## Ordinary Devices, Extraordinary Applications

Many believe that uncharted territory warrants unchartered

methodologies. However, novel methodologies are often costly to

create, difficult to produce, and simply unnecessary. I have

witnessed this concept both within and beyond the classroom.

From utilizing affordable sensors to create a motor disability

detection device for infants, to applying ancient mathematical

theorems to solve realistic world problems, I have witnessed

firsthand that there is no need to reinvent the wheel to invent the

car. Sometimes, what we need already exists and is just waiting to

be seen in a new context. My experiences have led me to

understand that innovation does not always require

creating the next big thing. Progression is not always a

result of a new theorem, technology or ancient scientific

breakthrough. In society today, innovation and

progression are greatly reliant upon new applications

and context of pre-existing methodology and technology.

When I first began to learn about mathematical theorems and the brilliant minds behind them, I was amazed. Many of the formulas responsible for some of the world’s most advanced technology were invented hundreds of years ago and still hold true. The field of mathematics stands on the shoulders of giants who laid the foundation all those years ago, without calculators! I began to learn the realistic 21st-century applications of such formulas early in my academic career. For example, the Fundamental Theorem of Calculus was first introduced by Isaac Barrow in the mid-1600s documenting the inverse link between differentiation and integration, the link between a function and its rate of change (Ponce-Campuzano, 2014). MATH 141: Calculus I and MATH 142: Calculus II collectively teach the rules and theorems of differentiation and integration—both of which I took as a freshman. The projects shown at the bottom of the screen show two programming projects from MATH 141 and MATH 142 which illustrate how these early formulas are being used today. One program uses differentiation to simulate a roller coaster’s trajectory and the other uses integration to simulate a three-dimensional goblet. Though these projects were just simulations, engineers use differentiation to assure enjoyable and safe rides when designing real roller coasters. Integration is also used by designers to assure that the center of gravity of a goblet will prevent it from falling over. These two impactful classes and their projects gave me a slap in the face. At such an early stage in my academic career, it was difficult to imagine such timeworn concepts to be of any practical use. Even with experiencing these pronounced examples of utilizing existing mechanisms, I was not convinced. However, this stubbornness did not last very long.

During the summer of 2016, I participated in a research experience for undergraduates (REU) in the HumAnS lab at the Georgia Institute of Technology inAtlanta, GA. During this experience, I worked on a project entitled the Infant Smart Anklet for Infants atRisk of Developing Cerebral Palsy. I was tasked with developing a robotic system that would be cost efficientand effective. Upon first glance, that seemed impossible.Similar systems on the market started at around $1,500; however, my budget was $200. How on earth was I supposed to compete with that? What I did not know at that time was that I would be able to develop a system that was only $150 by the end of the summer.

The developed smart anklet system collects live data during an infant’s spontaneous kicking and provides augmented reinforcement to improve their movements. This cost efficient system utilizes an inexpensive sensor in the form of an anklet that sends data to a free mobile app. The app then triggers a robotic mobile located above the infant when the data meets a specific threshold. In order to convince potential customers of the effectiveness of the system, I created an illustrative PowerPoint that expands on how the developed system works with the Texas Instruments sensors. This PowerPoint slide is at the bottom of the page.

This system provides a form of early intervention for infants that may be at-risk of developing cerebral palsy, a motor disorder caused by abnormal brain development either before or shortly after birth (Vincer, 2006). The sensors used in the $1,500 suits were nearly $400 - $500 alone. By using ordinary Texas Instrument sensors that were relatively cheap at a rate of approximately $50 altogether, I was able to get the desired results of the project using differentiation, a concept I had learned in MATH 141. Go figure! Here I was at a summer REU using a formula that I had learned years ago and that Barrow had invented decades ago. The overall problem that I was trying to solve depended on the results of this ancient formula. This modern application of differentiation is what really made the idea of progression and innovation clear for me.

