The poem-collage pair presented here is a work of collaboration between the mathematician and poet, Sarah Glaz, and the collage and ceramic artist, Mark Sanders. The piece is part of their larger joint poem-collage project involving the history of mathematics. Created at the height of the pandemic, the poem-collage pair reflects the reality of living during a plague and embodies the solace offered by long-distance collaboration and by the arts. Included as background is a brief discussion on the history and mathematics involved, information about Sarah’s poem and Mark’s collage, and a reflection on how the pandemic influenced both the choice of poem and the imagery appearing in the collage.
To see the poem-collage pair as originally envisioned by Sarah and Mark please place them side by side

Glaz, Sarah

Sanders, Mark

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Journal of Humanistic Mathematics Volume 11 | Issue 2 July 2021 The Music Is All That Counts! A Poem-Collage Pair Created During The Pandemic Sarah Glaz Department of Mathematics, University of Connecticut, Storrs, CT Mark Sanders Rushden, Northamptonshire, UK Follow this and additional works at: https://scholarship.claremont.edu/jhm  Part of the Arts and Humanities Commons, and the Mathematics Commons Recommended Citation Glaz, S. and Sanders, M. "The Music Is All That Counts! A Poem-Collage Pair Created During The Pandemic," Journal of Humanistic Mathematics, Volume 11 Issue 2 (July 2021), pages 522-529. . Available at: https://scholarship.claremont.edu/jhm/vol11/iss2/37 ©2021 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. The Music is All That Counts!A Poem-Collage PairCreated During the PandemicSarah GlazUniversity of Connecticut, Storrs, Connecticut, USAsarah.glaz@uconn.eduMark SandersRushden, Northamptonshire, UKsparkymarky63@btinternet.comSynopsisThe poem-collage pair presented here is a work of collaboration between the mathematician and poet,Sarah Glaz, and the collage and ceramic artist, Mark Sanders. The piece is part of their larger jointpoem-collage project involving the history of mathematics. Created at the height of the pandemic,the poem-collage pair reflects the reality of living during a plague and embodies the solace offered bylong-distance collaboration and by the arts. Included as background is a brief discussion on the historyand mathematics involved, information about Sarah’s poem and Mark’s collage, and a reflection on howthe pandemic influenced both the choice of poem and the imagery appearing in the collage.To see the poem-collage pair as originally envisioned by Sarah and Mark please place them side by side:Journal of Humanistic Mathematics Volume 11 Number 2 (July 2021)Pythagoras plays his lyre“What is the wisest thing? Number.What is the most beautiful? Harmony.”- Iamblichus (ca. 250-330), Life of PythagorasPythagoras plays his lyresurrounded by mathematicians.We sing paeans as he strikesthe cords:We discovered thelaw of the cosmos:All is number!Mysterious proportions!The way strings vibrateto harmonic ratiosmakes music soundlike heaven.The sacred beans sproutin the nearby fields.All animals are partof our family.In the interval betweenearth and the firmamentplanets circle and humin concert.Each One a notein the grand symphonyof all creation.We guardits innermost secret.The music wafts upwardlike smoke from burnt incensepleasing the gods who watch usplay and pass.523524Background: History, mathematics, poem, collage, pandemicThe collaboration between Sarah Glaz and Mark Sanders started in 2019, when David Greensladeinvited both of them to participate in the poem-collage project he was editing, “Imagined Invited.”The result is the poem-collage pair “Among Practitioners of Cossike Arte,” which appears onlineat the Bridges 2020 Art Gallery [6] and in the print publications [2, page 28] and [7].In the summer of 2020, Sarah and Mark decided to collaborate on a new poem-collage projectinvolving the history of mathematics. At that time the first wave of the pandemic was ravaging theUnited States, and Sarah found herself checking the “daily numbers” with obsessive conscientious-ness: number of coronavirus cases, number of hospitalizations, number of deaths in Connecticut, inthe US, in the world; speculations on the meaning of the up and down trends, other numbers usedaround the globe to measure the extent of the pandemic, and more. Whole numbers were every-where evident and seemed to dictate both the routines of daily life and the mood with which onewoke up every morning. The poet heard an echo of a voice from the deep past “All Is Number!” Inanother period of time long, long ago, people also believed the world around them was governed bywhole numbers and their ratios, and tried to understand the relations between numbers and realityin order to have some control over their destiny. This remote period of time is the 6th centuryBCE, and the people who proclaimed “All Is Number!” were Pythagoras and his followers. Andso, poems about the Pythagorean Brotherhood became a natural choice for the new collaborativeproject.