Phil, Extrapolation is really tough with complex systems. Usually there are distinct points where models break down (continuity goes out the window). For example, the Ideal Gas Equation of State is great for situations where the gas is nearly ideal. But once we reach certain limits (i.e. higher pressure or temperature) a different model is needed. So we go to something more complicated like the Van der Waals Equation of State or the good ol' Soave-Redlich-Kwong Equation of State. We can see that models of economies or populations will act in the same way. So our function either has to be able account for discontinuities which could arise in the future which we're trying to extrapolate. This means that we either have to use a universal equation (which is usually tough to create) for everything (but such an equation may not be computationally feasible for a large number of points), or we have to create a piecewise function which allows for the discontinuities... but if we're going to account for the discontinuities in such a complex and ill-conditioned system, we better know damn well where they are. Also, if we're going to use a computer, we have to worry about iteration error. Which means, if we base our extrapolation of point i+1 on point i, then the extrapolation of point i+2 has the error created in i to i+1 as well as the error created in i+1 to i+2. In chaotic systems (i.e. populations, economies, climates) this propagation of error is awful. That's why weathermen are only "accurate" for a few days. Mike