Showing posts with label Multiplication. Show all posts
Showing posts with label Multiplication. Show all posts

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

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

Wednesday, April 16, 2008

a+b+c Does Not Equal c+b+a

In Delancyplace's excerpt for 4/16/08 --as discussed by political advisor Frank Luntz, the sequential arrangement of information often creates the very meaning of that information:

"[In film, when] two unrelated images are presented, one after the other, the audience infers a causal or substantive link between them. A shot of a masked killer raising a butcher knife, followed by a shot of a woman opening her mouth, tells us that the woman is scared. But if that same image of a woman opening her mouth is preceded by a shot of a clock showing that it's 3 a.m., the woman may seem not to be screaming, but yawning. The mind takes the information it receives and synthesizes it to create a third idea, a new whole. ...

"The essential importance of the order in which information is presented first hit home for me early in my career when I was working for Ross Perot during the 1992 presidential campaign. I had three videos to test: a) a Perot biography, b) testimonials of various people praising Perot, and c) Perot himself delivering a speech. Without giving it much thought, I'd been showing the videos to various focus groups of independent voters in that order--until, at the beginning of one session, I realized to my horror that I'd failed to rewind the first two videotapes. So I was forced to begin the focus group with the tape of Perot himself talking.

"The results were stunning.

"In every previous focus group, the participants had fallen in love with Perot by the time they'd seen all three tapes in their particular order. No matter what the negative information I threw at them, they could not be moved off their support. But now, when people were seeing the tapes in the opposite order, they were immediately skeptical of Perot's capabilities and claims, and abandoned him at the first negative information they heard. ... I repeated this experiment several times, reversing the order, and watched as the same phenomenon took place. Demographically identical focus groups in the same cities had radically different reactions--all based on whether or not they saw Perot's biographical video and the third-party testimonials (and were therefore predisposed and conditioned to like him) before or after the candidate spoke for himself.

"The language lesson: A+B+C does not necessarily equal C+B+A. The order of presentation determines the reaction."

Dr. Frank Luntz, Words that Work, Hyperion, Copyright 2007 by Dr. Frank Luntz, pp. 40-41

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