Megan Cubberley, Nick Gratto, Alyssa Schabel,
Allsion Wengryniuk
The Healing Power of Music and Math

AwardWhite Ribbon Award

SchoolKenston High School

CityChagrin Falls, Ohio

TeacherGreg Koltas

Selected Research

Alternative Pain Therapies and Their Effectiveness in
Previously Medicated Surgical Patients, Marissa Rose

Selected ArtDripnote, Alina Raulinaitis

Selected LanguagePain Scales, Carl Buchwald

Our submission consists of an essay composed of three parts. Part one is an interpretation of mathematics found in the literature, "Pain Scales," by Carl Buchwald. Part two is an interpretation of the mathematics found in the sculpture, Dripnote, by Alina Raulinaitis. And part three is an interpretation of math found in scientific research. All of our interpretations are based off of the research, and the subsequent art and literature inspired by Marissa Rose’s experimentation. --Megan Cubberley, Nick Gratto, Alyssa Schabe, Allsion Wengryniuk

RATIONALE: The eXpressions™ Math Program submission we have composed and compiled is a direct representation of our goals to discover, interpret, and expound upon the mathematical principles found in the research, literature, and art provided to us by Cleveland Clinic. We decided to delve into the summer research project of Marissa Rose and discover the hidden mathematical undertones throughout her research, "Alternative Pain Therapies and Their Effectiveness in Previously Medicated Surgical Patients," the poem written by Carl Buchwald, “Pain Scales,” and the sculpture created by Alina Raulinaitis, Dripnote. In order to do so, we spent weeks observing and analyzing the mediums and then, subsequently, learning and applying new mathematical principles and techniques we saw represented and implemented in the research, poem, and sculpture. For our final interpretation, we chose to expound upon the concepts of symmetry, the Fibonacci sequence, catenary curves, and experimental design techniques.

MATH IN SCIENCE: The data compiled by Marissa Rose, which was later applied to the literature and art components, is presented as an experimental design. An experiment is the deliberate change of one or more process variables, also known as factors, in order to observe the effect the changes have on response variables. The process variable was whether or not the patient received the alternative therapy and the response variable showed how the patient's pain changed. The experiment was used with this research because it provided us with a clear, definite conclusion. An observational study could not have been properly applied to this data ecause it does not force the patients to change habits in order for the outcomes to prove conclusive. Thus, an experiment was necessary to properly assess the effectiveness of the alternate therapies.

The observational unit is the most basic element of any experiment. It is the individual whose characteristics will be evaluated. In this case, as in most medical situations, the patients, who have undergone surgery, are the observational unit. From the population, which is all surgical patients in pain, a sample of six individuals was chosen for representation. Following the surgery, patients' pain levels were evaluated on the Wong-Baker Pain Scale, where one is very little pain, and ten is immense pain. Next, the patients' pain was reevaluated following medication. Patients whose pain level was unaffected were placed in the first group. However, if pain levels decreased, then these patients became part of the second group. Thus, through a random process, the patients were separated into two groups. From here, patients were asked whether they would like to receive the alternative pain therapy, which in this case was music therapy. For the group where pain didn't decrease with initial medication, only one of the three chose to embrace the musical therapy, and they saw immediate results. Of the three who had seen pain improvement following the initial medication, all three opted to receive music therapy. However, only one of them saw pain reduction afterwards.

Following the music therapy, the pain levels were reevaluated. Original medication reduced the pain by about an average of 1.33 levels per patient. Three of the six saw improvement following the initial medication. Musical therapy showed an average of 0.75 levels of pain decrease per patient. Two of the four patients saw improvement after the alternative treatment. The beginning pain was an average of 6.83, and fell to 5.5 after medication. The average pain of the patient who endorsed music therapy was 6; however, this is misleading because those who chose the music medication all had pain levels higher than 6 before their alternative therapy.See attached graph.

Marissa successfully controlled the experiment and kept it true to definition. This was an experiment where there were only two groups, and only two variables were available. Patients either chose the alternative therapy, or stayed with the control group, which was refusing alternative therapy. Though the pain levels became a confounding variable, and affected the outcome, it didn't significantly harm the experiment, as a logical conclusion was drawn from this small, limited sample group.

MATH IN ART: Marissa Rose dedicated her summer to studying the effects alternative music therapy has on pain-stricken patients. The next step in the process involved local student, Alina Raulinatis, creating artwork, inspired by the tremendous research conducted. Incorporating math into the art piece was the next task. Math concepts and ideas are around us on a daily basis. In fact, we are exposed to them so frequently that they go unregistered. The sculpture, Dripnote, incorporates many mathematical concepts. The one that stood out to me specifically was the curvature of the simulated IV staff. This replication utilizes the concept of a catenary curve.

A catenary curve is the theoretical shape of a hanging cable when supported at both its ends and acted upon by a uniform gravitational force (its own weight) and in equilibrium. Galileo was the first to ponder the concept, yet deemed the curve nothing more than a basic parabola with the formula, y = A(x-h)2 + k. However, in the late sixteenth and early seventeenth centuries, Joachim Jourgis disproved Galileo's theory. In 1691 the exact equation for a catenary curve was discovered by Christiaan Huygens and Johann Bernoulli. The term catenary is derived from the Latin word catena, or chain, and was first used by Thomas Jefferson. We used the formula, y = a/2 [e ^x/a + ^e-x/a], to derive the exact line followed by the bottom line in the staff in Dripnote.

Our first order of business was to transfer the image of the sculpture onto a cartesian plane. Once transferred, an x-axis, y-axis, and origin were constructed spanning the image. The bottom line of the staff passed through the following three points, (2,1), (-2,1) and (-5,4) which we used to model the catenary. Trial and error was then used with these three points to determine the equation, y = 2.556 [e x/2.556 + e-x/2.556]. This line was derived from the basic formula, y = a cosh ax, based on the principles once dismissed by the legendary Galilleo. This curve is finite proof that math is present all around us, and we just need to discover it.

MATH IN LANGUAGE: The literature inspired by Marissa Rose’s research is rich in both metaphorical themes and mathematical concepts. Diving deeper into “Pain Scales” by Carl Buchwald, several math themes emerge. The first theme presented itself upon the initial viewing of the piece. The poem itself is centered, representing the mathematical phenomenon known as symmetry. Symmetry has long been beautified, as illustrated by the natural gravitation humans have towards it. Reflectional symmetry is shown by the centered words, with balanced margins. The Fibonacci sequence also shows itself in this piece. Leonardo of Pisa, the Italian mathematician, identified the Fibonacci sequence. The sequence has a second order recurrence relation, denoting that in order to produce the nth term, the previous two terms must be known and utilized in the formula shown in Table 1. These numbers are embedded subconsciously into the human mind, and are naturally occurring as well. The sequence was first derived from the breeding habits of rabbits. In Fibonacci’s sequence, the pairs of rabbits are counted as they age, reach sexual maturity, and reproduce. The sequence that emerged is the famous 1, 1, 2, 3, 5, 8, 13, etc. These naturally occurring numbers are also present in nature. For example, the number of leaves emerging from a flower stalk are all numbers from the Fibonacci sequence. Likewise, the poem "Pain Scales" also follows the Fibonacci pattern. There are 13 stanzas in the poem, a Fibonacci number. The poem is also laden with a Fibonacci undertone, with many of the lines containing five words or an eight beat rhyme scheme. These sequences may have emerged unbeknownst to the writer, only to be identified and admired by us.