Recently I was helping Mikayla review for a math placement test. First off, numbers have never been my strong suit. I can get by (on a good day) and that’s about it. We got to a spot where we were supposed to review subtraction of negative numbers. “Oh boy” I thought, and for a moment I started looking for an escape route. But then, by the grace of God, I remembered the rule about changing the sign of the negative number to positive and then changing the subtraction to addition. Wow, was I ever proud of myself for remembering that rule. I rattled it off with all the mathematical prowess I could muster and hoped we could move on.
But Mikayla, being who she is, asked “why”. I drew out a number line and attempted a half-baked explanation, but at some point fell back to some version of “I don’t know, ask your mother.” In this case, good advice because mom is darn good at math.
Later in the day I was shoveling manure. All great ideas come to me while picking manure; I should do more of that. What is it about manure that gets those neurons firing? Thats a question for another day.
I remembered some sage advice I’d received many years before. It was my first job out of school. I was a R&D scientist at a small biotech company, a newly minted PhD wanting to please EVERYONE and change the world. After working for only a few weeks, I soon realized that about 5% of our customers took up about 50% of the company’s R&D resources (mostly in the form of scientist time).
My manager Rob and I were talking one day about a customer who was especially “challenging” (a real pain-in-the synonym-for-donkey). Rob put on his serious face and looked me square in the eye. “Mike” he said “Listen-up, I’m about to tell you something very important; something they didn’t teach you in PhD-school. Rob then gave advice I have never forgotten: “Sometimes its better if the customer just goes away.”
My jaw dropped. My manager had just said something that was in direct conflict with the company’s “customer-driven” mission statement; a statement that I had just memorized and recited to complete my HR new hire training only weeks before. I wondered if I should report Rob directly to the company president for this infraction.
Before I could say anything Rob continued, “You see Mike, its called addition by subtraction. A customer like this goes away and can serve all of our other customers more effectively.” Having been an addition-man all of my life this was mind-blowing. Addition by subtraction, WOW!!
So you see I did actually have an explanation to Mikayla’s questions about subtracting negative numbers, but it involved experience rather than postulates or theorems.
I’ve come to appreciate the general applicability of this idea. There are two ways to add. We can add a positive, we can accumulate; if it truly is a positive, this is a good thing. We can also subtract a negative; dump stuff that is dead weight that maybe we only carry around out of habit or obligation. Another word for this simplify.
Math teachers say it and so did the man that lived in the cabin-in-the-woods, the one on Walden Pond.