Arnold Kling has a very good article about non-linear thinking. Nothing new (at least to me) but a cogent way of explaining the implications to those for whom it is.

OT comment, but is anyone in space blogging circles going to attend Space Resources Roundtable this year?
Some very valuable insights, according to http://www.mines.edu/research/srr/SRR%20V%20Preliminary%20Program-1.doc

The first part of the article seems like a good explanation of why it is important for people to learn calculus. With a calc background, the answer to the bacteria question pops out immediately.

If the culture doubles every minute then 1 minute before it was full it must have been 1/2 full. No calculus, just logic.

Moore's Law is a very poor example of "nonlinear" thinking because first and foremost it is the successful imposition of a linear model on what was previously a nonlinear problem. That is, an exponential growth model has a linear model as its exponent! In the case of Moore's Law, the log of the transistor density is more or less a linear function of time over forty or so years.

IMHO, the problem isn't whether we're using too many linear models or not thinking nonlinearly enough. Instead, it's the insistence on simulations and paradigms that back your biases and preconceptions but fail to model reality. Ie, many of these flawed models are used not because of the simplicity of the model or the inability of the user to understand complex systems, but because the model happens to confirm the beliefs of the entities using the model.

I also have a comment on the last section:

Hearing the nonlinear thinking of Pop!tech helps to soften my concern about the future of Social Security. When economists make predictions about Social Security or Medicare, we use linear approximations. Those approximations do not take into account nanotechnology or a successful war on aging or other scenarios that were spun out at Pop!tech. What I call The Great Race seems to pale by comparison. Instead, what is uncertain is the continuity of the human race.

What if our survival in the big unknowns is in part determined by our (in)ability to properly handle the small but predictable problems? Look at US Social Security. It's a trainwreck due to occur in 2015 or perhaps a bit earlier under our "linear" predictions. I think it irresponsible to ignore those predictions merely because the future might be better than we thought or at least beyond the horizon of the current political crowd.