Wednesday, January 21, 2009

Ed Schenk Predestination / Karma / Reincarnation


The following text are expressions by the Dutch Mathematical Poet, Ed Schenk

Predestination / karma / reincarnation

Some agnostics define death as:
death = life – life axiom 1)

In many religions the believe is there is something after or above death. This could be written as:
death ≠ 0 axiom 2)

Now if axiom 1 and axiom 2 are simultaneous valid, this leads to the postulate:
life ≠ life

This looks contradictory, however if we introduce the element time, axiom 1 could be written as:
death = life(n+1) – life(n),
where n is the current life. Moving variables yields: life(n+1) = life(n) + death. This could be written as:

next life = this life + death (predestination)

or

this life = next life – death This formula looks a bit strange, however this is due to semantics. If we take into account that time is not necessarily linear we could replace the word ‘next’ by the word ‘another’.

This leads to: this life = another life – death (karma)

Monday, January 19, 2009

Mathematickles by Betsy Franco


Mathmatickles by Betsy Franco
I would like to speak a bit about the book Mathematickles by Betsy Franco. The book is a wonderful collection of Mathematical Poetry showing addition poems, subtraction poems, long division poems, and multiplication poems. What I find refreshing about the poems is that they are constructed in a way that you can tell that Franco knows the difference between addition and multiplication in Mathematical Poetry for these poems are obviously not thrown together without thought. This may not seem like a big deal however, I find a lot of confusion about this topic among some intellectuals much less the general public. I think this book is an outstanding book for teaching young students how to use math as a language and have fun doing it. I would recommend it to all primary school teachers who are teaching math.

About Betsy:
Betsy Franco, a writer and a member of Suburban Squirrel comedy troupe, has written over eighty books-young adult novels, picture books, poetry, and nonfiction. A graduate of Stanford University, with an M.Ed from Lesley College, she particularly loves to show people how sassy, beautiful, and creative math can be. Her latest book is Bees, Snails, and Peacock Tails about geometry in nature. Mathematickles, also published by Simon & Schuster, was inspired by Bob Grumman's mathemaku and long division poetry. Metamorphosis, a novel illustrated by her son Tom, is forthcoming in fall 2009.

To give young adults a voice, she has compiled four anthologies of their work including: You Hear Me? poems and writing by teenage boys, and Falling Hard, 100 love poems by teenagers, published by Candlewick Press.

Betsy lives in Palo Alto, California, with her husband Doug who shares her interest in math. They have three creative sons, James and Dave (actor/writers) and Tom (sculptor, illustrator). See www.betsyfranco.com.

Saturday, January 17, 2009

The Long Division Poem

I would like to introduce the long division poem structure to this blog. The structure has been used for quite a few years primarily by Bob Grumman. It is similar to an orthogonal space poem with the exception that it uses a remainder. Because of its simplicity Betsy Franco and others including teachers have used it to help children play with mathematical ideas in the form of language. I think this is an excellent way to give children a fun way to play with poetic ideas and at the same time introduce them to the idea of applied mathematics. Here is a Christmas poem and one of my favorites by Bob Grumman:


Thursday, January 15, 2009

Joint Meeting of the American Mathematical Society and Mathematical Association of America Conference 2009


This blog entry is to share a few moments and images of the AMS and MAA Joint Meeting held this year in Washington D.C. The first lonely image is a view from my hotel room bed as I tried to get to sleep by counting the sheep jumping over the Washington Monument. The weather for the most part was cold and rainy and made my three-quarter mile walk to the conference a little trying at times. However the last day was nice and offered the image below which was shot from my hotel room window as the sun was rising in the east.

The shot below is a 180 degree panoramic view of 21 images sewn together to provide an overview of the entire show of mathart. The show is always modestly done due to its modest budget (relative to art galleries) but it is always done well and the people who work on it are wonderful enthusiastic individuals who feel mathart can make a difference. They even gave out prizes this year.
The shot below is of the past president of the Mathematical Association of America, Joseph Gallian as he was browsing the show.

