Why the compass rose has 32 points

Thirty-two is a strange-looking number until you see how it was arrived at. Nobody sat down and decided on thirty-two directions. The rose is what you get from halving an interval four times, and the naming scheme records each halving.

Four rounds of halving

Start with the two things any observer has: the direction the sun rises and the direction it sets. Add the axis perpendicular to that and you have four directions ninety degrees apart. These are the cardinals: north, east, south, west.

Halve each of those intervals and you get four more at forty-five degrees. These are the ordinals, or intercardinals, and their names are simply the two cardinals they sit between: northeast, southeast, southwest, northwest. No new words were invented, which tells you the scheme was meant to be learnable rather than elegant.

Halve again, twenty-two and a half degrees, and you get eight half-winds. The naming rule tightens here: the cardinal is always named first. It is north-northeast, never northeast-north. Once you know the rule you can generate all eight without being taught them.

Halve once more, eleven and a quarter degrees, and you get sixteen quarter-winds. These are the ones written with “by”: north by east, northeast by north, west by south. The word “by” marks a quarter-wind, and the point named first is the one you are measuring from.

Four cardinals, four ordinals, eight half-winds, sixteen quarter-winds. Thirty-two.

Reading the names

The system is generative, which is the whole point of it. Given a name you can reconstruct the bearing, and given the bearing you can reconstruct the name.

Take northeast by north. The base point is northeast, at forty-five degrees. “By north” means one quarter-point from it toward north, so subtract eleven and a quarter. Thirty-three point seven five degrees.

Or take west by south. West is 270. “By south” moves one quarter-point toward south, which from west means down toward 180, so subtract 11.25: 258.75 degrees.

Every one of the thirty-two names decodes this way, and every bearing on the card is an exact multiple of 11.25 degrees. There is nothing approximate in the system at all.

Why it stopped

It did not, entirely. Mariners divided further when they needed to, into half points and quarter points, giving cards of sixty-four and even 128 divisions. The finest subdivisions were used for recording a course precisely in a log.

But thirty-two is where the naming stopped being useful. A name has to be sayable under pressure, distinguishable from its neighbours when shouted across a deck, and memorable enough to be recalled without reference. “North northeast by north half east” fails all three tests. Past thirty-two points the names get longer than the precision is worth, and the sensible move is to abandon names and use numbers.

Which is exactly what happened. Modern practice gives bearings in degrees, written to three digits so they cannot be confused with anything else: 007, not 7. Boxing the compass, reciting all thirty-two points in order, was a standard test of a competent seaman and is now a curiosity.

What survives

The eight principal points are alive and well, because they are how people give directions in conversation. “Head northwest” is understood by everyone.

The half-winds survive in one specific place: weather reporting. A forecast says the wind is west-southwest because sixteen points is the right resolution for describing wind direction, precise enough to be useful and coarse enough not to imply accuracy the measurement does not have. Phone compasses report sixteen points for the same reason.

The quarter-winds are effectively extinct outside of historical texts and crossword puzzles. Which is a shame, in the small way that any lost vocabulary is a shame: there is something satisfying about a system where thirty-two directions can be named exactly, and every name tells you how to find it.