The greatest shortcoming of the human race is our inability to understand the exponential function.
That’s what Albert Bartlett, retired professor of physics at the University of Colorado in Boulder, says. I saw a lecture of his (granted, a low-budget video recording of it) last night. The concepts are not staggering in their complexity, the results simple and direct. Sure, he uses a little bit of statistical data taken out of context and applies them in vacuum-like situations, but the basic principle on which he bases his assertions on is quite solid and useful. And, frankly, slightly unnerving.
To illustrate his point, I will crib his example of the inventor of chess asking for payment from his king for his fancy new game. When the king offered him gold, he crafty man simply asked for the king to put one grain of wheat on the first square, then two grains on the second square, four on the third, and so on through all 64 squares. Without thinking too much about it, this does not seem like a great payment.
| Square # | Grains | Total |
|---|---|---|
| 1 | 1 (20) | 1 ((21)-1) |
| 2 | 2 (21) | 3 ((22)-1) |
| 3 | 4 (22) | 7 ((23)-1) |
| 4 | 8 (23) | 15 ((24)-1) |
| 5 | 16 (24) | 31 ((25)-1) |
| . | . | . |
| 63 | 1 (262) | (263)-1 |
| 64 | 1 (263) | (264)-1 |
The reality is, of course, that this function creates 9.22337204 × 1018 grains of wheat. 922,337,204,000,000,000 grains of wheat. 922 quadrillion, 337 trillion, 204 billion grains of wheat. That is more than all the wheat ever produced throughout all the history of mankind. That is how exponential growth works. Now imagine that this wheat is oil. We spent a few weeks in this country discussing the concept of “peak oil” and how we may or may not be approaching it. The talking heads and pundits all say we’re fine. But that just doesn’t make sense–every year we need more oil than the previous year. Do we anticipate that we’ll just continue to find more through time immortal? We hear Bush and McCain talking about drilling in ANWR–really liberal estimates are saying we’d be able to pull out 3.5 billion barrels out of there. This would surely be our savior, right?
The US says we demand around 20 million barrels of oil per day. If that rate remains constant, which is a ludicrous claim, ANWR at the most liberal estimate would give us 175 days worth of oil. At what cost? And if demand increases, as it is very likely to do?
Consider next an example using a fictitious bacterium, one who splits cellularly every minute. This is not an unusual bacterium. Place it in a bottle at 11:00am. By noon the bottle is completely full. This is not shocking. What is shocking is that one minute before noon, 11:59am, the bottle is only half full. “Half full” seems like a huge amount of space. But when your growth is unrestrained… Imagine if at noon the bacteria send out scouts who discover 3 other bottles. There is great rejoicing. If the growth continues, these three new bottles, this 300% increase in living space, will be filled up in 2 more minutes.
His talk also reminded me of how often we are lied to using numbers. We are told that growth is good, and that, say, 7% annual growth is a solid number, not frightening at all. But the reality is that 7% annual growth means that you’re doubling size every 10 years. Seven percent growth on $100 in the bank means that in 10 years, you have $200. If Denver, CO, my home, had a 5% sustained growth rate to affect our current 554,000 people, in 14 years we would have 1,108,000 people. This estimate is derived from the same growth estimates that have 7% interest on $100 doubling in 10 years–5% growth doubles in roughly 14 years. Denver is roughly 44 square miles–that’s over 25,000 people per square mile. Now, historically, Denver hasn’t had a 5% growth rate. On average, it’s been closer to 17%. For those counting at home, that’s doubling every 4 years or so. Thankfully, we’ve not kept a constant rate. But in 100 years, we went from almost 134,000 people to more than four times that.
Sit on that for a moment.
Let’s go back to our oil consumption. Let’s just pretend that US demand for oil grows at 1% per year. Remember that chart with the wheat and chess squares? Notice that the “Total” column is always one less than the amount added in the next iteration. If we keep 1% growth on US demand for oil, 70 years from today we’ll need as much oil as all the oil ever produced up to this point for just one year.
It’s simply not sustainable.
Bartlett’s main question, what he calls The Great Challenge drives this all home:
Can you think of any problem, in any area of human endeavor, on any scale, from microscopic to global, whose long-term solution is in any demonstrable way aided, assisted, or advanced by further increases in population, locally, nationally, or globally?