Speaking of browsing the show … The next image (below) is of our friend Ivars Peterson who writes about mathart for many publications including Science News.

From left to right: Reza Sarhangi the nucleus of the Bridges Conference on mathematical connections in art music and architecture , Annette Emerson, the Public Relations Officer of the AMS and Anne Burns, one of the Judges for the mathart exhibit and webmaster for the mathart exhibit webpage.
The next image is of Robert Fathauer who curates the mathart show each year and also owns and operated Tessellations a company devoted to selling objects that inspire the math aesthetic.

Here is Nat Friedman and one of his knots displaying a minimum surface by spanning a soap bubble film across the knot. Very interesting and simple stuff showing complex concepts.

The next image is of Reza Sarhangi with Arthur Benjamin who happens to spend a lot of time on stage racing calculators … I have seen him in action and yes, he can calculate in his brain faster than you can calculate on your hand calculator. Check out this video.




JoAnne Growney and Sarah Glaz recently edited an anthology of mathematical love poems titled “Strange Attractors”. The book was published by AK Peters and can be seen in the above photo at the bottom right of the image. Also in the photo are Klaus Peters (left) and his lovely wife Alice (Thus AK). The conference also provided a poetry reading session to deliver poems from the book. The event was organized by co-editor JoAnne and you can see the crowd gathering for the reading in the image below.





In the image above you can see JoAnne standing and speaking to the crowd and Sara sitting and listening (lower right). The image below is of fellow mathematical poet Bob Grumman as he delivers one of his long division mathematical visual poems.




The image above is of me delivering my poem "Prometheus's Epistle to Job"

Here is a link to a review of the poetry reading by
Karren Alenier.

Kempton's Mouth

Karl Kempton has expanded his mathematical paradigm poem “My Big Mouth” into a polyaesthetic series show below. Very nice Karl! I especially like the last image which I would love to see at the bridges show in Banff this summer.










Friday, January 02, 2009

Kempton's View

Karl Kempton has sent me a paradigm mathematical poem (above) in response to the last two blog posts; so let's look at it. The image shows the volume of a ellipsoidal solid with the three ellipse radii defined metaphorically. The first radii is a value of "lack of forethought" and the second being an radius of "ego" and the last radii being the ratio of "attachment" divided by "humility" and all of this is equal to "my big mouth".

Thanks Karl for illuminating my problem :)

Thursday, January 01, 2009

Primitive Clarification


I am sure that most of our general population will find this discussion pointless but those interested in language, visual language and mathematical poetry should not. We use addition and multiplication in our language everyday but most are not aware of it. I think a person could spend their entire life devoted just to the concept of exploring the ideas presented in this one blog post (I am serious). We are just scratching the surface of the possibilities with our few examples shown in this blog. It is not trivial to ponder the differences in addition and multiplication for they are crucial to our existence through our everyday decisions. However, I can agree that in mathematical poetry we are taking these operations into the nebulous areas of art and art aesthetics. Numbers are clear and easy to manipulate with mathematical operations however, extrapolating them into the realm of images or concepts is much more difficult and it is even more difficult to say something new and interesting with it.
This blog post is an extension from my last post where I was trying to clarify the difference between addition and multiplication in the context of mathematical poetry. The best way to approach this is to start by viewing the blog entry which lays it out pretty clearly. This blog entry is devoted to clarifying a visual mathematical poem which was posted on the blog for the artpolice. The visual mathematical poem on his blog (above) was executed in the form of three paintings and it is show in my last blog post. I realize that the interest of the artpolice and his band of followers due to the paintings being fraudulent copies of other works (I will take his word for it). I find this interesting and there seems to be a lot of controversy surrounding it as well however I am more interested in the exploration of the visual/math principals.
Our example (above) in this blog post concerns the three images in the original work found at the blog of artpolice. (which seems to have disappeared) My original statement was that the images are an example of using multiplication in mathematical poetry as opposed to using addition. What I have done here is to show the work corrected with the proper operational sign and also create a little piece showing a solution to the problem if indeed it were done with addition.
The Image below was submitted by the math poet PI. O. --- He obviously knows the difference between addition and multiplication of images as well as the artist Tisa Bryant. Thank you PI. O.!



