Dietrich von Freiberg

(b. Freiberg, Germany, ca. 1250; d. ca. 1310)

optics, natural philosophy.

In Latin his name is written Theodoricus Teutonicus de Vriberg (variants: de Vriburgo, de Vribergh, de Vriberch, de Fridiberg, de Frideberch, Vriburgensus). This has been anglicized as Theodoric of Freiberg and rendered into French as Thierry de Fribourg. Which of the many Freibergs or Freiburgs is the place of his birth is not known for certain; Krebs regards Freiberg in Saxony as the most likely. Dietrich entered the Dominican order (province of Teutonia) and probably taught in Germany before studying at the University of Paris, about 1275–1277. He was named provincial of Teutonia in 1293 and was appointed vicar provincial again in 1310. He earned the title of master of theology at St. Jacques in Paris before 1303. In 1304 he was present at the general chapter of his order held in Toulouse, where he was requested by the master general, Aymeric de Plaisance, to put his investigations on the rainbow into writing. Dietrich is sometimes cited as a disciple of Albertus Magnus; although he is in Albert’s tradition, there is no direct evidence that Albert actually taught him.

Apart from his role as a precursor of modern science, Dietrich wrote extensively in philosophy and theology. He is best characterized as an eclectic, although he generally followed the Aristotelian tradition in philosophy and the Augustinian-Neoplatonic tradition in theology. He opposed Thomas Aquinas on key metaphysical theses, including the real distinction between essence and existence. Crombie argues for an influence of Robert Grosseteste on Dietrich from similarities in their optics, but the evidence is meager; Dietrich certainly rejected the “metaphysics of light” taught by Grosseteste and Roger Bacon, and he did not subscribe to the mathematicist view of nature that was common in the Oxford school. Again, Dietrich’s interest in Neoplatonism was more theological and mystical than philosophical. He is credited with having influenced the development of speculative mysticism as it was to be taught by Meister Eckhart and Johannes Tauler, both of whom were German Dominicans.

Dietrich’s place in the history of science is assured by his De iride et radialibus impressionibus (“On the Rainbow and ‘Radiant Impressions,’” i.e., phenomena produced in the upper atmosphere by radiation from the sun or other heavenly body), a treatise composed shortly after 1304 and running to over 170 pages in the printed edition (1914). In an age when scientific experimentation was practically unknown, Dietrich investigated thoroughly the paths of light rays through crystalline spheres and flasks filled with water; and he deduced therefrom the main elements of a theory of the rainbow that was to be perfected only centuries later by Descartes and Newton. He also worked out a novel theory of the elements that was related to his optical researches and wrote on the heavenly bodies, although the latter of these contributions is more the work of a philosopher than of a physical scientist in the modern sense.

The anomalous character of Dietrich’s contribution poses a problem for the historian of scientific methodology. One is tempted to see in his use of experiment and mathematical reasoning an adumbration of techniques that were brought to perfection in the seventeenth and later centuries. That there is such a foreshadowing is undeniable, and yet the thought context in which Dietrich worked is so different from the Cartesian and empiricist world views that one must be careful not to force too close an identification in method. The mathematical basis for Dietrich’s reasoning stems from the perspectiva, or geometrical optics, of the Schoolmen and of Arabs such as Ibn al-Haytham (Alhazen); and his measurements are those of medieval astronomy, based on the primitive trigonometry of Ptolemy’s Almagest. Dietrich does not propose a “theory” in the technical sense, although there is a hypothetical element in his thinking that can be disengaged on careful reading. Rather, he explicitly locates his own method in the framework of Aristotle’s Posterior Analytics, which puts him on the search for the causes of the rainbow, through discovery of which he hopes to be able to deduce all of the rainbow’s properties. This demonstrative ideal of Aristotelian science, it may be noted, did not exclude the use of dialectical (or conjectural) reasoning by its practitioner, although later Scholastics have tended to overlook the latter element. Dietrich’s empiricism also derives from the Aristotelian tradition, even though portions of his theory of knowledge are markedly Augustinian. His optics makes implicit use of a method of resolution and composition that was already known to Grosseteste and that was to be refined considerably by the Averroist Aristotelians at Padua, who educated the young Galileo in its use. The general framework of Dietrich’s methodology is, thus, far from revolutionary. What characterizes his contribution is his careful application of a method already known in a general way but never hitherto applied with such skill to the detailed explanation of natural phenomena.

