Curious Omission In New-Style Formats

[Steven D'Aprano]

On Fri, 15 Jul 2016 06:40 pm, Jussi Piitulainen wrote:

> Antoon Pardon writes:
> 
>> Op 15-07-16 om 08:06 schreef Marko Rauhamaa:
>>>
>>> Common usage among educated speakers ordinarily is the yardstick for
>>> language questions.
>>
>> But educated about what exactly?
>>
>> Each time someone talks about "a steep learning curve" in order to
>> indicate something is difficult to master, he is using it wrong,
>> because actual steep learning curves indicate something can be
>> mastered quickly.

That's not necessarily the case. See below.


>> Now I suspect most people who talk about steep learning curves are
>> educated, they just aren't educated about learning curves and so I
>> think common usage among educated speakers is inadequate as a yard
>> stick.
> 
> I think I see your point, but I think it's also easy to think the axes
> of the metaphor so that it makes sense:
> 
> c      ,
> o     ,
> s    ,
> t . .
>  l e a r n i n g
> 
> First two steps l-e plain sailing. Next two steps a-r steep climb. Cost
> is the effort that makes the learner experience the learning as steep.
> (Spending more *time* without ever paying much attention may not be the
> best of ideas - it may be the worst of ideas - if the goal is to learn
> but it still fits the graph: cost goes up for little or no gain.)
> 
> Perhaps more proper to call that a cost-to-learn curve or something?
> But when it becomes unwieldy, it gets shortened to something shorter,
> and here the more informative component has won. Maybe.

"Learning curve" or "experience curve" is not just an metaphor, it is an
actual technical term. See the Wikipedia article:

https://en.wikipedia.org/wiki/Learning_curve


Now, there are a couple of ways that we can interpret the idiom of "steep
learning curve". One is the way Wikipedia interprets it: as a mistake.
According to this conventional explanation, people have *wrongly* imagined
a curve like this:

(for best results, view using a fixed width font like Courier)

K               x
n        x
o    x
w
l  x 
e
d  
g x
e
+ Effort or cost or time needed to gain that knowledge or skill


as being "hard to learn" at the beginning, when in fact it shows the
opposite: with just a little bit of effort, you can learn a lot. But (so
goes the conventional explanation) people think of steep in the sense of
climbing a steep mountain, and think that it shows that the learning
process is really hard at the start.

I believe Wikipedia is wrong. I think that there is a natural interpretation
of "steep learning curve" which matches *both* the idiomatic and technical
meanings, with the same graph.

Remember that the English idiom of a steep learning curve is not just hard
to learn. It means that something takes a lot of effort to gain mastery
over, after which things become easier.

Learning Ancient Etruscan is hard for beginners and experts alike, because
there is so little information available about Ancient Etruscan that even
the experts can hardly be said to have mastered the language. That would
not often be described as a steep learning curve, as it lacks the sense of
getting easier with time. Learning Etruscan might have a curve like this:

K
n                       x
o                 x
w             x
l           x 
e         x
d       x
g x
e
+ Effort or cost or time

It's hard at the beginning, because you don't know the language; then it
gets a bit easier, for a while, then it gets difficult again because you
run out of information about the language.

Here is a curve that matches the common idiom. It is (1) steep, (2) requires
a lot of effort for very little progress at the beginning, and (3) becomes
easier with time:


K                       x
n                      x
o                     x
w                   x
l                 x 
e              x
d          x
g x
e
+ Effort or cost or time


Mastery makes the going easy, but it takes a long time to see any real
progress. You can interpret the "steepness" in two ways: it's steep (easy)
for experts, and if you turn your head to the side, it's steep (hard, like
climbing a steep mountain) at the beginning).

Another way to interpret it is to ask, what's the *cost* (in time, or
effort) to gain a certain amount of knowledge? That's equivalent to
swapping the X and Y axes:

C            x
o       x
s    x
t
·  x
o
r
·
t x
i
m
e
+ Knowledge gained



That's not the conventional layout of the axis, but it does make sense, and
it's more likely that people have this reversed layout in mind when
thinking about "steepness of learning" than it is that they were thinking
about the original curve and misinterpreting the meaning of the gradient.






-- 
Steven
“Cheer up,” they said, “things could be worse.” So I cheered up, and sure
enough, things got worse.