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Learning curve
"It has a steep learning curve." This is, assuming we share a cultural background, a phrase you will be familiar with. But have you ever tried to figure out what it means? What exactly does the curve in question graph?
Well, a steep learning curve means something is difficult to learn, particularly as you get started. That simply means lot of time and effort has to be expended to gain a small amount of proficiency. So until t gets large, the output of the function stays fairly small. Let us see what that might look like.
But... that isn't very steep at all! (At least not early on, when it counts. The rest I was just being fancy with because a linear plot is dull.) And if we look at one that actually is steep, it's even worse.
Now a small amount of time and effort results in a very large amount of proficiency! That's the exact opposite of what we want! The only way we can fix it is if we invert the axes.
We've finally found the shape we want, with the interpretation we want. But at what cost? AT WHAT COST? We have made time a dependent variable! The natural order of nature itself must be turned upside down in order to satisfy the logical demands of this seemingly innocuous little saying!
(For certain tiresomely literal people in my audience: I am perfectly aware there is no grand universal rule preventing this from being done. But it's weird and uncomfortable and completely at odds with the intuitive nature of the original saying.)
Conclusions: Steep learning curves are actually quite shallow, and shallows ones steep. Whoever invented this metaphor did not work with graphs very often. And from now on, if something is difficult to learn you should say it has a very shallow learning curve!
Well, a steep learning curve means something is difficult to learn, particularly as you get started. That simply means lot of time and effort has to be expended to gain a small amount of proficiency. So until t gets large, the output of the function stays fairly small. Let us see what that might look like.
But... that isn't very steep at all! (At least not early on, when it counts. The rest I was just being fancy with because a linear plot is dull.) And if we look at one that actually is steep, it's even worse.
Now a small amount of time and effort results in a very large amount of proficiency! That's the exact opposite of what we want! The only way we can fix it is if we invert the axes.
We've finally found the shape we want, with the interpretation we want. But at what cost? AT WHAT COST? We have made time a dependent variable! The natural order of nature itself must be turned upside down in order to satisfy the logical demands of this seemingly innocuous little saying!
(For certain tiresomely literal people in my audience: I am perfectly aware there is no grand universal rule preventing this from being done. But it's weird and uncomfortable and completely at odds with the intuitive nature of the original saying.)
Conclusions: Steep learning curves are actually quite shallow, and shallows ones steep. Whoever invented this metaphor did not work with graphs very often. And from now on, if something is difficult to learn you should say it has a very shallow learning curve!
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However the first plots of "learning curves" were by Ebbinghaus, who among other things graphed the number of syllables of nonsense words on the horizontal and the number of repetitions required to memorize words of that length on the vertical.
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