Saturday, August 26, 2006

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.