Re: On Topic Wednesday: Universal Synthetic Languages

Wayne Throop wrote:
:: Also, what makes you think the curve is x=time y=accomplishment?

: Sean Case <seancase@xxxxxxxxxx>
: Because that's the definition of "learning curve."

It is? What standards body maintains this definition?

As Tevye would say, "Tradition!".

What are we, French?

Pas du tout.

Since I work with these annoying little buggers every day, let me try.

Traditionally, in military and manufacturing contexts learning curves
are expressed as either the average effort (in hours, dollars,
whatever) to produce the first N units of something, or the marginal
effort to produce the Nth unit of something, as a function of N. So,
quantity (accomplishment) on the X axis, effort on the Y axis.

These relationships are often well-fit by a negative exponential curve,
C(Q) = T*Q^b, where T is the "notional first unit cost" (and obviously
different depending on whether you're talking unit cost or average
cost) and b is the rate of learning. Given this, and the fact that
all of this predates computer spreadsheets, it is also traditional to
draw them on log-log axes, making a nice linear relationship. It's
also traditional to express the rate of learning base 2 -- how much
does the unit (or average) cost go down when you double the quantity?

Some quick algebra establishes that ln(C(2Q)) = b*ln(2)*ln(C(Q)), so
b*ln(2) is the 'slope' associated with doubling the quantity on a
log/log plot. There is a long tradition of saying "the slope is 92%"
when what you really mean is "the cost of unit 2N is 92% of the cost of
unit N". Bad notation, but traditional.

So, a higher "slope", which is (intuitively) "steeper", means the cost
of unit 2N is a higher fraction of the cost of unit N, which in turn
means that learning is "harder". A steep learning curve is thus not
one where the *graph* of the curve is steep, but (paradoxically) one
where the graph is flatter, leading to a large "slope". With no
learning at all, the graph is perfectly flat, which is as 'steep' as
you can get. Go figure.

Is this a complete and utter abuse of the term 'slope'? Yep. Is it
standard? Yep.

David Tate

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