———o———0———o———The poem “Pythagoras plays his lyre,” featured in this poem-collage pair, was written a few yearsbefore the pandemic. In the poem, the poet travels in a time machine to the distant past andjoins the Pythagorean Brotherhood. The poem was first published in the Journal of HumanisticMathematics [3], and later translated into Spanish and Galician.1 It also appears in Sarah’s poetrycollection, Ode to Numbers [4].———o———0———o———Sarah emailed Mark the poem to see if it would act as a source of inspiration for a collage.———o———0———o———Pythagoras was born circa 585 BCE on the Greek island of Samos. Most of what we know abouthis life filtered down to us through the ages as fantastic stories scattered through ancient writings.Some of these stories, along with the epigraph to the poem, were gathered in Pythagoras’s biographywritten over 500 years after his death by Iamblicus [11].1 You can see Elena Soto’s Spanish translation at https://establopegaso.wordpress.com/2016/02/16/pitagoras-toca-la-lira/, and Robin Urquhart’s Spanish translation at https://www.lamajadesnuda.com/poesia-en-la-voz-de-la-mujer/96-la-maja-desnuda/poesia-en-la-voz-de-la-mujer/1518-sarah-glaz.html.See https://tarabelateca.blogspot.com/2016/04/astropoemas-11-sarah-glaz.html for the Galician translationby Ánxeles Francis and Minia Bongiorno.525Pythagoras seems to have traveled widely through Egypt, the Middle East, and Babylon, where heacquired both mathematical knowledge and a reverential and mystical attitude towards numbers [1,5, 9, 11]. In his fifties he returned to Samos; he fled from there soon after to settle in Crotona,a Greek city that was part of Magna Graecia, the coastal area of southern Italy colonized byGreece. Here he founded the school of philosophy known as the Pythagorean Brotherhood. Theschool’s aims were at once philosophical, religious, and political. The Pythagorean Brotherhood,which in spite of its name included women, was a tightly knit community following rigid rules ofconduct and a common lifestyle and philosophy. Its members learned four mathemata (subjectsof study): arithmetica (arithmetic, in the sense of number theory, not computation), harmonia(music), geometria (geometry), and astrologia (astronomy). Those attending Pythagoras’ lectureswere divided into two groups: the acoustici (listeners) and the mathematici (mathematicians). Onlyafter a number of years as listeners did students advance sufficiently to become mathematiciansand be allowed to speak to, and to participate in mathematical investigations with the master.A fundamental belief of the Pythagorean Brotherhood was that whole numbers underlie all naturalphenomena. Whether in music, or astronomy, or philosophy, the central position of number waseverywhere evident. This belief led them to undertake investigations into the properties of numbersand to the discovery of many interesting mathematical results.Greek mathematics contributed to the discipline its most fundamental principle—the requirementthat mathematical results are validated by proofs. The Pythagoreans were among the first to provemany mathematical truths that were in common usage in the ancient world, like for example, thefamous Pythagorean Theorem of Right Triangles. They also discovered and proved numerous newresults in geometry and number theory. Many of their discoveries were kept secret, and when sharedwith outsiders, they were presented as a common accomplishment of the entire brotherhood.Like many ancient cults, the Pythagorean Brotherhood had esoteric initiation rites and dietaryand lifestyle restrictions. The symbol on which the members of the Pythagorean Brotherhoodswore their oath of allegiance was the Tetractys, or holy fourfoldness. As seen in Figure 1, theTetractys is a symmetric triangular arrangement of dots with 4 dots on the bottom row, 3 on therow above them, 2 on the next higher row and 1 on top. The total number of dots in the Tetractysis 1 + 2 + 3 + 4 = 10.Figure 1: The Tetractys of the Pythagorean Brotherhood. Public domain image from Wikipedia (https://en.wikipedia.org/wiki/Tetractys), last accessed on July 28, 2021.Numbers