Authors: Carl Sagan
In such interdimensional contemplations, we need not be restricted to two dimensions. We can, following Abbott, imagine a world of one dimension, where everyone is a line segment, or even the magical world of zero-dimensional beasts, the points. But perhaps more interesting is the question of higher dimensions. Could there be a fourth physical dimension?
*
We can imagine generating a cube in the following way: Take a line segment of a certain length and move it an equal length at right angles to itself. That makes a square. Move the square an equal length at right angles to itself, and we have a cube. We understand this cube to cast a shadow, which we usually draw as two squares with their vertices connected. If we examine the shadow of a cube in two dimensions, we notice that not all the lines appear equal, and not all the angles are right angles. The three-dimensional object has not been perfectly represented in its transfiguration into two dimensions. This is the cost of losing a dimension in the geometrical projection. Now let us take our three-dimensional cube and carry it, at right angles to itself, through a fourth physical dimension: not left-right, not forward-back, not up-down, but simultaneously at right angles to all those directions. I cannot show you what direction that is, but I can imagine it to exist. In such a case, we would have generated a four-dimensional hypercube, also called a tesseract. I cannot show you a tesseract, because we are trapped in three dimensions. But what I can show you is the shadow in three dimensions of a tesseract. It resembles two nested cubes, all the vertices connected by lines. But for a real tesseract, in four dimensions, all the lines would be of equal length and all the angles would be right angles.
Imagine a universe just like Flatland, except that unbeknownst to the inhabitants, their two-dimensional universe is curved through a third physical dimension. When the Flatlanders take short excursions, their universe looks flat enough. But if one of them takes
a long enough walk along what seems to be a perfectly straight line, he uncovers a great mystery: although he has not reached a barrier and has never turned around, he has somehow come back to the place from which he started. His two-dimensional universe must have been warped, bent or curved through a mysterious third dimension. He cannot imagine that third dimension, but he can deduce it. Increase all dimensions in this story by one, and you have a situation that may apply to us.
Where is the center of the Cosmos? Is there an edge to the universe? What lies beyond that? In a two-dimensional universe, curved through a third dimension, there
is
no center—at least not on the surface of the sphere. The center of such a universe is not
in
that universe; it lies, inaccessible, in the third dimension,
inside
the sphere. While there is only so much area on the surface of the sphere, there is no edge to this universe—it is finite but unbounded. And the question of what lies beyond is meaningless. Flat creatures cannot, on their own, escape their two dimensions.
Increase all dimensions by one, and you have the situation that may apply to us: the universe as a four-dimensional hypersphere with no center and no edge, and nothing beyond. Why do all the galaxies seem to be running away from
us?
The hypersphere is expanding from a point, like a four-dimensional balloon being inflated, creating in every instant more space in the universe. Sometime after the expansion begins, galaxies condense and are carried outward on the surface of the hypersphere. There are astronomers in each galaxy, and the light they see is also trapped on the curved surface of the hypersphere. As the sphere expands, an astronomer in any galaxy will think all the other galaxies are running away from him. There are no privileged reference frames.
*
The farther away the galaxy, the faster its recession. The galaxies are embedded in, attached to space, and the fabric of space is expanding. And to the question, Where in the present universe did the Big Bang occur? the answer is clearly, everywhere.
If there is insufficient matter to prevent the universe from expanding forever, it must have an open shape, curved like a saddle with a surface extending to infinity in our three-dimensional analogy. If there is enough matter, then it has a closed shape, curved like a sphere in our three-dimensional analogy. If the universe is closed, light is trapped within it. In the 1920’s, in a direction
opposite to M31, observers found a distant pair of spiral galaxies. Was it possible, they wondered, that they were seeing the Milky Way and M31 from the other direction—like seeing the back of your head with light that has circumnavigated the universe? We now know that the universe is much larger than they imagined in the 1920’s. It would take more than the age of the universe for light to circumnavigate it. And the galaxies are younger than the universe. But if the Cosmos is closed and light cannot escape from it, then it may be perfectly correct to describe the universe as a black hole. If you wish to know what it is like inside a black hole, look around you.
We have previously mentioned the possibility of wormholes to get from one place in the universe to another without covering the intervening distance—through a black hole. We can imagine these wormholes as tubes running through a fourth physical dimension. We do not know that such wormholes exist. But if they do, must they always hook up with another place in our universe? Or is it just possible that wormholes connect with other universes, places that would otherwise be forever inaccessible to us? For all we know, there may be many other universes. Perhaps they are, in some sense, nested within one another.
There is an idea—strange, haunting, evocative—one of the most exquisite conjectures in science or religion. It is entirely undemonstrated; it may never be proved. But it stirs the blood. There is, we are told, an infinite hierarchy of universes, so that an elementary particle, such as an electron, in our universe would, if penetrated, reveal itself to be an entire closed universe. Within it, organized into the local equivalent of galaxies and smaller structures, are an immense number of other, much tinier elementary particles, which are themselves universes at the next level and so on forever—an infinite downward regression, universes within universes, endlessly. And upward as well. Our familiar universe of galaxies and stars, planets and people, would be a single elementary particle in the next universe up, the first step of another infinite regress.
This is the only religious idea I know that surpasses the endless number of infinitely old cycling universes in Hindu cosmology. What would those other universes be like? Would they be built on different laws of physics? Would they have stars and galaxies and worlds, or something quite different? Might they be compatible with some unimaginably different form of life? To enter them, we would somehow have to penetrate a fourth physical dimension—not
an easy undertaking, surely, but perhaps a black hole would provide a way. There may be small black holes in the solar neighborhood. Poised at the edge of forever, we would jump off …
*
This is not quite true. The near side of a galaxy is tens of thousands of light-years closer to us than the far side; thus we see the front as it was tens of thousands of years before the back. But typical events in galactic dynamics occupy tens of millions of years, so the error in thinking of an image of a galaxy as frozen in one moment of time is small.
