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When I studied navigation as a kid in the 1970s, RYA/DOT Yachmaster
theory at nightschool, I was puzzled by the strange mariners mnemonics
for remembering if deviation or variation should be subtracted. The
mainly adult students at the time, as Frank said,  found algebraic
reasoning difficult. To me it was natural to just 1) decide which was
the "dominant" direction to convert and 2)  take E to be positive. The
rest is algebra. They insisted on "variation west compass best (ie
most)" .  Later my Yachtmaster ocean teacher went to great lengths to
explain if one was closer or further from the GP of a body if the
altitude was bigger or smaller. I didn't understand as I thought it
was obvious. She had navigated  all the oceans of the world several
times.  I began to understand that when you are tired, cold, lacking
oxygen or seasick, the  ability to do basic algebra seems to be the
first thing your brain shuts down, and yet you can still remember
silly rhymes.

On the subject of negatives I am old enough to have learnt the use of
log tables at primary school. There was a strange convention whereby a
negative real number x was represented as integer part `n of x, with
an over bar, dot  then   1+ fractional part (I am taking the
fractional part as negative).   I mention this as it puzzled me when I
was small if there was an alternative to negative numbers, some
quantity that did not obey the usual rules like -1 times -1 =1.  The
answer is largely NO, mostly you want things you can add and multiply
to work like a ring. Rings with a 1 for which  1+1=0 are perhaps the
strangest and of course arithmetic modulo two is important in logic
and binary electronics, for example.

Of course there is some wonderful hidden complexity in the compass.
The earth's magnetic field is a vector field (or perhaps a twisted
two-form). The compass has a magnetic moment, as do bits of metal
around the ship.  The dynamics of the compass are governed by the
interaction of the fields and the friction and drag of the compass
card, varying with the heal and pitch of the boat as well as its
accelerations. So it is complicated, and mariners have a knack of
boiling it down to simple approximations that are good enough and can
be done under non-ideal conditions for brain work.

Bill Lionheart

   

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