Mathematics and Poetry

Math G Kim Ly

Final Paper 11/25/02

"Mathematics speaks to the mind, poetry to the heart". (http://www.kavitanjali.com/pgmarch02/onpoetry.htm ), Finding the link between mathematics and poetry is a challenge. The reason for this is the fact that mathematics deals with reasoning, calculating, proving, and then resulting in one final answer; whereas poetry deals with rhymes, feelings, symmetry, and poetry always offers more than one solution. However, with the introductory quote above, a very interesting link can be drawn to connect two very extreme studies to be related together. This connection is made taking humans as a link between the two. That is, we use our mind to do mathematic calculations, we use our heart to express thoughts or feelings through poetry, and since our heart and mind are connected to each other, there should be a way to link mathematics and poetry together. Thus, with this research paper, I would like to go deeper into how poets and mathematicians were able to integrate the two studies together.

Math was not my favorite subject and poetry has always aroused interest in me. Ever since I take this Math G course as a liberal art class, I find that learning math does not have to be tied down with only calculations and intense problem solving. It can also be learned with a liberal art perspective.

From saying this, I decide to combine what I like a lot to something I don't really like and see how well one subject leads to a better understanding of another subject.

The poem below titled "Algebra One" written by poet Daphne N., Needham, MA, expressed how simple algebra can be. It lists out the general terms, formulas, and concepts that algebra has. In addition, it has a tone of humor in the poem. What I especially like is the similarity that exists between the poet and me. Because, just like myself, I had a hard time with math; I always get confused by looking at numbers and equations, but when I read this poem, I was able to get a very good overview of what algebra is about. The overview is explained in a very poetic way, which interests me very much.

"Remember all those rationals and irrationals, the ones we got confused?

I still get them wrong and I am not very amused.

Digits and decimals, too many D's

But wait until we start on those x,y, and z's.

Powers of 10 are expressed by exponents in many ways,

But, remember, there is only one and that is to have them raised.

Counting all those zeros makes me very crazy,

So use that scientific notation and don't be so lazy.

Collections of elements in sets are a breeze.

Elements follow a pattern just like 1,2, and 3's.

A variable is a symbol like x which has 1 value, not 2.

If you put the right variable in an open sentence, the statement will be true.

Factoring numbers can be such a bore!

But, prime numbers are the best since the factors are only 1 and itself, and nothing more.

Basic axioms of algebra leave you in awe,

But not to understand them is one major flaw.

The most important axiom is the distributive one.

It's the one we used the most, but it wasn't that fun.

Reciprocals are the numbers that always do a flip upside down.

Inverses are very different and in their own special way turn around.

Numbers are variables are jumbled disorderly,

Are called equations and are only solved algebraically

Solving inequalities can make you want to die,

But, there are only 3 choices: greater than, less than, or equal to, so there is no need to cry.

Polynomials can leave you in such a disarray,

But, just remember there are coefficients and constant terms and then you will be straightened out today.

Products of binomials can take you so long to do a few.

But, just skip the steps and use FOIL without a big to do.

Figuring out ordered pairs can leave you in such a mess.

But, if you remember the x-axis, y-axis, and origin, you'll do them with success.

Systems of linear equations can be solved in 4 different ways.

Substitution, addition method, determinants, and graphing with different rays.

The slope always equals rise over run.

If you remember this you'll always get those problems done.

Quotients of 2 polynomials are called Rational Algebraic Expression.

If you don't reduce them fully they will leave you in a great big depression.

Square roots and cubic roots leave me very puzzled,

But the index and radicand leave me troubled.

Square-free integers can't be broken down anymore.

They are like 2,3, and 5, but never integers like 16 or 4.

There are many other rules, guidelines and steps to Algebra 1

But, we still have Geometry, Algebra 2 and Analysis to continue the fun!!!"

