by Carl Sagan
* The crisis was resolved when Mr. Abdul-Rauf agreed to stand during the anthem, but pray instead of sing.
CHAPTER 4
THE GAZE OF GOD
AND THE
DRIPPING FAUCET
When you are risen on the eastern horizon
You have filled every land with your beauty …
Though you are far away, your rays are on Earth.
AKHNATON,
Hymn to the Sun (ca. 1370 B. C.)
In Pharaonic Egypt at the time of Akhnaton, in a now-extinct monotheistic religion that worshiped the Sun, light was thought to be the gaze of God. Back then, vision was imagined as a kind of emanation that proceeded from the eye. Sight was something like radar. It reached out and touched the object being seen. The Sun—without which little more than the stars are visible—was stroking, illuminating, and warming the valley of the Nile. Given the physics of the time, and a generation that worshiped the Sun, it made some sense to describe light as the gaze of God. Thirty-three hundred years later, a deeper, although much more prosaic metaphor provides a better understanding of light:
You’re sitting in the bathtub, and the faucet is dripping. Once every second, say, a drop falls into the tub. It generates a little wave that spreads out in a beautiful perfect circle. As it reaches the sides of the tub, it’s reflected back. The reflected wave is weaker, and after one or two more reflections, you can’t make it out anymore.
New waves are arriving at your end of the tub, each generated by another drip of the faucet. Your rubber duck bobs up and down as each new wave front arrives before it. Clearly, the water is a little higher at the crest of the moving wave, and lower in the little shallow between the waves, the trough.
The “frequency” of the waves is simply how often the crests pass your vantage point—in this case, one wave every second. Since every drip makes a wave, the frequency is the same as the drip rate. The “wavelength” of the waves is simply the distance between successive wave crests—in this case, maybe 10 centimeters (about four inches). But if a wave passes every second, and they’re ten centimeters apart, the speed of the waves is ten centimeters per second. The speed of a wave, you conclude after thinking about it a moment, is the frequency times the wavelength.
Bathtub waves and ocean waves are two-dimensional; they spread out from a point source as circles on the surface of the water. Sound waves, by contrast, are three-dimensional, spreading out in the air in all directions from the source of the sound. In the wave crest, the air is compressed a little; in the trough, the air is rarefied a little. Your ear detects these waves. The more often they come (the higher the frequency), the higher the pitch you hear.
Musical tones are only a matter of how often the sound waves strike your ears. Middle C is how we describe 263 sound waves reaching us every second; 263 hertz, it’s called.* What would be the wavelength of Middle C? If sound waves were directly visible, how far would it be from crest to crest? At sea level, sound travels at about 340 meters per second (about 700 miles per hour). Just as in the bathtub, the wavelength will be the speed of the wave divided by its frequency, or about 1.3 meters for Middle C—roughly, the height of a nine-year-old human.
There is a class of puzzle thought to confound science—which goes something like, “What is Middle C to a person deaf from birth?” Well, it’s the same as it is to the rest of us: 263 hertz, a precise, unique frequency of sound belonging to this note and no other. If you can’t hear it directly, you can detect it unambiguously with an audio amplifier and an oscilloscope. Now of course this isn’t the same as experiencing the usual human perception of air waves—it utilizes sight rather than sound—but so what? All the information is there. You can sense chords and staccato, pizzicato, and timbre. You can associate with other times you’ve “heard” Middle C. Maybe the electronic representation of Middle C isn’t emotively the same as what a hearing person experiences, but even that may be a matter of experience. Even putting geniuses like Beethoven aside, you can be stone-deaf and experience music.
This is also the solution to the old conundrum about whether, if a tree falls in the forest and there’s no one to hear, is a sound produced? Of course if we define a sound in terms of someone hearing it, by definition there was no sound. But this is an excessively anthropocentric definition. Clearly, if the tree falls, it makes sound waves, those sound waves can readily be detected by, say, a CD recorder, and when played back, the sound would be recognizably a tree falling in a forest. There is no mystery here.
But the human ear is not a perfect detector of sound waves. There are frequencies (fewer than 20 waves arriving per second) that are too low for us to hear, although whales communicate readily in such low tones. Likewise, there are frequencies (more than 20,000 waves arriving every second) too high-pitched for adult humans to detect, although dogs have no difficulty (and respond when called at such frequencies by a whistle). Realms of sound exist—a million waves per second, say—that are, and always will be, unknown to direct human perception. Our sense organs, as superbly adapted as they are, have fundamental physical limitations.
—
It’s natural that we should communicate by sound. Our primate relatives certainly do. We’re gregarious and mutually interdependent—there’s a real necessity behind our communication talents. So, as our brains grew at an unprecedented rate over the last few million years, and as specialized regions of the cerebral cortex in charge of language evolved, our vocabulary proliferated. There was more and more that we were able to put into sounds.
