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KRONOS Vol VII, No. 1

Metron

LIVIO C. STECCHINI

Copyright (C) 1981 by the Estate of Livio C. Stecchini

Science is a process consciously directed towards achieving knowledge that is explicitly formulated, general in scope, systematically ordered, and dependable. Since Kepler and Galileo, dependability is based on testing by measurement. The reason for which physics became the queen of the sciences is its consistent determination to introduce measurement into its discussions at the very earliest stage.

Modern science began when Galileo introduced the distinction between primary and secondary properties; primary properties are those that are measurable. Hence, science today is the art of formulating general statements that are verifiable by measurement. The precision of the measurements involved is the standard of the probable truth of a scientific theory.

Philosophers of science have recognized that this conception of science may be traced to Plato. But the historian must be concerned with the context out of which there grew Plato's formulations. The most radical statement of all Greek thought is Protagoras' "Man is the measure of all things". Werner Jaeger observes that Plato's philosophy could be summed up in one sentence, intended as a reply to Protagoras: "God is the measure of all things." These two thinkers disagreed on the metaphysical foundations of measurement, but they agreed on the proposition that measure is the ultimate reality, since the claim of God or man to be the ultimate reality depends on their connection with measure.

It is important to know how the Greeks operated empirically in the matter of measurements. The Greeks had a scientific system of measures connecting length, volume, and weight. This system was not their invention, but was developed in Mesopotamia before the origin of writing, before 3000 B.C.

All units of length, volume, and weight can be derived by a few simple arithmetical rules from a single lineal standard, the so-called Egyptian foot of 300 mm. This is proved through an extensive survey of the archaeological and written evidence for the Near East and Europe, including Russia; there is prima facie evidence that the same results would be obtained by examining the evidence for China and India. This system was maintained from early Mesopotamia and Egypt into medieval Europe and is continued today by English units. The English pound has not changed by a grain since the fourth millennium B.C. The units of length were maintained unaltered through millennia up to less than 1/100 of a millimeter. This shows that the concern with precision of measurement in the ancient world went beyond any immediate practical utility. Similarly, the geometry of Mesopotamian, Egyptian, and Greek buildings shows a concern with a precision that is irrelevant to the needs of architectural construction.

The inner structure of the ancient system of measures, in which a fundamental element is the scaling of the units in order to take into account the specific gravity of wheat and barley, suggests that measurement became important when agriculture was "invented" in the area that goes from Syria to Iran. Probably it was in the wake of agriculture that a single system of units spread East and West. As soon as farming became the main source of sustenance, it proved necessary to know how to distribute supplies between one crop and the next. Myths associate the establishment of measures with a famine. William Blake evoked a theme of the ancient past when he formulated the proverb, Bring out number, weight, and measure in a year of dearth. But the stimulus to the establishment of extremely precise standards came from the use of gold and silver as means of exchange and from the need of astronomy which was concerned with astrological predictions. Because of their connections with social justice and because of their connection with astronomy, measures acquired a transcendental meaning. The care needed for precision contributed to creating a religious atmosphere around them. Measures were preserved in temples (and in medieval churches), both because thereby they would be protected as holy and because it was felt that there was something holy about them.

In the middle of Mesopotamian cities there was the steptower which embodied the units of the system of measures, and represented the connection of the cities with the cosmic order. The Egyptians had measured the circumference of the Earth and realized that degrees of meridian become longer as one moves to the north. They had set up a geodetic system with benchmarks which had the purpose of showing that the main physical features of Egypt fit the patterns of meridians and parallels. At the beginning of the Middle Kingdom they set their capital at Thebes which is located at 2/7 of the distance between the Equator and the Pole.

Maimonides observes that, according to Jewish tradition, to use false measures is a crime worse than incest. A number of passages from the Old Testament make clear that the first element of Hebrew law is the system of measures. They are connected with the statements that God created the world numero pondere mensura; these texts were quoted with gusto by thinkers of the Renaissance. The Ark of the Covenant, where God was present, was nothing but an empty box representing a standard unit of measure. In some Greek temples, too, the divinity was represented by a unit of measure that was carried in procession on given occasions. The Brazen Sea and the other measures of the Temple of Solomon expressed the same notion; Jewish tradition preserved with great care the middoth of the vanished Temple.

Germanic tribes continued into the Middle Ages the ancient custom of placing in tombs an instrument of measurement.