This wonderful image is a work by Tisa Bryant, titled "Slave Lady" and will be part of the show:

WHEN DOES IT OR YOU BEGIN? (MEMORY AS INNOVATION)
Festival of Writing, Performance, & Video

JANUARY 9 – FEBRUARY 1, 2009
Curated by Amina Cain & Jennifer Karmin
at Links Hall
3435 N. Sheffield Avenue
Chicago, IL

Saturday, December 27, 2008

Me And My Big Mouth





Me And My Big Mouth
Well I have to confess that I have been a bit ornery. I ran across a blog that was discussing the painting shown above. I thought I would try to stir things up a bit and drop in the comment that the math was wrong and that it should have been multiplication as opposed to addition. This created quite a stir among this group of rowdy folk at the art police blog. You may want to follow it back to see their musings after I dropped the comment.
The text in green below is a response to my comment from the art policeman and my response to him is in white.

Kaz said:
"Well, I hate to be the mathart police however, the math is wrong ... it should be multiplication and not addition.

How can it be wrong when it was never right in the first place?

It is true that there is no 'correct' art however there is correct and incorrect mathematics. This is why you called up your mathematical art equation department ... you just didn't realize it was me. (I guess it was presumptuous of me to show up)

Well, the art at least that is....
But for the sake of even more pointless argument.
And you really have not argued a thing you have just brain-farted your opinion and have not backed it up with a damn thing. Have you?


You are correct that I didn't give you a direct hint Furthermore; I should not expect you to dig through my blog to find a hint so I owe you an apology and I will now supply the link to help with our discussion if you are so inclined. (Here it is)

So let us at least show you Kaz Mashorseshockey how to argue.
Here we go-
Are we not dealing with three paintings here in this particular equation?
Only three, so therefore if the factors were to be multiplied as in repeated addition, as you suggest, then the two said factors would result in a product of a multiple of the two.


I see your last statement being basically correct. Although, repeated addition is not how I would describe this situation within this context.

Unless the two factors were exactly the same then they would result in the same product,

Well the last statement seems to indicate that you think that 4 x 4 = 4 and not 16 … I doubt that was your intention so we are not clear here.

or if one factor was zero, then the resulting product would be zero or in this case no painting at all(which is what they should be in a perfect world)...that zero being the no product.

Again I see this last statement being correct.

However in this case we have two singular images resulting into another singular image and that clearly can only be stated in an equation of addition.
1painting + 1painting =2painting
or #1painting + #2painting =#3Painting
If it was a multiplication problem, as you Kaz Matdingdong have suggested , we would result in
1painting x 1painting =1painting
or #1painting x #2painting =#2painting


Here it seems that you are not making any sense for it seems that you are saying that the statement, "4 + 4 = 8" is a valid equation yet "4 x 4 = 16" is not valid or maybe you are trying to say that 2 x 4 = 4 which of course is not true mathematically furthermore, this is not the case in the artwork for the second image from the painting is not the same as the product image(Obama) -- I am not following your logic here.

Either way you look at it, and obviously you didn't, The multiplication scenario does not fit.

Maybe you can look at this again after checking out this blog post . Your comments would be appreciated.

We here at The Art Police feel you are horribly wrong in correcting us, so therefore you, along with our fine art friend from NC Karen on the other blog, have failed in trying to insult the intelligence of The Art Police.

