Getting the Numbers and Doing the Arithmetic

6 December 2008

Many questions that concern people can be answered by getting some numbers and doing arithmetic with them. Usually just multiplication and division are involved.

The water supply problem for California provides a good example, because the relevant numbers are available. California is a drier than average part of the United States, but it is also the country's leading agricultural state in value of crops produced. There was a seven year period in the 1980s in which the rainfall was much less than average, and this directed a lot of public attention to water supply.

California uses about 35 million acre-feet of water per year and has a population of about 30 million people. That's a bit more than an acre-foot per person. For present purposes, an acre-foot per person is accurate enough, because some of the other numbers are more uncertain.
2002 note: Now it's 32 million people and 43 million acre-feet. The trouble with statistics is that they become obsolete.

Q. Where did these numbers come from?

A. I remember the numbers, because I think about numbers quite a bit, but both numbers are available in The Statistical Abstract of the United States, a volume that is published every year by the Bureau of the Census. Actually the 1998 estimate of the population of California was 32,667,000, and the 1997 estimate of the population of the US was 267.2 million. If we ignore the discrepancy of years, we get that California has 12.2 percent of the US population.

Q. What if California became a total desert? Apparently this happened at least once in the last thousand years, judging from fossil sand dunes in the San Joaquin Valley. Would everyone die?

A. No. It would be quite a hit to the economy, but California could still maintain its agricultural production, although many products would be produced elsewhere. Here's where the arithmetic comes in.

During the seven year drought of the 1980s, the city of Santa Barbara constructed a plant for desalinating seawater. The cost of water from the plant would have been $2,000 per acre-foot. If California had to get all its 35 million acre-feet of water by desalinating seawater, it would cost $70 billion per year. The gross domestic product of the US is given as $8 trillion. So we estimate the GDP of California at $980 billion. Spending $70 billion on water would be 7.1 percent of the GDP of the state. We'd notice it, but life would go on, not much changed. (Actually, California has slightly more than average per capita income for the US, so the percentage would be somewhat lower, but we don't need more accuracy than we already have.)

Assuming California lost all its water is an extreme case, but it is useful to do that computation, because it tells us that one particular doom won't happen. Without the arithmetic, we wouldn't know, and the rhetoric of The Cadillac Desert might win out.

It doesn't suggest that California build a large number of desalination plants just in case. We can expect to solve our water supply problems much more cheaply than by converting entirely to desalination.

Someone reminded me that desalination of seawater requires substantial energy. I don't have the numbers to say what that cost, but it is surely included in the Santa Barbara estimated cost. As became evident during the summer of 2000, the customary sources of California's electricity are under stress. Someday California may be faced with the choice between going without lawns and resuming the construction of nuclear power plants. I'll bet the voters will choose the latter.

2008 note: 8 kWh per cubic meter using reverse osmosis. [Thanks to David MacKay, Professor of Physics, Cambridge]

Another example arose from a discussion in the newsgroup sci.environment. Someone argued that when oil became much more expensive, international grain trade would be infeasible and countries would have to raise their own food. It took a while to find the relevant fact, and I eventually telephoned a professor of ocean engineering at M.I.T. The relevant fact is that a large bulk carrier carrying grain uses one gallon of fuel for 1600 tonne-miles of transportation. Arithmetic tells us that even a 100 fold increase in oil prices wouldn't make international grain transportation infeasible, although it sure would damage the rest of the economy if there were no replacement for oil.

These examples are not important in themselves. They just illustrate the important point. Many questions can be settled by recourse to available statistics and arithmetic - arithmetic not higher mathematics, although higher mathematics is also useful. The converse is that failing to look up statistics and do the arithmetic is a recipe for ignorance.