Yes sir, helpful. Statistics is where the rubber meets the road, as the say,
in terms of sucking in data from the "empirical world" (as if there were others),
as I'm starting to re-appreciate.
DIGITAL MATH
As a worker on the digital mathematics railroad (formerly "discrete math"
but morphing), I'm keen to abet numeric content, so familiar from arithmetic,
with lexical content, as executable math notations (aka "programming
languages") tend to work with words, characters, semantic content
other than "just numbers".
SAME VS DIFFERENT
By focusing on the nominal (naming) functions of language, irrespective
of sorting and ordering, I get back to basic taxonomies such as mammals,
fungi, plants, micro-organisms... a biological beginning where the first
step is to tell things apart and to recognize when we have another one
of the "same thing". Simple counting (none, 1, 2, 3...) depends on
recognizing "this is another one of those" (sheep, apples....).
MATH OBJECTS
In the world of "math objects", we have a similar need to distinguish
different types of "thing" (object) without worrying about ranking them.
A "vector" is a mathematical "creature", as is a "polyhedron", a "set",
a "rectangular table" (of data) and so forth. The mathematical vista
is populated with these "animals" we distinguish nominally (by name).
NAMESPACES
Then comes the concept of "namespace", which sounds too advanced
in some contexts, but it simply means the names we're using depends
on the language in play. The concept of fluid. We might be talking
about Russian vs. English. We might be talking about a mathematical
language which invents new meanings for familiar words (happens
all the time).
NOMINAL VS ORDINAL
In my own experience, I've had a couple library jobs, both involved
with sorting books, putting them where they belong on the shelves,
in an order corresponding to cards in a card catalog. Sometimes
the titles were in Arabic. When being trained, I was exposed to
extended alphabetical rules that deal with the interleaving of
multiple languages and character sets (so-called collations, a
concept in unicode).
HOW IT WORKS
Mathematics classes don't typically deal with such as the Dewey
decimal system (that's library science), but the new digital math
track might go there (physical libraries are still a reality). I also
want to dissect the concept of URL in the context of the Web,
to tell stories about "how it works", about protocols, tcp/ip... all
"advanced topics" when studied in detail, but also useful and
relevant from the proverbial "10,000 feet". URLs, DNS, IP numbers...
-- lots of "nominalism" there.
Kirby