Friday, February 08, 2008

On "Steep" Learning Curves (Or: Hackling at Tilted Petards)

Okay, time to tilt against the windmills -- actually just one small, stupid windmill. But it's a windmill that particularly raises my hackles because it brings together my distaste for ignorant distortions of stock phrases with my interest in the history of psychology.

(You can bet that I double-checked the OED, after saying this, to confirm my use of "tilting" at windmills and raising "hackles". I don't want to be hoisted by my own petard. [Yep, double-checked that too.] Shouldn't we know what we are saying? -- what tilting and hackles and petards are?)

Here's a picture of a typical learning curve (from Stroop 1935):

(This curve charts the increasing speed with which subjects can name the colors of words on a list of color words printed in colors different from those named by the word [e.g., saying "blue" when seeing the word "red" printed in blue ink]. But the particular nature of the task is irrelevant to my point.)

Now consider this: If the curve were steeper, would that mean subjects were learning more quickly -- i.e., that the task was easier to learn -- or would it mean that the subjects were learning less quickly and the task was harder?

Next time you hear someone talk about a "steep learning curve" to mean the opposite of its proper meaning, tell her you're going to hackle her tilted petard!


Anonymous said...

Nice one,

I didn't even know that there are actual 'learning curves'. I was thinking of it as a metaphor for moving from the bottom (the lack of knowledge) and how hard is to get to the top.

Anonymous said...

The colloquial use makes sense, it just has the x- and y-axes switched around. On the y-axis, elapsed time, and on the x-axis, proficiency.

Eric Schwitzgebel said...

Yes, Sarah, there are learning curves that rise (in proficiency, etc.) as well as fall -- but for them, too, a steeper curve would indicate attaining proficiency more quickly, no?

Anonymous said...

Interesting, I have always used the phrase to refer to a skill or activity in which large improvements can be made in a relatively short amount of time. I had no idea this use was contrary to normal. The comfort I can take in knowing my usage is mathematically correct is out weighed by frustration. I wasn't trying for mathematical accuracy, I wanted to be like everyone else with my linguistic devices!

Anonymous said...

I made some sketches. I believe this one illustrates a steep learning curve where proficiency is obtained with difficulty:

MT said...

Yes, that usage always has gotten my goat too. But taken to extremes, such stickling could decimate our conversational options, and what would that mean? I think being normative, means being conservative.

Eric Schwitzgebel said...

Ah, Alan and MT, you're right. Maybe I shouldn't be such a stickler. Go ahead and hackle.

Sarah: I hadn't thought about it before, but as your graph shows, my point about "steep" learning curves depends on the independent variable (roughly, your activity or number of trials) being on the x axis and the dependent variable (roughly, outcome) being on the y axis -- which is the traditional layout. If you reverse the axes as in your example, you get the effect you say.

Now you could have the axes as you do, and not violate the dependent-independent convention if what you were doing was looking at students' exam scores and then asking them how many hours they studied (then hours studied would be the dependent variable). And then, indeed, your "steep learning curve" would mean slow learning early on!

That's not the normal behaviorist set-up, but maybe it's all the more reason not to stickle.

Anonymous said...

Yeah, I think Sarah's analysis is a good account of the colloquialism.

Tony said...

I think this overly-literal interpretation is a bit autistic. Doesn't cognitive linguistics teach us to accept our metaphors however they come embodied? What seems right is that the steep is supposed to trigger the idea of walking up a steep slope, which is hard work. To apply the steep to the 'learning curve', instead of leaving it do to that work and that work alone, is to be overly literal.
Anyhow, how is the steep learning curve for your newly re-enculturated child? I hope all is going well.
Best, Tony Jack

Eric Schwitzgebel said...

Hi, Tony! Yeah, I've got some weird etymological hangups, I suppose. Have I mentioned "processes" pronounced with a long e as though it were the plural of "processis"? I prefer to think of these matters as aesthetic rather than autistic, but who's to say, really?

Kate is trucking up that curve at amazing speed, by the way!

Tony said...

Hey Eric, you might like this - I am working on a test of figurative language comprehension to see if it correlates with theory of mind performance in normals. I think I'll try to include an item on the steep learning curve. So at some point soon, we should know if I was right whether that is an 'autistic' interpretation.

Eric Schwitzgebel said...

Cute, Tony! Be sure to let me know my diagnosis!