Bugs, bunnies, bombs and branches 1

Many growth processes proceed by ‘branching’. For example, bacteria split in two (‘binary fission’) at regular or irregular intervals, depending on the environmental conditions. Let us imagine a lonely bacterium with an infinite supply of all the nutrients it needs to grow and become two after about 20 minutes (e.g. E coli). In an hour there are three splittings and our bacterium has become 2×2×2 = 2³ = 8 bacteria. In 24 hours there have been 3×24 = 72 splittings, giving 272, or around 4.7 sextillion (4.7×10²¹ according to my calculator; sextillion is the name for 10²¹, according to most dictionaries) bacteria. That seems a lot, but bacteria are very small, usually of the order of 1 micrometre (1µm = 10⁻⁶m). So let’s imagine that our bacteria has a volume 1µm³ = 10⁻¹⁸m³. So in volume terms we have 4722m³ of bacteria. If the infinite source of nutrients was your body, it would be gone. Fortunately for most humans, biology has evolved mechanisms to fight back against unfriendly bacteria, and control the ‘friendly’ ones we’re told about in TV adverts (at least in the UK).