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: