'the richness of the world ... and, often, its inscrutability'

Whenever parts of a system interfere or cooperate with each other, there are nonlinear interactions taking place. Most of everyday life is spectacularly nonlinear; if you listen to your two favorite songs at the same time, you won’t get double the pleasure. The same goes for consuming alcohol and drugs, where the interaction effects can be deadly. By contrast, peanut butter and jelly are better together. They don’t just add up—they synergize. 

Nonlinearity is responsible for the richness of the world, for its beauty and complexity and, often, its inscrutability. For example, all of biology is nonlinear; so is sociology. That’s why the soft sciences are hard—and the last to be mathematized. Because of nonlinearity, there’s nothing soft about them. 

[…] 

Sofia Kovalevskaya helped us understand how different the world appears when we finally face up to nonlinearity. She realized that nonlinearity places limits on human hubris. When a system is nonlinear, its behavior can be impossible to forecast with formulas, even though that behavior is completely determined. In other words, determinism does not imply predictability. It took the motion of a top—a child’s plaything—to make us more humble about what we can ever hope to know.

—Steven Strogatz, Infinite Powers (2019)

'see the world in a pendulum's swing'

Galileo conceded that the study of pendulums “may appear to many exceedingly arid,” although it was anything but that, as later work showed. In mathematics, pendulums stimulated the development of calculus through the riddles they posed. In physics and engineering, pendulums became paradigms of oscillation. Like the line in William Blake’s poem about seeing the world in a grain of sand, physicists and engineers learned to see the world in a pendulum’s swing. The same mathematics applied wherever oscillations occurred. The worrisome movements of a footbridge, the bouncing of a car with mushy shock absorbers, the thumping of a washing machine with an unbalanced load, the fluttering of venetian blinds in a gentle breeze, the rumbling of the earth in the aftershock of an earthquake, the sixty-cycle hum of fluorescent lights—every field of science and technology today has its own version of to-and-fro motion, of rhythmic return. The pendulum is the granddaddy of them all. Its patterns are universal. Arid is not the right word for them.

—Steven Strogatz, Infinite Powers (2019)

Pursuing Sacred Magic

The practical aspect of the scientific ideal is revealed in the progress of modern science from the eighteenth century to the present day. Its essential stages are the discoveries and putting into man's service, successively, steam, electricity and atomic energy. But as different as these appear to be, these discoveries are based only on a single principle, namely the principle of the destruction of matter, by which energy is freed in order to be captured anew by man so as to be put at his service.... [T]he practical aspect of the scientific ideal is the domination of Nature by means of putting into play the principle of destruction or death.

Imagine, dear Unknown Friend, efforts and discoveries in the opposite direction, in the direction of construction or life. Imagine, not an explosion, but rather the blossoming out of a constructive “atomic bomb”. It is not too difficult to imagine, because each little acorn is such a “constructive bomb” and the oak is only the visible result of the slow “explosion”—or blossoming out—of this “bomb”. Imagine it, and you will have the ideal of the great work or the idea of the Tree of Life. The image itself of the tree comprises the negation of the technical and mechanical element. It is the living synthesis of heaven and earth, it constantly synthesis that which descends from above and that which ascends from below.

Now, the ideal of Hermeticism is contrary to that of science. Instead of aspiring to power over the forces of Nature by means of the destruction of matter, Hermeticism aspires to conscious participation with the constructive forces of the world on the basis of an alliance and a cordial communion with them. Science wants to compel Nature to obedience to the will of man such as it is; Hermeticism—or the philosophy of sacred magic—on the contrary wants to purify, illumine and change the will and nature of man in order to bring them into harmony with the creative principle of Nature (natura naturans) and to render them capable of receiving its willingly bestowed revelation. The “great work”, as an ideal, is therefore the state of the human being who is in peace, alliance, harmony and collaboration with life. This is the “fruit” of the Tree of Life.

—Anonomous (Valentin Tomberg), Meditations on the Tarot: A Journey into Christian Hermeticism (1980)

Is it not enough to believe?

It is often said: Why philosophize about the divine matters; is it not enough to believe in them and feel them? Certainly, it is enough ... in the absence of intellectual interest on the part of him who believes and feels. It is equivalent to saying: Is it not enough to believe that the sun exists, and to delight in its light and warmth? Why should we have any physical or astronomical theories about the sun or the solar system? They are not, of course, necessary for those who have no scientific interest. But on what grounds should the limitations of some people be made a law for all? If man has faith in the divine matters, and if at the same time he has the capacity as well as the need for thinking, then of necessity he must think about the objects of his faith ...

—Vladimir Soloviev, Lectures on Godmanhood (1878)

'something to reach for'

After that he had talked to Johnson every Saturday for the rest of the year. He talked at random, the kind of talk the boy would never have heard before. He talked a little above him to give him something to reach for. He roamed from simple psychology and the dodges of the human mind to astronomy and the space capsules that were whirling around the earth faster than the speed of sound and would soon encircle the stars. Instinctively he concentrated on the stars. He wanted to give the boy something to reach for besides his neighbor's goods. He wanted to stretch his horizons. He wanted him to see the universe, to see that the darkest parts of it could be penetrated. He would have given anything to be able to put a telescope in Johnson's hands.

—Flannery O'Connor, "The Lame Shall Enter First," Everything That Rises Must Converge (1965)

'Such omniscience ... would extinguish its soul'

In science greater knowledge is always and indisputably good; it is by no means so throughout all human existence. We know it from art proper, where achievement and great factual knowledge, or taste, or intelligence, are in no way essential companions; if they were, our best artists would also be our most learned academics. We can know it by reducing the matter to the absurd, and imagining that God, or some Protean visitor from outer space, were at one fell swoop to grant us all knowledge. Such omniscience would be worse than the worst natural catastrophe, for our species as a whole; would extinguish its soul, lose it all pleasure and reason for living.

—John Fowles, The Tree (1979)