I don't know how you come to the conclusion that it is a mathematical
absurdity but consider this: If you find that common usage propagates
something that is incorrect, should we just shrug it off or should we
attemp a correction? There is always a chance that one day you find
yourself exposed to a learning curve while going through a document.
If you just depend on common usage you will probably draw the wrong
conclusion.
The only way one could assume the "common usage" to be a mathematical
absurdity would be not to think about it or not to have much
mathematical insight or "maturity". Is a vertical cliff not steep no
matter how high it is? And is a gentle grade (say <= 10%) not
un-steep no matter how long it is? Is the slope of a curve dependent
on its length?
So the remark that " a steep learning curve means that the subject is
easily familiarized and that the learning period is short" is
completely incorrect on two points (i.e., all points that are
relevant): first, steep always implies much to learn in a relatively
short time (what else could the slope of a curve possibly mean
"mathematicallY" or logically?); second, steepness is independent of
length, so "steep" has no implication in general about how long the
learning curve will be--on the contrary, in fact, it's quite possible
that a learning curve will never have any great challenges (steep
portions) but be only a very long gradual process--as the learning of
many natural languages is.
A learning curve is conventionally the graph of a function of
"quantity to be learned" vs. time, and it may be steep or not and,
independently, may be long or not. And if it's long and complex
enough, it may have some portions that are steeper than others, and
some steep portions may be longer than others (and more or less
steeper than those they are steeper than).
A steep learning curve would imply there's a lot to learn in a short
time--at least at some point in learning the material, and usually
implied to be at the start--hence the slope is large (and the curve is
steep) for some significant portion of the learning process. A
non-steep learning curve would imply that at no time in the learning
process (or, at least, the period under consideration) is there a lot
to learn in a short time.
If there's little to learn about a language or package but all parts
are so interdependent that you need to learn all, or most, right at
the start, then the learning curve is steep but short.
Independent of steepness, a learning curve will be short if there is
not a lot to learn overall, and long if there _is_ a lot to learn.
True Basic has a short and non-steep learning curve, whereas BF has a
short and steep curve; and C++, in my opinion, has a steep and long
learning curve since you must learn a lot of C syntax and semantics as
well as general OO terminology and principles to get started, and
every time you think you're done there's yet another fix for a
previously unconsidered problem or to add yet another "feature".
More apropos, Perl probably has a steep and long learning curve,
whereas Python's is less steep overall (and especially at the start)
and perhaps not quite as long. Of course this brings up a third
difference: how much of what "needs to be learned" is actually useful
and how much is excess baggage caused by poor language design? The
area under the curve represents the amount of information _about that
particular topic_ that must be learned, and is not a measure of
knowledge or wisdom.
To learn enough to be able to peform many simple tasks, both Java and
Perl have much steeper learning curves than Python: Java requires
knowledge of at least some basic OOP terminology and Java syntax for
creating a class, and variable type declarations, to get started; Perl
requires learning special symbols for correct naming of different data
types and other syntax that can be "cryptic" to a beginner. A
beginning Java programmer or Perl programmer will not have learned
more useful information than a beginning Python programmer at this
point: one will have "learned more Java" and the other will have
"learned more Perl", but this only implies there's "more stuff" to
learn in these two than in Python before being competent at this
particular set of tasks. And this would imply that both Java and Perl
are less efficient in a fairly-well-defined way than Python to this
level of programmer competence.
There--that horse is dead!