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The first sentence from the article you linked to: "The learning curve refers to a relationship between the duration of learning or experience and the resulting progress."
This is exactly what I said: duration refers to time ("the length of time something continues or exists"(dictionary.com)) and is always the X, or independent, axis. The Y, or dependent, axis is the amount learned. The 'rate' of learning is the first derivative of this curve, the curve itself is not a rate.
The second definition, the only one you refer to, is the bastardized version that ignorance has created.