Tea for two, times two times two times two . . .

We have a social disease, and I’ve taken the presumptuous liberty to name it: exponentiosis stupiditus (“ES” as it is known among expo therapists). It’s a condition characterized by gleefully pursuing endless growth until its inherent impossibility clobbers us to smithereens. Generally incurable, it is highly contagious and endemic in the population of industrialized nations, with a prevalence of around 99%. Once infected at an early age, victims are afflicted with a compulsion to acquire stuff regardless of consequences. Many cultures and civilizations have suffered and expired from ES, but never before has it afflicted humans on such a planetary scale.


Despite the varied political rhetoric of the last few mercantile centuries, the issue is neither capitalism nor communism nor fascism nor socialism nor any ism. The issue is the prevalent cultural delusion that we can grow our portfolios of acquisitions without limits; indeed, if we don’t we’ll die.

Unfortunately, the opposite is true. And most of us have no idea why.

We are chronically factor-of-2 challenged. Also known as exponentiation, multiplying repetitively by the number 2 yields counter-intuitive and unimaginably large numbers in short order, as the emporer discovered when rewarding the extraordinarily clever inventor of chess (1). Here’s a puzzle that brilliantly illustrates our collective conundrum – see if you can figure it out before I give the answer away below:

“Bacteria grow by division so that 1 bacterium becomes 2, the 2 divide to give 4, the 4 divide to give 8, etc. Consider a hypothetical strain of bacteria for which this division time is 1 minute. The number of bacteria thus grows exponentially with a doubling time of 1 minute. One bacterium is put in a bottle at 11:00 a.m. and it is observed that the bottle is full of bacteria at 12:00 noon.

“Here is a simple example of exponential growth in a finite environment. This is mathematically identical to the case of the exponentially growing consumption of our finite resources of fossil fuels [as well as many other resources, greenhouse gas emissions, population explosion, etc.]. Keep this in mind as you ponder three questions about the bacteria:

“(1) When was the bottle half-full?

“(2) If you were an average bacterium in the bottle, at what time would you first realize that you were running out of space?

“(3) How long can the bacterial growth continue if the total space resources are quadrupled?” (2).

I’m about to give you the answer to the first question (which is also a hint for the other two) – so don’t read ahead yet if you’d like to wrestle with this one yourself.

Thinking . . .

thinking . . .

thinking . . .

thinking . . .

OK, here we go!


The answer is surprising but, in retrospect, obvious. The last doubling occurs at the last minute, so the bottle is half full at 11:59. If you’re an exponentially expanding anything (and we are currently an exponentially expanding practically everything), all looks well until a minute before noon. Then, less than sixty seconds later, ES pounces with a rapidity that leaves us reeling with disbelief, rage that “nobody told us,” and finally despair as the inevitable severe, violent and lethal limitations of the physical world make themselves known.

Yes, dear reader, here we are, at an exponentiating minute before high noon, acting like the ebullient, enthusiastic emporer with his new chess toy before accounts are settled. We are in the throes of the final doubling, yet it still looks like we have half a world left to exploit. Realistically speaking, we have quite possibly triggered exponential natural processes over which we have no control, that will run their course until they reach their physical limits (3) In any case, we have precious little time left to act.

Can we break through our blinding mythology and change for an immediate and urgent purpose? After all, given the nature of the problem, a rational response would be for all of us to focus the better part of all our waking hours on turning this lovely little blue spaceship around – because without it we have nothing.

Unfortunately, we can no longer console ourselves that we can work with the tools we’re accustomed to, such as our broken political processes – so clearly illustrated by the Bali conference on climate a few weeks ago (more on Bali in the next post). There’s little point in working with our current tools if they’re useless for the task at hand. It’s now a matter of creating whatever it is that we need to get the job done. After all, that’s the whole point of invention, and we’re very good at that (4).

We may each do it differently – although with the seas pounding at our doorstep we’ll all be fielding sandbags, no matter what our personal preferences may be. But whatever the parameters, we can direct our energies to the task. We have all the knowledge and technology we need right now, although certainly more may be helpful – what we lack are insight, will and the strength to end our terminal cultural addictions, and to overhaul the essence of our lives and change the course of planetary history.


We know how to focus intently on the task at hand during crisis – burning buildings, hurricanes, war. With climate change and what’s at stake, as difficult as it may be to grasp at times, surely we must do no less (5).

Next time: Bali Dancing.

Copyright 2007 by Adam D. Sacks, all rights reserved.

1. For a discussion of the emporer’s slight miscalculation when granting a doubling quantity of rice for each of the sixty-four squares on the chessboard, see http://in.answers.yahoo.com/question/index?qid=20070624005441AA41vJA. The hapless regent wound up an unpayable 16 quintillion grains of rice in debt, give or take.

2. From Albert A. Bartlett, “Forgotten Fundamentals of the Energy Crisis,” University of Colorado at Boulder, n.d., http://www.npg.org/specialreports/bartlett_section2.htm. See Bartlett’s web page for full discussion and answers.

3. That is, positive feedback loops or “tipping points,” in which exponential forces are unleashed; for example, melting permafrost releases methane which elevates greenhouse gas levels which raises temperature which melts more permafrost, until there’s no permafrost left to melt. For an excellent overview of tipping points, see Fred Pearce, With Speed and Violence, Beacon Press, Boston, 2007.

4. See our October 23, 2007 post, Zero Carbon Now – Part I for a glance at what a surviving world might be like.

5. For a graphic view of what exponentiation might look like, see Chris Jordan’s remarkable photographic series, “Running the Numbers,” at http://www.chrisjordan.com/current_set2.php.