From this poem, I like how they start off in the same situation as some people who have difficulty with math. Although really simple concepts and the simple differences between rational and irrational, sometimes I still get confused which is which. Next the poem mentions of the basis of algebra, that is in algebra, there are digits and decimals introduced together. Unlike in elementary math, where it is impossible to add a number with a letter, in algebra, it is possible. In algebra we also learn of exponential problems and using scientific notations. For example, if I want to multiply 10000 by 10000. It would be simpler to express this as 1 x 10^8. Moreover, sometimes learning math there are tricks or shortcuts. Instead of doing the regular multiplication problem, I can simply count the numbers of zeros in both of the numbers and conclude the exponent. So for the above example, there are 8 zeros therefore the scientific notation is 1 x 10^8. However, this only applies to some cases where the zeros are ending zeros and there shouldn't be any other numbers between the zeros.

One of the significant changes in the study of math is the understanding of variables. Although variables seem so mysterious at times since we do not know of its value or the number that it stands for, but it is of important uses especially when calculating an unknown number. Just as in reality, we sometimes have numbers in which we need to calculate for its unknown, therefore, the use of variables help make solving problems easier to understand. In the poem, it says, "If you put the right variable in an open sentence, the statement will be true." This means for example, we have an equation like 8x-4=20. If you can find a number for x, replace it, then calculate it, the number on both sides should be the same. If it is the same then the statement is true. Solving this problem, the value for x is 3.

Taking the study of mathematics and applying it to poetry, a lawyer from France by the name of Francois Viete had discovered that "the abstract nature of higher algebra depends on its symbolic language." (Miller, Charles, page 335) From this quote, I find that "symbolic language" also applies to poetry writing. Sometimes when writing a poem, feelings and thoughts are not expressed explicitly, but implicitly. Poets tend to use symbols or abstract description to portray what they see, what they feel, and what they think. In terms of mathematics, symbolic language signifies the use of letters or so-called variables to represent numbers. This similarity shows that both mathematics and poetry share the same notation of symbolic usage. Sometimes with symbolic usage, it makes the actual idea of a poem, or the actual concept of a math problem harder to understand at first if the reader does not have a clue of what the symbol stands for. However, if one is able to make a link between the actual concept and the symbolic representation, understanding comes easily.

Another point of this poem states that there is a pattern in mathematics. In comparison to poetry, poetry also has a pattern. Pattern makes a poem more stylish and interesting. Patterns in poetry consist of making each verse in the poem have the same number of syllables. Or patterns in poetry may consist of making each end word in a verse rhymes with the following verse. Thus, some poems bring about symmetry in its verses. Similarly when speaking of mathematics, an obvious pattern that comes to my head is the geometric series. Especially, when I consider the Fibonacci sequence, where 1,1,2,3,5,8, Ö are simply patterns established by adding the two previous numbers of the sequence to get the following number. Mathematics also involves symmetry. This is true when one works out a proof, or an equation as the one above. Taking the above equation as an example again, in order to test if x really does equals 3, one would need to replace x with 3, and so,

8 ( 3 ) ñ 4 = 20

24 ñ 4 = 20

20 = 20

Working out this problem, one would see how symmetry is incorporated into math problems. We start off the problem asymmetrically where the right and left sides of the equation are of different numbers. But to find if the equation is true or not, one needs to work the problem out and derive both sides to reach the exact same number, thus reaching symmetry. The above work shows that the equation is indeed true, since the left side calculates out to become 20 and the right side equals to 20 already.

It is believed that in art, people tend to seek pattern, repetition, and mainly symmetry. Taking this belief into account for the discussion of mathematics and poetry, through our observations and understanding, we do see that mathematics and poetry are in the form of art also. The other example of symmetry in mathematics is proof. "Mathematician seeks an elegant proof above one which demonstrates the same result through contradiction or examination of numerous cases." (http://kate.stange.com/mathweb/mathpoet.html) "He seeks the simple, the fundamental from which to build his great mathematical structures." (http://kate.stange.com/mathweb/mathpoet.html) From these quotes, I realize how mathematics is not simply developed. But they must be developed with "great mathematical structures." As the same with poetry, if one wants to have a good poem, one must develop a style and follow that style throughout. There are many ways of writing poetry. An easier version of writing poetry is called free writing, where rhymes and counts do not matter much, but the content itself does. It is up to the human himself as the poet or the mathematician to design and stylize the structure to make it as comprehensive and interesting as possible to attract readers or problem solvers respectively. The following quote is said by Kate Stange to clarify my point. "The artist or poet seeks a similar symmetry in many ways; the meter of poetry is a subtle counting, and the words chosen are a concise reflection of the experience of the poet. He seeks to give his poem a contained, elegant form, with verses and stanzas showing the inner symmetry of thought."

