A more descriptive title for this essay would be
“multiword idioms, typically not recognized by lexicographers as deserving
own-place headword entry paralleling that of any other multimorphemic
lexeme”. But cryptonym sounds snazzier; and the meaning you’ll find online
(“secret word”) is not actually used by those who deal daily with codewords and
cover-terms, so we here use it as we see fit.
Our lesson for the day concerns: up to.
As anyone learning a foreign language is well
aware, and as speakers considering their own native language are not aware at
all, the hardest words in any language -- the most difficult to characterize
definitionally, and the hardest for a nonnative speaker to use with real
Sprachgefühl -- are the shortest ones.
(This practically follows from Zipf’s Law.) And when you have two monosyllables cheek-by-jowl : Trouble!
~
One of the things that used to irk me when I
worked at Merriam-Webster dictionaries, was their characteristic disinclination
to deny own-place entry as a lexicalized, bold-face headword, to multi-word
idioms, provided these were written with spaces between the words. If written solid or with hyphens,
they were welcomed as own-place entries:
nevertheless, devil-may-care. This meant that some phrases whose senses were not predictable
from their parts, and which permitted only very limited variation in their
parts (cf. nonetheless,
the-devil-may-care) would be defined
only as run-ons to one of their constituents (kick the bucket at kick,
and not at bucket) -- or, far worse,
received no boldface status at all,
but had to be found at some postulated and by now rare or obsolete
sense, not called out typographically, and indeed disguised by the practice of
replacing the headword in angled-bracketed exemplifications with a tilde:
to
function with vitality and energy <still alive and ~ing at 75 years>
--
Webster’s Third New International Dictionary (Unabridged)
From this, the reader would have no idea that alive and kicking is about a million
times more frequent than breathing and kicking or raising begonias and kicking or what
have you.
Now, in this case, the M-W Collegiate actually
does give own-place entry to our quarry of the day: You can find up to
as a boldface headword, at its own alphabetical place: right after uptime, rather than as a run-on s.v. up. So far so
good. But the problem is, they
basically give it only one meaning (split unimportantly into two
subsenses): that of reaching as
far as a certain limit, that limit being the complement of up to. There
are, however, several other senses, which that dictionary does not there
record.
As:
Are
you úp to it?
Meaning:
Are you capable of doing it.
(Contrast: “Are you up for it?”, meaning: are you in the mood to do it; are you game.
And:
That’s
up to yóu.
Meaning: The decision is yours to make. -- Oddly, British English
apparently uses down to in the same
or similar sense. (“It’s down to
me, the change has come, she’s under my thumb.”)
Note, b.t.w., the accent marks, which are inherent
in these idioms, and which scarcely any dictionary thinks of noting. That the patterns are here
different suggests that we are actually dealing with subtly distinct entities,
cryptic even within the class of cryptonyms (for that is but a proper class,
and not a well-defined set); but that is a refinement with which we need not
grapple here.
And:
What
is he up to?
The usual meaning of this would be yet another
meaning: What (sketchy,
perplexing) thing is he doing?
What is he about?
There is another possibility here, the very same
that the Collegiate uniquely lexicalizes, and which requires a special context
to evoke. Namely, suppose that our person is
engaged on a stepwise-graduated task (like our diligent meso-hero in the fable Talesof Frontier Times). Here
the phrase would mean: How far has
he gotten? (Answer: four thousand
and seventy-two.)
~
Finally we arrive at a further, delicious use,
which is likely unfamiliar to you unless you have studied mathematics, and
which motivated this whole post in the first place. In mathematical writing, this use is extremely common
-- but probably unnoticed as being of the technical, special terminology of
that subject, whether by adepts or by laymen. An example:
Semisimple Lie algebras can be factored
in a unique way (up to rearrangement) as a
direct sum of simple Lie algebras.
-- Timothy Gowers, ed., The
Princeton Companion to Mathematics (2008), p. 232
(Here the “up to” clause modifies unique.) Which is to say: Their factors are unique, but the order
of these is not (just as 3 × 5 and 5 × 3
equally equal 15.)
Commonest of all: unique/uniquely “up to isomorphism”.
~
Suddenly the blood froze in my veins.
Here I thought I’d noticed something clever; but it is increasingly difficult to say
anything original these days, as Wikipedia’s omniscence takes in ever-larger
swaths of the noösphere.
And indeed -- unlike the offline lexicographers, Wiki has (like Kilroy)
already been there.
That article notes that, ‘in informal contexts’, modulo X is, like up to X, often used in
this sense of ‘considering as equivalent all entitites differing only in their X-value’.
The idioms are not quite equivalent, however. First, modulo -- and especially its abbreviation mod when followed by an integer -- originated strictly in one formal context, namely number theory. Second, modulo in non-number-theoretic uses has leaked out into the general educated population; as,
The idioms are not quite equivalent, however. First, modulo -- and especially its abbreviation mod when followed by an integer -- originated strictly in one formal context, namely number theory. Second, modulo in non-number-theoretic uses has leaked out into the general educated population; as,
Chairman: “And so, the ‘ayes’ have it
unanimously.”
A
handful of agitated spectators in the balcony: “No! No! Shame!”
Chairman
(unperturbed): “… modulo certain
yelps from the peanut gallery.”
Here it means no more than “apart from”, “setting
aside”. -- By contrast, up to is
never used in this extended way.
As an additional excellence, there is a
corresponding article in French:
But, in line with what we said earlier, that
article is contentually different,
since we are here dealing, not with an overt terminus technicus like homology/homologie, which are used the
same way withing mathematics, but
a cryptonym cobbled-together out of tiny unassuming semantically-multivalent
function-words. Thus, the nearest
French equivalent of “up to X”, namely “à X près”, is synonymous in some uses and not-quite-so in others.
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