As discussed in the last chapter, based on recent observations of the Kepler satellite, designed to search for “habitable” planets, we can estimate that the fraction of all material in the cosmos in living form is no larger than one-billionth of one-billionth. Life is indeed rare in space.

  The discovery of cosmic acceleration makes life rare also in time. That is, only for a brief phase in the long history of the universe can life exist. “Brief,” of course, is a relative term. Let me elaborate. Life and all complex structures require the larger atoms such as carbon and oxygen and nitrogen. (Even computers, which may someday be deemed alive, require heavy elements in the form of silicon.) The smallest atoms, hydrogen and helium, simply do not have enough structural components to build much of anything. We have a great deal of evidence that the larger atoms were made in the nuclear fusion reactions in stars. The first stars, in turn, could not form until the universe was about one billion years old, as they required a slow condensation and contraction of giant clouds of gas. So the beginning of the “era of life” was around one billion years after the Big Bang. At the other end, as previously discussed, life will probably not exist after the universe is about a thousand billion years old.

  How can we think of this range of the era of life, from one billion years to a thousand billion years? In dealing with such large numbers and their ranges, it is most useful to think in terms of powers of ten. So here we have three powers of ten, from one billion to one thousand billion. What should we compare this range to? We cannot compare it to infinity, the duration of an infinitely expanding universe. No number can be compared to infinity. Failing that, we can compare it to the longest period of time where we believe some final qualitative change occurs. That would be the time in the remote future, long after the era of life, when all matter in the cosmos disintegrates, in a process called “proton decay.” That era is estimated to be about a million billion billion billion (1033) years from now. Beyond that remote period, no further conceivable changes would occur as the universe spins away into nothingness.

  The earliest time when we have a fair understanding of the universe was about a millionth of a trillionth of a trillionth of a trillionth (10-42) of a second after the Big Bang, about ten times the Planck era, discussed in the chapter “Between Nothingness and Infinity.” From that earliest moment of understanding to the last moment of understanding, when all matter disintegrates, is a range of about 82 powers of ten. In sum, the evolving universe, as scientists believe they understand it, lasts for something like 82 powers of ten, while the era of life occupies only 3 powers of ten.

  Evidently, life in our universe is a flash in the pan, a few moments in the vast unfolding of time and space in the cosmos. What are we to make of such a fact? For this writer, a realization of the scarcity of life makes me feel some ineffable connection to other living things, in a manner I’ve not experienced before. Perhaps it is mostly an intellectual connection, but not all of it. There is a kinship in being among those few grains of sand in the desert, or present during the relatively brief era of life in the vast temporal sprawl of the universe. Even though I will never contact or know other life beyond planet Earth, I am part of something rare and unique, never to pass this way again. Almost certainly, there are other thinking beings out there in the infinity of space who have their own astronomers and physicists and biologists (and painters and writers), and who have reached the same conclusion. We will likely never exchange a single word, but we have all realized the rarity of our existence and connection to one another. As mentioned in the last chapter, we are connected in that we are “fellow” observers of the cosmos. But we are also connected simply by our rarity, in time and in space. It is a thought too grand to fathom. But then again the knowledge that the atoms in our bodies were made in stars—a concept unanimously endorsed by the scientific community—is also difficult to fathom.

  Early in the twentieth century, the Alsatian philosopher and polymath Albert Schweitzer introduced a concept he called Ehrfurcht vor dem Leben, which translates to “Reverence for Life.” According to Schweitzer’s autobiography, one day in 1915, while traveling on a river in Africa, the forty-year-old Schweitzer witnessed all at once the Sun shimmering on the water, the background of tropical forest, and a herd of hippopotamuses basking on the banks of the river. Suddenly he felt “the reverence for life.” Later, Schweitzer put it this way: “I am life that wills to live in the midst of other life that wills to live.”

  Schweitzer’s “Reverence for Life” became an underpinning of the more recent notion called “biocentrism”—a philosophical view that extends ethical value and connection to all living things. This view is explicitly nonanthropomorphic. Such an attitude is not new. It can be found in ancient religion and philosophy, including Buddhism. In modern times, the concept of biocentrism has been invoked by advocates of biodiversity, of protection of the environment, and of animal rights.

  With the discoveries of the Kepler satellite in the last five years, it is almost certain that life exists elsewhere in the universe. (Given the unimaginable number of habitable planets, the absence of life beyond Earth would be like the absence of fires in a million dry forests, year after year after year.) The Kepler discoveries, plus the rarity of life in time and in space discussed here, lead to a concept I will call “cosmic biocentrism.” By that, I mean that the rarity and preciousness of life provides a kinship to all living things in the universe. I cannot imagine what kinds of thoughts, what kinds of values and principles, other living beings might have. But we share something in the vast corridors of this cosmos we find ourselves in. What exactly is it we share? Certainly, the mundane attributes of “life”: the ability to separate ourselves from our surroundings, to utilize energy sources, to grow, to reproduce, to evolve. I would argue that we “conscious” beings share something more during our relatively brief moment in the “era of life”: the ability to witness and reflect on the spectacle of existence, a spectacle that is at once mysterious, joyous, tragic, trembling, majestic, confusing, comic, nurturing, unpredictable and predictable, ecstatic, beautiful, cruel, sacred, devastating, exhilarating. The cosmos will grind on for eternity long after we’re gone, cold and unobserved. But for these few powers of ten, we have been. We have seen, we have felt, we have lived.

