Coming of Age in the Milky Way - Timothy Ferris (2003)

Part III. CREATION

Chapter 20. THE PERSISTENCE OF MYSTERY

Drawn by my eager wish, desirous of seeing the great confusion of the various strange forms created by ingenious nature, I wandered for some time among the shadowed cliffs, and came to the entrance of a great cavern. I remained before it for a while, stupefied, and ignorant of the existence of such a thing, with my back bent and my left hand resting on my knee, and shading my eyes with my right, with lids lowered and closed, and often bending this way and that to see whether I could discern anything within; but this was denied me by the great darkness inside. And after I stayed a while, suddenly there arose in me two things, fear and desire—fear because of the menacing dark cave, and desire to see whether there were any miraculous thing within.

—Leonardo da Vinci

A great truth is a truth whose opposite is also a great truth.

—Niels Bohr

           In this book I have discussed how we inhabitants of this one world pieced together a credible picture of the (much) larger universe. I have described this process as a “coming of age,” by which I mean that we have, through centuries of fitful effort, finally begun to comprehend a few of the fundamental facts about the universe an acquaintanceship with which presumably is prerequisite to the most modest claim of cosmological maturity. We now know, for example, where we are—that we live on a planet orbiting a star located out toward one edge of a spiral galaxy, which in turn lies near the outskirts of a supercluster of galaxies, whose position has been determined relative to several neighboring superclusters that altogether harbor some forty thousand galaxies arrayed across a million billion cubic light-years of space. We also know, more or less, when we have come upon the scene—at about five billion years since the sun and its planets formed, in an expanding universe that is probably between twice and four times that old. We have discerned the basic mechanisms responsible for the evolution of life on Earth, found evidence of chemical evolution on the cosmic scale as well, and learned enough physics to investigate nature on a wide range of scales, from the jitterbugging of the quarks to the waltz of the galaxies.

These are accomplishments in which humanity can with justice take pride. Since the ancient Greeks first set the Western world on the path of science, our mensuration of the past has deepened from a few thousand years to over ten billion years, while that of space has expanded from a low-roof sky not much higher than the real distance of the moon to the more than ten-billion-light-year radius of the observable universe. We have reason to hope that our age will be remembered (if there is anyone around to remember it) for its contributions to the supreme intellectual treasure of any society, its concept of the universe at large.

And yet the more we know about the universe, the more we come to see how little we know. When the cosmos was thought to be but a tidy garden, with the sky its ceiling and the earth its floor and its history coextensive with that of the human family tree, it was still possible to imagine that we might one day comprehend it in both plan and detail. That illusion can no longer be sustained. We might eventually obtain some sort of bedrock understanding of cosmic structure, but we will never understand the universe in detail; it is just too big and varied for that. If we possessed an atlas of our galaxy that devoted but a single page to each star system in the Milky Way (so that the sun and all its planets were crammed on one page), that atlas would run to more than ten million volumes of ten thousand pages each. It would take a library the size of Harvard’s to house the atlas, and merely to flip through it, at the rate of a page per second, would require over ten thousand years. Add the details of planetary cartography, potential extraterrestrial biology, the subtleties of the scientific principles involved, and the historical dimensions of change, and it becomes clear that we are never going to learn more than a tiny fraction of the story of our galaxy alone—and there are a hundred billion more galaxies. As the physician Lewis Thomas writes, “The greatest of all the accomplishments of twentieth-century science has been the discovery of human ignorance.”1

Our ignorance, of course, has always been with us, and always will be. What is new is our awareness of it, our awakening to its fathomless dimensions, and it is this, more than anything else, that marks the coming of age of our species. Space may have a horizon and time a stop, but the adventure of learning is endless. As the philosopher of science Karl Popper writes:

The more we learn about the world, and the deeper our learning, the more conscious, specific, and articulate will be our knowledge of what we do not know, our knowledge of our ignorance. For this, indeed, is the main source of our ignorance—the fact that our knowledge can be only finite, while our ignorance must necessarily be infinite.2

It is widely though erroneously supposed that science has to do with explaining everything, and that unexplained phenomena therefore upset scientists by threatening the hegemony of their world view. The technician in the white lab coat in the low-budget movie slaps palm to forehead when confronted with something novel, gasping, “But … there’s no explanation for this!” Actually, of course, any worthy scientist will rush to embrace the unexplained, for without it science would get nowhere. It is the grand, mystical systems of thought, couched in terminologies too vague to be wrong, that explain everything and seldom err and do not grow.

