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Please stop talking about exponential growth

Published on 2017-11-20

How often do you read sentences like "the problem is growing exponentially" or "technological progress is exponential"? Do you understand what this should tell you? I don't.

It's a relation

First of all, "exponential" is not a property of a series. It is a relation. A problem cannot grow exponentially, but it can grow exponentially in relation to time or people involved or whatever.

It depends on units

Much more important, however, is this: "Exponential" depends on the unit that is used. For example, think about a tone whose frequency rises exponentially in relation to time. The key of that tone will rise linearly in relation to time. It is because adding one octave is the same as doubling the frequency.

Another mistake you often see in the wild is claiming that "consumption of resource X has grown exponentially over time". This is often the total consumption. If you look at per capita consumption instead, you may well find that it has stayed constant. Same for "price of X has grown exponentially": Have they taken inflation into account?

It is probably not the right thing

Here is the third issue: Remember when people at your bank tell you that a "1.3% interest rate does not seem like much now, but think about what it will bring you in 40 years"? They are basically telling you that exponential growth only really gets interesting in the long term. However, long-term exponential growth is rarely seen in the wild.

Think about a population of rabbits on an island: At first, they will reproduce exponentially. However, at some point the available foot will become scarce and the growth will stagnate. This is called logistic growth. It has similar short-term properties to exponential growth, but is vastly different in the long term. Again, the long term is what is interesting about exponential growth.

Conclusion

Maybe I should just accept that "exponential" has become a fancy way to say "hugely". That would be sad because exponential growth is a powerful concept if used correctly. So sad…