the shortest distance – observations

Airborne navigation, especially dead reckoning, continues to be a rich source of observations that apply to life and it’s journey.  Dead reckoning is the kind of navigation that begins with a known location, and then proceeds in a known direction at a given rate for a specified time. An alternate way of looking at this kind of navigation is the process of attempting to follow a line drawn on a map.

Figuring out what line to draw turns out to be a hard decision.

In a flight across North Carolina from Greensboro to Wilmington, for example, one could draw a single, straight line beginning at the point of origin and terminating at the destination. As they say, the shortest distance between any two points is a straight line.  This may not be the best choice though, because dead reckoning relies on accurately measuring and maintaining the direction, the speed, and the time, which is not as easy at is sounds. (Centuries of nautical disasters should be enough to convince the reader of this fact.)

On the other hand, in aerial navigation one has the option of changing the length of a given leg of the journey. This is done by examining the map and choosing suitable landmarks along or near the desired route by which to confirm one’s position. Once the position is accurately determined, the process of dead reckoning begins anew, and so, by a series of intermediate legs, the journey is made to final destination. Segmenting a journey in this way usually results in a zigzag path, but the benefits of an accurate position fix are worth the cost. The process becomes a trade-off. In the age of rudimentary navigation, before GPS, this trade-off was a necessity, because the precision of the navigation instruments required more frequent reference to the ground below and its depiction on the map.

There may be other, less obvious reasons for segmenting or zigzagging. Early roads circumnavigated obstacles like mountains, and chose to cross natural boundaries at particular spots. Though the air affords a certain amount of freedom from these constraints, the airspace itself has structural limitations and invisible obstacles as well as visible ones, like the occasional towering thunderstorm. In both cases, one finds the need to accurately fix one’s position, to crosscheck the accuracy of one’s dead reckoning.

In the first example, the longer one performs dead reckoning, the more likely it is to drift off course, falling prey to the effects of the wind or the magnetic compass. Many have spoken of this phenomenon, but to quantify its effect, briefly consider this: an error of one degree in heading adds up to being a full mile off-course for every sixty miles flown over the ground. This assumes, of course, that the pilot has held the heading perfectly steady for the entire time, which is also nearly impossible. It is also difficult to determine the effects of the wind on the speed of the aircraft over the ground, for the airspeed indicator only shows one’s speed through the air. More or less headwind than planned will only compound error, and again we have the added difficulty of maintaining the desired speed precisely.

As we ruminate on these principles of navigation, we might wonder thus: “If dividing a long leg into shorter segments improves our navigational accuracy, why not segment it into even more shorter legs.” In the extreme, we can see the fallacy of this reasoning. At the speed of the aircraft, it is impossible to consult the map every second, then adjust the course, cross reference the landmarks below…and so on and so forth. There is a practical limit that prevents us from scaling the navigation task to the infinitesimal.

So what is the best length of a given segment of the journey?

The answer to the seemingly benign question is complicated and depends on a number of variables. In the final effort, it will require a skill called judgment to synthesize the uncertainty, variability, and complexity, and thence to propose a solution. The best may, in fact, be indeterminate.  As it turns out, making our way through the pathless air isn’t easy.

This seems to be a reasonable analogy for life.

Sometimes learning to make these kinds of decisions takes trial and error. Other times, it helps to have an accurate map or a guide.

Life is a journey. And these are observations from ours.


You’ve just read observations, a column that illustrates in my personal life and leadership the technical concepts found in ATOMs.

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