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