The greatest shortcoming of the human race is our inability to understand the exponential function.
— Albert A. Bartlett
GDP, Moore's law, greenhouse gas emissions — Exponential goods are the some of our greatest blessings and dangers.
But what exponentials can a person create in their own life? Ask the internet and you'll learn that you're just one listicle away from bench pressing Mount Everest and eating grapes from the hands of your three million wives.
This is unfortunate. The giddiness of the messenger, and perhaps the confusion of "exponential" with "fast," confuses the ordinary but profound reality.
As far as I can see, there are exponentials both positive (growing unboundedly) and negative (decaying to zero) at the personal level.
For positives, only two come to mind:
Wealth — money, stocks, equity growth.
Influence — subscribers and views when directed outward; recommendations and opportunities when directed inward.
Both are straightforward but influence is more clearly zero-sum: the more my audience engages with me, the less they engage with something else. But given the state of attention in the modern world, I think this is an improvement.
There is also a third I'm less sure about:
- Idea exploration — finding good ideas (and ignoring bad ones), either through honing your intuition or by being able to try ideas out exponentially (e.g. through your network).
I put this in the exponential bucket because the wrong idea (even with good execution) is worth nothing, but the right one is worth billions.
I'm reminded again of the insight about Jeff Dean and Sanjay Ghemawat I quoted in my amateurs and professionals post. It's not that they type thousands of times faster; it's that their intuition leads them to the one good idea over the thousand bad ones.
And once again, this idea seems to be an important fundamental that cuts across domains. To quote the Go player Toshiro Kageyama 7-dan, whom I've mentioned before:
One must, without fail, learn the correct way to study.
— Toshiro Kageyama 7-dan, Lessons in the Fundamentals of Go
For negative exponentials, only one comes to mind: spaced repetition to memorize facts with exponentially less time. With spaced repetition our memory is bounded only by how fast we can add facts to the system. Note that while this is a breakthrough, our ability to memorize ultimately remains linear.
For all else, I think growth is mostly linear or sub-linear, with rare multiplicitave phases. But steady growth of any kind makes us incomparable to who we once were. It may not be exponential, but it's wonder enough.