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There are several ways to make predictions. Dynamic prediction is a method invented by Newton and Leibniz. Newton has been successfully applied to the movement of planets and their satellites.

Since it became the high prediction method applied in mathematics. Its scope is universal. Everything material, everything is in motion can be studied with the tools of dynamical systems theory. But it does not mean that it is necessary to know a system to know its dynamics. Otherwise we would not know much. The other major method of prediction is simply the ordinary use of reason. If you know the predictive laws you can make inferences that lead to predictions.

General definition of predictability

Generally, a predictive law determines conditions and a result; if conditions are observed, then you will have a result. As a condition and as a result we can consider everything sayable. So we have a wide variety of possibilities.

The conditions of a predictive law define a region of the space of the dynamics states, the set of states for which the conditions are met. You can call the set of starting points. The result defines the same set of states for which it was obtained. You can call the set of points of arrival of the predictive distribution. For convenience, let’s define the concept of achieving: a region B of the space of the dynamic states is achieved by region A when all paths passing through A then pass through at least one point, a state of B. A predictive distribution is true when all its end points are reached by all of its starting points. System is predictable when you can find results and conditions as the first to be affected by the latter.

We can consider that dynamic prediction is a very special case of rational prediction for which the only predictive laws are the laws of motion.

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