Thinking in math

-December 10, 2013

One of the prerogatives I enjoy as DesignCon Program Director is getting a first look as all of the papers as they arrive.  With over eighty papers on the schedule, I can only skim most of them.  Still, I find myself drawn into their contents, enough to notice shifts in certain trends over the years.

One thing that strikes me in reading this year’s crop is the amount of math I see.  I may be hypersensitive to essential role of mathematics in all of the engineering disciplines (I’ll explain in a minute), but I sense a greater richness of equations in these papers than in past years.

I may have mentioned in an earlier blog that our youngest son has begun his freshman year of college as an engineering major.  Like many of his classmates, he has been challenged by the rigors of first-year calculus.

When I ask him how it’s going with calculus, his answers tend toward his performance on the last test and his expectations regarding his grade in the course.  While I appreciate his recognition of the role of grades in demonstrating to others his mastery of a subject, I try to emphasize the greater importance of establishing a solid math foundation for his future studies and career in engineering.  “Mathematics is the language of engineering,” I tell him in my father-knows-best voice, “and you must become fluent in this language to succeed as an engineer.”

I am woefully deficient in my ability to speak in anything but my native Midwestern English (Chicago dialect), retaining just a smattering of the German I learned in high school.  However, I understand a sign of true fluency in a foreign language is finding yourself thinking in that language.  What does it mean, then, to think in math?

I think it means seeing manifestations of math in all your surroundings.  For example, as I ride my bicycle, I might visualize the path in space of the valve stem I just used to inflate the tires.  If I’m riding at a steady pace on a flat, smooth surface, the path looks like a sinusoidal waveform, moving up and down at a regular rate as it simultaneously moves forward in my direction of travel.  As I speed up or slow down, the frequency of the sinusoid increases or decreases accordingly.  If I’m riding through hills, the undulations of the road modulate the sinusoidal path of the valve stem; a rough surface introduces noise.

A closer look at the math in these DesignCon papers reveals another engineering truth.  Engineers need an intuitive understanding of the subject at hand, but mastering the math allows us to push performance to the physical limits.  A good mathematical model of a device and the circuit surrounding it can mean the difference between “I think this might work” and “I’m willing to bet my company’s future on this design.”

Some may say the ability to think in math fits the stereotype of the engineer who relates to things, not people.  To them I say, come to DesignCon to witness engineers relating to each other and putting their social side on display by speaking as well as thinking in math.  I might event suggest a new tag for DesignCon: Come for the networking, stay for the math.

Do you think in math?  What’s your favorite example?

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