Poetry, Music, and Math Published by Mir Samreen and Kunjika Pathak

Table of Contents

Introduction

Human interaction amongst themselves and with the elements of this world is interesting and amazing. No doubt connecting with people or nature is crucial in everyday life but connecting to own self through the aid of these is something beyond. There are different ways through which humans connect with things and every way has its own charm. But it makes one wonder, can there be some connection between the forms of connections as well? And can these connections further enrich human experiences?

Poetry helps us to appreciate things around us, music helps in modulating emotions and math helps us to understand it all. These three are the strongest and most efficacious means of connections between anything. There are deeper connections between the three than what appears at the surface level. Despite their different disciplinary approaches, connections can be drawn by examining the expressions and how they build on one another. Nevertheless, the fascinating relationship between the three is more promising.

Evidence that Proves Poetry, Music, and Mathematics are Interlinked

In order to show that in fact poetry, music, and math are interknitted, we shall be using a mathematical approach to prove apparent. Choosing a mathematical way means that the proof is going to be logically true and hence credible. After proving that the three are interconnected, the article delves into how the three can be implemented together in a classroom setting for students to learn. This would promote interdisciplinary thinking and approaches, giving rise to critical thinking and problem-solving skills.

Let’s look at the definitions of the three and consider our data from them.

Poetry: A piece of writing in which words are chosen for their beauty and sound and a careful arrangement is called a poem. Poetry is a collection of poems.
Music: Arrangement of sounds in time through the elements of melody, harmony, rhythm, and timbre.
Math: A field of study that deals with the logic of. shapes, quantity, and arrangement.

One can easily observe that the three are related to each other by the common word i.e., arrangement. So, we have established the relationship between them. The best way to prove the relationship between three entities is using the transitive property which says if a ̴b and b ̴c then a ̴c. Where “ ̴” means ‘related to’. We know the relationship and also the method we shall use for our proof so, let us begin step by step procedure as if solving a mathematical problem. This procedure is especially helpful when taking a mathematical approach to proving the connection between the three.

Poetry and Music [Claim]

Poetry and music have been related to each other from time immemorial. It is so strong that in spite of being challenged and questioned, their connection has survived the ages. Of course, they are two independent forms of art that have varieties of genres and can stand alone. But one cannot ignore how the two draw inspiration from one another and are closely connected when it comes to rhythmic patterns. Lyrics are the best example of the evidence of this claim. When poetry is accompanied by music, a masterwork is created like Greek rhapsodies, Japanese Tankas, or praise poetry in India and Pakistan.

Poetry and music are both performed art, have almost the same result on human emotions, are used to represent culture and history, and yet are still not seen as connected as they are in actuality. For example, rhythm is used to create both the flow of music and poetry. If poetry can be sung without music, music without words can also be poetry. This can be realized by the effect it produces on its audience. Poetry expresses just like instrumental music and has the same emotional captivation as music with words will have.

Sounds and paintings are also considered to be forms of poems that do not need words at all. In that sense music is poetry. Likewise, poetry is music, and to recognize it considers the quote by an Argentine short-story writer Jorge Luis Borges, “Truly fine poetry must be read aloud… Poetry always remembers that it was an oral art before it became a written art. It remembers that it was first song.”

Rise of Spoken Word Poetry

This is particularly interesting to note in current times where spoken word poetry has gained popularity. Several poets have gained prominence performing poetry that evokes the relationship between music and poetry. Performance poetry has an aspect of musicality to it as poets deliver in a certain rhythmic manner. These performances are often accompanied by light music such as the gentle strumming of a guitar in the background.

The performance aspect of both music and poetry also ties them together creating similar effects of tonality and harmony. To quote Sarah Kay, a prominent spoken word artist, “Spoken word poetry is the art of performance poetry. I tell people it involves creating poetry that doesn’t just want to sit on paper, that something about it demands it be heard out loud or witnessed in person”. These arguments try to bridge poetry and music together. However, to make this bridging look promising by being able to actually prove this connection is what we shall be doing here. We will arrive at the same conclusion with a stronger set of arguments using transitivity. So, we claim Poetry is related to Music.