You have misunderstood my correction for it was not to insult anyone I just thought that I would have some fun and stir things up at bit and try to get some discussion concerning the problem of addition and multiplication in math poetry. However I really didn't mean to give poor 'whirley gig man' a reoccurring nightmare from his high school days. And if he really knew me I think he would like me because I have more in common with him than he realizes.
Again my intent was certainly not to piss anyone off … Whirley gig man was right … I was just farting around … I just didn't realize it stunk so badly.

YOU Kaz Matahoowy FAILED!
And you will be added to our ART POLICE TIOI(Trying to Insult Our Intelligence) list of

Top That Killer!

We do appreciate your appreciation for Mathart and do encourage you keeping up with your craft.


I appreciate your appreciation and you will notice that I purposely have avoided talking about art in this blog post and especially the art aesthetic used in the painting.

Cheers Mr. Policeman

Friday, December 19, 2008

See the Mathart show in Washington D.C.


Here is the link for the mathart show in Washington D.C. this January. You can see the variety of work from the links presented. The image I chose to show (above) is titled:
“A Strange Dream”
Oil crayon on paper, 20" x 24" (framed), 2008. "

The work is by Karl Kattchee, Associate Professor of Mathematics, Mathematics Department, University of Wisconsin-La Crosse, La Crosse, WI

Professor Kattchee says, "I generally work in the abstract and typically with oil crayons or pencil on paper. Each drawing has an internal logic, mathematical in nature, which usually evolves while I work. My mathematical instincts urge me to keep the internal logic consistent, but my artistic side wants to bend the rules. The soul of my drawings is the balance between the two."

Tuesday, December 09, 2008

Prometheus’s Epistle Nominated For A Pushcart Prize In Poetry




I am extremely grateful and happy to announce that my orthogonal space poem “Prometheus’s Epistle to Job” was recently nominated for a Pushcart Prize in poetry by the poetry journal ZYZZYZVA.

Here is the Anouncement by ZYZZYVA - I see their blog has been moved or deleted - Here is my original letter from them


Friday, December 05, 2008

Michael Sussna show in Carlsbad California


Tonight I went to the opening of my friend Michael Sussna at the New Village Arts Theatre in Carlsbad California. There were 21 pieces curated by Laura Kurner from the Theatre. All of Michaels Images were done with Ultra Fractal Software and more can be viewed at his website. If you get a chance to see the show you can check it out at the address below.

New Village Arts Theatre

2787 State St
Carlsbad, CA 92008
(760) 729-8747

Wednesday, December 03, 2008

Binoy Majumdar



My friend Anand Bora has turned me onto the late Bharat (India) poet Binoy Majumdar. Today I have selected Three mathematics related poems by that were taken off of the website at this link. These were translated into English by Aryanil Mukherjee


flowers have no room for geometry or even its traces
they are all mixed up into a singular mess
geometry makes the landscape
all those lines we use in poems

from time immemorial have these poems existed
like serene mathematics
lying in an unseen corner
awaiting discovery this autumn evening
in the Bakul grove under faint moonlight

length, weight and time - these three worldly units
are talked about too often
like there's nothing else in the can...
also a unit that measures light, or
how audible are you could be measured too
in our world, man-day is another unit

Tuesday, December 02, 2008

Reality?



Mathematics is not the foundation of reality.
Reality is the foundation for math.

Sunday, November 23, 2008

“Strange Attractors” Poems of Love and Mathematics


Sacrifice and Bliss by Kaz Maslanka(below)

Mathemaku No.10 by Bob Grumman (below)


I just received a copy of “Strange Attractors” Poems of Love and Mathematics. Furthermore, I was fortunate and honored to have my poem “Sacrifice and Bliss” published in it. The book is edited by Mathematicians and Poets, Sarah Glaz and JoAnne Growney. It is full of many traditional language poems as well as a few mathematical poems of the flavor seen in this blog. One is “Mathemaku no. 10” which I believe is one of Bob Grumman’s better long division poems.

