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“OUT of FIXED PROPORTION, BEAUTY RISES”: a REVIEW of MATHEMATICS in FORMAL POETIC CONSTRAINT by Tiffany Nielander

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“OUT of FIXED PROPORTION, BEAUTY RISES”: a REVIEW of MATHEMATICS in FORMAL POETIC CONSTRAINT by Tiffany Nielander “OUT OF FIXED PROPORTION, BEAUTY RISES”: A REVIEW OF MATHEMATICS IN FORMAL POETIC CONSTRAINT by Tiffany Nielander A Thesis Submitted to the Faculty of The Harriet L. Wilkes Honors College in Partial Fulfillment of the Requirements for the Degree of Bachelor of Arts in Liberal Arts and Sciences with a Concentration in Mathematics and English Literature Wilkes Honors College of Florida Atlantic University Jupiter, Florida May 2018 “OUT OF FIXED PROPORTION, BEAUTY RISES”: A REVIEW OF MATHEMATICS IN FORMAL POETIC CONSTRAINT by Tiffany Nielander This thesis was prepared under the direction of the candidate’s thesis advisors, Dr. Meredith Blue and Dr. Gavin Sourgen, and has been approved by members of her supervisory committee. It was submitted to the faculty of The Honors College and was accepted in partial fulfillment of the requirements for the degree of Bachelor of Arts in Liberal Arts and Sciences. SUPERVISORY COMMITTEE: ___________________________ Dr. Meredith Blue ___________________________ Dr. Gavin Sourgen ___________________________ Dean Ellen Goldey, Wilkes Honors College ___________ Date ii ABSTRACT Author: Tiffany Nielander Title: “OUT OF FIXED PROPORTION, BEAUTY RISES”: A REVIEW OF MATHEMATICS IN FORMAL POETIC CONSTRAINT Institution: Wilkes Honors College of Florida Atlantic University Thesis Advisors: Dr. Meredith Blue and Dr. Gavin Sourgen Degree: Bachelor of Arts in Liberal Arts and Sciences Concentrations: Mathematics and English Literature Year: 2018 As Bertrand Russel once said, “The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry” (Russel 60). Poetry and mathematics are recognizably linked through aesthetics and counting at the most fundamental level, but these basic connections can be further extended to formal constraints in poetry. The link between mathematics and poetry, as well as formal poetic constraint based on mathematical structures and principles is inherently organic. The sestina and the sonnet are traditional poetic forms that contain intrinsic mathematical structures. The Fib, the S+7 algorithm, and computer-generated poetry are modern forms which have been explicitly based on mathematical structures. iii ACKNOWLEDGEMENTS Thank you to my advisors, Dr. Meredith Blue and Dr. Gavin Sourgen: Dr. Blue, you have been with me from my first days at the HC four years ago, and you have been there for every moment since. Dr. Sourgen, I regret that I only had the chance to take two of your classes, but Irony & Satire will always be one of the best classes that I have ever taken. You have both done so much for me this year, and I am so grateful for your time and support through the ups and downs of the process that has culminated in this document. Thank you to my family: Mom, Macy, and Dad, what do I even say to you? You have been there for me through everything-panic attacks, triumphs, and failures-and I could not have made it this far without you. I love you so much and I cannot imagine achieving anything without sharing it with you. Thank you to my loving partner, Tripp: I cannot put into words how grateful I am that you are a part of my life. Thank you for understanding my anxiety and stress, and always being there for me. Your constant support has gotten me through most of the last three years and I look forward to our future together. Thank you to my fantastic friends: Thank you for buying coffee, and snacks. Thank you for letting me cry in your laps. Thank you for the long nights of Netflix binging and Uno- playing, even though I almost died. Thank you for your unyielding support. Thank you for hugs, I-love-yous, cuddles. Thank you for late nights in the housing office. I love you guys so much. Kesh, you have been my best friend basically since day one, thank you for everything you have done for me these four years, and I will miss you so much. I love you. And to my roommates, past and present: I treasure the support and friendship of all of you, and I wish you all the very best in everything you do. iv Thank you to Adam “Dad-am” Schwarz: I appreciate you and everything you have done and still do for me as a member of the Housing team and as an individual. I could not have asked for a more supportive, involved, and understanding boss. I love you. *fist- bumps* Thank you to Dr. Warren McGovern: You have shaped so much of my experience at the HC, always for the better. Thank you for an incredible four years. Thank you to Professor Rachel Luria: Thank you for not only being an amazing professor, but also the most wonderful advisor we could have asked for in Cliché. Thank you to my HC professors, Drs. Michael Harrawood, Yasmine Shamma, Mark Tunick, Christopher Ely, William O’Brien, Terje Hoim, Christopher Strain, and Jacqueline Fewkes, for making the past four years memorable and absolutely incredible. v Table of Contents Chapter 1: Introduction: On Formal Poetic Constraint, the Organic, and Mathematics .... 1 Chapter 2: Mathematics in the Sestina and the Petrarchan Sonnet ................................. 12 Section 2.1: The Sestina and the Permutation .................................................... 12 Section 2.2: The Petrarchan Sonnet and the Pythagorean Theorem .................... 20 Chapter 3: The Fib, the S+7 Algorithm, and Computer-Generated Poetry ..................... 26 Section 3.1: The Fib .......................................................................................... 26 Section 3.2: The S+7 Algorithm ........................................................................ 29 Section 3.3: Computer-Generated Poetry ........................................................... 31 Section 3.4: Coding the Fib and the S+7 ............................................................ 33 Conclusion ................................................................................................................... 38 Appendix A .................................................................................................................. 40 Appendix B .................................................................................................................. 43 Works Cited ................................................................................................................. 45 vi List of Figures Figure 1 ........................................................................................................................ 15 Figure 2 ........................................................................................................................ 18 Figure 3 ........................................................................................................................ 19 Figure 4 ........................................................................................................................ 23 Figure 5 ........................................................................................................................ 30 Figure 6 ........................................................................................................................ 36 vii Chapter 1: Introduction: On Formal Poetic Constraint, the Organic, and Mathematics In his book How to Read a Poem, Terry Eagleton defines ‘form’ as “all those aspects of a literary work… which are relevant to how the work presents its materials” (Eagleton 166). Form in this definition pertains to the disjoint elements, such as rhyme and tone, posed by a poem to convey itself in the physical world; it is the characteristics of its shape as individual components. The ‘formal poetic constraint’ incorporates these elements into a predetermined external structure of patterned rhyme, meter, and more, such as a limerick, often termed a “form.” I will use the term “fixed form” in the cases that are in reference specifically to classified constraints. The notion of formal constraint and its application to the structures of poetry has been debated for centuries. Some have criticized fixed forms of poetry as acrobatics, being ostentatious but providing little to nothing of real substance to the overall reading of the poem. Oliver Wendell Holmes criticized fixed form in his novel Over the Teacups when he declares “Rhythm alone is a tether, and not a very long one. But rhymes are iron fetters” (Holmes 79). More often, form is criticized if it does not reflect the sentiments or essence of the ‘content of the poem’; i.e., if form and content can be distinctly separated, then the form is superfluous. There are others, however, who see new possibilities in strict formal constraint, or in fact, fixed forms as literature in themselves, worthy of study. This chapter will discuss the perspectives of two literary ‘movements’ and three particular authors who have all theorized on the importance and proper usage of strict formal constraints in poetry. The perspectives that this chapter examines will inform the 1 function of the fixed forms that I will be examining in the following chapters: by tracing the evolution of the purpose of constraint, I hope to illustrate the significance that mathematics has in forming such constraints. I will begin this discussion with British Romanticism because its writers were notorious for their extensive employment of formal constraints to contend with their untamed internal energies. Form and formal constraint in Romantic poetry, though they seem to be cognitively disnonant, are a necessity for the very reason that the Romantics themselves emphasized
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