A few years ago, I asked experts to estimate when the world's supply of oil will dry up. Most agreed that improved technologies will probably allow oil companies to extract it at current levels until at least 2050, and that new discoveries might bump the reserves well into the next century.

But a mathematician suggests that when we look at the supply of a finite resource, we also must look at the effects of increasing demand.

Evar Nering is a professor emeritus of mathematics at Arizona State University. He lives in Scottsdale, he is 80 years old, and he began teaching math during World War II. Nering wrote an essay, "The Mirage of a Growing Fuel Supply," that recently appeared in The New York Times. Nering said he often used consumption of a nonrenewable resource as an example of the exponential function in his calculus classes, and the simple equation might be helpful to those making decisions about national energy policy.

"Say you have a 100-year supply of crude oil," Nering would say to his students. "That is, the oil would last 100 years if consumed at its current rate. Now assume that people consume the oil at a rate that grows by 5 percent each year. How long would it last now?" Students had no problem with the calculation, Nering said. The oil would last 36 years.

"What if you had a 1,000-year supply of oil that people used at the same increasing rate of 5 percent each year?" he would ask.

Answer: 79 years.

"What if oil company geologists find an incredible bonanza -- a 10,000-year supply of oil, and that oil is consumed at the same rate. How long would that last?"

Answer: 125 years.

The 5-percent increase in oil consumption is not a real number; Nering used it as a handy example for his class.

The U.S. Energy Information Administra-tion predicts an average rise in world oil consumption of about 3 percent each year for the next 20 years. But the numbers don't matter as much as the fact that humans are using more oil each year than the previous year, Nering said.

"Increasing the supply of oil is not the way to make it last," he said. "Building more power plants and drilling for more oil is exactly the wrong thing to do, because it will encourage more use."

Cutting the growth rate of consumption by one half almost doubles the lifespan of a resource, Nering said. He suggests that people need to change their lifestyles to extend the lifetime of crude oil.

"Reducing the growth of consumption means living closer to where we work or play," he said. "It means telecommuting. It means controlling population growth. It means shifting to renewable energy sources."

After half a century of living in Arizona and watching subdivisions and highways blossom on the desert floor, Nering said certain examples of the increase in energy consumption are obvious.

He has a grandniece, for example, who commutes to work more than 20 miles each day, as does her husband in a separate car.

"Every time we build a new freeway around town, it invites people to commute farther," he said. "It's a way of life that encourages consumption. My concern is that nobody seems to be trying to figure out what to do about it."

Ned Rozell is a science writer at the Geophysical Institute, University of Alaska Fairbanks. He can be reached by e-mail at nrozell@dino.gi.alaska.edu.

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