From the Editor’s Desk: Math ⭐

By the time I got to high school, I knew what I liked and I paid little attention to what I didn’t. This didn’t go well for me academically. And it is somewhat ironic that two of the topics I didn’t care about much at all would come back to haunt me later in life.

The first was Spanish, which I took all four years of high school while barely paying attention and barely passing. When you consider that we later bought an apartment in Mexico City and spend half our time there now, you can see the irony. My calcified brain is barely capable of learning anything now, and I’d love to get that wasted time in high school back.

The second is math. And here, I mean math in all its forms. I did so badly across a few algebra classes in what was then called junior high school that I ended up retaking and barely passing algebra in high school. And then my high school offered its first-ever computer programming classes when I was a junior. And because those classes were considered math, I never moved on to higher level math classes like pre-calc and calculus like most of the other students. I could barely handle chemistry, and physics was beyond me.

The only math class I did well in during that phase of my schooling was geometry. In that class, I got all A’s, confusing my parents and teachers alike. But that’s because I was an artist, and to me, geometry was all about drawing, and so I actually paid attention. But don’t worry, there’s irony in that, too: I went from high school to an art school for college, but only for one year because I suddenly realized that was a path to never having a good career. So I was checked out by the second semester, mentally, and I dropped out of that school after the first year.

A series of re-do attempts followed at various schools, mostly part-time. But in 1993, my wife and I moved to the Phoenix area so I could go back to college, this time for computer science. I was going to become a programmer, a career I maybe should have considered in high school, given how much the topic interested me then. I had taught myself programming over many years, many computer platforms (starting with the Intellivision and its Entertainment Computer System add-on, but then the Commodore 64/128, Apple IIGS, and Amiga), and various programming languages (BASIC, of course, but also Pascal and C). And when I went back to school to study this formally, I of course moved to the PC, where I started off with Turbo Pascal before moving on to C, C++, and then Visual Basic and more.

This was when I met Gary Brent, a professor and programmer who jumpstarted my writing career. I’ve told these stories before, so here I’ll just say that Gary was possibly the smartest person I’ve ever met. And yet he, like me, was actually pretty terrible at math. So I was surprised one day when he complimented me on my ability to calculate restaurant tips in my head.

I dismissed this compliment by telling him that I was cheating because I wasn’t doing “real” math. At the time, 15 percent tips were the standard in the U.S., and it seemed obvious to me anyone could calculate that tip using a workaround: Calculating 10 percent was simple, and all you had to do was add half that number to whatever the 10 percent figure was.

Right, he said. That’s why you’re good at math. That’s obvious to you.

Hm.

I don’t think I’m good at math. But the real irony in all this—and it’s odd how that word keeps coming up—is that I probably could be. It’s clear to me now, all these decades later, that part of the issue I had with math early on was tied to the teachers I had, some of whom were terrible, and their presentation styles. This was an era well before we understood or acknowledged things like attention deficit disorder (ADD) and similarly common conditions that most people deal with. I’m a member of one of the last “suck it up” generations, and making subjects interesting for students wasn’t part of the plan back then. I suspect it is now based on my interactions with my children and the teachers they had growing.

The other irony (sorry) is that I actually use math all the time. And while this has been obvious to me for quite some time, it suddenly came together for me, for whatever reason, while we were in Berlin last week. My wife kicked this off with a simple enough question.

“What time should we leave for the airport?”

We’ve had this discussion hundreds of times. And I’ve done this kind of math, what I think of as “backwards time math,” thousands of times. Easily thousands. Maybe more. I bet a lot of you, maybe all of you, have as well.

Here’s how it works.

Our flight was scheduled to leave Berlin at 9:50 am on Sunday morning, and boarding was scheduled to start at 9:00. This has changed a bit over the years, and it can vary depending on where we are at the time, but my goal is to be through security one hour before boarding starts. So in this case, 8:00 am. We’re not overly-familiar with the Berlin Brandenburg Airport, but since we were flying early on a Sunday, and based in part on previous experience, I figured 30 minutes would be more than enough time to get through security. And so that put us at 7:30 am. It had taken us almost 40 minutes to get from that airport to our hotel when we had arrived, but that was a busier time and day, and looking at it on Google Maps, I figured it would be closer to 25 minutes that morning. So let’s call it 30 minutes, meaning we would want to leave the hotel at 7:00 am. And that meant we would set our alarms—we always set at least two—for 6:00 that morning.

My wife and I stepped through the above verbally, together, and arrived at the same times. We always do this conservatively, with the idea that we prefer to get there early and have time to kill rather than be running late and get stressed. To me especially, but to both of us, eliminating stress when traveling is important.

That morning, our alarms went off at 6:00, we got cleaned and packed, had time for a few coffees and a bit of news reading, and then we headed downstairs before 7:00 am. I arranged for an Uber, which arrived in literally one minute, and the drive was less than 25 minutes, during which time the driver regaled us with tales of German politics, immigration, and other worldly issues that were perhaps a bit much for our tired brains. Traffic was non-existent, and the security lines—this is Europe, so there were three of them—all went quickly. By the time we sat down at the gate, we had almost exactly one hour to kill before boarding started. Mission accomplished.

This is the way it usually goes because most of the travel we do now is pretty predictable—mostly to and from Mexico, these days—and because we’ve gotten pretty good at this, too.

But when my wife asked this question, I had a strange moment of clarity about math. Math, this topic I had come close to failing many times when I was required to take those classes, and have largely ignored in the years since. Or so I kept telling myself. The truth, I realized, is that I do math all the time. I am doing math fairly regularly.

