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The term exact science refers to certain areas of (scientific) knowledge, notably mathematics, physics, and others. In general use, it is associated with what is perceived as so-called "hard science", an equally unfortunate term. The standard definition, along the lines of "using mathematics" is nowadays considered inadequate. Nevertheless, there is an incontrovertible basis in fact that these terms are used. Such as accurate prediction of a future event, like a Solar eclipse. From the standpoint of method, what characterizes these fields of study is that, predictions are possible, and undergo testing by measurement, by experiment, and, at the very least, by observation. As well as by rigorous logical argument, wherever appropriate. And that theories may eventually get rejected, if it becomes agreed that they do not satisfy the tests. This availability-for-rejection is also known as "falsifiability", as advocated by the philosopher Karl Popper. Technically speaking, however, it applies to all the natural sciences, which can then be considered "exact", according to this criterion of testability. On the other hand, the mere application of mathematics does not in itself confer any greater degree of reliability to a subject. This was the origin of the term "exact". However, it is clear that, a completely correct, exact, mathematical computation, but based on faulty premises, and thus drawing equally faulty conclusions, would not in itself suffice. Likewise, a study can be quantitative, and yet be counting irreproducible entities. Therefore, without testability, there is no way to ensure reliability. For testability, it is essential that results and hypotheses be public, so that repeated testing and development is a universal endeavor. For this reason, it can be said that exact science, at least in the strict sense, did not arise until the invention of the publicly available scientific journal, say around 1640. Or at least with the availability of printed books, say around 1540, in Europe. This does not necessarily imply that results before that time were invalid. But many are seen that way today, in the light of the intense scrutiny that characterizes today's sciences. This relentless testing, and the ensuing error-correction, so to speak, translates into the very high degree of reliability of the established results in these sciences. Some fields of study, such as for example economics, share some of the features characteristic of the exact sciences. The primary distinction, of testability, lies in whether experimentation is feasible (or indeed advisable). Whether experiments can be designed so that they provide reproducible evidence, as distinct from anecdotal evidence, obtained from a single observation only. In this respect, astronomy could be hard put to qualify, precisely for the lack of experimentation. However, there are huge numbers of stars to be observed, in (almost) all relevant stages of the stellar life cycle, and this provides essentially as reproducible data as experiments otherwise do. And so do, indirectly, the branches of mathematics, physics and chemistry that are employed. Without which it would be impossible to interpret atronomical observations. It does appear as if the currently recognized laws of nature applied throughout the visible universe, at the epochs where the observed phenomena took place. However, this assumption is being tested, not taken for granted.
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