Explanations for Confused Little
Orderings
Often the items in a list have some natural ordering, for example, by size,
age or complexity. In such cases, the order in which the items are listed
should be the same as their natural ordering. (Sometimes there is more than
one natural ordering, in which case the list ordering should reflect the most
important natural ordering, for whatever the main purpose at hand may be.)
Here's what's wrong with each example:
- The first 4 items reflect increasing granularity of the social unit
involved, but last item has a different character from the others, because it
is a subcase of the 4th, rather than a still larger grain unit. (It could
also be argued that the 2nd is a special case of the 3rd.)
- These items have a natural ordering by the number of degrees of freedom,
and that ordering is not preserved. (Also the facts are wrong, e.g., wrists
have two degrees of freedom.)
- Units of time have a natural ordering by size, and the given ordering of
the components of a date violates that natural ordering. According to this,
the example date should be written 11 January 1998, which also has
the advantage that no commas are needed. It is interesting to notice that the
standard notation for time, e.g. 11:59:58, is consistently ordered,
but because it is by decreasing size of units, this ordering is not
consistent with any of the usual orderings for dates. Moreover, adding
"am" and "pm" after the time is also inconsistent, because
this represents a 12 hour unit. (Of course, it normally takes very little
effort to deal with these small inconsistencies, but more serious problems can
arise when it is not clear what conventions are being used, e.g., dates in
email sent from Europe to the US.)
- The different kinds of numerals may be ordered in several different ways.
One is by date of origin. Another, which is used in the exhibit on numerals, is by the complexity of computations
done using each notation. The ordering given in the list respects neither of
these two natural orderings.
In terms of semiotics, each little creature here is a complex sign that is the
image under some semiotic morphism into a sign system where the main
constructor is a list constructor, and where there is an important ordering in
the source sign system that should be mapped to the natural ordering of
elements associated with the list constructor. Of course, as dates and times
illustrate, things are not always so simple, because there may be multiple
orderings on both the source and target sign system. Moreover, the goal
and/or cultural background of the author and/or intended audience may play a
role in determining which ordering is appropriate, and this could be difficult
to determine; the is part of the "inverse problem" of inferring the source
space from a sign that (we assume) represents it.
It is very interesting to explore the representations of dates and times in
more detail. For example, there is an explanation for the conventional
ordering of times, with hours first and seconds last: usually we are more
interested in the hour than in the second. Notice that this assumes that we
are reading from left to right, which in fact is a culture dependent aspect of
reading; one imagines that cultures that read right to left may impose rather
different conventions.
12 February 1998, somewhat modified 23 January 2000.