Continuing the discussion of the "Algebra One" poem, this poem also refers to the system of linear equations, inequalities, reciprocals, inverses, polynomials, binomials, roots, slopes and ordered pairs. From just this one poem, a quick overview of algebra was introduced. The way the poem was presented was amusing as it has some humor as well as some friendly comments in it. The tone the poet uses to write this poem centers on an audience whom are not so very fond of algebra. Thus I called this poem very friendly to people who dislike mathematics, because through this poem, it may have a positive influence on some of these type of people. It may partially reduce their hatred in the study of math knowing that there are other people on the same boat as them.

The poem summarizes that systems of linear equations can be solved using four different methods. They are substitution, addition method, determinants, and graphing. Reading this part of the poem sort of simplifies all those chapters in my textbook and gave me a concise idea of all the possible methods that can be used to apply to linear equation systems.

The poem mentions of graphing terms also. It refers to x-axis, y-axis, and origin as the key terms that need to be known to successfully create a graph for an equation. In connection to that, there's also the term of the slope introduced, which states how a slope is determined. "The slope always equals rise over run." This equals the concept of a slope where a slope is the change of y-axis over the change of x-axis. The "rise" is spoken in terms of the vertical change. And the "run" is spoken in terms of the horizontal change.

The poem talks about polynomials and binomials, reciprocals and inverses. It briefly gives you a guideline of the importance of these two concepts. I really like this poem because it sort of outlines the poem with the most basic and important concepts that algebra contains. I think it would be a very good introduction to all algebra classes to share this poem. Not only does it has some humor in it, but it also covers a wide range of terminologies and it discusses the most prominent methods that is used to solve the problems.

Poetry and mathematic are two very distinct topics, yet I find it very similar in its formation and structure. I think the understanding and interest in one may lead into a better understanding and interest in another. I think in general, when we learn something, if we are able to grasp some slight idea of just one concept of something which we like, we can very easily build on that concept and expand our knowledge. Similarly, if we grasp that patterns exist in mathematics, and we enjoy working with patterns, we can easily build our interest in it. I guess, for me, many times I just say to myself, I hate calculating, I hate working with numbers, I hate solving problems, I hate doing proofs. I never look at a math problem as a poem. But if I had looked at a math problem as a poem, I will see that calculating is essentially the same as finding a pattern in the poem, working with numbers is the same as counting the syllables of each verse, solving problems is essentially the same as finding its rhymes at the end of each verse, and doing proofs is essentially the same as finding symmetry in the poem.

Therefore, in conclusion, although it may sound impossible to combine poetry and mathematics together at first look, but if one was to look deeper into the foundation of mathematics and poetry, one will see that the two have many common perspectives. There was a quote that states: "Mathematics is poetry to one who understands." (http://www.kavaitanjali.com/pgmarch02/onpoetry.htm) And another quote states: "For a person who does not read poetry or knows mathematics, much of the world is hidden from view." (http://www.kavaitanjali.com/pgmarch02/onpoetry.htm)

Indeed, the knowledge of both poetry and mathematics combined brought about a realization that no matter how different two things may seem, there still exists some kind of unique link between the two.

References:

Website on the Internet:

1. http: www.teenink.com/past/1990/668.html

2. http: www.ugcs.caltech.edu/~eveander/poem html

3. http://members.aol.com/LooseTooth/poem.html

4. http://teachers. Net/lessons/posts/617.html

5. http//kate.stange.com/mathweb/p_e.html

6. http://www.mathstudio.com/poetry.htm

Information on Books:

Mathematical Ideas by Francois Viete pg 335
The Weight of Number by Baumel Judith
Arithmetic Lesson Infinity: by Linda Pastan
Geometry by Rita Dove
"Pi" by Robert Morgan
The Prince of Algebra by JoAnne Growney