When we were hunter-gatherers, language became essential for planning the day’s activity, teaching the children, cementing friendships, alerting the others to danger, and sitting around the fire after dinner watching the stars come out and telling stories. Eventually, we invented phonetic writing so we could put our sounds down on paper and, by glancing at a page, hear someone speaking in our head—an invention that became so widespread in the last few thousand years that we hardly ever stop to consider how astonishing it is.
Speech is not really communicated instantaneously: When we make a sound, we are creating traveling waves in the air carried at the speed of sound. For practical purposes that’s nearly instantaneous. But the trouble is that your shout carries only so far. It’s a very rare person who can carry on a coherent conversation with someone even 100 meters away.
Until comparatively recently human population densities were very low. There was hardly any reason to communicate with someone more than 100 meters away. Almost no one—except members of our itinerant family group—ever came close enough to communicate with us. On the rare occasions that someone did, we were generally hostile. Ethnocentrism—the idea that our little group, no matter which one it is, is better than any other—and xenophobia—a “shoot first, ask questions later” fear of strangers—are deeply built into us. They are by no means peculiarly human; all our monkey and ape cousins behave similarly, as do many other mammals. These attitudes are at least aided and abetted by the short distances over which speech is possible.
If we’re isolated for long periods from those other guys, we and they slowly develop in different directions. Their warriors start wearing ocelot skins, for example, instead of eagle feather headdresses—which everybody around here knows are fashionable, proper, and sane. Their language eventually becomes different from ours, their gods have strange names and demand bizarre ceremonies and sacrifices. Isolation breeds diversity; and our small numbers and limited communications range guarantee isolation. The human family—originating in one small locale in East Africa a few million years ago—wandered, separated, diversified, and became strangers to one another.
The reversal of this trend—the movement toward the reacquaintance and reunification of the lost tribes of the human family, the binding up of the species—has occurred only fairly recently and only because of advances in technology. The domestication of the horse permitted us to send messages (and ourselves) over distances of hundreds of miles in a few d
ays. Advances in sailing ship technology allowed us to travel to the most distant reaches of the planet—but slowly: In the eighteenth century, it took about two years to sail from Europe to China. By this time, far-flung human communities could send ambassadors to each other’s courts, and exchange products of economic importance. However, for the great majority of eighteenth-century Chinese, Europeans could not have been more exotic had they lived on the Moon, and vice versa. The real binding up and deprovincialization of the planet requires a technology that communicates much faster than horse or sailing ship, that conveys information all over the world, and that is cheap enough to be available, at least occasionally, to the average person. Such a technology began with the invention of the telegraph and the laying of submarine cables; was greatly expanded by the invention of the telephone, using the same cables; and then enormously proliferated with the invention of radio, television, and satellite communications technology.
Today we communicate—routinely, casually, with hardly ever a second thought—at the speed of light. From the speed of horse or sailing ship to the speed of light is an improvement by a factor of almost a hundred million. For fundamental reasons at the heart of the way the world works, codified in Einstein’s special theory of relativity, we know that there is no way we can send information faster than light. In a century, we have reached the ultimate speed limit. The technology is so powerful, its implications so far-reaching, that of course our societies have not yet caught up.
We place an overseas call, and we can sense that brief interval between when we finish asking a question and when the person we’re talking to begins to answer. That delay is the time it takes for the sound our voice makes to get into the telephone, run electrically along the wires, reach a transmission station, be beamed up by microwaves to a communications satellite in geosynchronous orbit, be beamed down to a satellite receiving station, run through the wires some more, wiggle a diaphragm in a handset (halfway around the world, it may be), make sound waves in a very short length of air, enter someone’s ear, carry an electrochemical message from ear to brain, and be understood.
The round-trip light travel time from the Earth to geosynchronous altitude is a quarter of a second. The farther apart the transmitter and receiver are, the longer it takes. In conversations with the Apollo astronauts on the Moon, the time delay between question and answer was longer. That was because the round-trip light (or radio) travel time between the Earth and the Moon is 2.6 seconds. It takes 20 minutes to receive a message from a spacecraft favorably situated in Martian orbit. In August 1989, we received pictures, taken by the Voyager 2 spacecraft, of Neptune and its moons and ring arcs—data sent to us from the planetary frontiers of the Solar System, taking five hours to reach us at the speed of light. It was one of the longest long-distance calls ever placed by the human species.
—
In many contexts, light behaves as a wave. For example, imagine light passing through two parallel slits in a darkened room. What image does it cast on a screen behind the slits? Answer: an image of the slits—more exactly, a series of parallel bright and dark images of the slits—an “interference pattern.” Rather than traveling like a bullet in a straight line, the waves spread from the two slits at various angles. Where crest falls on crest, we have a bright image of the slit: “constructive” interference; and where crest falls on trough, we have darkness: “destructive” interference. This is the signature behavior of a wave. You’d see the same thing with water waves and two holes cut at surface level in the pilings of a pier on a waterfront.