I do want to make a comment for the record. Unfortunately there was a typo in the contributors notes whereby it mentions that Kaz Maslanka believes that mathematics is “the” language of art. It should have said that Kaz Maslanka believes that mathematics is “a” language for art. All that aside it’s a great book and it’s time to order your copy.

Saturday, November 15, 2008

The American Mathematical Society has accepted “The Empty Paradox”



I am grateful and honored that the American Mathematical Society has accepted “The Empty Paradox” to their annual art show which will be held in Washington D.C. this year. (To see The Empty Paradox click here)

Sunday, November 02, 2008

Bernar Venet in San Diego

The photo above is Bernar Venet and me.
    When going back and re-reading the section about Bernar Venet in Ursula Meyer’s book on conceptual art, I was fascinated again from the statements that the young Venet made in 1971. He presented math and physics not as art but as knowledge. I remember reading this in 1978 while studying with Robert C. Morgan and saw this work to be exciting yet I was confused by the idea that physics could be presented as art. Eventually, I focused on what his statement explicitly said and I separated the aesthetics of Physics from the aesthetics of art. Even though Venet did not directly take these different disciplines to have different aesthetics I eventually read them as such and focused on separating, understanding their differences, and then putting them back together (polyaesthetics) in a single context as in my physics paradigm poems.
    We are fortunate enough to have had the Scott White Gallery here in San Diego bring 13 pieces of Venet’s sculptures here to San Diego to be viewed for a year in certain urban locations of San Diego as well as along the waterfront of the bay. The image below is a photo I shot of one of the sculptures.

Thursday, October 16, 2008

Dog Dream Accepted for SDPUG


The polyaesthetic piece, "Dog Dream" has been accepted for the SDPUG group show at the California Art Institute in San Diego, California.

Art Institute of California - San Diego
7650 Mission Valley Rd
San Diego, CA 92108-4423

Map Quest:

http://www.mapquest.com/maps/map.adp?country=US&addtohistory=&formtype=addre
ss&searchtype=address&cat=&address=7650%20Mission%20Valley%20Rd&city=San%20D
iego&state=CA&zipcode=92108-4423

The opening reception is this Friday, October 17th from 6 to 8pm.


Who is in the show?

Thursday, October 09, 2008

ZYZZYVA Fall 2008


Kaz Maslanka’s Orthogonal space poem titled “Prometheus’s Epistle to Job” has recently been published in the latest edition of the West Coast Poetry Journal “ZYZZYVA”

Friday, October 03, 2008

Show at the Bonita Museum


Kaz Maslanka’s artworks titled, “The Empty Paradox” and “Temptation” will be part of “Urban Legends and Country Tales” an international Juried Art Show at the Bonita Museum - Oct 4 to Nov 15
The opening and public reception for Urban Legends and Country Tales will be 6 to 8:30 pm on Saturday, Oct. 4th. Admission is free to the Bonita Museum, 4355 Bonita Road, Bonita CA 91902. Hours are 10:00am - 4:00pm - Wednesday through Saturday. For museum information, contact Vicky DeLong, Museum Director, 619-267-5141.

Friday, September 05, 2008

What Is The Difference Between Multiplication And Addition In The Context Of Mathematical Poetry?

Before I talk about addition and multiplication in mathematical Visual Poetry I would like to present the following two paintings by Giorgio De Chirico. These were created in the beginning years of the 20th century.




     When I was visiting the inner harbor of Baltimore, Maryland I came across a most interesting tower. I later found the name to be "The Shot Tower". (Below)


      As you can see, it is tall, cylindrical and has a little flag on the top of it. It reminded me of the towers I have seen in many Giorgio De Chirico paintings. I only included two painting here in this blog post but, there are many more that can be found in art history books.
     So I got the idea to take it into Photoshop and turn the scene into a De Chirico-ish image.
I titled the piece: “THE QUESTION OF DE CHIRICO” and it poses the question: “Is the image on the right side of the piece equal to the ideas of Baltimore times De Chirico or is the image equal to the ideas of Baltimore plus De Chirico?