*
The object itself might be any color, even blue. The red shift means only that each spectral line appears at longer wavelengths than when the object is at rest; the amount of the red shift is proportional both to the velocity and to the wavelength of the spectral line when the object is at rest.
*
The dates on Mayan inscriptions also range deep into the past and occasionally far into the future. One inscription refers to a time more than a million years ago and another perhaps refers to events of 400 million years ago, although this is in some dispute among Mayan scholars. The events memorialized may be mythical, but the time scales are prodigious. A millennium before Europeans were willing to divest themselves of the Biblical idea that the world was a few thousand years old, the Mayans were thinking of millions, and the Indians of billions.
*
The laws of nature cannot be
randomly
reshuffled at the cusps. If the universe has already gone through many oscillations, many possible laws of gravity would have been so weak that, for any given initial expansion, the universe would not have held together. Once the universe stumbles upon such a gravitational law, it flies apart and has no further opportunity to experience another oscillation and another cusp and another set of laws of nature. Thus we can deduce from the fact that the universe exists either a finite age, or a severe restriction on the kinds of laws of nature permitted in each oscillation. If the laws of physics are not randomly reshuffled at the cusps, there must be a regularity, a set of rules, that determines which laws are permissible and which are not. Such a set of rules would comprise a new physics standing over the existing physics. Our language is impoverished; there seems to be no suitable name for such a new physics. Both “paraphysics” and “metaphysics” have been preempted by other rather different and, quite possibly, wholly irrelevant activities. Perhaps “transphysics” would do.
*
If a fourth-dimensional creature existed it could, in our three-dimensional universe, appear and dematerialize at will, change shape remarkably, pluck us out of locked rooms and make us appear from nowhere. It could also turn us inside out. There are several ways in which we can be turned inside out: the least pleasant would result in our viscera and internal organs being on the outside and the entire Cosmos—glowing intergalactic gas, galaxies, planets, everything—on the inside. I am not sure I like the idea.
*
The view that the universe looks by and large the same no matter from where we happen to view it was first proposed, so far as we know, by Giordano Bruno.
Now that the destinies of Heaven and Earth have been fixed;
Trench and canal have been given their proper course;
The banks of the Tigris and the Euphrates
have been established;
What else shall we do?
What else shall we create?
Oh Anunaki, you great gods of the sky,
what else shall we do?
—The Assyrian account of the creation of Man, 800
B.C
.
When he, whoever of the gods it was, had thus arranged in order and resolved that chaotic mass, and reduced it, thus resolved, to cosmic parts, he first moulded the Earth into the form of a mighty ball so that it might be of like form on every side … And, that no region might be without its own forms of animate life, the stars and divine forms occupied the floor of heaven, the sea fell to the shining fishes for their home, Earth received the beasts, and the mobile air the birds … Then Man was born:… though all other animals are prone, and fix their gaze upon the earth, he gave to Man an uplifted face and bade him stand erect and turn his eyes to heaven.
—Ovid,
Metamorphoses
, first century
In the great cosmic dark there are countless stars and planets both younger and older than our solar system. Although we cannot yet be certain, the same processes that led on Earth to the evolution of life and intelligence should have been operating throughout the Cosmos. There may be a million worlds in the Milky Way Galaxy alone that at this moment are inhabited by beings who are very different from us, and far more advanced. Knowing a great deal is not the same as being smart; intelligence is not information alone but also judgment, the manner in which information is co-ordinated
and used. Still, the amount of information to which we have access is one index of our intelligence. The measuring rod, the unit of information, is something called a bit (for binary digit). It is an answer—either yes or no—to an unambiguous question. To specify whether a lamp is on or off requires a single bit of information. To designate one letter out of the twenty-six in the Latin alphabet takes five bits (2
5
= 2 × 2 × 2 × 2 × 2 = 32, which is more than 26). The verbal information content of this book is a little less than ten million bits, 10
7
. The total number of bits that characterizes an hour-long television program is about 10
12
. The information in the words and pictures of different books in all the libraries on the Earth is something like 10
16
or 10
17
bits.
*
Of course much of it is redundant. Such a number calibrates crudely what humans know. But elsewhere, on older worlds, where life has evolved billions of years earlier than on Earth, perhaps they know 10
20
bits or 10
30
—not just more information but significantly different information.
Of those million worlds inhabited by advanced intelligences, consider a rare planet, the only one in its system with a surface ocean of liquid water. In this rich aquatic environment, many relatively intelligent creatures live—some with eight appendages for grasping; others that communicate among themselves by changing an intricate pattern of bright and dark mottling on their bodies; even clever little creatures from the land who make brief forays into the ocean in vessels of wood or metal. But we seek the dominant intelligences, the grandest creatures on the planet, the sentient and graceful masters of the deep ocean, the great whales.
They are the largest animals
†
ever to evolve on the planet Earth, larger by far than the dinosaurs. An adult blue whale can be thirty meters long and weigh 150 tons. Many, especially the baleen whales, are placid browsers, straining through vast volumes of ocean for the small animals on which they graze; others eat fish and krill. The whales are recent arrivals in the ocean. Only seventy million years ago their ancestors were carnivorous mammals who migrated in slow steps from the land into the ocean. Among the whales, mothers suckle and care tenderly for their offspring. There is a long childhood in which the adults teach the young. Play is a typical pastime. These are all mammalian characteristics, all
important for the development of intelligent beings.