In Greece, the concern with an organized system of measures and with the conception that the world was constructed numero pondere mensura was taken over in the seventh century B.C. It can be shown that phrases of Greek inscriptions dealing with measures are translated from a Semitic language. But among the Greeks the importance of measurement acquired a new dimension, because of their invention of the coin; they felt that monetary economy mathematizes human relations, since, as Marx puts it, the bond among human beings becomes the cash nexus. A number of fundamental texts, which have been either ignored or declared puzzling, make absolutely clear that the Athenians considered the system of measures the essence of their democracy. Democracy involved a mathematization of the constitution. However, it must be kept in mind that by democracy they did not mean anything resembling our representative institutions, since Athenian democracy, with its system of cross sections, fair samples, and lotteries, had features similar to those of our social statistics and public opinion polls. The revolt against mathematization and measurement, represented by Aristotle, is connected with the opposition to democracy. Up to now one of the most important parts of Aristotle, the discussion of justice in the Fifth Book of Ethics, has been badly understood, because there he criticizes the democratic conception of arithmetical equality and, at the same time, the mathematical interpretation of money and the notion that money is the essence of law, in the sense of being the basic determinant of human relations.

One of the first systematic bibliographies ever printed deals with works on measures. By the age of Galileo there had appeared at least fifty major works dealing with ancient measures. Even though Galileo did not write on units of measure (Kepler did), many of his correspondents wrote on the history of measures; among his antagonists Father Riccioli dealt with Roman measures and Father Grienberger with Hebrew measures. The French metric system did not derive from a desire to innovate, but from plans formulated in the course of two centuries to reform ancient measures by making them consistently decimal, as they were already in part.

It has been objected that the reduction of science to measurement makes the world dry and dull and stifles human creativity. This fallacy is based on a misconception about the nature of scientific theory; it is the insistence upon measurement that makes the construction of scientific hypotheses a field free for human imagination. One could hardly accuse Plato of being an opponent of imagination, although he declares that if number, weight, and measure are taken away from a discipline, little or nothing remains. Echoing some words of Bacon, it may be said that science consists of "anticipations, rash and premature" and of "prejudices"; but these marvellously imaginative and bold conjectures are carefully and soberly controlled by systematic tests. It is a common misconception that science results from the accumulation of perceptual experiences in the course of time. For this reason many find it difficult to explain the progress of science in Greece. It would seem that science advances in the periods in which human imagination is particularly stimulated. The outburst of science in the Renaissance is connected with the development in the arts and letters. Needham maintains that the technology of the Italian Renaissance was inferior to the technology of contemporary China.

As the origin of specific theories in the Renaissance is investigated, there appears their connection with neo-Platonism, Pythagoreanism, Cabalism, and mystical doctrines. Karl R. Popper has observed that the fallacy of deriving science from the accumulation of perceptual experiences leads to the superstition that science is bound to advance, since our experiences are bound to accumulate. This leads to a deterministic conception of history which implies that science can progress under totalitarian regimes. Science depends upon the free interplay of thought and therefore ultimately upon freedom. Hence, those who stress the role of measurement in science are the true friends of humanism, of those artistic and literary pursuits that increase the range of human imagination. The Newtonian conception of space has its roots in the mathematical perspective in the painting of the Quattrocento, which in turn was influenced by Pythagorean tenets. It is not accidental that Galileo was the son of the author of an important treatise on Greek music; it can be shown that this treatise had a direct influence on Kepler.

The problem of the relation of science to the humanities is discussed by Husserl in his final work, The Crisis of European Science. He stresses the importance of knowing the genetic relationship between the practice of metrology and the mathematical conception of the universe. Because this relationship has been forgotten, the scientific universe appears a reality independent of the mind of man, a monster that would crush humanity. For the Greeks science was the product of the rational attitude of man, an affirmation of the human mind: the logos discovered in nature is the human logos. This is the essence of humanism according to Husserl. The history of measures reveals man's option in specific historical circumstances to interpret the world in mathematical terms (Wille der geistigen Vorvater).

Such an investigation is concerned with the gathering of empirical data and with pursuing the minutiae that provide the proper evidence for a history of measurement; but it cannot help having some bearing on the conflict between realists and instrumentalists in the interpretation of scientific theories. Most modern instrumentalists have been motivated by an irreverent frame of mind and have aimed at destroying ontology; for this reason they have not seen that, in denying the connection between being and scientific theories, they transferred being to measures themselves. On the other side, the realists have tried to hold on to being, but have not seen that the source of the ontological force of scientific theories is measurement. Ancient thought had gone a long way in this direction. The Renaissance view is expressed by Guillaume Bude, the founder of Greek studies in France, who in 1514 A.D. published a monumental study of ancient measures for the purpose of reestablishing the coherence of the units that had been shaken by medieval practice; he prefaced it with a motto that equates measures to religion:

Una fides, pondus, mensura sit idem,
Et status illaesus totius orbis erit.

(Let there be one single faith, one measure, one weight, and the order of the world shall be free from harm.)

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