Within this setting Dietrich’s methodological contribution may be made more precise, as follows. He was not content merely to observe nature but attempted to duplicate nature’s operation by isolating the component factors of that operation in a way that permitted their study at close range. Most of his predecessors had regarded the rain cloud as an effective agent in the production of the rainbow; even when they suspected that the individual drop played a significant role, as did Albertus Magnus, they saw no way of isolating it from the collection that produced the bow. When, for example, they compared the colors of the bow with the spectrum resulting from the sun’s rays passing through a spherical flask of water, they tended to equate the flask with a cloud or with a collection of drops. It was Dietrich who apparently was the first to see “that a globe of water can be thought of, not as a diminutive spherical cloud, but as a magnified raindrop” (Boyer, p. 112). This insight, coupled with the recognition that the bow is simply the aggregate of effects produced by many individual drops, ultimately led him to the first essentially correct explanation of the primary and secondary bows. Dietrich, of course, used remarkable experimental acumen in working out all the implications of his discovery. But his genius consisted basically in immobilizing the raindrop, in magnified form, in what approximated a laboratory situation and then studying at leisure and at length the various components involved in the production of the bows.

Dietrich’s work represents a great breakthrough in geometrical optics, and yet a simple error in geometry prevented him from giving a correct quantitative theory of the rainbow. In essence, this came about through his using the “meteorological sphere” of Aristotle as his basic frame of reference. Here the observer was regarded as at the center of such a sphere, and the sun and the raindrop (or cloud) were thought to be located on its periphery. Thus, in Figure 1, the observer is at the center, B, while the sun is

behind him at point A on the horizon and the much magnified raindrop is elevated at point D in front of him. Although this schema permitted Dietrich to use a method of calculation already at hand from medieval astronomy, it automatically committed him to holding that the raindrop and the sun remain always at an equal distance from the observer—an assumption that perforce falsified his calculations.

On the detailed mechanism for the production of the primary, or lower, rainbow (see Figure 2), Dietrich

was the first to trace correctly the path of the light ray through the raindrop and to see that this involved two refractions at the surface of the drop nearer the observer, i.e., at points E and F, and one internal reflection at the surface farther from him, i.e., at point G. This provided an understanding of why the bow always has a circular form, which was already seen in a rudimentary way by Aristotle; but it also enabled Dietrich to deduce many of the remaining properties of the bow. He was the first to see, for example, that each color in the rainbow is projected to the observer from a different drop or series of drops. He also could deduce, as others before him had merely surmised, that an observer who changes his position sees a different rainbow, in the sense that a completely different series of drops is required for its formation.

This explanation of the primary rainbow alone would have gained for Dietrich a respectable place in the history of optics. He did not stop here, however, but went on to detail the corresponding mechanism for the production of the secondary, or upper, rainbow (see Figure 3). He saw that the light ray, in this case

follows a path quite different from that in the production of the primary bow, involving as it does two refractions at the surface of the drop nearer the observer, i.e., at points E and F, and two internal reflections at the surface farther from him, i.e., at points G and H. This insight led immediately to the correct explanation for the inversion of the colors in the secondary bow: the additional internal reflection reverses the ordering of the colors. Thus could Dietrich demolish the competing theories current in his time and go on to deduce other properties of the outer bow: that it is paler in appearance than the inner bow (because of the additional reflection) and that it often fails to appear when the inner bow is clearly seen.

A most interesting part of Dietrich’s De iride—which led him to compose a companion treatise, De coloribus (“On Colors”)—is his ingenious but unsuccessful attempt to explain how the colors of the rainbow are generated. It is in these portions of his work, generally passed over rapidly by historians of science, that one can discern in his procedure an interplay between theory and experiment foreshadowing the characteristic methodology of modern science. Dietrich was confident that he had discovered the true “causes” of the bows, and thus he proposed his geometrical explanations of their formation as apodictic demonstrations in the Aristotelian mode. He never was convinced, on the other hand, that he had gotten to the “causes” of radiant color; and thus he had to content himself with the search for the “principles” of such color formation. In this search Dietrich fell back on a Peripatetic argument involving “contraries,” the classical paradigm of dialectical reasoning. He used as his analogy the medieval theory of the elements, according to which the four basic contrary qualities of hot-cold and wet-dry, in proper combination, account for the generation of the four elements (fire, air, water, and earth). To employ this, Dietrich had first to establish that there are four colors in the spectrum-and this contrary to Aristotle and almost all of his contemporaries, who held that there are only three. His inductive argument here is superb, and the way in which he employs observation and experiment to overthrow the authority of Aristotle would delight any seventeenth-century thinker. Dietrich was less fortunate in explaining the origin of colors in terms of his two “formal principles” (clear-obscure) and two “material principles” (bounded-unbounded). He did, however, contrive a whole series of experiments, leading to various adhoc assumptions, in his attempt to verify the explanation he proposed. Yet it seems that he was never quite sure of this, and in fact a quite different approach was needed to solve his problem—it was provided by Sir Isaac Newton.

