[FRIAM] FW: Math emojis
lrudolph at meganet.net
lrudolph at meganet.net
Wed Jan 30 17:09:44 EST 2019
The joke (such as it is) is a discourse joke, playing upon the fact
(incontestable to all fluent writers/speakers of MathEng, i.e.,
mathematicians' English) that the fragment of MathEng "For every \epsilon
< 0" is perfectly well formed both syntactically and semantically, but
violates the established pragmatics of MathEng. (Excuse the TeX, but when
I try to paste the Greek letter epsilon into this window, hijinx ensue;
imagine it's there, instead of \epsilon.) [Added before mailing: it occurs
to me that you, as an expert on "pragmatism", may not be familiar with the
linguists' term-of-art "pragmatics", which I learned long ago from my
daughter Susanna, whom you met in Santa Fe. The first definition Google
gives is what I mean: "the branch of linguistics dealing with language in
use and the contexts in which it is used, including such matters as
deixis, the taking of turns in conversation, text organization,
presupposition, and implicature." In particular, the "joke" in question
depends on presuppositions and implicatures.]
Even as a hopeless non-fluent occasional witness of MathEng, Nick, you can
easily acquire evidence in favor of my claim about syntax by browsing
mathematical papers for fragments of the form "For every [glyph] <
[glyph]" until you are convinced of the proposition that the MathEng
discourse community accepts such a fragment as well-formed.
With perhaps more work than you can be expected to do, you might also
acquire evidence in favor of my claim about semantics by browsing for
contexts that convince you of several propositions about MathEng: (1) very
generally, the glyph (here expanded as) \epsilon is used in MathEng to
denote a "real number"; (2) the glyph 0, in both MathEng and colloquial
English, is used to denote the (real) number zero; (3) the glyph < is used
in MathEng to denote a relationship that two real numbers may or may not
bear to each other, namely, the string of glyphs p < q is used to denote
that p is less than (and not equal to) q; (4) there *are* real numbers
less than 0; ... and perhaps more; whence "For every \epsilon < 0" is a
meaningful fragment of MathEng.
*However*, without sufficient exposure to MathEng discourses (and
certainly exposure more than you have had, or would tolerate having in the
present or future) it would be unlikely that you could figure out on your
own that IN PRESENT PRACTICE within the MathEng discourse community all
the following propositions are true. (A) The glyph \epsilon is nearly
always used to denote a "small" real number (or an "arbitrary" real number
that "becomes" small), where in the context of "the real number system"
(among others) "small" means "close to 0". (B) More specifically, in many
(but not all) such contexts, "small" means "close to 0 BUT LARGER THAN 0".
(C) The most common context of type (B)--at least for mathematics
students and most, but probably not all, more fully-fledged Working
Mathematicians)--are the MathEng discourse fragments "For every \epsilon >
0", "For every sufficiently small \epsilon > 0", and their variants with
"every" replaced by "all". [This is an empirical claim. I have not done
anything to test it (although if you have read those Book Fragments I sent
you, you will see there several examples where I *have* accumulated strong
empirical evidence, from exhaustive queries of extensive corpora of
MathEng, for other claims about MathEng: which should convince you, I
hope, that my MathEng intuitions are not invariably pulled out of my ass).
I will bet you a shiny new dime that it's true.] THEREFORE, in the
actually existing community of contemporary fluent users of MathEng, the
syntactically and semantically impeccable fragment "For every \epsilon <
0" is pragmatically defective: nobody would say that!
If that hasn't explained any slightest \epsilon of humor out of the joke,
I don't know why not. Perhaps you could respond with a Peircean analysis
of the semiotics of the joke, and *really* kill it dead.
Lee
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