had their own personalities for the Pythagoreans. In particular, 1 was a male numberand the sacred creator of all numbers, since every number is the finite sum of 1s; 2 was a femalenumber and was associated with diversity of opinion; 3 was linked to harmony; and 4 stood forjustice. Thus 10, the total number of dots in the Tetractys, was considered to be the very bestnumber since it contained the first four whole numbers, and in dot notation it formed a perfecttriangle.526Among other dietary and lifestyle rules, the Pythagoreans considered bean plants to be sacred andwere prohibited from eating them. They were also strictly vegetarian. The latter was a result oftheir belief in the doctrine of transmigration of the souls. The Pythagoreans believed that the soulcan temporarily or permanently leave a body and inhabit the body of another person or animal,especially after death, and therefore refrained not only from eating animal flesh, but also from usinganimal materials in their cloths, such as, for example, leather or wool [1, 9, 11].———o———0———o———Mathematically, the focus of the poem is on the Pythagorean music theory and astronomy. Musicwas important to Pythagoras and his followers. According to Iamblicus [11], Pythagoras was welleducated, learning to play the lyre and to recite the poetry of Homer. In addition to valuingmusic for its beauty, the Pythagoreans used it to regulate mood and heal illnesses [11]. Pythagorashimself is credited with the discovery that the sound produced by vibrating strings depends onstring length. In particular, he noticed that a harmonious sound was produced by plucking twostrings, one twice the length of the other — a ratio of string length 2:1 (in modern language,an interval of an octave). Furthermore, he concluded that the most beautiful musical harmoniescorresponded to the simplest string length ratios 2:1, 3:2, and 4:3 — 1, 2, 3, and 4, like in themystical Tetractys. This was the start of music theory. It also reinforced the Pythagoreans’ beliefthat the whole cosmos is governed by whole numbers and their ratios.The Pythagorean astronomy, which can be seen as an extension of their doctrine of musical intervals,was a curious mix of facts and mysticism. Following the Greek scientific tradition of his times,Pythagoras believed that the Earth was a sphere and the center of the universe. He also taughtthat each of the seven known planets, among which he included the Sun and the Moon, revolvedaround the Earth encased in its own crystal sphere, and as it moved it produced a certain humaccording to its distance from the center. The whole system created a celestial harmony, whichcame to be known as the “music of the spheres” [1, 9, 11]. Nevertheless, Pythagoras recognizedthat the orbit of the Moon was inclined to the equator of the Earth, and that the planet Venusappears as both the morning star and the evening star [9].———o———0———o———While the poet remained immersed in the 6th century BCE for the duration of the poem, thecollagist responded to the poem using imagery that moves through time all the way to the present.The pandemic, although not foremost on Mark’s mind while working on the collage, neverthelessfound a way to show itself in the choice of images and the atmosphere created by their juxtaposition.———o———0———o———Pythagoras himself appears multiple times through the collage in various guises. In his role as majorphilosopher and mathematician, he is depicted surrounded by past and future disciples in Raphael’sfresco The School of Athens,2 and also as the lone figure in the 1955 Greek commemorative postagestamp on the occasion of the 2500th anniversary of the founding of the first school of philosophyby Pythagoras.2 See [10] for more on The School of Athens. Also note that this issue of the Journal of Humanistic Mathematicscontains an article about Raphael’s masterpiece and engages with several of the ideas in this essay. See [8].527Emphasising the music theme, which is central to both the poem and the collage, Pythagorasappears as the blind, multi-instrumentalist modern jazz genius, Rahsaan Roland Kirk, one of whoselandmark recordings was the album titled “The Case of the Three-Sided Dream In Technicolor” —a title evoking both the Tetractys and the Pythagorean Theorem of Right Triangles. To the rightof the image of Rahsaan Roland Kirk, the seated audience plays the role of the mathematicianssurrounding Pythagoras mentioned in the first stanza of the poem, as well as the role of the gods,mentioned in the poem’s last stanza, who watch from the highest seats in the theatre, while humansoffer music, poetry, and art in return for hope. Above Rahsaan Roland Kirk’s head, the Hand ofGod, originally appearing on the Sixteenth Chapel’s ceiling in Michelangelo’s fresco “The Creationof Adam,” creates not a man, but the muse which bestows on Kirk/Pythagoras the divine gift ofmusic. The lightning strike to the left of this scene represents the energy and power of creation,be it the creation of the world or that of a piece of art or mathematics; whilst also reflecting in itsshape the Tetractys.