Bacteria and Bricklayers
Bacteria
In bacteria populations, growth is fixed. Subject to the resource constraints of the environment they inhabit, bacteria grow at a constant rate indefinitely.
A simple example to illustrate the point:
Let's say we have some bacteria that reproduce on a fixed time schedule, one doubling per minute to keep the numbers simple.
We start with a single bacteria cell. After one minute, we'll have two bacteria. With time, the population grows as such:
- 1
- 2
- 4
- 8
- 16
- ...
Now we ask the question, how fast does our bacteria population grow (in percentage terms)?
The minute-over-minute growth rate is: 1 or 100%.
This is an example of perfectly compounding growth, also referred to as exponential or geometric growth.
Put simply, how fast the bacteria grow is entirely independent of population size. In other words, growth and scale are perfectly uncorrelated.
Importantly, most things do not work this way.
Layering on
Let's look at another example - constructing a brick wall.
Assume a bricklayer can lay 10 bricks per hour. The brick count will proceed as follows
- 0
- 10
- 20
- 30
- 40
- ...
The brick count grows by 10 bricks per hour.
Going through the same growth rate calculations from above: initially we are growing the brick count quite fast - 100% in fact. But by the time we reach 30 bricks, our forward-looking growth rate has fallen to 33%. At 100 bricks, we'll only be growing 10%.
Notice that the growth rate depends on how many bricks we've already laid. This is linear or arithmetic growth. Because the number of bricks laid each hour is static through time, growth (in percentage terms) necessarily slows down. Scale is in the denominator. Therefore, growth and scale are negatively correlated: more scale -> less growth.