German Cardinal of the Catholic Church, Philosopher, Theologian, Jurist, Mathematician and Astronomer
Nicholas of Cusa, also Nicholas of Kues and Nicolaus Cusanus
German Cardinal of the Catholic Church, Philosopher, Theologian, Jurist, Mathematician and Astronomer
All those who make an investigation judge the uncertain proportionally, by means of a comparison with what is taken to be certain. Therefore, every inquiry is comparative and uses the means of comparative relation. ... Hence, the infinite, qua infinite, is unknown; for it escapes all comparative relation.
Nor is the darkness of colour a proof of the earth?s baseness; for the brightness of the sun, which is visible to us, would not be perceived by anyone who might be in the sun.
Thus wise men have been right in taking examples of things which can be investigated with the mind from the field of mathematics, and not one of the Ancients who is considered of real importance approached a difficult problem except by way of the mathematical analogy. That is why Boethius, the greatest scholar among the Romans, said that for a man entirely unversed in mathematics, knowledge of the Divine was unattainable. ?
All visible things would not claim as their king some color of their region, which is actually among the visible things of this region, but rather would say, he is the highest possible beauty of the most lucid and perfect color.
Number, in consequence, includes all things that are capable of comparison. It is not then in quantity only that number produces proportion; it produces it in all things that are capable of agreement and differences in any way at all, whether substantially or accidentally.
Wonder is the reason we seek to know any reality whatsoever.
Consequently, if you want to have a better understanding of the motion of the universe, you must put together the center and the poles, with the aid of your imagination as far as you can; for if somebody were on the earth, under the arctic pole, and somebody else on the arctic pole, then just as to the man on the earth the pole will appear to be in the zenith, to the man on the pole it is the center that would appear to be in the zenith. And as the antipodes have, like ourselves, the sky above them, so to those who are in the poles (in both), the earth will appear to be in the zenith, and wherever the observer be he will believe himself to be in the center. Combine thus these diverse imaginations, making the center into the zenith and vice versa, and then, with the intellect, which alone can practise learned ignorance, you will see that the world and its motion cannot be represented by a figure, because it will appear almost as a wheel within a wheel, and a sphere within a sphere, having nowhere, as we have seen, either a center or a circumference.
Oftentimes our appetite is satisfied quite pleasantly by dishes that are less varied but savory. Accordingly, although you, Nicholas, have already generously served up teachings that show the way to undepletable nourishment of the soul, do not for that reason be annoyed, I ask, if I importunately request nourishment that is even more delicious.
You are therefore able to run on this path, on which God is found above all vision, hearing, taste, touch, smell, speech, sense, rationality, and intellect. It is found as none of these, but rather above everything as God of gods and King of all kings. Indeed, the King of the world of the intellect is the King of kings and Lord of lords in the universe.
Even if it might seem otherwise to us, neither the sun nor the earth nor any sphere can describe a perfect circle by its motion...nor is a sphere?s or a star?s motion at one moment ever precisely equal to their motion at another.
Otherness cannot be a form. For to alter is to deform rather than to form. Therefore, that which is seen in different things can also be seen in and of itself without otherness, since otherness did not give being to it.
You have now to consider attentively what follows: just as the stars move around the conjectural poles of the eighth sphere, so also do the earth, the moon and the planets move in various ways and at [different] distances around a pole, which pole we have to conjecture as being [in the place] where you are accustomed to put the center. It follows therefrom that though the earth is, so to speak, the star which is nearer the central pole [than the others] it still moves, and yet does not describe in [its] motion the minimum circle, as has been shown supra. Moreover, neither the sun, nor the moon, nor any sphere?though to us it seems otherwise?can in [its] motion describe a true circle, because they do not move around a fixed base. Nowhere is there a true circle such that a truer one would not be possible, nor is [anything] ever at one time [exactly] as at another, neither does it move in a precisely equal [manner], nor does it describe an equally perfect circle, though we are not aware of it.
