Fly by Numbers

Numbers define our airfoils and rotation speeds, our winds aloft and ILS minimums, our fuel burn and estimated time enroute. Numbers rule, and rule absolutely if we look deeply enough. If rotation speed varies from takeoff to takeoff, it's not because the math changes, but because there are other variables---temperature, runway surface, tire inflation or bugs on the leading edge---to be taken into account or, if lacking evidence, to be searched for more deeply. If we do the legwork, the math will reward us with answers and understanding.

Like most people, I think of mathematics as a tool to describe the world around us, but theoretical mathematicians these days are enchanted with the idea that math not only describes our reality (in the case of aviation, quantifying the physics of flight), but that math is our reality. In his 2014 book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, Max Tegmark argues just this point, that we are all, planes and pilots included, part of a "giant mathematical object." In creating everything from the satellite-based Global Positioning System (with its almanacs of satellite locations and speed-of-light distance-measuring triangulations) to carbon nanotube structures and laminar flow airfoils, we are, in a sense, leveraging preexisting elements of this giant math object by applying our hard-won understanding of them.

This distinction between math describing reality or being reality is at the heart of the use of the terms "discover" and "invent." Did Bernoulli discover the properties of fluids and pressure and, hence, lift, or did he invent it? While Bernoulli took full credit for the theory, the machine underlying that principle, Tegmark would argue, was there all along patiently waiting for some clever person to stumble across it.

What does this mean to us? My theory is that pilots come in two varieties, just two. Those who love to tackle the math and those, like me, who tend to get tackled by it. Since my introduction in grade school to long division, math and anxiety have gone hand in hand for me. So, as a teenager embarking upon my Private Pilot coursework, I was profoundly unsettled by the realization that this whole flying thing involved math and plenty of.

I loved flying, and I was good at the physical part of it. I loved the feel of the controls in my hands, loved the sense of playing out the last little bits of lift to chirp the Goodyears while settling back home. Figuring out raw data navigation solutions, on the other hand, would put me in the fetal position.

Luckily, I realized a couple of things early on or I'd never have kept flying: First was the realization that the airplane wouldn't fall out of the sky because I couldn't solve for X. Second was that there were shortcuts galore that could greatly aid us math-light types: To estimate time enroute, for example, with a 120 mph airplane like the Warrior I learned to fly in, just figure two miles per minute. Add in a few minutes for climb and you're going to be really close, often, I've discovered, closer than if I'd used the POH. Moreover, I like that shortcuts like this give no hard answers, a fact that resonates with my worldview, that with the infinite number of variables that invade our best attempts to arrive at a certain answer to any question, the best you can do is a really good approximation.

With the arrival in the late '80s in my flying world of area navigation (in the form of LORAN), I was ecstatic. Now I could let the instrument do the math for me, and I could luxuriate in the white light of warm and fuzzy information instead of hard, demanding data. I feel the same way today about onboard computers that calculate my landing speeds for me. And, yes, I love that magenta line.

At the same time, I don't pretend for a second that math isn't at the heart of all we do in an airplane. As I dive into the POH to calculate takeoff distances or fuel loads, I'm reminded of Tegmark's "giant mathematical object." I have no doubt that this pilot and whatever airplane I might be flying that day are simply a part of that grand expression of numbers swirling in their infinite and beautiful complexity. I'm good with that. And the chirping of those Goodyears still sounds as sweet.