Is the universe infinite?

Is this question useful in determining how well someone reasons? If that is the case, is it unfair to think that Nicholas of Cusa, while being a unique philosopher during the medieval period, might not be good enough to be a master of those seeking to know?

From the Closed World to the Infinite Universe, by Alexander Koyré, [1957], at sacred-texts.com,
(here):

Nicholas of Cusa denies the finitude of the world and its enclosure by the walls of the heavenly spheres. But he does not assert its positive infinity; as a matter of fact he avoids as carefully and as consistently as Descartes himself the attribution to the universe of the qualification "infinite," which he reserves for God, and for God alone. His universe is not infinite (infinitum) but "interminate" (interminatum), which means not only that it is boundless and is not terminated by an outside shell, but also that it is not "terminated" in its constituents, that is, that it utterly lacks precision and strict determination. It never reaches the "limit"; it is, in the full sense of the word, indetermined. It cannot, therefore, be the object of total and precise knowledge, but only that of a partial and conjectural one.9 It is the recognition of this necessarily partial—and relative—character of our knowledge, of the impossibility of building a univocal and objective representation of the universe, that constitutes—in one of its aspects—the docta ignorantia, the learned ignorance, advocated by Nicholas of Cusa as a means of transcending the limitations of our rational thought. (7-8)

Of course this judgment presumes that Aristotle and his followers are right in holding that the universe is finite.

And:

The universe of Nicholas of Cusa is an expression or a development (explicatio), though, of course, necessarily imperfect and inadequate, of God—imperfect and inadequate because it displays in the realm of multiplicity and

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separation what in God is present in an indissoluble and intimate unity (complicatio), a unity which embraces not only the different, but even the opposite, qualities or determinations of being. In its turn, every singular thing in the universe represents it—the universe—and thus also God, in its own particular manner; each in a manner different from that of all others, by "contracting" (contractio) the wealth of the universe in accordance with its own unique individuality.

The metaphysical and epistemological conceptions of Nicholas of Cuss, his idea of the coincidence of the opposites in the absolute which transcends them, as well as the correlative concept of learned ignorance as the intellectual act that grasps this relationship which transcends discursive, rational thought, follow and develop the pattern of the mathematical paradoxes involved in the infinitization of certain relations valid for finite objects. Thus, for instance, nothing is more opposed in geometry than "straightness" and "curvilinearity"; and yet in the infinitely great circle the circumference coincides with the tangent, and in the infinitely small one, with the diameter. In both cases, moreover, the center loses its unique, determinate position; it coincides with the circumference; it is nowhere, or everywhere. But "great" and "small" are themselves a pair of opposed concepts that are valid and meaningful only in the realm of finite quantity, the realm of relative being, where there are no "great" or "small" objects, but only "greater" and "smaller" ones, and where, therefore, there is no "greatest," as well as no "smallest." Compared with the infinite there is nothing that is greater or smaller than anything else. The absolute, infinite maximum does not, any more

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than the absolute, infinite minimum, belong to the series of the great and small. They are outside it, and therefore, as Nicholas of Cusa boldly concludes, they coincide.

Another example can be provided by kinematics. No two things, indeed, are more opposed than motion and rest. A body in motion is never in the same place; a body at rest is never outside it. And yet a body moving with infinite velocity along a circular path will always be in the place of its departure, and at the same time will always be elsewhere, a good proof that motion is a relative concept embracing the oppositions of "speedy" and "slow." Thus it follows that, just as in the sphere of purely geometrical quantity, there is no minimum and no maximum of motion, no slowest and no quickest, and that the absolute maximum of velocity (infinite speed) as well as its absolute minimum (infinite slowness or rest) are both outside it, and, as we have seen, coincide.

Nicholas of Cusa is well aware of the originality of his thought and even more so of the rather paradoxical and strange character of the conclusion to which he is led by learned ignorance.11

It is possible [he states] that those who will read things previously unheard of, and now established by Learned Ignorance, will be astonished.

Nicholas of Cusa cannot help it: it has, indeed, been established by learned ignorance12

. . . that the universe is triune; and that there is nothing that is not a unity of potentiality, actuality and connecting motion; that no one of these can subsist absolutely without the other; and that all these are in all [things] in different degrees, so different that in the universe no two [things]

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can be completely equal to each other in everything. Accordingly, if we consider the diverse motions of the [celestial] orbs, [we find that] it is impossible for the machine of the world to have any fixed and motionless center; be it this sensible earth, or the air, or fire or anything else. For there can be found no absolute minimum in motion, that is, no fixed center, because the minimum must necessarily coincide with the maximum]

[paragraph continues] Thus the centrum of the world coincides with the circumference and, as we shall see, it is not a physical, but a metaphysical "centrum," which does not belong to the world. This "centrum," which is the same as the "circumference," that is, beginning and end, foundation and limit, the "place" that "contains" it, is nothing other than the Absolute Being or God.