In my original post on this 'kogwork' I received a couple of responses that proved to me that it is an interesting question and the answer is not as esoteric as one might imagine. I will display and discuss the responses at the bottom of this blog entry.
     I gave a lecture on Polyaesthetics and Mathematical Poetry last year at the Salk Institute and within the boundaries of my presentation I had a section that addressed this very issue.   From that lecture I am going to borrow a few images to help illuminate this most interesting idea. Let us think about the equation 3 + 4 = 7 and let us look at a pie chart to help illuminate our quest. When we add 3 and 4 together we can distinctly see the separate pieces within the pie as well as seeing the entire seven pieces. (Shown below)

The Bottom line is that it is easy to remove the 3 slices or the 4 slices from the mix of 7 Now let us think about the equation 3 x 4 = 12 When it comes to multiplication our task gets a little trickier tracking where the numbers 3 and 4 end up (visually). The difficulty is due to them get integrated into each other to produce the number 12. It is though they form an augmentation from which each other play a part in constructing. If we look at a pie chart again we can see that the 12 pieces can be viewed as 4 groups of 3 or we can view it as 3 groups of 4. Both numbers influence the whole in their own way. Above we have 4 groups of 3 to yield the product of 12 Below we have 3 groups of 4 to yield the product of 12 So what we see is that the multiplier and the multiplicand both augment each other to produce the product. So how does all of this relate to mathematical poetry? How can we multiply concepts or even images? Let’s look at the next image titled "Americana Mathematics" and analyze its components. We see an the popular American icon depicting a NASCAR racing machine added to an 8 ball from the game of pool to yield a strange vehicle that is part race car and part pool table. Here in this example as in our pie chart we can see the two concepts added in such a way that it would be easy to pull them apart and break them out of the whole. The two concepts can be clearly separated in addition however; in multiplication it is again trickier. Let’s look at 8 x 8 = 64 Here again we can refer back to our pie charts showing how the multiplier and multiplicand each augment the other idea to create a whole that possesses much more amplitude than the originating two concepts. Here our product is not a race car but a rocket ship that is obviously involved in some sort of pool game. Now that we have the tools to understand the mechanics of this artwork we can then spend our time experiencing the interacting metaphors involved to come to our understanding of the signified. I now want to post two responses to the original question of De Chirico from the blog entry on August 7, 2008. The first being from the Math Poet TT.O. The text in Blue is from TT.O. and the text in white is mine My attempt at a solution to the difference in addition and multiplication in mathematical poetry is as follows:----- As the difference in nomenclature suggests, the above problem of A+B=C and A*B=C may be a issue of semantics, and in the case of "mathematical poetry" the said equations NOT equal. Consider One: A + B = C may mean let A abut B i.e. let image A physically touch image B, a kind of concatenation, a bringing together. Which would then go on to suggest that A + B = C1, and B + A = C2 since A + B ≠ B + A, and as their relative positions read from left-to-right would imply, the bringing together would result in an AB versus BA result. Notice that the collapse into a visual representation would suggest a kind of visual multiplication. I want to add for any mathematicians that are reading this -- when he says A + B ≠ B + A we all realize that this is definitely not true in pure mathematics however, it is debatable within the context of mathematical poetry due to syntax having some bearing on the results. From my perspective the influence of syntax is minimal when performing addition, although, I am willing to listen to all arguments. I will say that syntax is more important with multiplication. One can see the importance within the recent post I made called a+b+c does not equal c+b+a in this post our attention is brought to a problem with the order in which one experiences a phenomena. The author titled his observation a+b+c does not equal c+b+a however I believe that he should have realized what he was performing was multiplication not addition. Consider Two: A * B = C may depend on how it is read i.e. a issue of semantics (again) i.e. the number to be multiplied is called the "multiplicand", while the number of multiples is called the "multiplier". Perhaps