The Problem with Math

Industry is fond of the notion that designers and engineers fail to see eye-to-eye and this tension results in avoidable design and engineering failures. It’s a bizarre point of pride among the two camps. Designers, and particularly the industrial designer crowd of which I was and still am a part, think of engineers as narrow-minded in their blind focus on numerical empiricism derived from mechanistic purity. Conversely, engineers find the work of the designer to be so hand-wavy and ungrounded that it becomes fantasy. I play for both teams. After a decade as one of those hand-wavy designer types, I enrolled in the biomedical engineering Master’s program at Brown University.

Brown University’s engineering curriculum, especially at the undergraduate level, is focused on a theoretical approach to engineering. Most of the low-to-mid level courses are exercises in calculation and not in practice. This pedagogy is not unique to Brown. As a designer I was fortunate to work closely with mechanical engineers and, due to this crossover experience, I was invited into classrooms of higher education to share my experience with undergraduates. I remember one such presentation at Roger Williams University in scenic Bristol, Rhode Island wherein a wide-eyed freshman mechanical engineer haltingly asked how much math I used on a daily basis. When I replied that both me and the mechanical engineers on my development teams used very little beyond basic multiplication and division, he pumped his fist and several other students audibly exhaled in relief. His professor (who remains a good friend of mine even after that uncomfortable moment) immediately interjected to state that it was nevertheless important for all students to understand the fundamental mathematics of engineering. In deference to her deep prowess as a professor, I do not agree with that sentiment.

To be fair, after nearly three decades I still recoil at the memory of Mrs. Toskas’ smoker’s-lung-inflected instruction in my third grade math class. I didn’t memorize or understand multiplication and division tables fast enough for her liking and she was fond of public shame as a motivation tool so I was often a target of her attention. While I generally lacked prescience at that age, I distinctly remember thinking that I would never be without a calculator in later life. The iPhone-shaped wear pattern over the righthand pocket of my jeans suggests that I was right. Regardless, my ridiculous inability to let go of this minor trauma contributed in part to a lifelong critical distance when examining the use of theoretical mathematics in design and engineering.

As humans, we are endowed with a such a complete comprehension of our world that we are the pinnacle apex predator of our time. There’s not even a close second. While this is partly due to the influence of math as an invented tool for the rationalization of natural phenomena, I believe that our dominance has far more to do with our ability to contextually interpret our environment. We smell a ripe berry and, deep from within our hippocampus, memories of flavor, texture, and a thousand other tangentialities such as how berries can be used as dye in the processing of cotton textiles begin to bubble forth. We can pick up a baseball and feel its weight and shape which in turn naturally inform how far we can throw that ball, how much it will hurt if we drop it on our foot, and how the texture of the stitching likely aids in our ability to torque the ball while pitching which results in an atypical ballistic trajectory. In the split second prior to release and without any conscious mathematical calculation, we then accurately intuit where in the strike zone the ball will cross home plate.

Modern engineering and engineering education, for all their successes as exemplified by the thankfully stable bridges we drive over and the satellite-laden rockets we send to orbit, fail to value that natural computational power that we all have because it’s not easy to communicate or quantify. Instead, we talk about ideas like acceleration due to gravity using inscrutable abstractions like 9.8 meters per second per second as if this is a reasonable practice. Forget the bit about meters; what is a second per second? Althought I’ve hunted, I’ve never seen one myself. For a large part of the population, this type of abstraction is incomprehensible. As science and engineering tackle deeper and more difficult questions, the mathematical abstractions have become progressively more abstracted to the point where there is a whole field of serious physics which requires the invention of as many as 10⁵⁰⁰ extra universes; this is string theory. Abstractions that underly string theory and ideas like it are at least partially driven by a love of The Math for The Math’s sake. Consequently, we also now recognize the importance of the “science communicator” or, in other words, the esteemed quantifier who came out the other side of their trial with The Math in possession of a deep enough understanding of self to realize that someone needs to translate that abstraction layer — something that we impose over that which we experience every day! — to everyone else. My love for a great Neil deGrasse Tyson or Carl Sagan thinkpiece is unflinching but the efforts of science communicators are a stopgap measure and, at best, a droplet in the ocean that is the sustained output of the science and engineering community.

The current popular answer to this conundrum is specialization. The thinking is that it is perfectly okay that some people don’t understand engineering, science, and all the mathematical abstractions because those people can become artists, fishermen, or any other vocation free of The Math. This is a dangerous notion and one that will continue to sap our lifeblood. Technology is inextricably embedded in modern life: fishermen monitor their nets and fishing grounds using advanced weather mapping tools and GPS and artists use artificial intelligence algorithms to clean and process image data. In the face of overwhelming global challenges with catastrophic consequences like human-caused climate change or another pandemic, we all need to be onboard. The infuriating response of the science and engineering community to these existential crises has been to layer in more abstraction. In turn, these abstractions serve to dehumanize the threat so, for example, a not-insignificant portion of the American adult population does not believe in climate change despite overwhelming scientific consensus indicating the contrary. While I am uncertain what the contribution of the scientist-artist looks like in the fight against climate change, I know with absolute certainty that the contribution of the scientist-artist is necessary for humanity to thrive.

We spent the last thousand years building abstraction layers under the guise of scientific method and refinement of mathematics. Over the next thousand years, we need to inclusively redefine how we empirically describe the world. This will be exceptionally difficult especially because math in its current form is not the answer to this summons. In the immediate future, the steps for improvement are much clearer. John Maeda, former Director of the MIT Media Lab and President of the Rhode Island School of Design, laid out his vision for a more inclusive science in his 2013 paper, “STEM + Art = STEAM”. This is a good start. Maeda’s vision is pure, equitable, and fundamentally empathetic to our natural interpretive abilities. In reference to engineering education specifically, it is also critical that budding engineers be given immediate and continuous exposure to real-world engineering in the form of the practical making and designing of things that serve actual functional purpose. What would happen if, instead of starting an introductory course on thermodynamics with equations and calculations, students were tasked on Day One with constructing a radiative system for the dissipation of heat from a thermal generator? While abstractions may be helpful for theoretical optimization and design, they have nothing to do with actually building the damn thing.

Whereas engineering for the sake of abstraction is just masturbation, engineering for the sake of making things is valuable. Let’s not forget that key point.