the first issue comes out.

Saturday, November 04, 2006

Upcoming Show in Chicago

For over twenty-five years, PHSColograms, the integration of photography,holography, sculpture, and computer graphics, have created a post-canvas three-dimensional medium that has expanded the visual imagery of the work of a variety of scientists, mathematicians, engineers, architects, and artists.

Paradox. The vessel is a metaphor of our human existence, the body symbolized as a box or bowl is the vessel for the soul. The paradox between the need to belong and the need for individuality; attraction and repulsion; the inside and the outside; materiel expansion and contraction.

Paul V. Galvin Library, Illinois Institute of Technology
35 West 33rd Street, Chicago, IL 60616

Exhibition hours: Monday - Thursday: 12 - 6 pm, Friday: 12 - 5 pm
Saturday: 8:30 am - 5 pm, Sunday: 2 - 6 pm

Sunday, October 29, 2006

Bridges London Conference Proceedings

I just received my Bridges 2006 Conference Proceedings today! It is full of wonderful papers for which some of them I plan to review. I recommend you going down to your local bookstore and ordering it! ISBN 0-9665201-7-3

Friday, October 27, 2006

Tuesday, October 24, 2006

New Design For My Main Website

I have redesigned my main website with an attempt to make the navigation easier. Any feedback will be greatly appreciated!


Sunday, October 08, 2006

Multiple Universe Show Opening Today

“Multiple Universes” show opening today 2 pm to 5 pm … If you are in southern California come join the fun. Above is the map to the show

Wednesday, October 04, 2006


I would like to thank the young lady by the name of Tifinie who sent me the link to a ‘’ account which had a copy the following essay posted. I am always interested in anyone expressing mathematical poetry. Here is a link to the original source of her information.

The following essay is by Allen L Roland a psychotherapist and political activist who can be found at Dr. Roland’s essay is a perfect example of mathematical poetry in his metaphorical use illuminating his philosophy. I went to his website and found much of his spiritual and socio-political views to be similar to mine although he is much more aggressive than I.

His poem reminds me of a poem I had done a poem using this same equation. I haven’t published it on my blog because I haven’t made an electronic version of it yet. Maybe this will motivate me to post it later just to contrast this poem and show how the same equation can be used for many vastly different metaphors.



Since we now know that the particles of light ( photons )
are subject to another force ~ and I would argue that that force is a psychic energy field of love and soul consciousness ( The Unified Field ) which exists beyond time and space and whose principle property is the universal urge to unite ~ it's time to add another dimension to Einstein's famous equation ~

E=mc² in Einsteinian terms means that the energy contained in matter is equal to its mass multiplied by the velocity of light squared.

Unfortunately, man, in his limited consciousness, has used this equation to create nuclear bombs and the means to completely destroy mankind.

But we now have growing scientific evidence that light is not the one constant of the Universe and may very well be a condition of state within a greater constant.

David Adam, science correspondent for the Guardian, in an April 11th article entitled Why Einstein may have got it wrong , reports some startling findings as physicists gather in England to celebrate Einstein's work;

"Astronomers will tell experts gathering at Warwick University to celebrate the anniversary of the great man's "miracle year" that the speed of light - Einstein's unchanging yardstick that underpins his special theory of relativity - might be slowing down. Michael Murphy, of the Institute of Astronomy at Cambridge University, said: "We are claiming something extraordinary here. The findings suggest there is a more fundamental theory of the way that light and matter interact; and that special relativity, at its foundation, is actually wrong."

The Bose/ Einstein Condensate established that photons, and now even atoms have a tendency to unite and dance in perfect unison.
Einstein was in a quandry about this phenomenon so he dismissed this obvious attraction of photons as not only spooky but evidently a " tendency to want to travel together " ~ and Einstein later died never realizing he had found his elusive Unified Field.

For, as I have written before, it was Einstein's consciousness that kept him from grasping that he had indeed discovered the Universal primal urge to unite that exists from atoms to human beings ~ and that even galaxies are subject to its universal pull.

As such, this psychic field of love and urge to unite deepest within us cannot be observed through the most powerful electron microscope nor through the lens of the largest telescope, for it is an energy which must be surrendered to and experienced before it can be perceived through the consciousness of the observer.

So now, let us breath fire into Einstein's most famous mathematical equation E=mc² and apply it to a Unified field of love and soul consciousness which could lead us instead to our ultimate fulfillment as human beings;

E = Love ~ The ultimate totalization of human energy ( The Unified Field )

M = Man, the most complex and conscious form of matter that we know.

c²= Consciousness squared.

