Small mistakes

We compare old and new examples of unforgiving calculations.

Our navigator was going through some of his old files this past week and found a couple of sight forms.  These are the organized mathematics of celestial navigation, the calculations that come between the sextant measurement of an altitude and the plot on the chart of a position.  They are not sophisticated calculations in themselves, mostly adding or subtracting and pulling numbers out of tables; the highest-level skill required is interpolation.  But there are many opportunities to make mistakes.  And, since the result is the small difference between two big numbers, small mistakes have enormous results.  Misreading the sextant altitude by a degree, for instance, means the result is off by a minimum of sixty nautical miles.

It was, our navigator says, a very useful discipline.  He learned to do math without making mistakes.  More accurately, he learned ways to check his work, so that his mistakes would be caught at once rather than propagating through the sight form.  He has recently been trying to recall the various techniques he used, because in explicit form they are of some use to our tutor.  For instance: double-check each number coming into or going out of a table (a remarkable number of student errors are just clerical); if you subtract one number from another, the result should be smaller; even if you’re sure, refer to the printed rules (add East longitude, subtract West); double-check that you’re on the right page of the table, and the right section of each page (latitude and declination same or opposite).  And it was all done under time pressure, because each minute spent working through the form took the ship that much farther from the calculated position.  Into, that is, the unknown.

It is certainly unreasonable to require anything similar of students nowadays.  Even in the old days, the number of officers who could do reliable celestial navigation by hand was limited, and now computers handle most of the fiddly bits.  But our tutor sometimes wishes he could run some of his students through a sight form.  Or two.  Or several.  And insist on a correct answer.

Meanwhile, students are now learning a process that is equally unforgiving, though in different ways.  Writing a computer program requires that one’s syntax be just so and not otherwise.  A misplaced parenthesis can cause havoc, and error messages may or may not point to the right source.  While there is some leeway for different algorithms, or different implementations of the same algorithm, once an approach is chosen there is little scope for small mistakes.

There are differences between the disciplines, of course.  Even with the tightest of deadlines, computer programming does not suffer under the tyranny of the clock the way navigation does.  On the other hand, the sight form is straightforward and already laid out; one need not try to set up the algorithm.  But a program may give the wrong answer without any clue that it’s incorrect.

Life today is probably no more forgiving of small mistakes than in the old days.  Maybe some practice with a sight form would be useful.