Er hat den archimedischen Punkt gefunden, hat ihn aber gegen sich ausgenutzt, offenbar hat er ihn nur unter dieser Bedingung finden dürfen. – Franz Kafka
(He found the Archimedean point, but he used it against himself; it seems that he was permitted to find it only under this condition.) >> archimedean point
~
ARENDT, Hannah, 1998. The human condition. wikipedia 
2nd ed. Chicago: University of Chicago Press. ISBN 978-0-226-02599-5, p. 248.
ARENDT, Hannah, 1972/2015. Vita activa oder Vom tätigen Leben. Ungekürzte Taschenbuchausgabe, 15. Auflage. München Berlin Zürich: Piper. Serie Piper, 3623. ISBN 978-3-492-23623-2, p. 318.
See also "Archimedean point" wikipedia
This difference in relevance between the Copernican system and Galileo's discoveries was quite clearly understood by the Catholic Church, which raised no objections to the pre-Galilean theory of an immobile sun and a moving earth as long as the astronomers used it as a convenient hypothesis for mathematical purposes; but, as Cardinal Bellarmine pointed out to Galileo, "to prove that the hypothesis … saves the appearances is not at all the same thing as to demonstrate the reality of the movement of the earth." […] (p. 260)
p. 267: Under this condition of remoteness, every assemblage of things is transformed into a mere multitude, and every multitude, no matter how disordered, incoherent, and confused, will fall into certain patterns and configurations possessing the same validity and no more significance than the mathematical curve, which, as Leibniz once remarked, can always be found between points thrown at random on a piece of paper. For if "it can be shown that a mathematical web of some kind can be woven about any universe containing several objects … then the fact that our universe lends itself to mathematical treatment is not a fact of any great philosophic significance." (Bertrand Russell, as quoted by J. W. N. Sullivan, op. cit., p. 144.) >> pattern mathematical curve
See also Whitehead's distinction between the traditional scientific method of classification and the modern approach of measurement: the former follows objective realities whose principle is found in the otherness of nature; the latter is entirely subjective, independent of qualities, and requires not more than that a multitude of objects be given. >> whitehead distinction classification measurement otherness nature
It certainly is neither a demonstration of an inherent and inherently beautiful order of nature nor does it offer a confirmation of the human mind, of its capacity to surpass the senses in perceptivity or of its adequateness as an organ for the reception of truth. >> beautiful order nature
p. 267–268: The modern reductio scientiae ad mathematicam has overruled the testimony of nature as witnessed at close range by human senses in the same way that Leibniz overruled the knowledge of the haphazard origin and the chaotic nature of the dot-covered piece of paper. And the feeling of suspicion, outrage, and despair, which was the first, and spiritually is still the most lasting consequence of the discovery that the Archimedean point was no vain dream of idle speculation, is not unlike the helpless outrage of a man who, having watched with his own eyes how these dots were thrown arbitrarily and without foresight onto the paper, is shown and forced to admit that all his senses and all his powers of judgment have betrayed him and that what he saw was the evolution of a "geometrical line whose direction is constantly and uniformly defined by one rule." >> leibniz geometric line
p. 268–269: It took many generations and quite a few centuries before the true meaning of the Copernican revolution and the discovery of the Archimedean point came to light. Only we, and we only for hardly more than a few decades, have come to live in a world thoroughly determined by a science and a technology whose objective truth and practical know-how are derived from cosmic and universal, as distinguished from terrestrial and "natural," laws, and in which a knowledge acquired by selecting a point of reference outside the earth is applied to earthly nature and the human artifice. There is a deep gulf between those before us who knew that the earth revolves around the sun, that neither the one nor the other is the center of the universe, and who concluded that man had lost his home as well as his privileged position in creation, and ourselves, who still and probably forever are earth-bound creatures, dependent upon metabolism with a terrestrial nature, and who have found the means to bring about processes of cosmic origin and possibly cosmic dimension. If one wishes to draw a distinctive line between the modern age and the world we have come to live in, he may well find it in the difference between a science which looks upon nature from a universal standpoint and thus acquires complete mastery over her, on one hand, and a truly "universal" science, on the other, which imports cosmic processes into nature even at the obvious risk of destroying her and, with her, man's mastership over her. Foremost in our minds at this moment is of course the enormously increased human power of destruction, that we are able to destroy all organic life on earth and shall probably be able one day to destroy even the earth itself. However, no less awesome and no less difficult to come to terms with is the corresponding new creative power, that we can produce new elements never found in nature, that we are able not only to speculate about the relationships between mass and energy and their innermost identity but actually to transform mass into energy or to transform radiation into matter. At the same time, we have begun to populate the space surrounding the earth with man-made stars, creating as it were, in the form of satellites, new heavenly bodies, and we hope that in a not very distant future we shall be able to perform what times before us regarded as the greatest, the deepest, and holiest secret of nature, to create or re-create the miracle of life. I use the word "create" deliberately, to indicate that we are actually doing what all ages before ours thought to be the exclusive prerogative of divine action.
