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

Sherrill's Music

The similar triangles poem above titled Sherrill's Music is inspired by Robert Sherrill's 1970 book titled "Military Justice is to Justice as Military Music is to Music"

A Math Art Moment #12

In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it’s the exact opposite. —Paul Dirac

To see more delineations click here

The Lotto

Here is a polyaesthetic piece of mathematical visual poetry based on the similar triangles poem titled “LOTTO” The photo was shot in Las Vegas. The inspiration for the piece came while being part of a shared "lotto pot" in an office setting. Watching all of the people fantasizing about winning was fascinating.

The poem can be read multiple ways including the following:

The lotto is to financial fantasy as ogling pornograpy is to sexual fantasy. 

-or-

The lotto is to ogling pornograpy as financial fantasy is to sexual fantasy.

Math Test Results (Math Jokes)

Kevin Watters sent me a few math jokes the other day and I thought it may be nice to share them. ------------------------------------------------------------------------------


This is pretty close to being visual mathematical poetry. The student is probably a fine art major and got lost in his/her own thoughts --- why answer the question when you can be creative?
:)

You would think the student would get some extra credit for this ... ok maybe not.

This student deserves no extra credit.



I know this feeling.

Freshness

Here is a Polyaesthetic piece with a 'Similar Triangles Poem' titled "Freshness"

The Question of De Chrico

I have noticed many small mathematical poems on the internet that are in the form of A+B=C . This form is a perfectly legitimate form however, there are times when I think the author intended you to understand it in terms of A*B=C . There is some confusion as to what is the difference between addition and multiplication within the realm of mathematical poetry. I would love to hear anyone try to explain the difference between the two. In the mean time I have posted a piece above that asks that very question.

The piece is titled: “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?

I invite anyone to choose between the two statements and explain why and I will post the answers.

The King's Crown

Here is another Similar Triangles Poem entitled "The Kings Crown"

Natural Selection

This entry is a polyaesthetic piece titled "Natural Selection" the structure of the poem inside is a similar triangle poem.

Read Me First

Read me first

In this section of the side bar there are four articles.

The first article is a paper that was published in the journal of mathematics and the arts titled “Polyaesthetics and Mathematical Poetry”. This paper is a good introduction to Mathematical Poetry for it shows some of the main ideas as well as some techniques used to create mathematical poetry. One of the more important ideas it addresses is that of mathematical metaphor. The paper addresses basic theory as well as providing examples.

The second article is a paper published in the 2006 Bridges Proceedings titled “Verbogeometry, The confluence of words and analytic geometry” This paper explains the mechanics of how mathematical poetry can use Cartesian space as a medium for words. It provides examples of analytic geometry as well as the mathematical poetic counterpart.

The third article is an interview published online at word for/word a journal of new writing. The interview was conducted by poet/theoretician Gregory Vincent Thomasino and is formulated in three groups of questions. The first group of questions is about the influences of Kaz Maslanka and the second and third address mathematical poetic theory.

The forth article is a list of terminology that is related to the area where the arts and mathematics meet.

Substitution in Mathematical Poetry

Substitution in Mathematical Poetry

If you have no understanding of similar triangles poems then please read about it at the following link: “Similar Triangles Poem”

This Blog entry will show an example of substitution in mathematical poetry. Substitution can occur when we have two equations that have a common term. For example let’s look at the two equations which have the same form as two similar triangles poems: A = BD/E and A = HJ/U since both equations have the term ‘A’ in common and consequentially they both happen to be solved for ‘A’ then we can set both equations equal to each other as such:

BD/E = HJ/U

We know that we can solve for any of the variables in our new equation and get a new equation in terms of one variable. Let do so and solve for ‘J’ so we now have: J=UBD/EH

So now let’s apply what we have just witnessed to two similar triangles poems.

First of all we must look at the following two poems.

We know from our earlier example that we can solve a mathematical equation for any term in it. If we take the first poem and solve it for “my memories” we then can present the poem as:

Notice (below) that we have the two poems solved for the same term (my memories).

Now we can set each poem equal to each other because they both have identical terms. (see below)

We also know that we can solve this poetic equation for any of the terms in it. So let us solve this poem in terms of “Delaware River”

Now we can see that the later poem was derived from the two similar triangles poems shown at the top. What is interesting is that all of the logical processes used to create the first two poems are contained in our resultant poem including the subtle differences in the contexts of each initial poem.
Substitution can also be used in poems created by different poets as long as they have a common term. Follow this link to collaborative substitution poems.

The following polyaesthetic piece uses the image of a shipping beacon located at Cedar Swamp on the Delaware side of the Delaware River. The full Delaware River Poem from our example is nestled in the lower left hand corner of the image. The physical size of the digital image is 67” x 31”

Delaware River Correction

I actually made a mistake on my last blog entry. I meant to post the two similar triangles poems (above). If you were on your toes you would have noticed that the last blog entry was actually the same equation (poem) solved for different terms. Today’s entry is two different poems that also share a common term. What is interesting is what we will do with these two poems on the next blog entry. Can you guess what I will do?

Delaware River Memories

Here are a couple of similar triangles poems inspired by a romantic encounter around ‘Cedar Swamp’ on the Delaware River. Notice that they both have one term in common.

My Response To a Critic

I would like to address a comment made in reference to the piece “Peano’s String; A History of Spiritual Stories”(displayed above) … the following (text in green) is a copy of a comment from my blog entry “New Work Accepted At The Bridges Show In Leeuwarden Netherlands Aug 2008”:

This is a strange place. Im all for maths, dont get me wrong. Anyone who's any good at maths needs to make it part of themself but democrats? Abraham? maths is made a cliche with these comparisons. Everything can be expressed in maths but some things shouldnt. Just make a billboard with euler's formula

My response:

I appreciate you giving me some feedback to my blog and I would love to engage you in discourse on any concerns that you may have. I am certainly not going to imply that I am always correct in my assumptions of anything. Furthermore I consider myself a student.

