No Comment, Quotation — December 19, 2009, 7:46 am

Pascal’s Principle of Convergence

bosch-earthly-delights

Le monde juge bien des choses, car il est dans l’ignorance naturelle qui est le vrai siège de l’homme. Les sciences ont deux extrémités qui se touchent, la première est la pure ignorance naturelle où se trouvent tous les hommes en naissant, l’autre extrémité est celle où arrivent les grandes âmes qui ayant parcouru tout ce que les hommes peuvent savoir trouvent qu’ils ne savent rien et se rencontrent en cette même ignorance d’où ils étaient partis, mais c’est une ignorance savante qui se connaît. Ceux d’entre deux qui sont sortis de l’ignorance naturelle et n’ont pu arriver à l’autre, ont quelque teinture de cette science suffisante, et font les entendus. Ceux-là troublent le monde et jugent mal de tout.

The world judges things well, because it is in that state of natural ignorance which is the true place of the human. The sciences have two extremities, which converge: the first is that state of pure ignorance, in which we are left by nature; the other extremity is that at which great minds arrive, which, having traversed everything which man can know, discover that they know nothing, and recognize once more the point from which they set out. But this is a learned ignorance, which knows itself. Those who have set out from the stage of natural ignorance, and have not yet been able to arrive at the other, have but a hint of that real and adequate knowledge; and these are the assumers and pretenders to reason. These disquiet the world: and judge everything worse than the others.

Blaise Pascal, Pensées pt 1, art vi, sec 25, pensée No 327b [308] (Frag. Sel. No. 117)(ca. 1649) in the Œuvres complètes p. 1166 (J. Chevalier ed. 1954)(S.H. transl.)

That Pascal’s theory of convergence emerges from his examination of Descartes and a series of Cartesian mathematical principles is revealed by this manuscript page on which the original appears. It is scribbled, with emendations, in the midst of a discussion of Cartesian texts.

sel117

But the profundity of the thought is great and it demonstrates well the force of mathematical principle applied to philosophy and the study of humankind. Like only a handful of other figures of his age, Pascal struggled for a reconciliation of his deeply felt religious convictions with science and reason. He firmly embraced faith and science. He denied that a gap necessarily existed between them. Key to that is his brilliantly formulated circumscription of the limits of scientific understanding, and of human reason and perception altogether. The notion of convergence can be seen in images of antiquity, as, for instance in the hermetic serpent that coils to grab its own tail by its jaws. The extreme of human wisdom and the vacuous ignorance of nature meet in the same place, it suggests. But that is not to suggest their identity, because one is learned ignorance–and on this point it cannot be coincidental that Pascal takes the formulation of the great Nicholas Cardinal Cusanus (De docta ignorantia, 1440), who struggled two centuries earlier to force back the barriers religious doctrine would impose on science. The struggle to learn and understand is not a vain exercise, it counsels. Humankind’s earnest effort to try to understand is essential, both to its advancement in a scientific setting and its redemption in a spiritual one. But Pascal warns us about those humans who quickly form judgments of others and who claim more wisdom and knowledge than they can field. “These disquiet the world.” In the end, humans must be conscious of the limits of their perceptions and their reason, they must accept the natural role of doubt accounting for those limits. In this way, the mandates of faith could be reconciled with those of science, and the door could be opened for the great scientific advancement which would follow in the next centuries. Conversely, Pascal counsels the solace of religion as a necessity to the scientist. “The man without god,” he writes, will inevitably find himself “engulfed in the infinite immensity of spaces of which I am ignorant and which know me not…The eternal silence of these infinite spaces frightens me.”


Consider the exterior panels of Hieronymus Bosch’s The Garden of Earthly Delights, completed around 1504, and likely reflecting the influence of the thinking of Cusanus, with which Bosch was in any event well familiar. The original can be found in the Museo del Prado in Madrid. The earth is presented in grisaille with a moss-green tint as a fully encapsulated sphere intersected by a plane on which the new life takes shape. The earth is in the midst of the creative process described in Genesis, probably on the third day. It is vested with plant life, an atmosphere and clouds–but not yet with human beings (whose appearance is marked on the reverse side, in what may be Bosch’s most famous works). In the upper left corner, God the Father appears, supervising the process of creation, a Bible on his lap. An inscription across the top reads: “Ipse dixit, et facta sunt: ipse mandavit, et creata sunt“—”For he spake and it was done; he commanded, and it stood fast.” (Psalm 23) The earth in the course of creation is surrounded by a dark void reflecting the infinite, and unknowable, universe. Note that Pascal’s most important reflections start from his studies of the concept and proof for the existence of a void or vacuum, and its justification from both scientific and theological perspectives and that Pascal begins his study with geometry and built his early reputation with a study of the calculations necessary to measure the area of a sphere intersected by a plane. The rapport between geometry, with its mathematical attempt to describe relationships, philosophy, and the mysteries of life are carefully explored in Bosch’s work, just as they are unfolded by Pascal.


Listen to Johann Sebastian Bach’s Cantata BWV 132, “Bereitet die Wege, bereitet die Bahn!” (“Make Ready the Paths, Make Ready the Way!”), for the Fourth Sunday in Advent (premiered on Dec. 22, 1715), including the introductory aria and the aria which presents the philosopher’s challenge “Frage dein Gewissen: Wer bist Du?” (“Ask your conscience: Who are you?”) all taken from texts drawn from Salomon Franck’s Evangelisches Andachts-Opfer (1715); the performance is by Gustav Leonhardt and the Leonhardt Consort of Vienna with the Hannover Knabenchor.

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