The Speed of growth

On this page…

  1. The SPEED of Growth over one human lifetime of 70 years
  2. Doubling Times
  3. Jimmy Carter on Doubling Times
  4. The Australian Federal Senate concludes growth is the real killer

1. The SPEED of Growth over one human lifetime of 70 years

The following table illustrates the sheer SPEED of growth so powerfully that every high school kid in the world should be forced to memorize it, and be tested on it each year. At this stage I find myself having a lot of sympathy for Professor Albert Bartlett when he says,

The greatest shortcoming of the human race is our inability to understand the exponential function.”

The following table illustrates the power of exponential growth over one human lifetime of about 70 years. If anything grows at the same steady rate each year, this is what you can expect.

For example, if your city is increasing its use of oil at the rate of 1% per year, how much extra oil is that over one lifetime of 70 years? OK, let’s take a look.

1% growth per year = 2
2% growth per year = 4
3% growth per year = 8
4% growth per year = 16
5% growth per year = 32
6% growth per year = 64

So in other words, if we are increasing our use of oil by 1% per year in 70 years we will have doubled our daily use of oil. Only a tiny, measly, insignificant little number like 1% per year certainly adds up in one lifetime. On the other hand, 5% growth means the city will consume 32 times the oil each and every year thereafter!

Or, as Professor Bartlett says, if your city has one run down old sewerage treatment plant, how many sewerage treatment plants will you need if the city population is growing by 4% per year? Check the graph… you’d need 16 sewerage treatment plants at the end of just one lifetime of growth! It’s truly astonishing that this is not common knowledge, and that people just accept that populations can and will continue to grow indefinitely into the future.

There are no tricks here, this is very ordinary maths illustrating the extraordinary power of exponential growth.

Another important concept to get used to is that of the Doubling Time. There is an easy way to figure out how many years it will take for steady growth to double your use of resources (or whatever you are counting), but before I borrow this directly from Bartlett’s lecture let me advertise his excellent 50 minute online movie. You can learn everything you need to learn about the sheer speed, power and problem of growth in this movie.

2. Doubling times

Well, if it takes a fixed length of time to grow 5%, it follows it takes a longer fixed length of time to grow 100%. That longer time’s called the doubling time and we need to know how you calculate the doubling time. It’s easy.

You just take the number 70, divide it by the percent growth per unit time and that gives you the doubling time. So our example of 5% per year, you divide the 5 into 70, you find that growing quantity will double in size every 14 years.

Well, you might ask, where did the 70 come from? The answer is that it’s approximately 100 multiplied by the natural logarithm of two. If you wanted the time to triple, you’d use the natural logarithm of three. So it’s all very logical. But you don’t have to remember where it came from, just remember 70.

I wish we could get every person to make this mental calculation every time we see a percent growth rate of anything in a news story. For example, if you saw a story that said things had been growing 7% per year for several recent years, you wouldn’t bat an eyelash. But when you see a headline that says crime has doubled in a decade, you say “My heavens, what’s happening?”

OK, what is happening? 7% growth per year: divide the seven into 70, the doubling time is ten years. But notice, if you want to write a headline to get people’s attention, you’d never write “Crime Growing 7% Per Year,” nobody would know what it means. Now, do you know what 7% means?
From Albert Bartlett’s transcript

3. Jimmy Carter on Doubling Times

Then Professor Bartlet introduces us to a famous speech by Jimmy Carter, the energy crisis “Malaise” speech.

The world has not prepared for the future. During the 1950s, people used twice as much oil as during the 1940s. During the 1960s, we used twice as much as during the 1950s. And in each of those decades, more oil was consumed than in all of mankind’s previous history.

So not only does the amount consumed DOUBLE in this time, but it also happens to work out to be slightly MORE than the original amount you started growing from. It means that even if a miracle happened and the “oil pixies” suddenly put ALL the oil we had EVER consumed right back in the ground, at 7% consumption growth it would only give us just less than 10 more years.

4. The Australian Federal Senate concludes growth is the real killer

However, we are only growing our oil consumption somewhere between 2% to 3% per year, so we are off the hook right? No. Sadly, exponential growth in our resource use has already accumulated up to an incredibly high number. As the Australian Federal Senate Committee found:-

For example, adding 900 billion barrels – more oil than had been produced at the time the estimates were made – to the mean USGS resource estimate in the 2 per cent growth case only delays the estimated production peak by 10 years.

That means that we’ve already doubled our oil use, and doubled it again — as President Carter said — and now even just the economic growth rate of 2% per year means that an extra 900 billion barrels magically put down on paper by the late peak optimists actually only delays peak oil 10 years.

This maths of course applies to everything that is growing exponentially, from a dangerous virus in our bloodstream to our consumption of resources as the human population itself grows exponentially. However, it can also apply to positives such as the speed of alternative energy deployment, scientific knowledge and progress, the roll out of political solutions across dysfunctional continents like Africa (if the African Union ever come to real agreements!), and the exponential growth in computer power. We are witnessing a race between both negative and positive exponential growth on a number of trends. Interesting times indeed!


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