FUTUROLOGY

Playing with logistic functions

Omar Campos Ferreira
Course of Nuclear Sciences and Techniques - UFMG
Energy Planning Department
English Version:
Frida Eidelman
frida@password.com.br

 

Overview
1 - Introduction
2 - Probabilistic model of the logistic "law"
3 - Examples of the logistic "law"
Bibliography


Overview
or a quick glance at Omar’s article

The need of predicting the future can be partially satisfied by a simple scientific methodology, attested by hundred of examples, that permit to project the development of a certain type of phenomena.

The most indicative example of these phenomena is the propagation of an "epidemic"(disease, fashion, slang, financial speculation, etc.). The same methodology applies to the use of equipment or to one form of energy, to the discovery of chemical elements or still to the construction of Gothic churches.

In these phenomena the epidemic propagation occurs according to a logistic function. The growth of an accumulated number of the affected elements (N) takes the shape of the letter s as it approaches the limit value (N). The initial growth conforms to an exponential function.

As it is usual in the scientific field., it is chosen an adequate scale which permits to represent the function by a straight line. In the present case, the function is a fraction of the affected population (F=N/N) that behaves according to a logistic function.

 

An elegant deduction using the probabilistic model is presented in the article.

The method is applied to make projections in two cases:

 

logistic function

 

A: The Brazilian population

The logistic function F=1/(1+Exp(-at-b)) can be represented by a straight line in an adequate scale Ln(F/(1-F))

 

 

 


 

The Brazilian population will be stabilized around 260 million inhabitants at the end of the next century.

B: Installed hydroelectric power

 

The installed hydroelectric power shows a quite adequate logistic fit. The behavior indicates saturation of the installed power at 80 GW and is much lower than the potential that is presently considered economical. This result refers to the present historical cycle based essentially on government capital. It remains to be answered if a new cycle based on private capital would be possible or - as it happened in several countries - other economic considerations would limit the use of hydroelectric power.

 

Top Main Document

 


1 - Introduction
2 - Probabilistic model of the logistic "law"
3 - Examples of the logistic "law"
Bibliography

 

Top Main Document