Forrester’s Limits To Growth Model For Your Personal Computer

Posted by President Barbicane on May 31, 2007, 01:31 AM | #

Are there any testable predictions in the world model?

Posted by James Bowery on May 31, 2007, 02:25 AM | #

The graphs of curves of various quantities vs time are the predictions.

Posted by karlmagnus on May 31, 2007, 09:10 AM | #

Don’t know about this version, but the original model included exploding exponential error terms. IF you have a model like Forrester’s with exponentials all over the place, and run a 40 year projection, the error terms explode off the screen, so “catastrophe” of some kind is unavoidable whatever assumptions you put in.

I told Forrester this in a public meeting in October 1971; didn’t stop the charlatan propagating his nonsense.

Posted by James Bowery on May 31, 2007, 09:54 AM | #

When you say “error terms” are you referring to the numerical methods used to run the differential equations or to something about the exponential propagation of input uncertainty?

Posted by Frank McGuckin on May 31, 2007, 01:14 PM | #

The late Donella Meadows was a fanatical multiculturalist who for the most part supported open borders.  What a piece of shit.

There is no environmental movement in the US.

Go to Wildlands website. I made a post there. If Dave Foreman has his way, White Americans will nothave the option of running away from non-whites much longer. And this would be good, for once the froniter is closed to White Americans, a race war will start which is the only way White Americans can prevent their racial dispossesson in America.

Posted by karlmagnus on May 31, 2007, 01:43 PM | #

James, the input uncertainty. When run on 1971 computers, the error terms exploded in about 40 iterations. I had studied the same problem a few months earlier, on a different problem, and so knew how it happened and what algorithms one might use to suppress the problem (it was impossible to eliminate entirely, as far as I knew.)

Forrester and Meadows had apparently ignored the problem altogether, at least that’s what it appeared from their output, which continued from plausible disasters to completely implausible ones that happened even when you made problem-suppressing and unlikely assumptions about rapid reversals in population and pollution growth.

Posted by karlmagnus on May 31, 2007, 01:48 PM | #

Sorry, to be clear, the rounding error caused at each year the projection extended further—the computer rounded everything and produced a “right answer plus epsilon” for the next year. Then the epsilon was included in the input for the iteration for the following year, and after 30-40 iterations the exponential functions in the equations caused it to explode off the screen.

Posted by SDLEE on August 31, 2010, 12:51 PM | #

>>Sorry, to be clear, the rounding error caused at each year the projection extended further—the >>computer rounded everything and produced a “right answer plus epsilon” for the next year. Then the >>epsilon was included in the input for the iteration for the following year, and after 30-40 iterations >>the exponential functions in the equations caused it to explode off the screen.

This (rounding error) is an artifact of using digital computer in solving “any” ordinary differential equation, not the “world dynamics.”  The mathmatics of the ‘world dynamics” is called “ordinary differential equation”  Reduce the delta (DT) with “Runge-Kutta 4” then, the rounding error can be reduced considerable so that we don’t need to worry about the rounding error anymore.  See Dr. Moler’s book at Matlab (available free).  Advancements in “numerical anaysis” and computer make the rounding error as of little concern. 

SDLEE

Posted by SDLEE on September 23, 2011, 11:14 AM | #

Dr. Cleve Molder’s free e-books on numerical analysis and MATLAB.  He is one of the founder of the Matlab and world-renowned numerical analyst.

http://www.mathworks.com/moler/index.html

Almost all engineering analyses and models especially for dynamic system are to solve “differential equations” such as the famous Newton’s law (sum of F=M*a=M*d(velocity)/dt, where velocity = d(displacement)/dt).  Some examples are structural dynamics (such as bending shape of a skyscraper, bridge, and car, etc.).  Computer-Aided-Engineering (CAE) is entirely based on differential equations (called finite element analysis (FEA)).  Rounding error is a serious issue in computer analysis and due attention should be paid.  However, rounding error is nothing to do with the World Model.