Galileo devised a method that exhibits some provocative similarities to, and differences from, a Rasch approach to instrument design: Viewed as a whole, Galileo's method then can be analyzed into three steps, intuition or resolution, demonstration, and experiment; using in each case his own favorite terms.
That Galileo actually followed these three steps in all of his important discoveries in dynamics is easily ascertainable from his frank biographical paragraphs, especially in the "Dialogues Concerning Two New Sciences."(all italicized quotations from Burtt)
Galileo's first step is organized observation: Facing the world of sensible [perceptible by sense] experience, we isolate and examine as fully as possible a certain typical phenomenon, in order first to intuit those simple, absolute elements in terms of which the phenomenon can be most easily and completely translated into mathematical form; which amounts (putting the matter in another way) to a resolution of the sensed fact into such elements in quantitative combinations.
The term elements is ambiguous. Initially elements appear to correspond to test items, survey questions or rating scales, but in the next sentence those same elements are already quantities. This leap from the ephemeral specifics of the data (sensed facts) into quantities is what Edmund Husserl terms Galileo's "fateful omission" of the means by which nature is mathematicized.
The means of quantification seemed self-evident to Galileo (as well as Descartes and Newton). There is also a common willingness in the social and human sciences to assume that one's intuitions of a variable's content and structure are enough to resolve (bring into focus) its quantitative elements (i.e., to separate them from all other variables, thus satisfying Rasch's separability theorem). But this self-evidence has proven to be unwarranted.
Burtt presents us with Galileo's formulation of what Ronald Fisher called "sufficiency": [If we have] performed this step [the intuition of elements] properly, we need the sensible facts no more; the elements thus reached are their real constituents, and deductive demonstration from them by pure mathematics (second step) must always be true of similar instances of the phenomenon, even though at times it should be impossible to confirm them empirically.
Once the quantitative status of the variable has been treated as a hypothesis, substantiated, and its elements derived from data, we need the sensible facts no more... Deductive demonstration from them [the sensible facts] by pure mathematics ... must always be true of similar instances. A continuing basis of all science is that quantitative differences among different aspects of the phenomenon should hold constant across similar observations. This requires that scale values be invariant, even when empirical evidence is unavailable (as, for example, relating to items not administered in computer-adaptive testing).
Galileo also perceived the value of descending from the world of mathematical manipulation of quantities into that of sensory perception: For the sake of more certain results, however, and especially to convince by sensible illustrations those who do not have such implicit confidence in the universal applicability of mathematics, it is well to develop, where possible, demonstrations whose conclusions are susceptible of verification by experiments [his third step]. Then, with the principles and truths thus acquired, we can proceed to more complex related phenomena and discover what additional mathematical laws are there implicated.
Since there are many who do not have such implicit confidence in the universal applicability of mathematics, it is necessary to substantiate with evidence what Galileo would intuit. Galileo's deductive, logical necessity of the way quantitative elements follow from sensible facts is for us experimental. We must add, as Galileo did not, that deduction is circularly complemented by induction, that logic is not simply rational, but also metaphorical, poetical, social, economic, political, and cultural.
Galileo contributed to Western culture's mind/body dualism by discrediting the trustworthiness of sensible facts in favor of intuited elements, deductive demonstrations, and experimental verification of how elements (quantitative units of measurement) follow from sensible facts. We, however, need to realize that our scientific instruments are extensions of our bodies' sense organs. The elements read off these extensions are also sensible facts dependent upon the existence of particular kinds of technology and on people who value them.
The technical aspects of Galileo's methods have been continually improved. Even his "fateful omission" of the step from observation to quantification has been remedied. Now it is up to us to give science a human face - to flesh out these technical advances with the meaning and sensitivity required to make measurement work in the complex applications we face today.
E. A. Burtt, The Metaphysical Foundations of Modern Science. Garden City, NY: Doubleday Anchor Books. 1924/1954
Galileo and Scientific Method, W Fisher Jr … Rasch Measurement Transactions, 1993, 6:4 p. 256-7
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