And yet light also behaves as a stream of little bullets, called photons. This is how an ordinary photocell (in a camera, for instance, or a light-powered calculator) works. Each arriving photon ejects an electron from a sensitive surface; many photons generate many electrons, a flow of electric current. How can light simultaneously be a wave and a particle? It might be better to think of it as something else, neither a wave nor a particle, something with no ready counterpart in the everyday world of the palpable, that under some circumstances partakes of the properties of a wave, and, under others, of a particle. This wave-particle dualism is another reminder of a central humbling fact: Nature does not always conform to our predispositions and preferences, to what we deem comfortable and easy to understand.
And yet for most purposes, light is similar to sound. Light waves are three-dimensional, have a frequency, a wavelength, and a speed (the speed of light). But, astonishingly, they do not require a medium, like water or air, to propagate in. Light reaches us from the Sun and the distant stars, even though the intervening space is a nearly perfect vacuum. In space, astronauts without a radio link cannot hear each other, even if they are a few centimeters apart. There is no air to carry the sound. But they can see one another perfectly well. Have them lean forward so their helmets touch, and they can hear one another. Take away all the air in your room and you will be unable to hear an acquaintance complain about it, although you will for a moment have no difficulty seeing him flailing and gasping.
For ordinary visible light—the kind our eyes are sensitive to—the frequency is very high, about 600 trillion (6 × 1014) waves striking your eyeballs every second. Because the speed of light is 30 billion (3 × 1010) centimeters a second (186,000 miles per second), the wavelength of visible light is about 30 billion divided by 600 trillion, or 0.00005 (3 × 1010/6 × 1014 = 0.5 × 10-4) centimeters—much too small for us to see were it possible somehow for the waves themselves to be illuminated.
As different frequencies of sound are perceived by humans as different musical tones, so different frequencies of light are perceived as different colors. Red light has a frequency of about 460 trillion (4.6 × 1012) waves per second, violet light about 710 trillion (7.1 × 1012) waves per second. Between them are the familiar colors of the rainbow. Every color corresponds to a frequency.
As with the question of the meaning of a musical tone to a person deaf since birth, there’s the complementary question of the meaning of color to a person blind since birth. Again, the answer is uniquely and unambiguously a wave frequency—which can be measured optically and detected, if we so wish, as a musical tone. A blind person, properly trained and equipped in physics, can distinguish rose red from apple red from blood red. With the right kind of spectrometric library, she might be able to make much better compositional distinctions than the untrained human eye. Yes, there’s a feeling of redness that sighted people sense around 460 trillion hertz. But I don’t think that’s anything more than what it feels like to sense 460 trillion hertz. There’s no magic to it, as beautiful as it may be.
Just as there are sounds too high-pitched and too low-pitched for us to hear, so there are frequencies of light, or colors, outside our range of vision. They extend to much higher frequencies (around a billion billion* —1018—waves per second for gamma rays) and to much lower ones (less than one wave per second for long radio waves). Running through the spectrum of light from high frequency to low are broad swaths called gamma rays, X rays, ultraviolet light, visible light, infrared light, and radio waves. These are all waves that travel through a vacuum. Each is as legitimate a kind of light as ordinary visible light is.
There is an astronomy for each of these frequency ranges. The sky looks quite different in each regime of light. For example, bright stars are invisible in the light of gamma rays. But the enigmatic gamma ray bursters, detected by orbiting gamma ray observatories, are, so far, almost wholly indetectable in ordinary visible light. If we viewed the Universe in visible light only—as we did for most of our history—we would not know of the existence of gamma ray sources in the sky. The same is true of X-ray, ultraviolet, infrared, and radio sources (as well as the more exotic neutrino and cosmic ray sources, and—perhaps—gravity wave sources).
We’re prejudiced toward visible light. We’re visible light chauvinists. That’s the only kind of light to which our eyes are sensitive. But if our bodies could transmit and receive radio waves, early humans might hav
e been able to communicate with each other over great distances; if X rays, our ancestors might have peered usefully into the hidden interiors of plants, people, other animals, and minerals. So why didn’t we evolve eyes sensitive to these other frequencies of light?
Any material you choose likes to absorb light of certain frequencies, but not of others. A different substance has a different preference. There is a natural resonance between light and chemistry. Some frequencies, such as gamma rays, are indiscriminately gobbled up by virtually all materials. If you had a gamma ray flashlight, the light would be readily absorbed by the air along its path. Gamma rays from space, traversing a much longer path through the Earth’s atmosphere, would be entirely absorbed before they reached the ground. Down here on Earth, it’s very dark in gamma rays—except around such things as nuclear weapons. If you want to see gamma rays from the center of the Galaxy, you must move your instruments into space. Something similar is true for X rays, ultraviolet light, and most infrared frequencies.
On the other hand, most materials are poor absorbers of visible light. Air, for example, is generally transparent to visible light. So one reason we see at visible frequencies is that this is the kind of light that gets through our atmosphere down to where we are. Gamma ray eyes would be of limited use in an atmosphere which makes things pitch black in gamma rays. Natural selection knows better.
