It’s easier when you can have it all

Life was more complicated in the old days. Not only were many things more difficult and tedious to accomplish, often you had to work out which of several methods you should use depending on what you really needed done. It’s much easier now. Really.

Our scientific consultants remember a different time. The need to do a calculation, say multiplying or dividing a couple of numbers, was as pressing then as now. But you had two choices: the slide rule or the log table. The first, a very ingenious device, would serve you the answer in an instant. If you were careful and in practice, you could get the answer reliably to within about a percent. (It is not true that our consultants have slide-rule competitions on slow Tuesday afternoons. But there probably are some of these things around the offices somewhere.)

If you needed something more exact, however, you had recourse to log tables. By laboriously looking up numbers in tables, adding or subtracting them, and looking up that number in other tables, you could come up with something right to within one part in a million. That’s what you wanted when designing a rocket to the Moon, or a photographic lens. You needed to be very careful about going to the right page and picking the right column, though, and carrying the number into the next column properly. In fact a 1917 book on lens design, the acknowledged reference work on the subject until sometime in the 1990s, had an entire chapter on how not to make mistakes with log table calculations.

That’s over. With the appearance of the electronic calculator you could have more accuracy than you could use, instantly. You don’t have to weigh how much time you can spend against how exact you need to be.

And in marine navigation, out at sea beyond sight or smell of land you had your sextant and sometimes LORAN. They could tell your position to within, at best, a mile or so, and sometimes not very often, but in the open ocean that was all you needed. In sight or radar range of land, when you needed to be more precise, ranges or bearings allowed you to do so. Some people remarked on how it worked out that you had the accuracy when you needed it. (They had never been faced with shoal water out of sight of land, as our navigator has, or thick fog near low-lying swamp that doesn’t return radar worth a damn.)

Well, now we have GPS, which can tell the navigator which side of the ship he’s on even in a dense overcast, when he’s so far from land he’s forgotten what it looks like. And you don’t even have to record and plot the position on a chart; the computer does it for you.

It’s far, far better for safety at sea, never mind the peace of mind of the captain.

And yet—

Our navigator has his Rules of Navigation, derived from many years of practice. The First is: “Always have at least two entirely independent ways of doing anything you need to do: fix the position, find your speed, work out your direction.” If you only have one way, regardless of how accurate or convenient it is, well, you only have one.  How do you know it’s right?