The experimental method was designed for studying natural phenomena and is structured in three phases that make it truly special.

The first phase is that of observation and measurement; the phenomenon to be studied must be observed; the exam should not vary by changing the observer and must therefore be independent from the person who observes; in this case it is said that the observation is objective. In order to be objective and accurate, it is searched in the phenomenon all that can be measured. If you ask ten people if a table we chose is large or small, it is very likely that some will say that it is large and others small, because everyone compares with his own table at home or to the large one their grandma had; if we ask them instead how big this table is and we give them carpenter meters to measure it, all of them will give the same answer, except for measurement errors, of course. The use of measuring tools, further to making the observations objective, all referring to the same units of measure, makes them even more precise and accurate, in accordance with the precision of the utilized instrument.

It is appropriate to mention the fact that the accuracy of the instruments is always limited, as there is inevitably a margin of error; for example, with a normal tailoring meter we cannot see differences of a tenth of a millimeter, but for the tailor this type of imprecision is irrelevant; it is however important to highlight that there are methods to know how is the error extent and therefore how our instrument is precise; this way, we know of how much the error was and if such error is relevant or not. The scientist, like the tailor, knows that his measures are not infinitely precise, but they are enough accurate; even if from a geometric or mathematical point of view they will always be a little wrong, the competent scientist always knows of how much they are inaccurate and can evaluate whether the error is small enough to be negligible.

A new element of this method is therefore the accuracy and a more rigorous objectivity.

The second phase consists in developing a mathematical or ideal model. For taking the measures you need to know what to measure, but a natural phenomenon often involves several different factors (temperature, distance, weight, speed, area, volume and many others); a scholar from the first observations must therefore make an analytical and schematization work, identify all the different factors / units involved in the issue and the relations between them, until he finds a main cause to be isolated to study the effects on the measures linked to it. A classic example is the fall of heavy objects in which the main cause is weight, while the effect is the movement, the speed, the acceleration and so on; the secondary components will be after added, like the force of friction, the irregular shape of the object, the mechanical constraints and other factors.

During the observation therefore there is already an interpretation of the facts and a simplification of reality that tends to form a model in which only one cause acts, and in which one effect at a time is examined. In this way the phenomenon is studied a piece at a time, step by step, gradually finding the appropriate units to be measured.

At this stage, the phenomenon is represented through the variations in its characteristics, whose measures are listed in appropriate tables and whose relations are now those between numbers (measures) usually represented with mathematical formulas called functions. The result is a mathematical model of the phenomenon, a sort of geometric representation, as precise as the measures on which is based are; this model becomes progressively more complex as new measures are added (both related to causes and effects), but it still remains a model in which something may be missing, although something secondary if the model has been well constructed.

From simple observation, as accurate as it can be, then we moved to something which is the fruit of our mind, a mental model having mathematical precision; this is the second step of the method and there is no doubt that this is an improved version, more rigorous, more objective, of the natural process that we all use in forming our personal mental models. The purpose is basically the same: to form in our mind a picture, a description of reality, that is understandable and that tells us how nature works, to satisfy our curiosity and take all possible advantages.

The third phase is the experimental verification. We saw that the observations are objective, while for forming a mathematical model we spoke of scholar intuition through which are assumed relations of cause and effect between the variations of the different factors; there is therefore a subjective contribution that may give rise to two incidents:

– by the same observations, several different models can arise, born by interpretations of the various scholars;

– further observations may deny the assumed relations.

In the first case, the different models are all consistent with the observations made and then perfectly equivalent in describing the nature; we have already seen a classic example in astronomy: is Earth rotating on its own axis or are the stars that revolve around the Earth? In both cases we’d see the Sun, the Moon and all the stars moving from east to the west, then how things really are? How to determine which is the right model or the closest to the truth? The scientist has to add new observations to the starting ones that are consistent with a single model and deny all the others; for this purpose, various models are used to make predictions about what should happen in situations not yet observed, and when the various models lead to different estimates in a specific situation, then a test is designed, called experiment, to verify which forecast is the right one; this is the experimental verification, the third important step of the method, on which outcome depends the choice of the best model.

Anyway, nothing guarantees that later a new model, consistent with the new observations, would not appear, in which case new verification experiments will have to be devised for selecting the best model.

In the second case suggested above, it might happen that appear, perhaps during the experimental tests, new observations that deny even the latest model left; in this case we must admit that the model is not valid at all times, but only for a limited number of cases and therefore we must start again searching for a better model, perhaps by changing the old one.

In any event, the refining and validity of the models depends on the number of cases observed, i.e. on the number of experiments made; the experimental verification leads to two important results:

– it allows to select the best models;

– it allows to determine the extent of its validity, or under what circumstances is valid, waiting for a better model.

It follows that if the research has produced only one model, and it is always subjected to experimental verification, because scientists know that its validity may however be limited, that it is not an indisputable truth and that it is better to verify as soon as possible whether there are cases for which this model cannot be used.

**ROYAL BOX
** GALILEO GALILEI

**ABSTRACTS
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