Thus, the energy of conscious unconditional love, which is deepest within all living matter, is equal to man times his consciousness squared.

British physicist, Steven Hawking, regarded by many as today's successor to Einstein, wrote that there ought to be something special and simple about a theory of everything .

And what could be more special and simple than love.

Finally, at this critical moment for mankind ~ it is imperative that we now recognize that love, not light, is the one constant of the Universe.


Allen L Roland

Thursday, September 28, 2006

The Energy To Break My Heart

Unfortunately to see it you must click here

This poem uses the physics equation for energy E = Fd Energy is also called work "W"

Energy (or work) is the force applied to an object multiplied by distance that object travels
If we pull force out of the context of the sentence above and look at what defines force we will find that Newton’s second law states Force is equal to the mass of an object multiplied by the acceleration the object is experiencing. Now if we look at acceleration we find that acceleration is the change in velocity per the change in time. In our energy equation we are multiplying the F times the distance the object is traveling. The way we calculate distances is with the distance formula. The poem above uses the distance formula in a nine dimensional space where every verbogeometrical axis is described in the poem underneath the radical.

Saturday, September 23, 2006

Optical Illusion Contest

Here is something unrelated to mathematical poetry but interesting none the less. I received this information from my vision science list today. These are the results from the best optical illusion contest of 2006 --- If you are an interested vision scientist, they are now calling for submission to the 2007 contest.

Check out the winners of 2006 here
Go to this page then click on TOP 10 finalists

Tuesday, September 19, 2006

The History Of Numbers

Karl Kempton sent me this link ... all I could say was WOW!
check out all these books (click here)

Sunday, September 10, 2006

Infinity In Science / Poetry

I tend to think that without logic, you cannot communicate and without communication, you cannot have a philosophy. To me logic presupposes philosophy ... Logic is the supportive structure for thought without it everything would fall apart, no one could predict where our next meal would come from, much less anything else. The other side of the coin is that without a philosophy coloring ones theory of logic, ones logic has no starting point. In this sense, ones logic can have no logic without a philosophical stone to stand on. It is a vicious circle!

The clipping below originally came from a polytope list and was sent to me by my friend the mathematician Paul Gailiunas. My original question to him a few weeks ago concerned the importance of infinity within modern scientific equations. Math poets seem to gravitate toward using infinity in our math poems and as professor Gailiunas told me scientists tend to avoid infinity as much as they can. The following is an example of scientific thinking in this area.

This came from a completely different direction.
I thought you might beinterested.

On Thu 7 Sep 2006 (21:46:48 +0100), wrote:On Wed, 6 Sep 2006 08:54:09, "Wenninger, Magnus" wrote:>the word Finitism caught my attention. Wow! I thought ...>This is something I have to bring to the attention>of our List. You can find it at:> In schools of divinity it is often said that philosophy is the handmaid of theology. But I think it is equally true that philosophy is the handmaid of>mathematics as well. How about that? At risk of wandering a little off the List's home territory, I find it hard to think of a discipline which does *not* rely on philosophy as its handmaid. Without philosophy there can be neither meaning nor logic, and without these there can be no rational thought or communication of ideas. I was of course intrigued to find another discipline where the broken natureof Euclidean lines causes a broken theory. I get the impression from Mathworld that discrete projective geometry is a fairly developed discipline, and I wonder whether finitists would, like us reciprocists (I shy away from"dualists" where theology appears in the same message!), do better to keep their distance from old Euclid's ghost. It seems to me that finitism is intimately bound to the philosophy of science. I recall the verification principle, favoured by logical positivists, that no statement has any meaning unless it can, at least in principle, be verified byexperiment. As a philosophical principle it fell at the first hurdle - how do we verify the verification principle itself? - and logical positivism soon faded from all but the history books. The principle remains a cornerstone of the scientific method - an article of faith that reality has an ultimate order. A finitist might observe that if something is suspected to be infinite, then this cannot be verified by experiment, and therefore no infinity has any scientific value. It follows that any mathematical model of any scientific phenomenon should preferably contain no infinities. Of course, if we seek a mathematical model of the underlying reality rather than the scientific observations alone, then we are using our maths to do philosophy and are not restricted to finitism.Modern quantum mechanics and general relativity are both plagued by infinities. Does this mean that they are in truth philosophical theories, with little to offer the hardworking scientist but approximations and embarrassing work arounds? If so, then where should philosophy end and theology begin? And why?

