A.3.3.PI:2 - Problem

A description can correctly report the present while omitting what determines its continuation. Recovering every underlying detail is often impractical, and a useful future distinction may require only a small part of that detail.

Adding observations does not automatically solve the problem. Their timing, the actions taken between them, measurement error and the assumed law determine what can be inferred. A fitted predictor can also work for one interval and accumulate consequential error when repeatedly applied.

The practical problem is to retain enough information for the future question, and to know what result remains obtainable when the available information supports only a range, a conditional probability or a shorter horizon.