Inside the developed mobile app, I would calculate the running average of the infant’s kicking motion. Next, I would use the derivative, the rate of change, of the infant’s kicking to identify when a significant kick occurred and trigger the mobile to spin. Instead of complaining about the seemingly unmanageable task, I was able to use a concept I was familiar with to implement an algorithm into a $150 system that would provide essentially the same service as the $1,500 system. This experience not only reinforced the importance of research in the scientific community, it demonstrated the power of resourcefulness and creativity in the workplace. This work was recently published at ARSO2017 for its innovative approaches with preexisting technology. The accepted paper can be found at the bottom of the page.

What drove this insight home for me was going to see the movie Hidden Figures with Women in Computing. I have been a member of Women in Computing at UofSC for four years. Through this group, I have been able to attend conferences such as the Grace Hopper Celebration of Women in Computing, discuss important issues facing the community such as dealing with macroaggressions, and collaborate greatly with other women in the department. The Women in Computing group went to see the movie as one of our social bonding events for the spring 2017 semester. Hidden Figures, based on true events, documents a group of mathematicians who were trying to put the first man on the moon during the space race. They originally thought that because no one had ever been to the moon, new math was needed for the mission to be successful, new math that hadn’t been invented yet. However, they soon realized that they did not need new math after all. They used Euler’s method. Aha! I learned about Euler’s method in both MATH 520: Differential Equations and in MATH 527: Numerical Analysis. The method is used to approximate the results of an equation given an interval and trajectory. As soon as it was mentioned in the movie, I knew that if they were using the appropriate numbers, Euler’s method could be extremely accurate. For example, see the comparison of the Euler’s method approximation of an equation to the actual solution of the equation from a MATH 527 project at the bottom of the page. You can see how the approximation is nearly identical to the actual solution. This knowledge of Euler’s method made seeing the movie an even greater experience for me and took me back to my experience at Georgia Tech using differentiation.

Euler’s method may have been old, but it worked. They did not need new math, after all, they just needed to look at old math in a different light. It was this impactful movie that helped me to appreciate that I had learned essentially the same lesson in my four years at the University of South Carolina that the mathematicians learned at the Langley Space Center decades ago. I am no longer the freshman with a mindset that is set on changing the world by inventing the next big thing all by myself. I have come to realize that some of the world’s most notable inventions and discoveries exist solely because of the concepts, devices, and developments that occurred before them. For example, cars would not exist without the wheel, Facebook would not exist without the internet, and computer science would not exist without mathematics. It is not always about pure novelty and innovation. The best invention uses prior invention. Whether the task may be designing roller coasters, crafting goblets, developing affordable robotic systems for infants or landing the first man on the moon, sometimes the most ordinary devices—with a little creativity—can have the most extraordinary applications.

Artifacts:

WTC Artifacts: MATH 141: Designing a Roller Coaster Project, MATH 142: Designing a Goblet Project, MATH 527: Euler’s Method Actual vs. Approximation Matlab Program & Graphs

BTC Artifiacts: PowerPoint selling Infant Smart Anklet, www.deairabryant.com/DREU, ARSO accepted paper

References:

Hutzenthaler, M., Jentzen, A., & Kloeden, P. E. (2011, June). Strong and Weak Divergence in Finite Time of Euler's Method for Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (Vol. 467, No. 2130, pp. 1563-1576). The Royal Society.

Ponce-Campuzano, J. C., & Maldonado-Aguilar, M. Á. (2014). The Fundamental Theorem of Calculus within a Geometric Context Based on Barrow's Work. International Journal of Mathematical Education in Science and Technology, 45(2), 293-303.

Vincer, M. J., Allen, A. C., Joseph, K. S., Stinson, D. A., Scott, H., & Wood, E. (2006). Increasing Prevalence of Cerebral Palsy Among Very Preterm Infants: a Population-Based Study. Pediatrics, 118(6), e1621-e1626.