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Benjamin Kuipers's avatar

Sure, it's good to understand exponentials. But it's also important to understand sigmoids (what happens when an exponential growth encounters an exponential counter-force), and the impact on the system of violating hard constraints that allow it to function (what happens when an exponentially growing population outgrows its limited source of food, or oxygen, or other critical resource).

The first part of a sigmoid looks just like an exponential, so your cheerful entrepreneur happily climbs aboard. But almost always, there are countervailing forces, and you actually have a sigmoid, which levels off at a higher plateau. If you are lucky, and the system is strong enough to resist the higher forces, so nothing breaks.

But in a Malthusian system, the growth breaks the system, which transitions to a different system, which might not support a large population, or even any population. Malthus observed that population growth is exponential, and predicted catastrophe when it outgrew the limited ability to grow food. It didn't work out that way, because (a) we got better at growing food (thought not exponentially better), and (b) we discovered that increasing prosperity decreases the population growth rate. We still don't know how high the population sigmoid might turn out to be, but we may have dodged the population growth bullet.

If you just learn about exponential, and not these other things, you are like a kid in a candy store, but you're likely to be in big trouble soon.

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