Mathematical physics: the radiation of virtue.
In view of Grosseteste’s interest in physical and astronomical matters, and his training, if we believe Bacon, for some thirty or forty years in mathematics, it is not surprising that he realized something of the value of mathematics in the study of natural science. He believed that a knowledge of geometry was of great aid to the “diligent investigator of natural phenomena” in explaining the causes of all natural effects. In a treatise “On lines, angles and figures,” or “On refraction and reflexion of rays,” Grosseteste holds that not only vision or light but every natural agent sends forth its virtue to the object affected and acts upon sense or matter along geometrical lines.[1444] This doctrine of radiation or emanation of force seems to date back at least to Plotinus, and we have heard Alkindi among the Arabs in his treatise on Stellar Rays say that the stars and all objects in the world of the four elements emit rays of this sort. From any given agent virtue radiates forth in all directions, but a perpendicular line is the shortest and strongest line of force between it and any other single point or object. From a point or center of influence to a larger surface we get pyramids or cones of radiated force. The same theory is set forth by Roger Bacon under the name “multiplication of species” but even this wording is not new with him, since Grosseteste speaks of the natural agent as “multiplying its virtue” from itself to the thing affected, and then explains that this virtue is also sometimes called “species” and sometimes “similitude” and is the same in whatever way it is named.
The Computus and calendar reform.
The Computus, or treatise on reckoning time and keeping track of Easter especially and also other church festivals, had been a variety of mathematical and astronomical exercise indulged in by the clergy even in the darkest periods of the early middle ages. The Computus of Grosseteste pointed out the need of reforming the Julian calendar then in use, and he also called attention to this need in his treatise on The Sphere. From the later use made of it by Roger Bacon[1445] and by Cardinal Pierre d’Ailly[1446] in the early fifteenth century one infers that Grosseteste’s Computus remained an authoritative work upon the subject of calendar reform.[1447]
Juggling with numbers.
On one occasion at least Grosseteste’s interest in mathematics degenerated into one of those puerile reveries on the relations and perfection of certain numbers in which so many authors since Pythagoras, if not before him, had indulged. Having stated that in “the supreme body” there are four things, namely, form, matter, composition and compound, Grosseteste states that form is represented by the number one, matter by two, and composition by three, “since there is patent in it formed matter and materialized form and the property of composition itself.”[1448] The compound besides these three things has its own nature and so is represented by four. Now 1 + 2 + 3 + 4 = 10. “Wherefore every whole and perfect thing is ten.”
From mathematics to astronomy to astrology.
That Grosseteste’s “mathematics” includes astronomy is indicated by his citing “mathematicos” as explaining that the sun burns the regions under the tropic of capricorn more than those under the tropic of cancer, because an eccentric of the sun when it is in capricorn brings it closer to the earth.[1449] These mathematicians disagree on this point with the commentator upon Aristotle who believed that the sun burned more in Cancer. If for Grosseteste mathematics included astronomy, astronomy also included astrology—although he does not usually employ the word mathematicus for an astrologer. To his attitude toward astrology we now turn.
Astrology in natural philosophy, agriculture, alchemy, medicine and music.
Grosseteste accepts astronomy or astrology as the supreme science and says in his treatise on the liberal arts that natural philosophy needs its aid more than that of the others.[1450] There is scarcely any operation whether of nature or of man, such as the planting of vegetables, or transmutation of minerals, or cure of diseases, which can dispense with astronomical assistance. For inferior nature does not act except as celestial virtue moves and directs it. He then goes on to detail the effects of the moon, Saturn, and Mars on the hour of planting, and then to emphasize the importance of selecting the favorable hours astrologically in medical practice and in alchemy where he associates the seven planets with seven metals.[1451] He also argues that the harmony of the movements of the celestial spheres is found also in their effects upon the inferior world.[1452] Therefore he who knows the due proportion of the elements in the human body and the concord of the soul with the body, can restore any lack of harmony in the same to its proper state.[1453] In other words, diseases and even wounds and deafness should be curable by music based upon a knowledge of astrology and mathematics, and one should also be able to control such emotions as joy, grief, and wrath.