Mathematical Frustrations in the Office

This morning, I found myself at the AVP's office, explaining to him the discount scheme that our client was bargaining for. We spent several minutes discussing, a few times I had to run back to my computer to check the rates and other data. As I was new to this business process, I was listening intently to what this businessman had to say. He asked for too many details, which meant more data-digging and additional workload for me. Nonetheless, I believed in him. "It's good that he considers different forms of analysis to come up with a sound business decision." I thought.

My respect for him was high. He's an AVP and I'm sure he knows what he's doing. He must have gone a long way to reach this far. I should just shut up and follow all his instructions.

"From A to B, the discount is 20%, am I right?" he asked, snapping me back to reality. I nodded.

"From B to C, the discount is around 20% also, right?" Again, I nodded.

I swallowed hard. "Uhm, sir, no." I politely countered, avoiding his eyes. "It's 35%... 34.9 to be exact."

"How can that be?" he asked, looking directly at me.

"Sir, it's because you have different bases." I simply said.

"What?" His voice was getting more irritated this time. For some reason, I didn't want to nod along with the boss this time. I wanted to prove my point.

"For me, it's as simple as this," he began to explain. He scribbled the following:

"From A to B it's 20%, B to C it's 20%, so from A to C, it's 40%." His voice was growing more and more impatient, and I felt like a dumb grade schooler. Good thing I knew he was wrong.

"Sir, it's like this," I, too, began scribbling some numbers. I felt guilty while writing the most "unmathematical" equation I've ever written. I prayed that none of my students would ever see what I wrote:

"Sir, to get the discount from A to C, you can't just add the discounts because we have different denominators." I said the last word with utmost care, lest he didn't know what the heck a denominator was. His face didn't change a bit, which meant one of two things - either he was not at all convinced, or my suspicion was correct - that he didn't know what denominators were.

"Sir, the discounts aren't additive because you have different bases." I tried to sound more business-like and less like a math teacher.

He didn't know I used to be a math teacher. I think my explanation offended him in some way. He, too, tried to reason out "mathematically".

"Isn't it like this?" He scribbled:

"Uhm, no."

"Are you sure? Can you show me the numbers?" he asked, making me more convinced now that he didn't care about denominators at all.

So I tapped the rates on my scientific calculator (which probably agitated him more), while he impatiently watched my poorly-manicured nails. Too bad for him, I was correct. Hah!

"I'm not so sure about that…" was all he could say. "Can you try it again?" Of course, I did. I was really correct. Promise.

"Hmmn, how can that be?" he wondered.

"Sir, you saw the numbers…"

He closed his eyes while nodding.

I just smiled and said, "Sir, sorry, I couldn't give you a convincing explanation right now, but, well, you saw the numbers…"

"Yes."

He continued to give me more stuff to do, and as I was leaving his office, I was shaking my head.

Later that day, I was eating alone at Greenwich, and I just could not resist. I grabbed a scratch paper from my bag and started my simple proof. As I was scribbling, I imagined that I was discussing the proof to my students. In my mind, I can see my students nodding along, while copying the "notes", their eyes sparkling, proudly beaming that they understood the lesson. After all, my students keep an open mind and are very intelligent people. I closed my eyes, and in my mind, I searched the classroom for the AVP. Yes, there he was. At the back of the room was a Chinese guy in his early forties, with a laptop on his desk, wearing a crisp, white polo shirt, with his secretary on his left, taking notes for him. His eyes were confused as ever, and then he raised his hand. "I can't believe this. Please prepare a PowerPoint presentation on this one," he would say. I could almost hear my sarcastic remark, "Mr. AVP, can you please review your arithmetic first?... Now, on to our next lesson…"

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