  The Man Who Knows Infinity

  In Jorge Luis Borges’s story “The Book of Sand,” a mysterious stranger knocks on the door of the narrator and offers to sell him a Bible he came by in a small village in India. The book shows the wear of many hands. The stranger says that the illiterate peasant who gave him the book called it the Book of Sand, “because neither sand nor this book has a beginning or an end.” Opening the volume, the narrator finds that its pages are rumpled and badly set, with an unpredictable Arabic numeral in the upper corner of each page. The stranger suggests that the narrator try to find the first page. It is impossible. No matter how close to the beginning he explores, several pages always remain between the cover and his hand. “It was as though they grew from the very book.” The stranger then asks the narrator to find the end of the book. Again, he fails. “It can’t be,” says the narrator. “It can’t be, but it is,” says the Bible peddler. “The number of pages in this book is literally infinite. No page is the first page; no page is the last.” The stranger pauses and reflects. “If space is infinite, we are anywhere, at any point in space. If time is infinite, we are at any point in time.” (Note to the observant reader: We cannot be at any point in time. Life can exist only during a relatively short period of cosmic history, as discussed in the last chapter.)

  Thoughts of the infinite have mesmerized and confounded human beings through the millennia. For mathematicians, infinity is an intellectual playground, where an endless string of fractions can add up to 1. For astronomers, the question is whether outer space goes on and on and on and on ad infinitum. And if it does, as cosmologists now believe, unsettling consequences abound. For one, there should be an infinite number of copies of each of us somewhere out there in the cosmos. Because even a situation of minuscule probability—like the creation of a particular individual’s exact arrangement of atoms—when multiplied by an infinite number of trials, repeats itself an infinite number of times. Infinity multiplied by any number (except 0) equals infinity.

  Measurements of infinity are impossible, or at least impossible according to the usual notions of size. If you cut infinity in half, each half is still infinite. If a weary traveler arrives at a fully occupied hotel of infinite size, no problem. You simply move the guest in room 1 into room 2, the guest in room 2 into room 3, and so on ad infinitum. In the process, you’ve accommodated all of the previous guests and freed up room 1 for the new arrival. There’s always room at the infinity hotel.

  We can play games with infinity, but we cannot visualize infinity. By contrast, we can visualize flying horses. We’ve seen horses, and we’ve seen birds, so we can mentally implant wings on a horse and send it aloft. Not so with infinity. The unvisualizability of infinity is part of its mystique.

  The first recorded conception of infinity seems to have occurred around 600 BC and is attributed to the Greek philosopher Anaximander, who used the word apeiron, meaning “unbounded” or “limitless.” For Anaximander, the Earth and the heavens and all material things were caused by the infinite, although infinity itself was not a material substance. Other ancient Greek philosophers held that infinity was a negative, even an evil, because the inability to measure a thing was considered a shortcoming of the thing—with the exception of the infinite and immeasurable One. About the same time as Anaximander, the Chinese employed the word wuji, meaning “boundless,” and wuqiong, meaning “endless,” and believed that the infinite was very close to nothingness. (An interesting perspective on Pascal’s ideas, discussed in “Between Nothingness and Infinity.”) In Chinese thought, being and nonbeing, like yin and yang, are in harmony with each other—thus the kinship of infinity and nothingness. A few centuries later, Aristotle argued that infinity does not actually exist. He conceded something he called potential infinity, such as the whole numbers. For any number, you can always create a bigger number by adding one to it. This process can continue as long as your stamina holds out, but you can never get to infinity.

  Indeed, one of the many intriguing properties of infinity is that you can’t get there from here. Infinity is not simply more and more of the finite. It seems to be of a completely different nature, although pieces of it may appear finite, like large numbers, or like large volumes of space. Infinity is a thing unto itself. All we see and experience has limits, boundaries, tangibilities. Not so with infinity. For similar reasons, St. Augustine, Spinoza, and other theological thinkers have associated infinity with God: the unlimited power of God, the unlimited knowledge of God, the unboundedness of God. “God is everywhere, and in all things, inasmuch as He is boundless and infinite,” said St. Thomas Aquinas.

  Beyond the religious sphere of the immaterial world, physicists believe that there may be infinite things in the material world as well. But this belief can never be proven. You can’t get there from here.

  Most of us have our first glimmerings of infinity as children, when we look up at the night sky for the first time. Or when we go to sea, out of sight of land, and gaze upon the ocean extending on and on until it meets the horizon. But these are only glimmerings, like counting to a few thousand in Aristotle’s potential infinity. We’re overwhelmed. But we haven’t come close.

