I may have written a post on this topic in the past so apologies if I am retreading old ground but I stumbled across this fascinating thought experiment once again earlier this week, and just had to talk about it (again?). It comes courtesy of University of Colorado physicist Albert Bartlett who studies the mathematics of overpopulation. Bartlett describes a colony of bacteria that live in a Coke bottle. Bacteria grow by a process of binary division, so one cell becomes two, two becomes four, four becomes eight, etc. (Technically this only occurs during the exponential phase of bacterial growth, bacteria have other growth/life phases when this does not apply, but for purposes of this discussion those can be ignored). He asks us to imagine a scenario in which they double their population by this process once every minute. This is very much a hypothetical scenario because the data we have say that under ideal conditions even for the fastest growing gram negative bacteria (E. coli, Salmonella, etc.), twenty minutes is about the biological maximum speed limit. Gram positive organisms (Staphylococcus, Listeria, etc.) double more slowly, with 30–45 minutes being the more common doubling time range under ideal conditions. In any event, in Bartlett’s non-realistic scenario of 1 minute doublings the bacteria start growing at 11 a.m., and by doubling every minute the bottle is overflowing with bacteria by noon. It has reached a point of saturation, it is full, in human terms it is over-populated.
To conclude the train of thought Bartlett’s proceeds to ask what time it would be before even the most forward thinking bacteria began to worry about the problem of overpopulation? If one does the math it is easy enough to see that there would be no warning of impending doom of any sort before 11:58 because at that point the bottle would only be one-quarter full (two doublings away from full). Thus the bacteria remain blissfully unaware that the complete exhaustion of all their resources is a short two minutes away. To make matters worse, once their bottle is full, because of the mathematics of doubling, even if they were to go exploring and find new territories (in this case let’s say three new empty Coke bottles), it would be of little help because it would only take two minutes for those to be filled completely as well.
And so with this one thought experiment we have an illustration of the non predictable nature of the problem of human overpopulation in the two minutes to disaster portion of the tale, which itself relied upon a clever demonstration of the doubling nature of bacterial growth, which in turn served as a stark reminder of the difficulty humans have in imagining large numbers and concepts like mathematical doubling. As thought experiments go this is one of the greats.