Leaving aside the recent tendency for use of the word “exponential” by people who don’t understand what the word actually means, it would be nice if people understood the underlying concept. A professor (now emeritus but not “gone emeritus”) Albert Bartlett has been trying to explain this for quite a number of years now.

In the late 1960’s I began to realize that people didn’t understand the large numbers that result from steady growth rates. So, forty years ago I developed the talk; I’ve given it an average of once every 8.7 days for 40 years.

That’s from a (relatively) recent interview of Bartlett by Miguel Barbosa, appearing on a “Stock Market Insight” page. Another interesting point is this:

Do you think most politicians understand growth rates, but prefer to look the other way?

These are chamber of commerce types: promoters, builders, architects. Their business is promoting growth. But the single thing to note is that, both at the community level and national level, growth doesn’t pay for itself. The more you grow the greater your debt load. Colorado has had decades of wild and largely uncontrolled growth and is now practically bankrupt. People become fed up with the constant increases in taxes needed to pay the costs of growth and they vote for tax limitation measures. Unfortunately, the growth promoters seem to find ways around these limitations, so the growth continues and the consequent problems escalate rapidly. We can see this happening in California and we have a similar situation brewing in Colorado.

I say “relatively recent” because though the article is dated Jan 15, it seems to refer to Bush as the current president. But I’m inclined to blame the venue, and not the interviewee, as a great deal of other sensible things get said.

Wikipedia does a decent job in English:http://en.wikipedia.org/wiki/Exponential_growthThey also throw in an explanation of logarithmic growth, which explains why I can hear my keyboard now and still go to a Metallica concert.Dot Earth has an exponential hamster on it today:http://www.impossiblehamster.org/

To someone who already has notions of differentiation and integration, it is easy to explain the exponential function as the solution of the equation dX/dt = a X. Otherwise it is very difficult.I am afraid many economists and business people usually make quantitative calculation of short time duration only, where linear and exponential extrapolations make no essential difference. Assessment of costs of climate change requires a sort of thinking they do not do.By the way, Ms. Junko Edahiro, an environmental journalist and the Japanese translator of "Limits to Growth – The 30-Year Update", says that we need double decoupling to achieve sustainability, namely, decoupling CO2 emission from GDP, and decoupling GDP from happiness. This statement does not explicitly refers to exponential growth. But I think that that is the reasoning behind it.

wow, dude, this is not only exponentially quantum .. it's NONLINEAR! Up to approximately 10-90% of people won't get that.Oh, and "resonance."(I've just determined that science runs from Galileo through Tesla to me.)

Solved if all costs were internalized?Thought experiment only as determining "all" seems impossible…

All of the best teachers seem to have speeches that run – “people do not understand exponential growth.” I got that speech over and over. However, I do not believe it. I believe that “anybody that did not get very high grades in 2 semesters of college level calculus does not understand exponential growth.”