Poetry and Math [Argument 1]

JoAnne Growney, a mathematician, and a poet say, “Mathematics and Poetry are both the formats that can convey multiple meanings”. In math, we find different ways through which we can represent and demonstrate a concept, shapes, theorems and etc. For example, a system of equations can be understood both graphically or through traditional algebraic methodologies. Similarly, in poetry, poems have multiple interpretations, even a single line can have several meanings. The abstract nature of both fields of study leads to multiple interpretations and embodying various approaches.

Mathematical Approach to Writing Sonnets and Haikus

A mathematical structure in a poem makes it more appealing by deepening its effect. We have sonnets and haiku that provide evidence for the same. In sonnets, we follow rules such as the rhyming scheme having to follow a specific arrangement. A 14-line sonnet is written in three sets and each set has 4 lines, in addition, there is another set with 2 lines. There has to be a metric pattern of stressed and unstressed syllables in each line. It might appear puzzling to be actually able to write a sonnet that is meaningful, it surely requires one to have skills that one can endure via a mathematical approach to its concoction. But once we have a sonnet, we know its power of expression. Shakespeare’s sonnets are a remarkable example of the same.

Haiku found its roots in Japan, a short poem that consists of only three lines with 17 syllables formed in such a manner that there are 5 syllables in the first and the last line and 7 in the second line. Its specialty is that it expresses human nature by describing nature. Again, the mathematical structure magnifies the influence of poetry. Here is an example of a haiku,

The sonnets and haikus are similar in structure in a way that both use some restrictions of a number of lines and number of syllables. However, there is a newer form of connection as well and that is the ‘philosophy of OULIPO’.

What is the Connection Between Poetry and Mathematics?

Poetry and mathematics are considered to be quite antithetical to each other. Founded in the 1960s by French mathematician Francois de Lionnais and writer Raymond Queneau, Ouvoir de Litterature Potentielle (workshop of potential literature) seeks to connect the two. They aim to find ways in which they can write verses of poems by using constraints or a form that follows a set of guidelines. Constraints work as both; a restrictive format as well as a freeing one. It is essential to note that the beauty of mathematics lies within its constraints. Furthermore, such constraints have also opened doors to newer mathematical and poetic possibilities.

As an example, we have “fib” or a Fibonacci poem. It is experimental Western poetry sharing similarities with haiku. The poem contains multiple line verses that are based on Fibonacci’s sequence.

Fibonacci’s sequence: 1,1,2,3,5,8, …

Here each term after the first two is the sum of the two terms before it. Similarly in the fib, a poem pattern is followed using the number of syllables per line as given below:

This relationship between math and poetry is not a recent discovery. Not only is there math in poetry but there is also poetry in mathematics. Several mathematicians use poetic lines, metaphors, and images as well. For example, Euclid’s proof of the infinitude of primes, Pythagorean theorem, or Pigeonhole Principle that can be formulated as a statement quite poetic: ‘if the number of pigeons residing in your pigeon house is more than the number of pigeonholes, then at least one pigeonhole must have more than one pigeon’. (JoAnne Growney)

Beliefs of Prominent Mathematicians and Poets

Ezra Pound, an American poet stated that “poetry is a sort of inspired mathematics”. And 19th-century mathematician Karl Weierstrass is also reported to have said that, “it is true that a mathematician, who is not somewhat a poet, will never be a perfect mathematician”. Many historical figures who were great mathematicians have always proclaimed it. E.g., Einstein has said, “Pure mathematics is, in its way, the poetry of logical ideas”. Mathematicians and poets both focus on language and imagination is the predominant factor for both. Other common elements are the use of patterns, symmetry, and symbols to understand abstraction.

Math and poetry both make one twirl on the journey of our own composition. They aren’t the result or an interpretation in needs to be discovered or worked out. These are de-facto languages that open up our perspectives and cognizance. By building on one another through form, patterns, and especially abstraction, they are recognized as profoundly interconnected.

Thus, the relationship between poetry and math is well established from factual descriptions.