Science is inherently open-ended and exploratory, and makes mistakes every day. Indeed that will always be its fate, according to the bare-bones logic of Kurt Gödel’s second incompleteness theorem. Gödel’s theorem establishes that the full validity of any system, including a scientific one, cannot be demonstrated within that system itself. In other words, the comprehensibility of a theory cannot be established unless there is something outside the frame against which to test it—something beyond the boundary defined by a thermodynamics equation, or by the collapse of the quantum wave function, or by any other theory or law. And if there is such a wider reference frame, then the theory by definition does not explain everything. In short, there is not and never will be a complete and comprehensive scientific account of the universe that can be proved valid. The Creator must have been fond of uncertainty, for He (or She) has given it to us for keeps.

Which is, I would argue, a salutary finding and cause for good cheer. Hell would be a small universe that we could explore thoroughly and fully comprehend. Alexander the Great may have wept upon being told that there were infinite worlds (“And we have not conquered even one,” he sobbed) but the situation looks more sanguine to those inclined to untie rather than to cut nature’s gordian knot. No thinking man or woman ought really to want to know everything, for when knowledge and its analysis is complete, thinking stops.

René Magritte in 1926 painted a picture of a pipe and wrote beneath it on the canvas, in a careful schoolboy script, the words “Ceci n’est pas une pipe”—“This is not a pipe.”3 His painting might suitably be made the emblem of scientific cosmology. The word “universe” is not the universe; neither are the equations of supersymmetry theory or the Hubble law or the Friedmann-Walker-Robinson metric* Nor, more generally, is science very good at explaining what anything, much less the entire universe, actually “is.” Science describes and predicts events, but it pays for this power in the coin of the ding an sich—the thing in itself.

Why, then, does science work? The answer is that nobody knows. It is a complete mystery—perhaps the complete mystery—why the human mind should be able to understand anything at all about the wider universe. As Einstein used to say, “The most incomprehensible thing about the universe is that it is comprehensible.”4 Perhaps it is because our brains evolved through the workings of natural law that they somehow resonate with natural law. Nature exhibits a number of self-similarities—patterns of behavior that recur on different scales, making it possible to identify principles, such as the conservation laws, that apply universally—and these may provide the link between what goes on inside and outside the human skull. But the mystery, really, is not that we are at one with the universe, but that we are to some degree at odds with it, different from it, and yet can understand something about it. Why is this so?

In search of an answer, let us pause to slake our thirst one last time at symmetry’s bubbling spring. Symmetry, we recall, implies not only the existence of an invariance under a transformation, the basis of all natural law, but also a “due proportion” between the invariance at hand and some larger, more comprehensive frame of reference. In this relationship may be found parallels with the process of scientific thought. The mind with its inherent limitations makes a frame within which our ideas can cavort; even the most expansive theory is “framed” in a specific mathematical or verbal or visual vocabulary. We then test our ideas against a piece of the outer world, which, however, itself has a frame around it. This process will work so long as we never reach an unframed, limitless arena. Gödel’s theorem suggests that we never will—that a theory by its very nature requires for its verification the existence or contemplation of a larger reference frame. It is the boundary condition, then, that provides the essential distinction between mind and the universe: Thoughts and events are bounded, even if the totality is not.*

And where did the boundaries come from? Quite possibly from the breaking of cosmic symmetries at the moment of genesis. We look out across a cosmic landscape riven by the fractal lines of broken symmetries, and draw from their patterns metaphors that aspire to be as creative, if not always quite as flawed, as the universe they purport to describe. (All metaphors are imperfect, said the poet Robert Frost, that is the beauty of them.)