Possibly because of an interest in the elements aroused by his optical studies, Dietrich wrote opuscula entitled De elementis corporum naturalium (“On the Elements of Natural Bodies”), De miscibilibus in mixto(“On Elements in the Compound”), and De luce et eius origine (“On Light and Its Production”). These are neither mathematical nor experimental, but they do shed light on Dietrich’s theories of the structure of matter and his analysis of gravitational motion. He also composed treatises relating to astronomy, De corporibus celestibus quoad naturam eorum corporalem(“On Heavenly Bodies With Regard to Their Corporeal Nature”) and De intelligenciis et motoribus celorum (“On Intelligences and the Movers of the Heavens”); the latter has been analyzed by Duhem, who sees it as a retrogression from the astronomical contributions of Albertus Magnus.

For the influence of Dietrich on later optical writers, which was mostly indirect, see the works of Boyer and Crombie cited in the bibliography.

BIBLIOGRAPHY

I. Original Works. De iride et radialibus impressionibus, edited by Joseph Würschmidt in “Dietrich von Freiberg: Über den Regenbogen und die durch Strahlen erzeugten Eindrücke,” in Beiträge zur Geschichte der Philosophie und Theologie des Mittelalters, XII, pts. 5–6 (Münster in Westfalen, 1914), contains Latin text, with summaries of chapters in German; an English translation of significant portions of the Latin text with notes, by W. A. Wallace, is to appear in A Source Book of Medieval Science, Edward Grant, ed., to be published by the Harvard University Press. The Latin text of De coloribus, De luce et eius origine, De miscibilibus in mixto, and portions of De elementis corporum naturalium is in W. A. Wallace, The Scientific Methodology of Theodoric of Freiberg, Studia Friburgensia, n.s. no. 26 (Fribourg, 1959), pp. 324–376, which contains references to all edited opuscula of Dietrich published before 1959; to these should be added a partial edition of De visione beatifica in Richard D. Tétreau, “The Agent Intellect in Meister Dietrich of Freiberg: Study and Text,” unpublished Ph.D. thesis for the Pontifical Institute of Mediaeval Studies (Toronto, 1966). A French translation of excerpts from De intelligenciis et motoribus celorum is in Pierre Duhem, Le systéme du monde, III (Paris, 1915; repr. 1958), 383–396.

II. Secondary Literature. Biographical material can be found in Engelbert Krebs, “Meister Dietrich, sein Leben, seine Werke, seine Wissenschaft,” in Beiträge zur Geschichte der Philosophie und Theologie des Mittelalters, V, pts. 5–6 (Münster in Westfalen, 1906). Dietrich’s work on the rainbow is well detailed in Carl B. Boyer, The Rainbow: From Myth to Mathematics (New York, 1959), pp.110–124 and passim; and in A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100–1700 (Oxford, 1953), pp. 233–259. Fuller details on Dietrich’s methods are in W. A. Wallace, Scientific Methodology..., cited above. For an account of Dietrich’s other scientific accomplishments, see the following articles by W. A. Wallace: “Gravitational Motion According to Theodoric of Freiberg,” in The Thomist, 24 (1961), 327–352, repr. in The Dignity of Science, J. A. Weisheipl, ed. (Washington, D.C., 1961), pp. 191–216; ‘Theodoric of Freiberg on the Structure of Matter,” in Proceedings of the Tenth International Congress of History of Science, Ithaca, N.Y., 1962, 1 (Paris, 1964), 591–597; and “Elementarity and Reality in Particle Physics,” in Boston Studies in the Philosophy of Science, III, R. S. Cohen and M. W. Wartofsky, eds. (New York, 1968), 236–271, esp. 243–247.

William A. Wallace, O. P.