Exponential Growth Starts Like Zero Progress

It takes off as soon as you’re convinced it isn’t working.

It took me 20 years of teaching to figure out that all growth is exponential.

By contrast, my classes are arithmetic. We meet twice a week, for ninety minutes each week, and the material we cover accumulates at a constant pace. But personal growth in a student is not merely the accumulation of time spent with new material, because all growth is exponential.

For example, when my kids were in elementary school, they did a demonstration of seed germination using lima beans, cotton, and a clear plastic bag. The kids put wet cotton in the bags, and then inserted the lima beans, so they could see the beans sprout.

For days nothing happened.

Then, there were little tiny roots. Just a little bit bigger each day.

Then, leaves, and more rapid progress now.

If it weren’t for the plastic bag, the changes going on would still be hidden from view underground,until finally the leaves burst through the surface of the soil. It looks like this:

That’s exponential growth.

The thing is that kids aren’t patient enough to wait for beans to burst up into view all at once. Kids need feedback sooner than that. That’s the reason for the clear plastic bags, so the kids don’t give up on the demonstration too soon.

My students are like lima beans.

When I teach, there’s a lot going on under the surface of any student. Things are happened on an exponential growth trajectory. Except that all those things on the student interior are invisible to me until they come bursting to the surface.

From my perspective as a teacher, there may be absolutely nothing happening with a student, and then there’s a huge leap forward as if they were learning everything we’d gone over all at once.

And that’s the problem with the beginning of an exponential growth curve: for a long time, it looks like nothing is happening.

That’s the case whether we’re talking about lima beans, engineering students, start up ventures, new product launches, or anything. The difficult thing about exponential growth is that it always looks like nothing is happening… for a long time.

You might have witnessed this when the media touts some newly famous celebrity as an “overnight success” (Zat Rana explains and Charles Chu describes how a napkin sketch takes decades). In fact, it takes years of hard work to become an overnight success. It only looks sudden to the people who aren’t doing the work.

Even the little signs of progress could be indications that you’re putting down roots, or forming leaves beneath your metaphorical soil.

Or… maybe just you’re not making any progress.

When working with students, I do my best to default to the expectation of exponential growth and the patience that requires. Sometimes, they come bursting through the soil. Sometimes, it turns out there was nothing happening there after all.

Next semester, I’ll get a fresh batch of new seeds, and I’ll attempt to impose upon them the artificial timeline of a 16 week, 3 credit course.

You likely have no such constraint or artificial deadline, which makes it difficult to know when to quit or change strategy.

At the beginning of any exponential growth trajectory, you’re going to need some positive cognitive distortions. You’re going to have to imagine exponential growth, even without the evidence of it.

Some people might call that denial, which gets a bad rap.

Others might call it faith.