Tuesday, September 05, 2006

The Equation For Aesthetic Measure By Birkhoff

My friend Keith Rowley pointed me at the equation above by 19th century American Mathematician George David Birkhoff. The equation comes from Birkhoff’s 1933 book entitled “Aesthetic Measure”. Here is a perfect example of an equation intended for artistic purpose and yet denotative. Here Birkhoff intends to write an equation to measure levels of aesthetic based on a ratio of order and complexity. Personally, I feel trying to quantify something as broad as the word ‘aesthetic’ is extremely difficult and elusive. I have not read his book so I withhold more comment until I have read what he has to say. My intuition tells me what he is doing is much like my syncopation theory. It will be interesting to see what differences there are.

Sunday, September 03, 2006

Scott Glassman Responds

Detail of Factorial for Scott Glassman (above)

Scott Glassman responds to my posting of his poem with my translations. I believe this gives even more detail to the workings of Scott’s poetry:


Your analysis is fantastic, and takes the poem to a very intricate term-bound level, one maybe lurking in logic + subsconscious forces. I always find the tension between emotions and quantification to be wonderful and you elucidate this beautifully in the visualized quotients.

I see how "I" an "I" is divided by elements, sun, burning, moon, etc. "I" or identity, or body, is a ratio of dust and cosmic energy, no better expressed than the direct equations you write out. Seems to cut through the bull to the crux of the matter.

The you - myself graphic you present is compelling because it made me think more about what I was, or my subconscious, was getting out. you - myself = luck. Or getting out of my own head, the ego, is a positive thing and will bring all the benefits. This is a frequent theme in what I write because I often try to disable the "I" and write from some central, unified place. luck = myself + you recognizes that in addition to self-disabling ego-dissolution work, there must also be an outside energy one connects with, an "other" on which "luck" is contingent. (Not really "luck" then anymore I guess is it). love is another product of myself + you.

myself + you = luck / love

an equal ratio of these elements, for someone in love is lucky and vice versa, seemingly to an equal degree

The final part you elucidate is probably the most fascinating because it appears at first to turn the whole logic on its head.

love = myself - you

What I think this is saying, or getting at, is the importance of letting go, of surrendering that which makes one most complete. That human beings or forces ALTHOUGH they may complement one another and co-exist in a single orbit, as do electrons of an atom-- one is not made subservient to the other, one is not made solely for the other's pleasure. Now I'm aware this is entering into the realm of the philosophical, the why-are-we-here-and-seperate question? And I suppose it speaks to the inherent integrity of nature, the particles that solid matter is made from, always particulate, having their boundaries as does the earth, moon, dewdrop, etc. Just above the unified plain, what is visible to the most powerful microscopes. Might be expressed:

myself - you = integrity / love

I'm linking the image and post to my blog. Thanks again for your attention to the poem, opening its dimensions for me.


Thursday, August 31, 2006

Factorial By Scott Glassman

am a
quotient of the

i am
a quotient of

moon i
am a quotient

the one
i am a

of the
two i am

quotient of
the burn i

a quotient
of the dew


am a
multiple of the

i am
a multiple of

sea i
am a multiple

the birth
i am a

of the
tree i am

multiple of
the word i

a multiple
of the air


subtract myself
from you for

i add
myself to you

love i
subtract myself from

for luck
i add myself

you for
love i subtract

from you
for luck i

myself to
you for love


am zero
over you +

i am
zero over you

2 minus
0 over you

1 minus
0 over you

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.

Tuesday, August 29, 2006

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

Monday, August 28, 2006

art@IIT Upcoming Show

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

Saturday, August 26, 2006

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

Friday, August 25, 2006

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

Thursday, August 24, 2006

Tuesday, August 22, 2006

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

Monday, August 21, 2006

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)

Sunday, August 20, 2006

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.

Thursday, August 17, 2006

Wednesday, August 16, 2006

Monday, August 14, 2006

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

Sunday, August 13, 2006

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.

Friday, August 11, 2006

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!

Thursday, August 10, 2006

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?

Wednesday, August 09, 2006

Geof Huth's Mathematical Poetry # 2

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

Tuesday, August 08, 2006

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.

Monday, August 07, 2006

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

Sunday, August 06, 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.

Saturday, August 05, 2006

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

Wednesday, August 02, 2006

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.

Tuesday, August 01, 2006

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

Monday, July 31, 2006

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



Six Alone In

Zen Poems

About Karl Kempton:


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


Friday, July 14, 2006

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.

Visit the National Gallery of Writing