Although often attributed to Nicholas of Cusa (1401-1464), in fact the claim derives from a pseudo-Hermetic text of the twelfth century, “The Book of the XXIV Philosophers.”43 This statement of early medieval origin was destined to become a mot celebre: not only Cusa but Giordano Bruno and Blaise Pascal (in the sixteenth and seventeenth centuries, respectively) cite it without attribution, each as if he had composed it himself.
Bruno’s version is unusually instructive: “Surely we can affirm that the universe is all center, or that the center of the universe is everywhere, and that the circumference is not in any part, although it is different from the center; or that the circumference is throughout all, but the center is not to be found inasmuch as it is different from that.”44 Considered as a challenge to Aristotle—to his closed and centered world—this complex proposition has two parts: (i) In saying that the center is everywhere, it proposes that there is no single privileged center such as the earth—or any other heavenly body, not even the sun (Copernicus’s efforts, known to Bruno, notwithstanding). The Arisotelian cosmographic model of a hierarchical universe with an immobile earth situated at the still center gives way to the idea that any part of the universe can be considered a fully valid center: the universe is “all center.” This in turn implies that every place is a center—a center of perspectival viewing from which all other places can (at least in principle) be seen. As Cusa was the first to insist, the perception of the universe is relative to the place of the observer.45 In other words, place is anywhere you choose to take up a point of view, and the universe yields an indefinite number of such places, (ii) In holding that the circumference is “throughout all”—that is, not in any single region, not even at the delimiting edge of the universe—Bruno maintains that it is in effect nowhere, “not in any [single] part.” The circumference is all over the place, which is tantamount to saying that it is located in pure space and not in a particular place or set of places. Nor is such space a mere composite of places that are parts of the whole. It is a radically open field that is coextensive with the universe in its totality. In terms of Archytas’s conundrum, we would have to say that no one could ever get to the edge of the world in the first place: nothing is at the edge since nothing can serve as the edge, as a simple circumference. There is no outer limit, no end to space. As Bruno himself comments, “Outside and beyond the infinite being, there exists nothing that is, because [such being] has no outside and no beyond.”46
What is remarkable, then, about the claim in question—whether in its initial or its Cusan version—is that it manages to combine recognition of the importance of place with an equal acknowledgment of the value of infinite space. In this respect, it reflects its historical origin at the beginning of the Middle Ages: at the very moment when Aristotle was being rediscovered, yet also when burgeoning interest in the possible infinity of space was colluding with theological speculation as to God’s uncontainable immensity. That the Renaissance took up the pseudo-Hermetic saying so enthusiastically indicates that the tension between place and space was still very much alive centuries after its first formulation in the twelfth century. Aristotle’s celebrated utterance retained its relevance: place still “has some power.” And it was just because it continued to have this power that the triumph of space was so slow in coming and so hard won during this same period. A considerable part of the struggle was due to the sheer fact that the looking-back was to place in its confinement (perspective is as confining as surface), just as the looking-forward was to a space unencumbered by such confinement. The situation was Januslike, exhibiting all the tension that looking in two opposed directions always brings with it. Instead of being surprised, we should ask instead: How could it be otherwise?
Nevertheless, the finally “triumphant beast” of Renaissance cosmology and theology is, indisputably, infinite space.47 This becomes evident in Cusa’s conception of space as modeled on the Absolute Maximum (absoluta maximitas), that is, the unqualifiedly great, that than which there can be no greater. Earlier medieval notions of absolute magnitude and of God’s perfection (especially as invoked in the ontological argument) are detectable in the Cusan idea of the absolutely maximal, but what is new in this idea is that it makes infinity and the finite radically incommensurate. For Cusa, whatever is finite is subject to degrees of greatness—thus to comparison—but what is infinite is incomparably great: “Where we find comparative degrees of greatness, we do not arrive at the unqualifiedly Maximum; for things which are comparatively greater and lesser are finite; but, necessarily, such a Maximum is infinite.”48 It follows that we can never get to the infinite from any addition or compilation of the finite, no matter how massive or prolonged our efforts may be.49 “The absolutely Maximum is all that which can be, it is altogether actual.”50 It also follows that the Absolute Maximum is equivalent to the Absolute Minimum—a palmary instance of Cusa’s celebrated principle of coincidentia oppositorum. (For example, neither extremity can tolerate anything greater or lesser, since each is complete in itself.)51 Further, the Absolute Maximum is incomprehensible and “beyond all affirmation and all negation.”52 Such a Maximum is numerically one (i.e., it is unique) and logically necessary (i.e., cannot not exist) as well as infinite.53 We are thus not surprised to be told that the Absolute Maximum is God—and vice versa. By a very different route, then, we attain the divinization of the infinite first encountered in Bradwardine and Crescas.
Yet the route and the result are very different. This becomes clear when we ask ourselves: Is the Cusan infinite divinity infinite space? With his usual subtlety, Cusa distinguishes between two kinds of infinite, one applicable strictly to God and the other to the universe. God—the absolutely Maximum—is “negatively infinite.” God is infinite in a negative mode insofar as He is not the sheer summation of finite things. The universe, in contrast, is “privately infinite,” by which Cusa means that it is unbounded yet not actually infinite.54 We can even say that the universe is “neither finite nor infinite,” but by this Cusa only means that “it cannot be greater than it is.”55 Not being able to be greater than it is—and not being as great as God—it is finite; but as it is, it is privately infinite, since it is as great as it can possibly be as something physical. As physical, the universe is the “contraction” (contractio) of divine infinity: it is this infinity in a compressed state. But precisely such a “finite infinity”56—another coincidence of opposites—characterizes infinite space.
When Cusa remarks that “the world, or universe, is a contracted maximum” and “is, contractedly, that which all things are,”57 he means that this world or universe (between which he does not distinguish) is a spatially maximal whole, even if it is not an absolutely maximal whole. As maximal, it is infinite; but as nonabsolute, it is finite: it is this world, a world that “sprang into existence by a simple emanation of the contracted maximum from the Absolute Maximum.”58 The finite infinity of the world, we might say, is the world put into its place: its “contracted infinity” is “infinitely lower than what is absolute, so that the infinite and eternal world [i.e., our world] falls dispro-portionally short of Absolute Infinity and Absolute Eternity.”59 But the distinctive privative infinity of this world remains unbounded, and in this format it contains, in contracted form, the very “Absolute Infinity” that it does not possess in itself without qualification.60 The same special infinity of the cosmos is contained contractedly in the particular things of the world, and in this latter capacity it is irrevocably spatial: What else other than space could be the medium of universal contraction, with the result that “all things are in all things” in “a most wonderful union”?61 If God is “in the one universe,” the universe itself is “contractedly in all things.”62 Double contractio ensures at once the spatial infinity of the world and its failure to be divinely infinite. The world is unbounded yet undivine. Spatial infinity is secured only by the loss of divinization—just the reverse of what Bradwardine and other fourteenth-century theologians had held. The infinitization of space requires its dedivinization.
To be unbounded is to be without circumference. Cusa does not assert the lack of circumference dogmatically, or just to repeat his pseudo-Hermetic source. He argues that insofar as the earth is not a “fixed and immovable center”—it cannot be such a center, since fixity and immobility are always relative to the movement of something else—it cannot have a set boundary: if the world