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

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

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.

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

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

Happy Halloween!

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!

Thanks!

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

Allen L Roland -- EQUATION FOR LOVE AND WORLD PEACE2

I would like to thank the young lady by the name of Tifinie who sent me the link to a ‘myspace.com’ 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 allenroland.com. 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.

--Kaz

E=mc² / A NEW MATHEMATICAL EQUATION FOR LOVE AND WORLD PEACE

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.

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.

ONLY LOVE HEALS

Allen L Roland

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.

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

The History Of Numbers

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

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.

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

On Thu 7 Sep 2006 (21:46:48 +0100), guy@steelpillow.com 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:>http://plato.stanford.edu/entries/geometry-finitism/ 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?

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.

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:

Kaz,

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.

Scott

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