Math and Music [Argument 2]

Galileo Galilei, an astronomer observed that the entire universe is written in the language of mathematics and surprisingly the introduction of passion and emotion in music composition is also based on mathematical relations. If one tries to uncloak the elements of music such as chords, scales, octaves, keys, pitch, beats, tempo, meter, time signatures, and formulaic progressions, they all can be understood well using simple math and logic. The mathematical properties of sound are already known to us.

The regulation of pitch, vibration, frequency, and loudness in order to change the effects of sound all fall under the physics we study at the school level. Even the wave nature is taught to us while still in school. So, the effect of music; the melody, rhythm, and harmony have mathematics in it does not come across as a surprise. However, the fact that even the cause of music is mathematical is quite enthralling, since this is yet again a pair just like math and poetry, which many don’t find compatible. We have already established a close relationship between poetry and music in terms of rhythm, tonality, etc. Similarly, music and math are closely related through patterns, form, and more.

Ancient Greek philosophers such as Pythagoras believed that music was built on mathematical ratios. Since then, the relationship between math and music is sought and musicians have also begun to study mathematics, for example, Brian May, Dan Snaith, and Ethan port are a few musicians who have degrees in mathematics.

How is Math-n-Music Interconnected?

Let’s explore the math-n-music relationship. Music set theory can be simply related to set theory in math where musical instruments and objects are organized and their relationships with each other are well defined. It is done to analyze the structure of music. Even abstract algebra is used in the analysis of music. As an example, a piece of tonal music with notes separated by the interval of a semitone makes use of chromatic scale which is a set of 12 pitch classes that has a free and transitive action of the cyclic group Z⁄12Z, with the action defined by transposition of notes. The chromatic scale can be seen as the torsor (principal homogenous space) of the group.

Listening to music makes human emotions fluctuate as the dynamics produced by music fluctuate. To determine the changing dynamics, variations, or even the balance of volume, calculus plays a vigorous role. Great mathematician Gottfried Leibniz, one of the inventors of calculus has said, “Music is the pleasure human mind experiences from counting without being aware that it is counting”. Several musicians have composed their music based on the golden ratio and famous Fibonacci’s sequence such as Bach by Variazioni Goldberg and even Mozart and Beethoven have composed pieces which have led to musical applications of number theory.

Music Complements Mathematics

While math makes music beautiful, music too reciprocates by complementing mathematics. In 2012, a study showed that music can enhance learning math skills. In fact, it was shown that during an examination of mathematics, listening to music could improve performance by 40%. Even though, listening to music has the ability to improve cognitive and mathematical skills, being able to perform music definitely serves added advantages. It is reported that when Einstein was stuck solving a math problem, he played music as we know he was also a pianist and a violinist.

It is because some researchers have found that music activates the hemisphere of the brain which is used in order to solve reasoning problems such as in mathematics. In fact, a recent study has shown that listening to music (theory of Mozart effect) activates certain portions of our brain. On the right side, classical music and minor tones, and on the left, we have upbeat and major tones. Complex mathematical problems or fine motor problems can become simple to deal with if you can play any musical instrument.

An audio analysis of audio “*a”-**DRUMS* *& “b”-**SOUND OF CLAPS*.

Periodogram of “a” and “b”

From the above discussion, proof of the relation between math and music is very well established by research-based arguments.

Therefore, Poetry is related to Math and Math is related to Music, by transitivity we get Poetry is related to Music.

Power of the Three

We have established the relationship between Poetry, Music, and Math and shown how the three are interwound. The three are the most helpful tools that let us connect to our own self as well as the universe, to the abstract and concrete. An example to know how three are intertwined together to produce worthwhile results, let us talk briefly about Lateralus by Tool.

‘Tool’ is an American rock band from Los Angeles formed in 1990. In 2001, they released a song named ‘Lateralus’ (Lateral thinking and viewing problems through a new light). Lateralus is a very famous and much-appreciated work of this band and is often considered to be a masterpiece of the 21^st century at par with compositions by legendary Beethoven and Mozart. What is so special about it? It is the result of the three incorporated intelligently in this piece by Tool.

