potential names

[Paul Taylor <pt10@PaulTaylor.EU>]

Todd Trimble wrote:
> Of the choices offered here, I like "precarious", "unstable", or
> "fragile".  I just thought of "risky" myself.  Good, experienced
> mathematicians will know when it's okay to take "risks" (and
> will be aware of what the risks are).
>
> "Unstable" seems like a very sober choice, not too likely to
> ruffle feathers.

Mathematical terminology should not employ words that are merely
value judgements, without relevant content.  It doesn't make any
difference whether they are offensive or inoffensive value-judgement
words.  This is not how we should choose scientific terminology.

We are already cursed with vast over-use of the words "regular"
and "normal" in mathematics.   Roughly translated, these mean
"the objects that I want to study" - other people may have very
good reasons for studying other kinds of objects.

("Stable" and "sober" already have several meanings.)

There is a problem here in that there is nothing in the education
of a pure mathematician that teaches how to make a professional
judgement.   I never thought I would find myself defending
software engineering (the religion whose creed it is that programs
are better if their authors wear suits, draw diagrams and attend
committee meetings) but when computer science students are subjected
to this at least they learn that, whatever they do, they are making
professional judgements.

Since pure mathematicians do nothing similar in their training
they are easily mis-led by the use of terminology that is based
on value judgements.   They just think that they are taking
dictation from God.

Even if there is a very strong argument in favour of a particular
value judgement (as there may well be in the case under discussion)
we should still not use words that have no other content, simply
because we will want to make OTHER value judgements in future.

The English language reportedly now contains over a million words.
Can you really not find anything in this vast thesaurus (=treasury)
that describes the situation more appropriately and precisely?
There is less, not more, of an excuse if you speak French, Spanish
or another language: English allows almost completely free
immigration of words.

Let's have a bit of imagination with language, please.

Despite the abuse that I received for it here, I am rather pleased
with my introduction of the words "prone" and "supine" for the two
different orthogonal notions to "vertical" in a fibration.

A word was needed to replace "open" for an object whose terminal
projection is an open map, since subobjects with this property
have a habit of being closed subspaces.   The rich English
vocabulary offered "overt", which means "explicit".   Since I first
used this word, it has emerged that this idea is very closely related
to recursive enumerability, ie to having an explicit presentation,
so this has turned out to be a very good choice of word.

On the other hand, I regret introducing "bilimit" and "bifinite"
in domain theory.

In the case under discussion we need to distinguish between equal
and isomorphic objects.   In existing terminology, a category in
which isomorphic objects are equal is called "skeletal", although
I doubt whether this word ever gets another outing after the
definition of a category and basic concepts therein has been
given for the first time to students.

So my suggestion is that you play around with skeletons, bones
or even the Grim Reaper for something more suitable.

Paul Taylor



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