It may be, then, that the universe is comprehensible because it is defective—that because it forsook the perfection of nonbeing for the welter of being, it is possible for us to exist, and to perceive the jumbled, blemished reality, and to test it against the ghostly specter of the primordial symmetry thought to have preceded it. We are, therefore we think. (Or, as the fabulist Jorge Luis Borges put it, “In spite of oneself, one thinks.”)6

Science is a process, not an edifice, and sheds old concepts as it grows. “Theories,” said Ernst Mach, “are like withered leaves, which drop off after having enabled the organism of science to breathe for a time.”7 The process depends upon error—as Popper notes, a theory is valuable only if it is capable of being disproved —as if to testify to the ubiquity and efficacy of cosmic imperfection. “Error can often be fertile,” remarked the historian A.J.P. Taylor, “but perfection is always sterile.”8 Taken as a whole, the scientific endeavor is as open-ended as the expansion of the universe—which, I think, is what Bohr had in mind when on his deathbed he complained of the philosophers that they too often “have not that instinct that it is important to learn something, and that we must be prepared to learn.”9 Every answer opens up new questions: Like Atalanta stooping to gather up the golden apples, we pause to marvel at each new discovery, only to realize that we have fallen behind in the race and must hurry on to the next turn in the path, where another golden apple awaits us.

Our explications of nature will always be inadequate, if only because it is the difference between the idea and the reality that makes the idea possible. Nature may be counted upon forever to retain the mysterious, magical quality that arises from the contrast between her innumerable splendors and the limitations of our metaphors. As Wheeler put it:

    There is nothing deader than an equation. Imagine that we take the carpet up in this room, and lay down on the floor a big sheet of paper and rule it off in one-foot squares. Then I get down and write in one square my best set of equations for the universe, and you get down and write yours, and we get the people we respect the most to write down their equations, till we have all the squares filled. We’ve worked our way to the door of the room.

We wave our magic wand and give the command to those equations to put on wings and fly. Not one of them will fly. Yet there is some magic in this universe of ours, so that with the birds and the flowers and the trees and the sky it flies! What compelling feature about the equations that are behind the universe is there that makes them put on wings and fly?

… If I had to produce a slogan for the search I see ahead of us, it would read like this: That we shall first understand how simple the universe is when we realize how strange it is.10

Science is young. Whether it will survive long enough to become old depends upon our sanity and courage and vigor, and, as one always must add in this nuclear age, upon whether we blow ourselves up first. “Nothing that is vast enters into the life of mortals without a curse,” as Sophocles said, and the knowledge of how the stars shine is very great, and its dark side is very dark indeed. Needless to say, science in itself will not deliver us from the dangers to which its knowledge has exposed us. “Scientific statements of facts and relations, indeed, cannot produce ethical directives,” wrote Einstein, though he allowed that “ethical directives can be made rational and coherent by logical thinking and empirical knowledge.”11

Viewed from so cold a perspective, we may esteem ourselves less but will know ourselves better, as creatures of darkness and light, in love with death as well as with life, as eager to destroy as to create. Our lives are suspended like our planet in a gimbals of duality, half sunlight and half shadow. If we plead with nature, it is in vain; she is wonderfully indifferent to our fate, and it is her custom to try everything and to be ruthless with incompetence. Ninety-nine percent of all the species that have lived on Earth have died away, and no stars will wink out in tribute if we in our folly soon join them.

Epictetus the former slave remarked that

every matter has two handles, one of which will bear taking hold of, the other not. If thy brother sin against thee, lay not hold of the matter by this, that he sins against thee; for by this handle the matter will not bear taking hold of. But rather lay hold of it by this, that he is thy brother, thy born mate; and thou wilt take hold of it by what will bear handling.12

Therefore, we say—speaking as living and (we think) thinking beings, as carriers of the fire—therefore, choose life.

* Numbers get closer to the rationally intelligible reality than do words—as Bohr said, “When it comes to atoms, language can be used only as in poetry”—but this is true only because mathematics is less ambiguous and more logical in structure than is ordinary language. The efficacy of mathematics in scientific research does not in itself establish that God is a geometer (if such a statement can have any meaning) or that the universe is a mathematical puzzle.

* Similar ideas appeared quite early in Greek thought, as when Philolaus of Tarentum wrote, in about 460 B.C., “Nature in the cosmos was fitted together of Unlimit and Limit, the order of the all as well as all things in it.”5