This is the third in a series of posts on mathematical metaphors. Don’t let the topic scare you. We all use these metaphors, most of us use them every day.
This is a graph of a logistics function. It is not a common function and is rarely discussed. However, it is a good one to learn as it is a much more accurate metaphor.
Just as the exponential takes a broader view than the linear, the logistics curve is broader than the exponential. While small sections of the exponential look like linear graphs, small sections of the logistics curve look like exponentials.
The metaphor recognizes that while things can growth quickly and change rapidly, this condition can not continue indefinitely. Eventually, growth slows down.
For example, Facebook increased its total users exponentially until it ran out of people. When virtually everyone with a phone or a computer was on Facebook, it couldn’t grow anymore. This is the truth of the logistics curve metaphor.
The logistics curve recognizes that things do not expand forever. In politics and economics, this metaphor is expressed as diminishing returns; what work well yesterday, barely works at all today.
This metaphor provides balance. It discourages the winners and encourages the losers.
Reality often matches this metaphor even though most people ignore this model.
The interesting thing is that all three models/metaphors are what mathematicians call: monotonic-they always increase. They never turn around. linear goes up, exponential goes up really fast, and the logistics curve ultimately goes up really slow.
While this arcane curve is a good metaphor, it is nor the best.
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