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Any discussions about the periodicity of natural occurrences must also take into account the fact that events may not be reproducible. In fact, what is a reproducible event? Both periodic or sporadic event may be involved, observable or not. In summary:
Definition 3
1. Reproducible phenomena: some information is known about their occurrence conditions so as to render them repeatable. E.g.: chemical reactions;
2. Irreproducible phenomena: events that cannot be reproduced at will either by knowing their occurrence conditions or because such conditions are themselves irreproducible. Ex.: E.g. climate or weather phenomena.
It is easy to see that, in order to be reproducible, it is necessary (but not sufficient) to know certain conditions. Reproducibility is associated to the ability to control the circumstances of a natural episode, which is a truly sufficient condition. The ‘laboratory reproducibility’ is a subset of Definition 3 (first type). Here it is important to emphasize the difference between ‘condition’ and ‘cause’ or ‘explanation’. As we have seen, it is possible to reproduce a phenomenon for which no suitable explanation exists (since it is sufficient to reproduce its conditions). This is often misinterpreted as an explanation mainly when someone manages to reproduce the event in the laboratory. Sometimes the knowledge of the operational conditions may lead to many purely phenomenological explanations that are not complete in face of the possibility of other explanations at a deeper level (1). As in the case of periodicity, the scientific community quite understandably prefers reproducible events. The task of the scientific exploration is the search for plausible causes to explain the reason beyond the occurrence conditions. Moreover, irreproducible events may become reproducible when knowledge of their operational conditions becomes available. Even though much is already known when the conditions are unveiled, science only happens when the causes or phenomenological sources are found.
As the causes are revealed, what was previously improbable becomes certain to the point of being possible to forecast the result by controlling the occurrence conditions. Therefore, irreproducible events could be further divided into two subclasses: predictable and unpredictable phenomena:
Definition
4
1. Predictable phenomena: events whose occurrence or details can be forecasted by knowing in advance a sufficient set of occurrence conditions. E. g.: weather phenomena;
2. Unpredictable phenomena: events that are inherently statistical in nature and, therefore, cannot be forecasted. E. g.: meteorite falls; the result of successive measurements of two non-commuting operators on a quantum state of a microscopic system.
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| Fig. 2 Another possible way of classifying phenomena according to Definition 3. |
Irreproducible events are common in Astronomy and Meteorology, and many can be simulated by computers (Pasini, 2003). It is clear here that such numerical ‘reproducibility’ has no relationship whatsoever with Definition 3.1. Again, it is interesting to compare our definitions of aperiodicity (Definition 2.2) and unpredictability (Definition 4.2). They are interrelated, however ‘unpredictability’ implies some sort of irreducible randomness. Yet, Definition 4.2 makes explicit reference to the operation conditions which are absent in Definition 2.2. Most unpredictable phenomena result from the inherent indeterminism of microphysics (Bohm, 1952; Popper, 1950; Penrose, 1989).
Reproducibility can be added to the diagram of Fig. 1 resulting in another branch as shown in Fig. 2. The four phenomenological features: observability, visibility, periodicity and reproducibility are of paramount importance when validating and developing whatever explanation for a given natural phenomena. Such features are ‘weak’ or defective in many anomalistic events in the lack of any theoretical framework to justify their existence.
An extended ‘entity-relationship’ diagram can be arranged in favor of any particular property. So far there are 8 classes which could be associated to the feature ‘visibility’, performing a total of 12 phenomenological classes. Fig. 3 shows the result of our general classification scheme starting with the main feature ‘reproducibility’.
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| Fig. 3 Adding more features in a more extended classification. |
Footnotes
(1) An example was the development of thermodynamics in physics. Thermodynamical principles were later explained or reduced in terms of statistical physics and microscopic entities such as atoms and their interactions.
