Key events in the history and potential future of the world's population seem to be associated with prime number multiples of minimum happiness (life satisfaction). This may be a coincidence, or it may be an indicator of some deep biological connection with Nature's limits. Whichever is the case, it's extremely fascinating.

First, some background: Happiness, as a fraction between zero and 100%, appears to be related to how many natural resources we each consume per year. By estimating this per-capita consumption for the world's population, we can calculate what the happiness is. I have a mathematical model that does this, along with estimating the size of the population, how many resources there are, and how fast we must be able to move what we consume (transport speed). The model and its results are detailed both in this blog and on my Web site.

I became interested in happiness in an attempt to explain how population and per-capita consumption appear to be in synch with each other, and have been recently focusing how fast population and resources change. The clearest connection with happiness comes from how fast these growth rates themselves change, similar to the familiar concept of acceleration (the speed of something's speed). A pattern emerged when I compared these accelerations to multiples of minimum happiness for the past and for potential futures.

Minimum happiness is simply how happy people are when consuming the least amount of resources, which I expect to be equivalent to today's poorest people. Everyone was at this minimum more than two-thousand years ago, and the world had a stable amount of resources that humanity could eventually use. As the population grew, there was enough labor to extract more resources, which enabled further growth. Because total consumption – how much everyone was consuming – is proportional to the square of population, the total amount of resources decreased more and more rapidly (it accelerated).

By the time 10% of the initial resources had been consumed, in the late 1800s, happiness had doubled (the multiple of happiness was two). This also translated into an increase in life expectancy of nearly half. The speed of the population rate (the acceleration of population size) stopped increasing and began decreasing.

In 2008, we passed the tripling of happiness (a multiple of three). The population has already stopped accelerating, corresponding to a peak in the population rate, and the population rate is now decreasing toward what I project will be an eventual crash as it continues to fall past zero. At that zero point, when the population is as high as it will ever go, resources will once again be at a 10% point, but this time only 10% of the initial amount will remain, and happiness will be at a peak of 3.1 times the minimum. Life expectancy will be close to doubling (reaching a maximum of about 1.9 times its maximum), but never get there.

The only way to keep happiness increasing (but not the only way to avoid the crash) is to increase the number of resources. If we could do that, probably by settling much of the Solar System, we might be able to achieve 100% happiness for everyone, which would be nearly five times the minimum (actually, 4.9). It is odd and possibly significant that life expectancy would be a multiple of 2.7 times its minimum, very close to the value of one of the most important constants in mathematics: the base of natural logarithms.

There may very possibly be a biological limit associated with 100% happiness; but assuming there isn't, there is an ultimate limit to how much mass we can consume, set by transportation speed: the speed of light. Here is where we meet our last prime number. At the speed of light, happiness would be about seven times the minimum (actually, 7.3; the multiple of 7 would correspond to 0.4 times the speed of light). Life expectancy, meanwhile, would reach its highest level at 3.8 times its minimum.

I find it interesting that life expectancy shows an equally memorable pattern by nearly doubling when Earth's resources are exhausted, nearly tripling when 100% happiness is achieved, and nearly quadrupling at the ultimate limit. Perhaps the most amazing aspect of this analysis is the existence of both patterns existing simultaneously. Whether it's coincidence, an artifact of my math, or the discovery of a fundamental aspect of our relationship with the Universe, finding it has been both a lot of fun and confirmation that asking questions and exploring the implications of their answers is well worth the effort.

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