Types of numerals

I've been thinking about numerals lately. Particularily, of all the possible
different types of them. So here goes loads of rambling on the topic. Feel
free to steal and/or shoot down any ideas contained. Commenting on them I
even welcome. :)

.:DEFINITIONS:.

First off, I confess that I not sure if you'll recognize "numeral" as a word
for the class of "number words" (never seen it used in that way in English;
only Finnish.) If it actually is something else instead, do tell. Also,
whenever I'm talking about "series", I mean an ordered infinite series where
each member is related in meaning to the respective natural number. By my
definition, all numerals must belong in some series (won't be much of a
numeral otherwise).

.:BASIC SERIES:.

Every language probably has the two basic series - the natural cardinals
(one, two, three...) and the natural ordinals (first, second, third...) But
is it always the former which is the open lexical category? Does any
language have ordinals as the unmarked series instead?

I presume that another universal feature is that while numerals are an open
class (theoretically more open than any other word class - but lets not go
there now), after a certain threshold, all words relating to a certain
number will be derived similarily. Typically there is a system to derive
infinitely many cardinals and a system to derive other series from them.
However... isn't it theoretically possible to have more than one "root
series"? This would probably need a base of 5 or less, given that languages
usually have only very few non-cardinal numerals which are unrelated to the
corresponding cardinal words. In fact, all languages I know of have 2 per
series tops, but I imagine languages with trial as a lexical number might
have 3? Does this happen? And in a conlang, would a little more, maybe 5, be
plausible?

Hm, what I'm proposing might be a little hard to grasp from the previous
paragraph, so I'll construct an example using English and base 2. So suppose
the cardinal series goes "one, two, onety-one..."; but meanwhile, the
ordinal series goes "first, second, firsty-first..." rather than
"...onety-first...". That is, NO ordinals would be derived from the
corresponding cardinals - but rather simpler ordinals in a way similar, but
perhaps not identical, to how more complex cardinals are derived from
simpler cardinals.

One could then split the class of numerals into "cardinal-derived" vs.
"ordinal-derived" - maybe even contrasting other series purely by their
roots. This is almost trivial to extend into mathematical series (half vs.
halfth), but it might be possible to carry it over to grammatical series too
- eg. contrasting the (cardinal-derived) word "trio" with an
(ordinal-derived) word meaning maybe something along the lines of "third
member of a trio".

.:A MATHEMATICAL P.O.V.:.

"Mathematical series" are technically still cardinal series, formed by
filtering the natural numbers {0, 1, 2, 3...} thru some random function.
AFAIK, only reciprocals (half, third, quarter...) and exponents of the base
number (ten, hundred, thousand...) are lexical anywhere. Unusually geeky
loglangs might have more, but even then, I doubt whether expressing eg. -6
as something along the lines of "unsix" would be useful.
...And speaking of negative numbers, why doesn't -1 have a name on its own,
but i does?

There are also often a handful of numbers which have an original name in
addition to a derived one. Most of the ones I know have been used as units
of measure (eg. Finnish "tiu" is a unit of 20 eggs), but are there others?
Eg. is the Latin prefix sesqui- really a *root* morpheme? If yes, I could
imagine lexicalizing other simple fractions too, like 2/3 and 3/4. Also I
might add the golden and silver ratios (the latter is sqrt(2)) to uwjge...
Have any of you lexicalized any unusual numbers in your conlangs? I'd be
interested to hear.

.:OTHER NUMERALS:.

So what other numerals are there? English has at least the "group numerals"
(single, duo, trio...), the "repeat numerals" (once, twice, thrice...)
Polygons, time-period names ("biweekly") etc. are probably best considered
compound words. In Finnish, the simplest polygon names are derived instead
(with the generic agentative affix -iO), and we also have a series which are
used as the names of the number symbols, as well as sort of pronouns for
things with ID numbers... What other series are you aware of? I might be
overlooking some obvious one.

There's also the possibility of adding "generic" numerals to each series.
"Number" is essentially a generic cardinal, and "nth" might count for a
generic ordinal... but it's a little iffy beyond those. Would you think
others were likely to exist?

---
That's all I can think of now; more maybe later, if the topic gathers any
discussion...

John Vertical

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