Nicholas of Cusa

1400-1464

German Philosopher, Mathematician, Astronomer, and Futurist

Nicholas Cryfts (or Krebs), known as Nicholas of Cusa (the German city Cues or Kues, his birthplace), was one of the first great polymathic (learned in many areas) minds of the early Renaissance, and one of the first "Renaissance men" with all the spirit implied in the title. Cleric, statesman, philosopher of seminal humanism, mathematician, astronomer, and futurist, Nicholas's early schooling included the universities of Heidelberg, Padua, and Bologna (1416-1423). Although he studied law for a short time, he turned to the clerical life with a move to theology at the University of Cologne (1425). Then followed diplomatic and administrative duties on behalf of the church, which led to his being honored with the designation cardinal priest (1449) by Pope Nicholas V, although he declined at first.

Nicholas of Cusa had begun formulating a theory of knowledge based on his premise of the incompleteness of humanity's knowledge of the universe. In regard to this, and having both the nominalist's and mystic's distrust of realism, he rejected the entrenched late medieval scholasticism with its dependence on Aristotelian method as a proper baseline. Instead he defined three stages to knowledge: phantasy (fantasy, meaning of the senses), reason (abstraction and discursive knowledge), and intellect (what hecalled mystical or ultimate knowledge found in the only perfect reality, that is, from God).

By 1439, Nicholas completed the first of his twelve philosophical/scientific treatises in which he underlined the limits of human understanding of science (defined generally as knowledge) and also the means to surpass those limits. This was the famous De docta ignorantia (On learned ignorance) wherein the knowledge of intellect can reconcile the differences in the states of finite and infinite, called "the coincidence of opposites." He used the squaring of the circle as an example: a square circumscribed or bounded by a circle will, if the number of sides are increased toward infinity, approach the shape of the circle. In other words, a line and a segment of a circle almost become the same (coincidence of opposites)—but not quite. The latter provided a philosophical and metaphysical aspect to the example as well. Through intellect, humanity can approach perfect wisdom but can never achieve it. The obvious mathematical parallel to the example provides seminal concepts in the study of infinity and infinitesimal theory.

This treatise also contained his early ideas on the cosmos, particularly his intuitive idea that logic was better served with the earth revolving around the sun and not being the center of the universe. This idea was probably based on Paris School physical theorist Nicole Oresme (c. 1320-1382). He also decided that the stars were other suns (although, he also defined the earth as a star) and that other habitable worlds like earth orbited them. He anticipated the question of the infinity of the universe, calling it unbounded but perhaps not spatially infinite. Another of his treatises (1436) foretold the need for calendar reform that came to pass with the Gregorian calendar reform of 1582. About 1444 he began more serious instrumental astronomical study. He improved on the earlier medieval Alphonsine Tables with a more practical method of finding positions of the sun, moon, and planets. A small scientific treatise Idiota de staticis experimentis (Static experiments) is important in physical statics and meteorology with regard to Nicholas's observations and experiments dealing with objects absorbing moisture and gaining weight and using that as a measure of atmospheric humidity.

Nicholas's intellectual pursuits were tempered by his duties as a papal legate. In 1460 he ran afoul of the unscrupulous Duke Sigmund of Austria and the Tyrol with regard to church authority. He was imprisoned by the Duke and illtreated to the point that he never fully recovered. On his way to Pope Pius II in 1464, he died at Todi in Italy, but he left behind the gifts of a hospital (at Cues), his extensive library, and his scholarly achievements, all of which are still in use to this day.