  The concept of infinity remains a controversial and paradoxical topic today, galvanizing international conferences and heated scholarly disputes. Can physical forces ever be infinite in strength? Can physical space extend beyond galaxy after galaxy without limit? Is there an infinity between the infinity of the whole numbers and the infinity of all numbers? In May 2013, a panel of scientists and mathematicians gathered in New York City to discuss the profound conundrums surrounding infinity. William Hugh Woodin, a mathematician at the University of California, Berkeley, put it this way: “It’s kind of like mathematics lives on a stable island—we’ve built a solid foundation. Then, there’s the wild land out there. That’s infinity.”

  * * *

  —

  The person on planet Earth who may have come up with the most expansive conception of spatial infinity is the theoretical physicist Andrei Linde, a professor at Stanford University. Professor Linde works only with pencil and paper. Now seventy-two years old, he was born and grew up in Moscow and received his PhD in physics there from the Lebedev Physical Institute. Both of his parents were physicists. He married a physicist, Renata Kallosh (also a professor at Stanford). In 1990, Linde and Kallosh moved to the United States, where he took up his current academic position.

  In the early 1980s, Linde proposed a radical theory of the origin of the universe. Linde’s theory, a revision of MIT physicist Alan Guth’s 1981 theory, itself a revision of the 1927 Big Bang model, is called “eternal chaotic inflation.” The theory posits that in its infancy, our universe went through a period of highly rapid expansion, much faster than in the standard Big Bang model. In a tiny fraction of a second, a region of space smaller than an atom “inflated” to a size large enough to encompass all of the matter and energy that we can see today. That much of the inflation theory was articulated in Guth’s paper. Linde’s theory goes further. It predicts that our universe is necessarily one of a vast number of universes, each of which is constantly and randomly spawning new universes in an unending chain of cosmic creation, extending into the future for eternity. Some of those universes, and perhaps our own, should be infinite in extent. In our particular universe, the period of highly rapid expansion would have been completed and done with when our universe was 0.00000­00000­00000­00000­00000­00000­01 seconds old.

  It would be easy to dismiss such speculations as science fiction. But the fantastic speculations of scientists have often found a grip on reality. Two hundred years ago, who would have thought we would be able to decipher the microscopic chemical code that creates living organisms and to alter that code as if rearranging a deck of cards? Or build tiny boxes that could communicate pictures and voices through space? Linde’s speculations are backed up by serious equations, and a number of important predictions of the Guth-Linde inflation theory (but not the existence of infinity) have been confirmed by experiment.

  In the scientific community, Linde is widely regarded as a physicist of the first rank. He has won most of the major prizes in physics except for the Nobel. To name a few: the Dirac medal of the International Center for Theoretical Physics in Trieste (shared with Guth and Paul Steinhardt); the Gruber Prize in cosmology (shared with Guth); the Humboldt Prize in Germany; the Kavli Prize of the Norwegian Academy of Sciences and the Kavli Foundation (shared with Guth and Alexei Starobinsky); the Medal of the Institute of Astrophysics in Paris; and, in 2012, the inaugural Fundamental Physics Prize (shared with Guth and others), which carries an award of $3 million per person, more than twice the prize money of the Nobel.

  Linde does not have a small opinion of himself. When I met him the first time, in 1987, a few years after his most important work on the inflation theory, he told me about his discovery with these words: “I easily understood what Guth was trying to do. But I did not understand how it [inflation] could be done, since we have seen that the inhomogeneities [in Guth’s original theory] were large [contradicting observations]. I just had the feeling that it was impossible for God not to use such a good possibility to simplify His work, the creation of the universe…I was simultaneously discussing similar matters with Rubakov [by telephone]…I was sitting in my bathroom, since all my children and my wife were already sleeping at the time…After the whole picture had crystallized, I was very excited. I came to my wife and I woke her up and I said: ‘It seems that I know how the universe originated.’ ”

  I visited Linde recently at his home in Stanford, California, to get an update on his theory and its place in our view of the world. Linde and his wife live in a lush neighborhood of winding streets, tropical gardens, and houses set up on hills. He was casually dressed in a black fleece sweater over a black T-shirt, black pants, and sandals with black socks—all in dramatic contrast with his snowy white hair. His English is good but retains a thick Russian accent. We sat at the kitchen table. On the wall, a clock, a map of Tuscany, painted ceramic jars on a shelf. His wife prepared a delicious lunch of tortellini and salad.

  First off, I asked Professor Linde if he believes that spatial infinity truly exists. “Do you think dinosaurs truly existed?” he replied and paused. “Everything works as if spatial infinity exists.” Linde is careful with language. He distinguishes between reality, which we can never know, and our models and inferences about reality. Linde has always had a strong interest in philosophy. He remembers having debates with high school classmates about science versus art. One of his teenaged philosophical ideas, and an idea that he has not completely abandoned, was that “feelings” are actual objects. Young Linde theorized that when two people are communicating, verbally or nonverbally, their feeling-objects are shared simultaneously. However, in his science classes he learned that Einstein’s theory of relativity forbids any communication faster than the speed of light. He decided that he had better study physics first, so as not to make such “mistakes.”

 

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