A learning curve is a hypothetical graph of how much time and energy must be invested before a tool can be used productively by the average user. If a tool has a high learning curve, it requires substantial study and experimentation before it will actually be useful. If a tool has an extremely low learning curve, the average user will be able to pick it up and intuitively know how to use it.

A lower learning curve is generally prefered, but sometimes a higher learning curve is acceptable if it results in a more powerful and flexible tool.

As an example, the Macintosh is generally considered to have a smaller learning curve than Unix.

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Secondary Plot: A new crime boss tries to take control of Downbelow.

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From the day that we are born until the day that we finally sail off on that great tax-free holiday in the sky we are constantly on a learning curve.
Whether it be learning to sit without our mom's having to hold our heads up or learning to play by the rules or even learning to do a writeup. It never stops.
Of course nobody's learning curve is identical to anyone else's. Nor is there ever only one learning curve to life. It's more like a roller coaster without the loops (or perhaps not).

But there are certain milestones along the way on each learning curve which can help you to orientate yourself on the curve.

  1. euphoria - 'Hey! this is easy'
  2. on the up - 'uhm, okaaay.. who put this bump here?'
  3. climbing - 'sheesh! Are you kidding me? Perhaps I should've stayed at home.'
  4. doubt - 'nope, can't do it - sorry, goodbye'
  5. perseverance - now this is where it gets hard...
  6. success - it speaks for itself doesn't it?
  7. euphoria - 'sure, no problem'

In the end there probably isn't a fool-proof approach to learning curves, but it all comes together in the perseverance bit.

Interestingly, the common use of this term is completely, unutterably, WRONG! Wherever I look (particularly in rigourous, exact disciplines such as computing, but also one of the softlinks below does this) I see "steep learning curve" meaning hard to learn.

Really? As explained by Agthorr above, the learning curve is a (hypothetical, mythical, nonexistent) graph of how much one knows of something after spending X effort+time. Steep curves are the one which go up faster (we assume the learning curve is the graph of a monotone function here...). Would you rather (assuming -- incorrectly -- that you could do both and end up with the same amount of knowledge) Teach Yourself C++ In 21 Hours or Teach Yourself C++ In 21 Years?

Thought so. Yet many insist on claiming that the necessarily steeper learning curve of Teach Yourself C++ in 4 Hours is worse!

A probable source for this confusion is the intuitive expectation that steep ascents are "harder". This is true -- trying to learn C++ in 7 days wastes time rather than saving it, as you waste the first 7 days "learning" C++, the next 28 days discovering that you need to learn in properly, and only then can start studying C++. But all this shows is that the "2.4 days strategy" is ineffective. And the reason it is ineffective is that it gives a very shallow learning curve: you spend the first 14 days learning nothing.

Learning curves typically also factor in effort. So there really is no excuse.

What is a learning curve and what does it tell us?

In popular discourse, we sometimes say a learning curve is 'steep' or 'high' to mean that something is hard to learn. That shows a completely wrong understanding of what a learning curve represents.

Put simply, a learning curve is a line graph that plots of how much is learned in how much time. The degree of learning is the vertical axis of the graph, and time is the horizontal axis. Points on the graph show how much has been learned (and remains learned) after a particular time has passed since learning began. Data points high on the graph indicate that much has been learned. 

Thus, a curve that rises sharply (a steep curve) indicates that much is learned in a short time, suggesting that the subject is easy to learn. A 'high' learning curve is sort of a meaningless expression, as the 'height' of a data point on the curve depends on the scale, which depends on the units of measurement for mastery and may be normalized as a percent. Using 'steep' or 'high' to mean 'difficult to learn' is incorrect, and may result from naively and ignorantly interpreting the curve as representing a wall that must be climbed, which it is not at all. 

Defined better, a learning curve plots the measured degree of mastery of a task or a subject against a measure of the effort applied to the learning (the usual measure being time). In math, we say that the curve represents ability as a function of effort. So what truths a learning curve can tell us depends on how mastery is defined and how valid are the measures of mastery and effort.

Predictive value

A learning curve is measured for an individual learner and a particular task over a measured period of time. It is meant to say something about the ability of that learner to acquire and retain the skill needed to perform the task successfully.

If we take the learning curves of (preferably) very many learners for the same task obtained under the same conditions and somehow average them, we have a learning curve that might say something about the general learnability of the task itself (at least for the statistical population that is fairly represented by the sample of learners). That is to say, we can use it to predict how difficult the learning would be for an 'average' learner. When time is the measure of effort, we can predict how fast learning may happen and how fast forgetting or loss of skill may happen. We need to be very careful in making predictions from learning curves (or any statistics), because there are always assumptions.

Assumptions are the devil in science, and in our daily lives as well. They are necessary, but evil only if you are not aware of them and how they affect your results or if you fail to be very clear about them in your conclusions and explanations.

Examples of things to question when creating and using learning curves (and any statistical results preseted as graphs):

  • How valid and reliable are the measurements of ability and time?
  • How well does the sample represent the population? (the sample on which the curve is based and the sample or population for which predicion is made)
  • Do the choice of scales in the graph suggest incorrect interpretation of the data?

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