On Human Competency and Calculus

“A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.”— Robert Heinlein, Time Enough for Love

American science fiction writer Robert Heinlein chooses the polymath as the central character type in his books- men and women who span many disciplines of knowledge and who seek to develop their abilities in multiple areas of accomplishment including the intellectual, social, and physical spheres. These people may more commonly be known as “Renaissance men and women” in today’s lingo.

In the modern economy there is a strong pressure towards specialization of skills and industry. The division of labor was a concept introduced during the Industrial Revolution that enabled companies to get the most out of their labor forces by having workers focus on limited and unskilled tasks to reduce training and wage costs, while increasing company productivity. A cursory view of Linkedin profiles reveals to what extent we’ve committed ourselves to a specialist economy:

“A data-driven marketer with 7 years of experience in shopper marketing and digital execution. I graduated with a BA in Marketing Management from XX University and am looking for opportunities in the Marketing Analytics & Big Data space!”

Rarely does one find and *take seriously* a description like the following:

“A data-driven house-builder, engineer, and artist. Graduated with a degree in Music and currently working as product designer and lead fitness instructor for an early-stage startup.”

It’s not a surprise that people end up with narrow skill sets that allow them to optimize their attractiveness on the job market. For those of us who are invested in being a modern-day Renaissance men and women, I’d hazard that the path to becoming a polymath is much less isolated than one would think.

Take calculus for example.

Most colleges require introductory calculus and if you’re someone who is not naturally inclined towards mathematics, it seems to be more of a prerequisite to getting to the exciting stuff than a fundamentally valuable discipline of knowledge. But it is valuable, even if it’s not readily apparent. Take me for example:

Today, I consider myself a product marketer. In my quest to be polymathic, I also want to be a designer, entrepreneur, engineer, and athlete. Somebody who knows that I graduated from a liberal arts college in political science might scoff at my ambitions since I’ve already “specialized” in the social sciences.

But I’ve taken calculus.

And I know that calculus is central to product and industrial design. Calculus enables me to calculate the area of an planar surface or solid beyond the symmetrical shapes we learned in grade school. More importantly, calculus helps me derive the analytical models I need to understand performance of my product, like stress testing. It also helps with:

  1. Package Design: I want to create packaging for my product using the least amount of material. How do I do this?
  2. Cost Optimization: One aspect of my product is less expensive to produce than the other. How do I optimize to make the product for the least amount of cost?
  3. Industrial Design: What’s the maximum amount of material I would need to build a product?

At its core, calculus is the study of change and how change might affect a system. In calculus, limits help us understand what it means to get close to a target point and the characteristics of measuring a continuous quantity. In an applied technology like wearables, this might mean being able to measure motion through a product like Fitbit and being able to determine how fast a user is going at a given time to inform future design changes. If we measured how rapidly and how often someone changes direction while running, can we design better sport-specific shoes? Yes, sudden directional changes would appear as changes in the sign of the derivative of the speed curve (the 1st derivative of speed is velocity).

In today’s world of specialization, being a Renaissance woman is a hard task indeed, however approaching multiple disciplines of knowledge with an open mind and willingness to think laterally can enhance innovation for everyone. Perhaps this is why human-centered design is rapidly gaining acclamation as one the foremost approaches to developing new products and processes to drive engagement and growth. Because real people are at the heart of human-centered design, one must consider the wide range of intellectual, social, and bodily ways in which real people interact with the physical world. Human-centered design principles can go beyond the Research-Design- Build framework and involve integrating knowledge from multiple domains even though this may be antithetical to modern day labor pressures. This will only grow more important as we become an even more data-driven world and rush to create products that resonate more with our shared experience.


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