p. 269–270: This thought strikes us as blasphemous, and though it is blasphemous in every traditional Western or Eastern philosophic or theological frame of reference, it is no more blasphemous than what we have been doing and what we are aspiring to do. The thought loses its blasphemous character, however, as soon as we understand what Archimedes understood so well, even though he did not know how to reach his point outside the earth, namely, that no matter how we explain the evolution of the earth and nature and man, they must have come into being by some transmundahe, "universal" force, whose work must be comprehensible to the point of imitation by somebody who is able to occupy the same location. It is ultimately nothing but this assumed location in the universe outside the earth that enables us to produce processes which do not occur on the earth and play no role in stable matter but are decisive for the coming into being of matter. It is indeed in the very nature of the thing that astrophysics and not geophysics, that "universal" science and not "natural" science, should have been able to penetrate the last secrets of the earth and of nature. From the viewpoint of the universe, the earth is but a special case and can be understood as such, just as in this view there cannot be a decisive distinction between matter and energy, both being "only different forms of the selfsame basic substance."
p. 270 (/344 de): With Galileo already, certainly since Newton, the word "universal" has begun to acquire a very specific meaning indeed; it means "valid beyond our solar system." And something quite similar has happened to another word of philosophic origin, the word "absolute," which is applied to "absolute time," "absolute space," "absolute motion," or "absolute speed," in each usage meaning a time, a space, a movement, a velocity which is present in the universe and compared to which earth-bound time or space or movement or speed are only "relative." Everything happening on earth has become relative since the earth's relatedness to the universe became the point of reference for all measurements.
Philosophically, it seems that man's ability to take this cosmic, universal standpoint without changing his location is the clearest possible indication of his universal origin, as it were. It is as though we no longer needed theology to tell us that man is not, cannot possibly be, of this world even though he spends his life here; and we may one day be able to look upon the age-old enthusiasm of philosophers for the universal as the first indication, as though they alone possessed a foreboding, that the time would come when men would have to live under the earth's conditions and at the same time be able to look upon and act on her from a point outside. (The trouble is only—or so it seems now—that while man can do things from a "universal," absolute standpoint, what the philosophers had never deemed possible, he has lost his capacity to think in universal, absolute terms, thus realizing and defeating at the same time the standards and ideals of traditional philosophy.
Instead of the old dichotomy between earth and sky we have a new one between man and the universe, or between the capacities of the human mind for understanding and the universal laws which man can discover and handle without true comprehension.) Whatever the rewards and the burdens of this yet uncertain future may turn out to be, one thing is sure: while it may affect greatly, perhaps even radically, the vocabulary and metaphoric content of existing religions, it neither abolishes nor removes nor even shifts the unknown that is the region of faith.
p. 271: While the new science, the science of the Archimedean point, needed centuries and generations to develop its full potentialities, taking roughly two hundred years before it even began to change the world and to establish new conditions for the life of man, it took no more than a few decades, hardly one generation, for the human mind to draw certain conclusions from Galileo's discoveries and the methods and assumption by which they had been accomplished. The human mind changed in a matter of years or decades as radically as the human world in a matter of centuries; and while this change naturally remained restricted to the few who belonged to that strangest of all modern societies, the society of scientists and the republic of letters (the only society which has survived all changes of conviction and conflict without a revolution and without ever forgetting to "honor the man whose beliefs it no longer shares"), this society anticipated in many respects, by sheer force of trained and controlled imagination, the radical change of mind of all modern men which became a politically demonstrable reality only in our own time. Descartes is no less the father of modern
p. 272: philosophy than Galileo is the ancestor of modern science, and while it is true that after the seventeenth century, and chiefly because of the development of modern philosophy, science and philosophy parted company more radically than ever before – Newton was almost the last to consider his own endeavors as "experimental philosophy" and to offer his discoveries to the reflection of "astronomers and philosophers," as Kant was the last philosopher who was also a kind of astronomer and natural scientist – modern philosophy owes its origin and its course more exclusively to specific scientific discoveries than any previous philosophy. That this philosophy, the exact counterpart of a scientific world view long since discarded, has not become obsolete today is not only due to the nature of philosophy, which, wherever it is authentic, possesses the same permanence and durability as art works, but is in this particular case closely related to the eventual evolution of a world where truths for many centuries accessible only to the few have become realities for everybody.
p. 275: […] As we said before, not ideas but events change the world—the heliocentric system as an idea is as old as Pythagorean speculation and as persistent in our history as Neo-Platonic traditions, without, for that matter, ever having changed the world or the human mind—and the author of the decisive event of the modern age is Galileo rather than Descartes. Descartes himself was quite aware of this, and when he heard of Galileo's trial and his recantation, he was tempted for a moment to burn all his papers, because "if the movement of the earth is false, all the foundations of my philosophy are also false." But Descartes and the philosophers, since they elevated what had happened to the level of uncompromising thought, registered with unequaled precision the enormous shock of the event; they anticipated, at least partially, the very perplexities inherent in the new standpoint of man with which the scientists were too busy to bother until, in our own time, they began to appear in their own work and to interfere with their own inquiries. Since then, the curious discrepancy between the mood of modern philosophy, which from the beginning had been predominantly pessimistic, and the mood of modern science, which until very recently had been so buoyantly optimistic, has been bridged. There seems to be little cheerfulness left in either of them.
~
⇒ God’s Eye View ⇒ Leverage Points (at least plural instead of singular)
DOT FROM two-level-diagram