Probable Impossibilities: Musings on Beginnings and Endings

by Alan Lightman

Between these two endpoints of the imagination are we human beings, fragile and brief, clutching our thin slice of reality.

Nothing will tremble at the sight of these marvels…[Man] is equally incapable of seeing the Nothing from which he was made, and the Infinite in which he is swallowed up.

The universe could be infinite in extent, but we cannot see beyond a certain distance because there hasn’t been enough time since the Big Bang for light to have traveled from there to here. It is as if we found ourselves in a vast dark palace, with unlit chandeliers covering the ceiling, and suddenly the lights are turned on (the Big Bang). In the first few moments, we would see only the nearest chandeliers, because the light from the more distant ones has not yet reached our eyes. As time passed, we would see more and more distant parts of the palace. But at any given time, there would be an outer region beyond which we couldn’t yet see. Thus, in our search for Pascal’s infinity of the large, we reach a limit brought about by the finite age of our universe and the finite speed of light.

Quantum physics, also developed in the 1920s, shows that in the subatomic realm, particles take on a hazy, nondefinite character, behaving as if they existed in several places at once. Although we don’t yet have a theory of “quantum gravity,” we can still estimate the size of the region in which quantum physics and gravitational physics would merge. This ultra-tiny scale is called the “Planck length,” named after the physicist Max Planck, a pioneer in quantum physics. The Planck length is 10-33 centimeters, a hundred million billion times smaller than a quark. Another way to visualize the infinitesimal size we are talking about: the Planck length is smaller than the nucleus of an atom by about the same ratio as the nucleus is smaller than the state of Rhode Island. It staggers the mind that we have anything at all to say about such infinitesimal elements of reality.

The Planck world is a ghost world. It is a world without “time” and without “space.” Just as Pascal suggested, we find ourselves at the abyss between nothingness and infinity. And in doing so, we have found limits to the smallest and largest things observable, limits imposed by the science of two and a half centuries after Pascal.

Einstein once wrote, “The most beautiful experience we can have is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science.”

Now it is well known in the science of order and disorder that, other things being equal, larger spaces allow for more disorder, essentially because there are more places to scatter things. Equivalently, smaller spaces have more order.

Somewhat surprisingly, nature not only requires disorder but thrives on it. Planets, stars, life, even the direction of time all depend on disorder. And we human beings as well. Especially if, along with disorder, we group together such concepts as randomness, novelty, spontaneity, free will, and unpredictability.

Diffusion is a key mechanism for transporting vital substances throughout the body. Take oxygen, the essential gas for energy production. With each inhalation, we produce a high concentration of oxygen in our lungs. The tiny blood vessels embedded in the lungs have a relatively low amount of oxygen. That allows the vital gas to “diffuse” from the lungs to the blood, and then, for the same reason, from the blood to individual cells throughout the body. Such directed movement results from random collisions, tending to transport oxygen molecules from areas of high to low oxygen concentration. Without random bumps and knocks, oxygen in the lungs would remain trapped in the lungs, and the cells of the body would suffocate.

In scientific terms, such an event would require a sustained and highly directed column of wind blowing at hurricane force, a phenomenon that could be created only on a small scale in a human-made wind tunnel of the twentieth century. But the parting of the Red Sea occurred three thousand years ago. It was ordered up by Moses and delivered by God. It was a “miracle,” at odds with the behavior of nature, beyond nature, a “supernatural” event, inexplicable except by recourse to divine intervention.

would argue that we have been fooling ourselves. Nature, in fact, is mindless. Nature is neither friend nor foe, neither malevolent nor benevolent. Nature is purposeless. Nature simply is. We may find nature beautiful or terrible, but those feelings are human constructions. Such utter and complete mindlessness is hard for us to accept, as creatures with minds. We feel such a strong connection to nature. But the relationship between nature and us is one-sided. There is no reciprocity. There is no mind on the other side of the wall.

Paradoxically, if we can give up the belief that our bodies and brains contain some transcendent, nonmaterial essence, if we can embrace the idea that we are completely material, then we arrive at a new kind of specialness—an alternative to the specialness of vitalism. We are special material. Not special because our atoms are different from atoms in rocks and water, and not special because we have a nonmaterial essence inside us, but special because our atoms are arranged in a special way as to create life, and consciousness. We humans living on our one planet wring our hands about the brevity of our lives and our mortal restraints, but we do not often think about how improbable it is to be alive at all. Of all the zillions of atoms and molecules in the universe, we have the privilege of being composed of those very, very few atoms that have joined together in the special arrangement to make living matter. We exist in that one-billionth of one-billionth. We are that one grain of sand in the desert.

A universe with no living matter at all could function without any trouble—mindlessly following the conservation of energy and the principle of cause and effect and the other laws of physics and biology. A universe does not need minds, or any living matter at all. (Indeed, in the recent “multiverse” hypothesis endorsed by many physicists, the vast majority of universes are totally lifeless.) But in this writer’s opinion, a universe without comment is a universe without meaning. What does it mean to say that a waterfall, or a mountain, is beautiful? The concept of beauty, and indeed all concepts of value and meaning, require observers. Without a mind to observe it, a waterfall is only a waterfall, a mountain is only a mountain. It is we conscious matter, the rarest of all forms of matter, that can take stock and record and announce this cosmic panorama of existence before us.

if you traveled to the Sun on a high-speed train, say at two hundred miles per hour, it would take about fifty years. She nodded. To get to the nearest star beyond the Sun on the same train would take about fifteen million years.

Human beings have done better at contemplating very long periods of time. In ancient Hinduism, the life span of a deva (minor god) was thought to be about 10,000 deva years, each deva year about 100 Earthly years, for a total of a million years. One day in the life of Brahma, the Creator God, was 1,000 deva lifetimes, estimated at about 4 billion years. That long time unit was called a kalpa. Evidently, these successively longer time scales were arrived at simply by multiplying the previous time scale by a few factors of ten, without any knowledge of the physical world. The Hindus believed in a cyclic universe. The life cycle of the entire universe was thought to be a hundred years in the life of Brahma, working out to be about three hundred thousand billion years. By accident, this time period is about the time required for all stars to burn out.

One of the first people to propose the existence of life beyond planet Earth was the early Roman poet Lucretius (ca. 50 BC).

“I am life that wills to live in the midst of other life that wills to live.”