Vol. 12, No. 2,856W - The American Reporter - March 18, 2006


On Media
EXPONENTIALLY WRONG

by Robert Gelfand
American Reporter Correspondent
San Pedro, Calif

SAN PEDRO, Calif. -- My savings account is growing exponentially, but also very slowly. The Internet is probably not growing exponentially. These statements are arguably true but would likely be challenged by a large number of mathematically-challenged writers and editors who increasingly misuse an important term.

The debasing of the phrase "growing exponentially" by writers who want an expression suggesting large and out of control is growing, not quite exponentially perhaps, but to use a less mathematical term, irritatingly.

We are likely to read a comment on the Internet such as, "The amount of information available to help a business make critical decisions is growing exponentially" (from DM Review), or consider a column by Julie Packard of the Monterey Bay Aquarium remarking that when it comes to the harmful effects people have on coastlines, "our impacts are growing exponentially."

James Flanigan, a respected journalist at the Los Angeles Times wrote, "The links between factories and continents have grown exponentially in recent years, thanks to heavy investments in computing and communications and the development of the Internet." When the same term "growing exponentially" is used in all these ways and even in an editorial by my local daily newspaper, it becomes obvious that people who should know better just don't.

Our civilization frowns on the split infinitive and the misplaced modifier, but looks the other way when writers misuse science and math. Of late, the phrase "growing exponentially" has become commonplace as it increasingly finds its way into newspaper stories and editorials, advertising and the Internet.

To some, this may seem a small thing, but the concept of exponential growth actually means something quite specific. In mathematics, what are known as exponential functions provide powerful tools used by engineers, scientists, and mathematicians to analyze everything from Internet bandwidth to the growth of the human race. Whole shelves of books have been written on exponential functions and hundreds of thousands of students have studied them.

You can think of exponential functions as representing growth characterized by a proportional increase each tick of the clock or each passing year. A population which doubles its own numbers every year is growing exponentially. Compound interest is an example of exponential growth, as is the growth of cancer cells in a culture flask.

The popularity of the term probably stems from the widespread publicity that accompanied publication of Paul Ehrlich's book, "The Population Bomb," in the late 1960's. Ehrlich explained in particular that systems growing exponentially are characterized by defined doubling times. That is, they double, then double again and so on, and each new cycle takes the same amount of time as the preceding one.

This is a mathematically demonstrable characteristic of this kind of system (imagine a single bacterium which divides to form two bacteria, which in turn divide to make four, which divide to make eight, and so on). Exponential functions as defined mathematically have strange sounding names such as exp(t) or "two to the n," but they all have these well defined characteristics in common. It is obviously a long stretch to claim that the same mathematical attributes apply to concepts as vaguely defined as the amount of information available to businesses, beach visitation, or the links between factories and continents.

True, exponential growth can at some stage be rapid. It is easy to see that an initial population of two dozen humans who double their population every twenty years would fill Europe or Asia in under five centuries. The last twenty years of those five centuries would see a population increase on the order of half a billion. What the popular imagination fails to notice is that things are much different early in the time series.

Even after a full century, the initial population of 24 souls has grown to less than a thousand. At the end of the second century it is just twenty-five thousand, smaller than many a present day rural town. In other words, exponential growth need not be rapid, nor does it necessarily imply large absolute increases at any particular time. Given unlimited time and resources, an exponentially growing system will eventually get to the point of rapid growth.

To the mathematically inclined, both aspects are understood, namely the rapid growth at some point and also the fact that it may require a very, very long time to get to that point. Take my savings account for example. At its current interest rate, the doubling time for my money is about 70 years. (To calculate the doubling time on your investments given a certain interest rate, divide the percent into 70. My one percent interest rate results in a seventy year doubling time. Likewise, a 3.5 percent yearly growth in population results in a twenty year doubling time.)

The problem in our material world comes when an exponentially growing population has grown large enough that it takes up most of the living space and consumes most of the available resources. At that point, the rapid growth that characterizes doubling every twenty years runs into real world limits. In this sense, the term exponential growth implies a threat.

It cannot go on indefinitely. Our civilization may be able to handle the current six billion people, but the doubling to twelve billion and the doubling after that to twenty-four billion will not happen with the same rapidity as the last cycle that took us from three to six billion because there is not enough food, water, land or petroleum to allow for it. This then is the dark side of the expression "exponential growth." It implies serious problems for our species in the near future. Use of the term in this particular sense is at least technically correct, whereas the current widespread use simply to imply that something is big and getting bigger is incorrect.

Perhaps this is making too much over a semantic point. After all, most of us understand what writers mean when they say that the Internet is growing exponentially, even if it doesn't fit the correct mathematical model. Or this from The Limerick Leader of Limerick, Ireland: "Limerick's Shannon Bridge, when opened by the then-Taoiseach Charles Haughey in a drenching downpour, was already demonstrably inadequate and traffic volumes have been growing exponentially ever since." We might not necessarily know what a Taoiseach - the leader of ireland - is, but we understand that there are lots of cars and trucks trying to cross.

Even our religious leadership have caught the bug, as a column in The Free Methodist Church Website warns: "The sleep industry is growing exponentially as we look for the perfect mattress to give our overcommitted bodies." Perhaps this explains the number of mattress commercials on the radio lately, if not necessarily the number of evangelical programs. But all these examples represent incorrect usage, whether the term was used (as it also has been) to refer to social spending in rural Australia, e-mail submissions to magazines, or shipping traffic at our west coast ports.

The increasing use of the term exponential in popular discourse is apparent, but it has not been made sufficiently clear that the term is now being used in two very different ways. The more traditional (and largely pessimistic) usage refers to the human population explosion and to the increasing volume of traffic and garbage clogging our streets and dumps. By contrast, the newer popular usage so beloved by business consultants and corporate advertisers implies wide open growth and vast frontiers of developing commerce ripe for the taking.

As his detractors make clear, Ehrlich's 1968 opus was wrong in many of its detailed forecasts, but the overall point that exponential growth cannot continue forever in the material world is correct. The hucksters who want to suggest that the Internet has a few more rounds of doubling left in it may or may not be correct, but consumers and investors need to understand the real meaning behind the term "growing exponentially" and be appropriately wary.

Of course, it would be nice if editors would demand and writers would select a more appropriate collection of adjectives to describe concepts such as rapid, large, huge, or uncontrolled. There are many available. Writing is, after all, about communicating clearly, and the incorrect use of a technically meaningful term not only communicates less but also damages the language.

Copyright 2006 Joe Shea The American Reporter. All Rights Reserved.

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