The most obvious example is the quarterly financial reports that I routinely cover every three months for a dozen or more tech companies. I’ll use Microsoft here as an obvious example. If you go to the Microsoft Investor website, you can find its latest earnings report, which consists of a press release, the PowerPoint slides used during the post-earnings conference call, the earnings call transcript, an SEC 10K filing, and other documentation. The income statements have all the numbers, and when it comes to financial reporting, the comparisons one makes are all year-over-year (YOY). That is, you compare any given fiscal quarter or fiscal year with the same period from one year ago.

In the quarter depicted above, Microsoft earned a net income of $27.233 billion (which I write as $27.2 billion) on revenues of $76.441 billion ($76.4 billion) during the quarter in question. And you can see that these figures are compared to the same quarter a year earlier. What’s not there is the math that determines how much these figures grew (in Microsoft’s case) or fell. Microsoft does provide those numbers, too, as it turns out. It’s just not there; it’s in the press release. So in this case, it reported that net income grew 24 percent YOY and revenues grew 18 percent. Which is what I wrote when I covered the announcement.

Not every company provides this math. Worse, sometimes the math these companies provide isn’t entirely accurate.

In the former case, this means I have to do the math. And I do this math all the time, so it’s stuck in my brain on auto-pilot. I didn’t actually check the accuracy of Microsoft’s math when I wrote about that quarter, but this is the math I would do if needed: Take the current net income/revenue figure, multiply it by 100, and then divide it by the year-ago number. For Microsoft’s revenue numbers, the answer to that math is 118.0975481638265, or what I would write as 118.1, or 18.1 percent. I’m curious now they didn’t use that figure.

Interestingly, when I was doing similar math for Apple’s most recent quarter, I came across a discrepancy that made me doubt myself. In its press release, Apple claimed that it experienced 10 percent revenue growth YOY. But when I looked at its financial statements, that number seemed off. So I did the math. And the answer to that math is 109.6284551802931, which I would write as 109.63, or 9.6 percent. Which is what I wrote when I covered the quarter.

(Don’t misunderstand me here. I’m not claiming that Apple is “lying” here. There’s always some form of rounding that occurs with these things, and I’m sure this is some established convention. But this is also Apple tilting toward the positive, if you will, which makes one wonder where else they take these liberties. Compare that to Microsoft “under-reporting” its revenue growth in the same quarter.)

That I do this kind of math repeatedly all year long is no surprise me, I’m obviously aware of it, and it’s been a constant for many years. But when my wife had asked me about leaving for the airport, other examples popped into my brain.

Tied to the airport “backwards time math,” I spend much of my time on long drives doing math because Google Maps will provide an estimated time of arrival and I always establish a realistic goal for when I or we will really arrive based on the number of times I think we’ll stop for food and/or gas (or not) and the duration of those stops. In recent years, this has usually occurred going back and forth to Boston for trips when we catch up with friends and family there. But we also drove to Charlotte back in August, which was a particularly long trip, and then back, stopping first in Washington D.C. for a few days. And that was a lot of math.

But let me keep this simple since I’m sure this is getting tedious. If I get in the car and Maps tells me that my expected arrival time is 3:00 pm, which we’ll assume is five hours from the start time, I may factor in a single stop for gas and lunch, ideally at the same location. And so I might come up with 3:15 to 3:30 as the hopeful real-world arrival time, based in part on my ability to “make up time” while driving like a bat out of hell to get there earlier.

This sometimes works, and sometimes not. But I am constantly reassessing this time based on how the drive goes, and so I am regularly glancing at the Maps display, evaluating whether we’re doing well—with the arrival time colored green—or, more often than not these days, doing poorly because there are accidents or other traffic-related issues occurring ahead of us as we go. (In which case the arrival time turns orange or even red.) The whole time, I’m doing math.

Whether this is healthy is debatable. But it at least keeps my mind occupied, which is something I do need. I can say this with certainty, though: If it’s the two of us on such a drive, and it’s going well, we can alternate between talking and periods of silence, and it’s fine. But if things are going poorly, really poorly, I will invariably suggest turning on a podcast or whatever because then I’ll need that distraction to keep my mind occupied in a way that’s better than me stressing over our ever-stretched-out arrival time.

Tipping has evolved over the years, but it’s also different in different places. And we’ve recently started trying to use cash for tips whenever possible because that’s better for the person being tipped, especially here in the United States. 20 percent is common now here in a restaurant, and that’s easy. In Mexico, 5, 10, and 15 percent are more common presets in the handheld payment terminals everyone uses. We try to do the right thing wherever we are. But one exception in Mexico, for us, is Uber. I can’t explain this, but Ubers are cheap there, and even a 20 or 30 minute ride to/from the airport or some other reasonably distant destination will typically cost under $10 US. And I cannot bring myself to tip a person who just spent 30 minutes with us in their own car, a person making next to nothing as it is, $1 or $1.50. So I usually tip more. And then get a later thank you note, indicating how rare this must be.

I’ve written about tipping a few times here and there—this, for example—but we always Google the norm when we travel to other countries. In Berlin as we were last week, for example, it’s customary to tip 5 or 10 percent in a restaurant, and cash is preferred. So we did that, and we tried to cash as much as possible. Common sense.

There’s more, so much more. Airfare prices compared over various dates and times. Whether we have time to watch a movie when it’s whatever time and the movie is whatever length. If we have time to start watching a new series based on what day of the week it is and which nights we’ll be out in the coming week. On and on it goes. But this is already longer than I expected, and I think you get the idea. I grew up expecting to be an artist, almost failing math routinely along the way, and then in meeting a genius who was nonetheless terrible at math, I started down a path to become a programmer only to end up being a writer. Who nbow does math all the time. Despite still not being any good at it.

What are the odds?

Hm. That’s math too. Let me think on that a bit.