Some Math

Most people hate even the simplest mathematics. This is too bad, because a little bit of it can often be used to illuminate a confusing situation.

Following are some simple examples that are relevant to the future of civilization.

Consumption of Energy - Climate Change

Americans make up about 5 percent of the world's population. We consume approximately 20 percent of the world's energy, most of which is in the form of fossil fuels.

Most people of the world would love to have the American way of life. What if the rest of the world consumed at our rate? We can calculate the total energy consumption of the world in this case quite simply:

First, an equation that expresses current energy consumption as the sum of US consumption and that of the rest of the world in relative per-capita rates Rusa and Rworld:

(0.05 * R_usa) + (0.95 * R_world) = 1

Because these are simple calculations, we have defined total world energy consumption as 1. We could plug in real numbers and get the same answer, because we are just using different units.

Second, knowing that the US uses 25 percent and the rest of the world uses 75 percent, we can calculate the relative rates of consumption:

0.05 * R_usa = .25 --> R_usa = 5

0.95 * R_world = 0.75 --> R_world = 0.79

So on average, Americans consume 5/.79 = 6.3 times as much energy as residents of the rest of the world. Of course, this varies by country. Canada uses about as much per capita as do we. Europe, Japan, and the former Soviet Union about half. Developing countries, about a tenth.

These numbers allow us to calculate how much energy would be used by the whole world if everyone consumed at America's rate. Given using the original equation, and substituting the R_usa rate for R_world, we get

(0.5 * 5) + (0.95 + 5) = 5

This means that the world would be consuming 5 times as much energy.

It would also be putting out about 5 times as much CO₂. This is clearly not a favorable direction. We have already increased the atmosphere's CO₂ by a third over its pre-industrial levels, and it is increasing. This increase is generally believed to be adversely affecting the climate of the planet.

It has been suggested that we need to CUT our worldwide fossil fuel use by 60 percent in order to stabilize the climate. If we were to cut our consumption by this much, what would that mean to Americans?

Of course, the first hurdle is to define an equitable distribution for the energy. For this exercise, equitable will be defined to be that each person on earth burns the same amount of fossil fuel.

If the total consumption is reduced by 60 percent, it is now 0.4. Assuming equal energy distribution per capita, our equation for world consumption becomes the trivial

R = R_usa = R_world = 0.4

To achieve the required reduction, the US and Canada reduce their energy consumption 12.5 fold. Europe, the Former Soviet Union and Japan reduce theirs about sixfold. The rest of the world needs to reduce just a bit, overall.

Doesn't sound good, does it? Perhaps we should work a little harder on energy conservation and renewable energy sources.

Chuck Wright's home page.

Per Capita consumption data taken from "BP Statistical Review of World Energy, 1998"