this is better seen in the following equation A ( B + C ) = D. Here, the multiplier is A while the multiplicand is (B + C). The semantics of the equation would then suggest that ( B + C ) A ≠ A (B + C) in mathematical poetry, since it would depend on which was the multiplicand and which the multiplier, and in what order they were being taken to be (or read) i.e. what was to be infused by what, or what was to be increased by what i.e. a kind of what is being "acted on" (passive) and what active. Here TT.O. has provided a good argument to warrant attention being paid to the syntax of the equation within the context of mathematical poetry. However, there could be an argument that within the realm of pure math syntax makes no difference and therefore the poet needs to create his/her metaphor to reflect this mathematical truth. In other words make the product reflect an equal amount of the conceptual essence of the multiplier and multiplicand. From where I stand, in the equation A + B = C, A cannot infuse into B (or visa versa), but can only stand-by it. Multiplication, in the equation A * B = C, on the other hand (to carry on the metaphor) "impregnates" B but not visa versa. I don't understand your poem properly, because I don't understand the basic essence of De Chirico's work (i.e. a specific painting???) or who or what Baltimore is i.e. a City? An Artist? An attitude? However, I would suggest that Baltimore × De Chirico is different from De Chirico × Baltimore and different to Baltimore + De Chirico, and De Chirico + Baltimore, and that we should be mindful of it in our equation making. TT.O. I want to thank TT.O. for commenting on “The Question of De Chirico” and I must ask forgiveness for not explaining that the image is one of my photographs of a tower that resides on the inner harbor landscape in downtown Baltimore, Maryland USA. I modified the image to be in the style of the twentieth century painter Giorgio De Chirico. (See Google) Here is a few excerpts from a response from Todd Smith: Here's my take on it: The painting on the right seems to fit the style of the painter Giorgio de Chirico, so I assume that it is his work. If this is the case, I would vote for the equation: de Chirico (Baltimore) i.e., multiplication. Multiplication implies a combination (almost a mixing of two elements) and it generates something more than the sum of the two entities being combined. I would suggest that a snap shot of de Chirico with Baltimore in the background to be represented by the equation de Chirico + Baltimore. But a work of art produced by de Chirico in which Baltimore is featured would mean multiplication to me. The painting is as much de Chirico as it is Baltimore. The two are inextricably intertwined. Multiplication seems to be a more complex combination than addition to me. Two spools of thread might be added together when placed in a shopping bag, but they would be multiplied together if they were woven into a shirt. Here is an image (above) which illustrates Todd's idea of a mathematical weave between two axes. The image is titled "Distance" and it uses the distace equation: Distance = velocity multiplied by time. Also, addition seems to be one-dimensional, while multiplication seems to create two dimensions. Addition happens along the number line, while multiplication can be graphed along the x and y axis. They say you can't add apples and oranges. In addition you have to find a common denominator before you can add. This implies the number line again. As soon as two things are on the same dimension they can be added. For example, de Chirico and Baltimore are both physical things and so they can both be photographed together and said to be "added together" in the picture. But with multiplication there is less restriction. You don't need a common denominator to multiply two things. The combination creates something new that is not merely more quantity of a common denominator. In pure mathematics 3 x 4 creates a rectangle of area 12. Before there were only lines (one dimension), after multiplication there is area (two dimensions). New space is created. In the example of de Chirico, Baltimore x de Chirico created a new vision of Baltimore colored by de Chirico's own inspiration. No one had seen Baltimore in quite the same way. It is as if a new dimension was opened when these two were combined. Well, I didn't plan to write this much, but it's fun to think about. Thanks, Todd

I also want to thank Todd Smith for his wonderful comments as well. I think the point that we all would like to assert is that this idea of adding and multiplying images (or concepts) is easy to understand. I would love to see more from everyone out there.

Thanks. Kaz

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