# Exponentials

I just read a [[very interesting article | http://globalpublicmedia.com/node/461]] about the inability of the human mind to comprehend exponentials. Exponential growth happens whenever there is a constant growth rate mentioned. So, when you hear about a ‘5% growth a year’, that’s actually an exponential growth: it grows faster and faster. So fast in fact that our minds fail to measure how fast it grows. |

The article gives easy tips to estimate the exponential computation:

- 7% growth per year means doubling every 10 years. Doubling your electricity consumption every 10 years means that if you have one nuclear station today, you’ll need 32 in 50 years.
- Over 70 years (about one life-time) an increase of x%/year results in a growth by a factor 2^^x^^ (which is 2 multiplied by itself, x times: 2^^8^^ is 2x2x2x2x2x2x2x2 which is 256). So a tame 4% growth rate means multiplying everything by 16 over 70 years.

The author then explains what should be self-evident: anything that’s based on continuous growth is doomed to stop some day. That applies to the population on earth, power consumption and so on. The only point I disagree with is that this does not actually apply to inflation or GDP, which are abstract values that can actually grow boundlessly: with 100% inflation a year, life can go on happily for decades, it’s just pretty bad for my savings.

On the other hand, overpopulation is a real problem, because, as the author says, “we can debate whether we like zero population growth or don’t like it, it’s going to happen”. Either through war, famine, and disease, or through drastic birth control.

And our lack of understanding of exponentials also means that things are probably much more urgent than we think. He imagines a model of bacteria growing in a bottle. Each minute, each bacteria splits and the population doubles. You start the experiment at 11:00, and at 12:00 the bottle is entirely full. At what point do the bacteria start to think they’re running out of space? 5 minutes before 12:00, they’re only using 3% of the bottle. With 97% of the known universe to fill, surely they’re fine? 5 minutes later, fighting starts over that last spot on the head of a pin.

Now, how many humans do we think the earth can comfortably sustain? How many can it sustain at all? How many minutes have we got left?