I will illustrate why.įirst, we have to think about the problem in a slightly different way. The old sailor is correct! According to our notation, that ONLY depends on the number of N's, E's, S's or W's, we can ALWAYS create another 'finer' degree of precision. Is the old sailor's claim true? Can you come up with some combination of 'north's and 'east's (or some other combination of two adjacent cardinal points) that doesn't correspond to a point on the infinite compass rose? 'That's cool,' said Stewart, now turning his attention to a wind-up clock. But I assure you, I can tell you the direction of any combination of two adjacent cardinal directions you like.' 'You can only name directions with two of the four cardinal directions that are next to each other. 'It'll take more than that to outfox me,' laughed John. 'What about north-west-south-east?' asked Stewart smartly. John had his fingers out counting how many 'south's and 'west's his young pupil had uttered out (six and eleven, respectively). He then blurted out, 'How about west-west-south-south-south-west-west-south-west-west-west-west-south-south-west-west-west?' 'Okay then,' said Stewart, frowning in thought. You can't use a number of 'south's and 'east's with a common factor,' explained John. 'How about south-east-east-south?' asked Stewart. 'Only the number of norths and easts matters, not their orders.' 'That's the same as the last one, 9/64 from north,' explained Stewart. 'And north-north-north-east-east-east-east?' You can name any number of 'north's and 'east's as you like, and I can tell you what fraction it is.'

Stewart then decided to ask, 'What about east-east-east-north-north-east-north?' Check for yourself.' Stewart located the arrow pointing 5/32 of the way around the circle, and sure enough, it read north-east-east-north-east. 'So what would north-east-east-north-east be?' Stewart decided to challenge the old sailor on this. Just like north-east is between north and east, and east-north-east is between east and north-east.' Each direction is named the combination of the two directions it's between. These directions are just for decoration on the compass. Stewart asked his great-uncle, 'Uncle John, how did you keep track of all these directions? Didn't you use degrees like we do today?' And it also had the 1/128 bearings and the 1/256 bearings, and so on down until they were so small that Stewart couldn't see them anymore. And between those were thirty-two markings for the 1/64 bearings, starting from north-north-north-north-east. There were sixteen markings for each of the 1/32 bearings, starting from north-north-north-east. Halfway again between those markings were eight markings for the 22.5° (1/16) bearings corresponding to north-north-east, east-north-east, and so on.īut what was special about this giant compass is that the markings went further down. Halfway between those markings were four more markings for the 45° (1/8) bearings of north-east, south-east, south-west, and north-west. It was beautifully constructed, with hand-printed markings for north, east, south and west. One item caught his eye, which was a giant compass like one would find on a table inside the ship. Stewart was fascinated by all the trinkets. An old sailor, by the name of John, was in his attic with his bright young great-nephew Stewart, showing him all the old tools they used to use while at sea.

Compass rose puzzle uncharted