let's watch grass grow!

A handful of seeds in a good patch of soil will do well. In just one or two growing seasons, the area will fill nicely, and you'll perhaps need a goat.

The goat is a nice solution, since it will give back by keeping the grass trimmed and fertilized.

A goat and pasture make a nice illustration of simple balance. There's more needed like rain and sunshine, good soil and drainage, but still, it's a nice picture of balance.

Over the years, the goat grows and the grass grows. Simple, probably easy to manage. It gets a bit more complicated with a breeding pair.

Two goats, in our simple illustration, will of course become four and then eight. Not a problem at first, since we have a large and fertile pasture for our example.

For our example, lets say that after 30 generations, the goats are consuming half of the pasture's production. How long do we have before the capacity is exceeded?

One more generation.

*Just one.*

So, if it took a thousand years to go from 200 million to 300 million people in the world, that means it will take another thousand years (or maybe ten thousand) to go from 2 billion to 3 billion, right? Hardly; it took 30 years. Then it took less than half that time for the next billion.

Population grows exponentially. Despite our intellectual preference for linearity and a steady pace forward, exponential growth is the norm, right up to the point where you have to expand the pasture or get rid of some goats. If unmanaged, the die-off can be massive.

For those who hope that perhaps

the many concerns are exaggerated,

here are a few thoughts that might be worth a moment.

The interesting part for all of us is figuring out what comes next.

**Note:**Feral goats, to clarify a bit, have an actual fertility rate of between 10% and 35% under favorable circumstances. Populations tend to retreat in line with unfavorable conditions; high juvenile mortality accounts for most of the decline. A generation varies; females begin reproduction at a year or so and will continue fertile for perhaps 8 breeding seasons.