Nominal characters once aga

[Warren Lamboy]

                       Subject:                               Time:8:05
  OFFICE MEMO          Nominal characters once again          Date:09/04/1995

Renaud Fortuner asks if there are any nominal characters that cannot be
represented by ordered characters.  I think that the answer is "yes".  For
example, leaf shapes in the genus I work in, Aster, have a several different
states (ovate, obovate, linear, lanceolate, . . . ), and yes, there is some
intraspecific variability.  Of course, you could always recode these shape
characters into several ordered characters (length, width, area, etc.), so
perhaps this disqualifies leaf shape as a nominal character, according to
Fortuner.  One must be cautious about such recodings, however, for one can
always recode nominal characters into several ordered characters, for
everything that exists, exists in some amount, some quantity, that can be
measured on an ordered scale.  I would venture to say that the only
characteristic that is always nominal and cannot always be recoded is
presence/absence, that is existence/nonexistence.

The point of my previous message concerning nominal characters was that
someone can always object that macroscopic (morphological) characters are not
"really" nominal, but they could always be ordered in some way by breaking
them down into more basic characters or their biochemical origins.

If one is allowed to answer the question in terms of protein or DNA
characters, then the answer is a resounding "Yes, there are nominal characters
that cannot be ordered, and yes, they show intraspecific variability."
Alleles at isozyme loci are one such example, so are DNA sequences and all the
types of data that depend on them, such as random amplified polymorphic DNA
markers, simple sequence repeats or microsatellite markers, restriction
fragment length polymorphisms and so on.  Most of the time there is no
rational way to order the variability observed at such DNA loci, although of
course, if we had perfect historical knowledge of the evolution of the DNA
sequence we could order them chronologically.  As I write this it occurs to me
that one could order the sequences by the number of A's, C's, G's, and T's, in
some 4-dimensional space, and then map that to a strict ordering of sequences,
using 2**A+3**B+5**C+7**D (where ** here represents the power function).  That
could impose an ordering on sequence data.  Perhaps my "Yes" above, should be
a meek and timid one, instead of a resounding one?

I am still confused about whether Renaud Fortuner's question concerns nominal
characters as they appear to us (with our imperfect knowledge of their
biochemical origins and/or evolution and without recoding as several ordered
variables) or as they "really" are (assuming we had perfect knowledge of their
biochemical origin and evolution).  In the former case, then the answer is
"Yes."  We have many such nominal characters, and many of the other writers in
this thread have given good examples of them.  If the latter case, the answer
is "No."  We could always order the characters somehow, if we had perfect and
complete knowledge.  Of course, if we had this knowledge, we wouldn't need to
use characters at all, and the question would never arise in the first place.
[Recodings of the types I mentioned above, simply for the purpose of doing
away with a nominal character, is an artificial means of answering the
question in the affirmative, in my opinion.]

As I tried to indicate in my previous email on nominal characters,  whether we
treat a character as nominal, ordinal, ratio, etc., should depend primarily on
WHAT WE WANT TO USE THE CHARACTER FOR, AND WHAT TYPE OF CHARACTER FACILITATES
HUMAN UNDERSTANDING.

Am I missing something?

-Warren