For all the [body?s] members seek nothing except inseparable union with the intellect, as with their beginning, ultimate good, and everlasting life.
Paul indeed wanted to reveal the unknown God to the philosophers and then affirms of Him, that no human intellect can conceive Him. Therefore, God is revealed therein, that one knows that every intellect is too small to make itself a figuration or concept of Him. However, he names him God, or in Greek, theos.
For when we say that what is different is different, we affirm that what is different is the same as itself. For what is different can be different only through the Absolute Same, through which all that is is both the same as itself and other than another.
Since beings desire to exist, because to exist is a good thing: they desire the One without which they cannot exist.
Furthermore the very center of the world is no more inside the earth than outside it; for neither this earth, nor any other sphere, has a center; indeed, the center is a point equidistant from the circumference; but it is not possible that there be a true sphere or circumference such that a truer, and more precise one, could not be possible; a precise equidistance of divers [objects] cannot be found outside of God, for He alone is the infinite equality. Thus it is the blessed God who is the center of the world; He is the center of the earth and of all the spheres, and of all [the things] that are in the world, as He is at the same time the infinite circumference of all. Furthermore, there are in the sky no immovable, fixed poles, though the sky of the fixed stars appears by its motion to describe circles graduated in magnitude, lesser than the colures or than the equinoctials and also circles of an intermediate [magnitude]; yet, as a matter of fact, all the parts of the sky must move, though unequally in comparison with the circles described by the motion of the fixed stars. Thus, as certain stars appear to describe the maximal circle, so certain [others], the minimal, but there is no star that does not describe any. Therefore, as there is no fixed pole in the sphere, it is obvious that neither can there be found an exact mean, that is, a point equidistant from the poles. There is therefore no star in the eighth sphere which by [its] revolution would describe a maximal circle, because it would have to be equidistant from the poles which do not exist, and accordingly [the star] that would describe the minimal circle does not exist either. Thus the poles of the spheres coincide with the center and there is no other center than the pole, that is, the blessed God Himself.
Since it always appears to every observer, whether on the earth, the sun, or another star, that one is, as if, at an immovable center of things and that all else is being moved, one will always select different poles in relation to oneself, whether one is on the sun, the earth, the moon, Mars, and so forth. Therefore, the world machine will have, one might say, its center everywhere and its circumference nowhere, for its circumference and center is God, who is everywhere and nowhere.
God is not something... God is beyond nothing and beyond something... God cannot be called this rather than that.
The ancients did not arrive at the things that we have brought forth, because they were deficient in learned ignorance. But for us it is clear that this earth really moves, though it does not appear to us to do so, because we do not apprehend motion except by a certain comparison with something fixed. Thus if a man in a boat, in the middle of a stream, did not know that the water was flowing and did not see the bank, how would he apprehend that the boat was moving?18 Accordingly, as it will always seem to the observer, whether he be on the earth, or on the sun or on another star, that he is in the quasi-motionless center and that all the other [things] are in motion, he will certainly determine the poles [of this motion] in relation to himself; and these poles will be different for the observer on the sun and for the one on the earth, and still different for those on the moon and Mars, and so on for the rest. Thus, the fabric of the world (machina mundi) will quasi have its center everywhere and its circumference nowhere, because the circumference and the center are God; Who is everywhere and nowhere.
If full knowledge about the very base of our existence could be described as a circle, the best we can do is to arrive at a polygon.
The earth, which cannot be the center, cannot lack all motion. In fact, it is even necessary that it be moved in such a way that it could be moved infinitely less.
In God we must not conceive of distinction and indistinction, for example, as two contradictories, but we must conceive of them as antecedently existing in their own most simple beginning, where distinction is not other than indistinction.
The fact is that man has no longing for any other nature but desires only to be perfect in his own.
It has been asserted that there is a separate species on the earth to correspond with each one of the stars. Now if the earth provides in each species a focus for the action of each star, why may not a similar provision be made among other heavenly bodies that are subject to the action of their fellows?