The Miracle of Exponential Growth

“Truly I tell you, if you have faith as small as a mustard seed, you can say to this mountain, ‘Move from here to there,” and it will move.” (Matt. 17:20)

The mustard seed is Jesus’ preferred reference for all things tiny. We know now there are objects many orders of magnitude tinier, but without the aid of magnification it’s rare to encounter anything significantly smaller than a mustard seed. If one does find something smaller, it is likely to be inert—a grain of sand or a speck of dust. The mustard seed is dynamic, growing into a bush which begets more mustard seeds.

How exactly does it accomplish this remarkable transformation? The secret is exponential growth. The basic idea behind exponential growth is doubling: one doubles to two, two doubles to four, four to eight, and so on. At first, it doesn’t seem that impressive, but after just ten iterations we’re over 1,000 copies, and in twenty iterations we exceed 1,000,000 copies. If the cells of a mustard plant are doubling, we can begin to see how that one tiny cell can produce something so big in a short period of time.

We don’t commonly witness exponential growth, which is why the parable is illuminating. Most things that we make grow linearly. As children, before we can even speak, we can stack one block on top of another on top of another. Pretty soon we have a nice tower, but it can only grow one block at a time. If mom or dad helps, we can double our productivity, but parents still only have two hands, so the growth of the tower is still linear. We write one word at a time, we walk one step at a time, we score goals one at a time—all the ways we can mark our progress are done on a linear ...

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