———o———0———o———From the point of view of the imagery alone, the coronavirus arrived among us like a lightning strike.The microscopic virus itself is a thing of unquestionable visual beauty. Were it a sea anemone or aflower, we would be admiring its other-worldly colors and shape. Lightning appears in the sky justas impressively, lighting up the darkness and fabulous to behold. However, both have the capabilityto be utterly disruptive and destructive—beauty taking on a sinister and terrifying form.———o———0———o———Pythagoras, embodying the values and beliefs of the Pythagorean Brotherhood expressed in thepoem, is also represented symbolically by the five Tarot cards placed in the lower part of the collage:The card Il Bagatto/the Magician, representing the sacred, religious, and cultish mysteries andsecrets of the society of the Pythagoreans; L’Appeso/The Hanged Man, representing the ultimatesacrifice, which alludes to Pythagoras’s assassination; Il Mondo/The World, representing cosmicconsciousness and a union with the One power of the universe; Il Sole/The Sun, representing thelight shining on truth; and La Morte/Death. Often misread to mean death itself, this last cardrefers to rebirth and represents the Pythagoreans’ belief in the doctrine of transmigration of thesouls. Interspersed between the tarot cards are images of the sacred fava bean pods. Legend tellshow Pythagoras fleeing from his enemies was struck down and killed because he refused to run tosafety through a bean field for fear of trampling the sacred plants. The radar image at the bottomright represents the Pythagorean’s search for the ultimate laws of the cosmos. These images conveythe attempt to understand the mysteries of life and death, the seeking of information and truth,the search for solace and spiritual guidance — all too relevant in a time of pandemic as they werein the time of the Pythagoreans.———o———0———o———For interested readers, Sarah and Mark’s other poem-collage collaboration involving the Pythagore-ans and their mathematics, “Square Root of 2,” can be accessed at https://www2.math.uconn.edu/~glaz/Square_Root_of_2/index.html.528References[1] David M Burton. The History of Mathematics, McGraw Hill, 2011.[2] Conan Chadbourne, Robert Fathauer, Nathan Selikoff, and Bruce Torrence, editors, Bridges2020 Art Exhibit Catalog, 2020.[3] Sarah Glaz, “Pythagoras plays his lyre,” Journal of Humanistic Mathematics, Volume 6 Issue1 (January 2016), page 291.[4] Sarah Glaz, Ode to Numbers, Antrim House, 2017.[5] Sarah Glaz, “Mathematics in the poetry of Sefer Yetzirah,” Proceedings of Bridges 2021, pages39–46, 2021. Available at http://archive.bridgesmathart.org/2021/bridges2021-39.html, last accessed on July 27, 2021.[6] Sarah Glaz, Mark Sanders, and David Greenslade, “Among Practitioners of CossikeArte,” Mathematical Art Galleries, 2020 Bridges Conference, available at http://gallery.bridgesmathart.org/exhibitions/2020-bridges-conference/sarahglaz, last accessedon July 13, 2021.[7] David Greenslade, editor, (with artwork by Mark Sanders), Imagined Invited, Hafan Books,2020.[8] Frode Sirnes Larsen, “Leonardo da Vinci in Raphael’s School of Athens,” Journal of Hu-manistic Mathematics, Volume 11 Issue 2 (July 2021), pages 196–243. Available at https://scholarship.claremont.edu/jhm/vol11/iss2/9.[9] John J. O’Connor and Edmund F. Robertson, “Pythagoras of Samos,” MacTutor Historyof Mathematics Archive, last updated January 1999. Available at https://mathshistory.st-andrews.ac.uk/Biographies/Pythagoras/, last accessed July 13, 2021.[10] Jessica Stewart, “The story behind Raphael’s masterpiece ‘The School of Athens’,”My Modern Met, September 6, 2018. Available at https://mymodernmet.com/school-of-athens-raphael/, last accessed on July 13, 2021.[11] Thomas Taylor, Iamblichus’ Life of Pythagoras, Inner Translations International, Ltd., 1986.529

The Music Is All That Counts! A Poem-Collage Pair Created During The Pandemic

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The Music Is All That Counts! A Poem-Collage Pair Created During The Pandemic

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