[FRIAM] Learning curves (was, Abduction)

[Marcus Daniels]

Figure B is how R&D works, and Figure A describes a good student.  

On 1/2/19, 2:32 PM, "lrudolph at meganet.net" <lrudolph at meganet.net> wrote:

    Nick wrote, in relevant part,
    > This reminds me of the misuse of the "learning curve"
    > metaphor.  People speak of a steep learning curve as something to be
    > feared.  In fact, people who learn quickly have a steep learning curve.
    
    Behold, complete with ASCII art (so be ready to view this in a monospaced
    font, or forever hold your peace), an ancient USENET post of mine to
    alt.usage.english, from 1995 (!):
    
    ===begin===
    Robert L Rosenberg (rros... at osf1.gmu.edu):
    >: A learning curve should be the graph of a non-decreasing function (time
    >: on the horizontal axis, knowledge of the topic on the vertical axis).  A
    >: fast learner would have a generally steeper learning curve than a slow
    >: learner.  At least that's the way I've always pictured it.
    
    kci... at cpcug.digex.net (Keith Ivey) writes:
    >I agree that this makes sense, but it doesn't seem to correspond with
    >the way the phrase is used.  In my experience, something that is hard
    >to learn is said to have a steep learning curve.
    
    Rosenberg's explanation not only makes sense, it accords with the
    original use by rat-runners and other operant conditioners (cf.,
    e.g., _Psychology_ by James D. Laird and Nicholas S. Thompson, p. 164:
    "The ... steeper the curve, the faster the animal is learning").
    More precisely, *during an interval of time where the curve is
    steep, the animal is learning quickly*.
    
    The present use is muddled; as Ivey points out, "something
    that is hard to learn is said to have a steep learning curve."
    Here's how I unmuddle it (but I don't know what, if anything, is
    going on in the heads of most people who use the phrase): by the
    Mean Value Theorem, or common intuition, if a (smooth) nondecreasing
    function f(t) with f(0)=0 and f(1)=1 is "steep" (has large derivative)
    somewhere, then it MUST be "flat" (have small derivative) somewhere
    else.  Typical learning curves (I gather from the illustrations in
    Laird and Thompson) look either like Figure A or like Figure B:
    
                                x                                    o
                        x
                   x                                                o
               x
             x                                                    o
    
           x                                                    o
                                                            o
                                                     o
          x                                o
    
                  FIGURE A                          FIGURE B
    
    In the first case, you learn almost everything in a short period of
    time near the beginning of the training, then reach a plateau and learn
    the rest very slowly.  In the second case, you learn very slowly for a long
    time, then take off near the end of the training.
    
    So the question is reduced to another one: which of Figures A and B is
    a "steep" curve to the average speaker?
    
    Lee Rudolph
    
    ===end===
    
    
    
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