I want to note that I may not defend mathematical poems made by others so if you wish to criticize the axiomatic poem concerning Barack Obama and the democrats you may wish to address your concerns to its author. I also wish to make this same disclaimer concerning any mathematical poetry posted on this blog that is not authored by me. However, I will be happy to address any concerns or criticism involving my work. My Job at this blog is to promote interest in mathematical poetry not criticize it. Yet, I may someday express criticism of someones work if I feel “the discipline” of mathematical poetry is being subverted.

To get to your concerns let’s look at the term cliché and what Wikipedia has to say about it:

A cliché (from French, pronounced [klɪ'ʃe]) is a phrase, expression, or idea that has been overused to the point of losing its intended force or novelty, especially when at some time it was considered distinctively forceful or novel. The term is most likely to be used in a negative context.

It seems that you have applied this term ‘cliché’ to my axiomatic poem titled, “Peano’s String; A History of Spiritual Stories”. So I can only assume that there is something about this mathematical poem that you would consider overused. It is hard to imagine that you may be referring to mathematical poetry in general since there is so little of it. What is it that is overused here? Is your concern related to my references to biblical history? Are you feeling that I have taken biblical references out of context in jest? I can only say that while I can see how one may find this mathematical poem humorous, the root of it can be taken very serious. Maybe, what you may really be trying to say, is that mathematical poetry is aesthetically trivial. This may be is a little more difficult for me to defend due to my belief that just because I find something beautiful I can never assume that anyone else would find it such. However, I do find mathematical poetry extremely beautiful especially in its use of dual aesthetics. My fear is that you, or anyone else for that matter, will discard this entire proposition and never really answer the following questions.

1. From a cognitive scientific point of view what is a metaphor, what are the parts within the structure of a metaphor and what are their relationship to mathematics in general and mathematical equations in particular?

2. What is the difference between connotation and denotation and how do they apply to the language of mathematics?

3. When looking at the structure of a mathematical equation how does that structure relate to other phenomena that can be described with that same mathematical structure?

4. Are the commonalities between identical mathematical structures purely linguistic? Or are they physical?... Or maybe spiritual? Could there be something such as archetypical equations?

5. What are the differences between the aesthetics of mathematics and the aesthetics of poetry or art? How can those differences be delineated when analyzing a mathematical poem?

6. How does mathematical poetry relate to the history of art, poetry and applied mathematics? Can mathematical poetry be considered a legitimate field of applied mathematics?


And now let’s address this mathematical poem in particular:


7. What is the relationship of Natural numbers to linear historical events?

8. What do the descendents of Abraham have to do with current cultural events especially ones that concern the military of the United States of America? Who are the children of Abraham and what is the historical and spiritual relationship that they share.

9. How are cultural stories passed from generation to generation?

10. How are mytho-spiritual (religious) stories created? How does deities and deification come to be? What is the source of the ‘so called’ divine inspirations that create works of poetry and art? And what is their relationship to this piece of art in particular.

11. What is the relationship of cats in mytho-spiritual literature? What is the meaning of cat when applied to a human being? What is the meaning of a cat when applied to a God?

12. When looking at the proofs using these axioms what can be said poetically from the proofs.

13. What are the proofs that can be created from Peano’s axioms?

14. How do questions 7 through 13 relate to questions 1 through 6?

I am not going to discount that you may provide an argument to the idea that my work is cliché and trivial but I would hope you address the latter questions within your argument.

Thanks!

Kaz

The Gift of San Shin 산신 (Polyaesthetic)

Here is the Polyaesthetic version of "The Gift of San Shin" which utilizes a Similar Triangles Poem.

In the vernacular this mathematical poem can be spoken four ways but the two most important ways are: 1.) Wisdom is to Adversity as the Wind is to a Cage  2.) Wisdom is to the Wind as Adversity is to a Cage.  It can also be put into the syntax of an orthogonal space poem.   I like to think of the denominator of  orthogonal space poem as some kind of valve that controls the value on the other side of the equal sign. For example I like to look at the limit of "The Cage" as it approaches zero thereby making "Wisdom" near infinite. 

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General Music

Here is another “Similar Triangle Poem” Titled “General Music” Inspired by the differences in their philosophy of battle execution.

공의 옉 설 The Empty Paradox

Here is the Korean version of “The Empty Paradox” "공의 옉 설"

The Empty Paradox

Here is a new piece titled "The Empty Paradox"
C= Compassion and W= Wisdom
The Chinese character is 'Buddha's mind'
So we have C multiplied times W equals the limit of (1/x) as 'x' approaches Buddha's mind.

The equation is the familiar function of x equal to 1/x which yields a hyperbolic curve when graphed and results an asymptote when x = 0. Compassion multiplied by Wisdom is equal to 1 over X as the limit of X approaches Buddha’s mind. Buddhist philosophy tells us that Buddha’s mind is emptiness yet the philosophy also tells us that emptiness is different than nothingness or zero. In fact it is quite paradoxical for we are told that emptiness is very much something. This piece also uses visual imagery for poetic expression with Buddhist symbolism of flexibility and eternity represented by bamboo and pine trees respectively.

산신 의 선물

Here is the Korean version of the Similar Triangle Poem titled “The Gift of San Shin / 산신 의 선물

” shown in the previous post.