Lateralus and Fibonacci’s Sequence

Lateralus is based on Fibonacci’s sequence. Not only is the music based on it but also lyrics (poem) follow the same pattern. The drum beats follow the fib progression of the time signature. The rhythmic movements follow the ratio of

9/8, 8/8, 7/8

An interesting observation is that 987 is the 16th term in the Fibonacci sequence. Vocals in this song start right after 1:37 seconds in the song which is 1.618 minutes. And 1.618 is the value associated with the golden ratio. Even the lyrics are structured as per fib sequence and are represented in each syllable of each phrase. It then reflects back and moves in the same procedure. Consider the lyric in the first verse

Lateralus Powerful Lyrics

Also, the lyrics are deeply poetic and fascinating, representing mathematical concepts that connect to the universe, and the music of the specific structure makes one feel the power of every word and instrument’s charm through their own language. The mention of spiral in the songs is no surprise and the way it represents the golden spiral is charted out from of Fibonacci number sequence an ever-expanding sequence.

And the way we find in lyrics the same geometrical representation through poetic words, “We’ll ride the spiral to the end and may just go where no one’s ever been.” This spiral, we know will end at infinity in mathematical language, and this when connected with the divine notion of losing oneself in the pathway and stating that we may go where no one has ever been just making it astoundingly deep. One might not be able to appreciate this song at the beginning. Just like it takes time to understand a mathematical equation, or express an idea in words or compose music, it will take time to understand how great Lateralus is.

And now that little details are given regarding the way it is constructed, one can listen to and feel the magic of good music. The detailed description of the song can take a while, so we can stop here with brief details enough to convince ourselves that poetry, math, and music interwound together has the full potential to create a masterpiece of any sort.

Finally, we confer different forms of means to connect to the universe, nature, and even people, as a matter of fact, subsumes relationships amongst them as well. They tend to compliment and inspire each other in such a way that the end result is exquisite!

Implementing the Power of the Three

The article has established the interconnected nature of the three which are vast fields of study. The three disciplines are taught widely at different levels in schools and colleges. With the interrelation in mind, we can make a case for the three being taught together in a classroom setting. This will promote interdisciplinary thinking amongst students and give rise to innovative pedagogy. Furthermore, it will enhance critical thinking and problem-solving skills by finding patterns and similarities across disciplines.

As per Scotland’s Curriculum for Excellence, the onus of numeracy teaching rests upon all classroom teachers and not only the mathematics department. This helps in broadening numerical understanding beyond just the math classrooms and encourages finding patterns in other classes. The production of new meanings in a classroom setting helps learners’ imagination and facilitates a better understanding across disciplines.

Oulipo an Interesting Teaching Technique

Using the example of Oulipo is an effective way to teach in class. It introduces students to a new form but also grabs their interest further because Oulipo has probably been introduced to them in history lessons. This works not just in favor of math and poetry but also adding further aspects like history and culture. It is also a good practice because it pushes students to move away from their regular practices and put themselves in a spot and write in a constrained format.

A child in kindergarten is usually taught counting numbers in a singsong rhyme format and most children’s poetry books have ‘a counting poem’ as a part of their writing. Counting is the backbone of mathematics and is one of the oldest forms as well. There are several temple hymns across cultures as old as 1800 BC, which talk about counting cattle and other animals. The divine is merged with literature and math and that also gives it a superpower of sorts. There are several references to the counting problem because of the barter system.

Modern-Day Approach towards Teaching

The poems written in different shapes can be used in several classes because it brings together visual imagery, words, and math together. The visual experience along with the written one enriches one’s understanding of mathematics and poetry further. Also, it is interesting because a large number of students have typically been taught to think, write and read in a restrictive format. Musicality is also associated with visuality and encourages a comprehensive understanding of the different disciplines. Thus, this is a fresh approach, which opens up new conversations about visual representation.

In conclusion, this article has made an argument to prove the interconnected relationship between math, music, and poetry and has also gone to show how the three can be implemented together in a classroom setting. The three add to an enriched understanding of human experiences through means of entertainment, studying, or even thinking.

Poetry, Music, and Math Published by Mir Samreen and Kunjika Pathak

Introduction

Evidence that Proves Poetry, Music, and Mathematics are Interlinked