### 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.**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