Measurements in the physical world of Euclid and
Newton are either lengths or angles. Angles are cyclic in nature and
so can be mapped with a modular type. However, this leaves scaling in
the hands of the user and is machine dependent. Consideration was given
to the possibility of a cyclic form of fixed point. Sadly, there was
much hidden complexity and so no solution was agreed. (See
AI-175).
One might have thought that it would be easy to use
the natural wrap-around hardware. However, with a binary machine, if
180 degrees is held exactly then 60 degrees is not which excludes an
exact representation of an equilateral triangle. The whole point about
using fixed point is that it is precise but it just doesn't work unless
the hardware uses a base with divisibility by 60. The Babylonians would
have understood. The text of
AI-175
includes a generic which might be useful for many applications.
© 2011, 2012, 2013 John Barnes Informatics.
