Essays

by Gregory Benford

  Einstein's theory contrasts strongly with visions such as Wells' in The Time Machine, which treats motion along the (dt) axis as very much like taking a train to the future, then back. In Einstein's geometry, only portions of the space can be reached at all without violating causality (the "light cone" within which two points can be connected by a single beam of light). Paradoxes can abound.

  Logical twists have inspired many science fiction stories. The issues are quite real; we have no solid theory which includes time in a satisfying manner, along with quantum mechanics, as a truly integrated fourth dimension. I spent a great deal of space in my novel Timescape wrestling with how to make this intuitively clear, but the struggle to think in four dimensions is perhaps beyond realistic fiction; perhaps it is more properly the ground of metaphor.

  Physicists began envisioning higher dimensions because they got a simpler dynamic picture, at the price of apparent complication. More dimensions to deal with certainly strains the imagination, and is at first glance an unintuitive way to think. But they can lead to beauties which only a mathematician can love, abstruse elegances. Thus Einstein, in his 1916 theory of general relativity, invoked the simplicity that objects move in "geodesies" -undisturbed paths, the equivalent of a straight line in Euclidean, rectangular geometry, or a great circle on a sphere -in a four-dimensional space-time. The clarity of a single type of curve, in return for the complication of a higher dimension.

  Einstein's general relativity said that matter curved the four-dimensional spacetime, an effect we see as gravity. Thus he replaced a classical idea, force, with a modem geometrical view, curvature of a 4D world. This led to a cosmology of the entire universe which was expanding and therefore pointed implicitly backward to an origin.

  Einstein did not in fact like this feature of his theory, and in his first investigations of his own marvelously beautiful equations fixed up the solution until it was static, without beginning or end. His authority was so profound that his bias might have held for ages, but Edmund Hubble showed within a decade that the universe was expanding.

  Even so, the concept of a beginning land perhaps an end) may be an artifact of our persistent 3D views. Implicitly, space and time separate in the Einstein universe. They are connected, but can be defined as ideas that stand alone.

  The essence of talking about dimensions is that they can be separately described. But this may not be so. At least, not in the beginning.

  Even Edwin Abbott did not foretell that in the hands of cosmologists like Stephen Hawking and James Hartle, time and space would blend. Though the universe remains 4D, definitions blur.

  Following the universe back to its origins leads inevitably to an early instant when intense energies led to the breakdown of the very ideas of space and time. Quantum mechanics tells us that as we proceed to earlier and earlier instants, something peculiar begins to happen. Time begins to turn into space. The origin of everything is in spacetime, and the "quantum foam" of that primordial event is not separable into our familiar distances and seconds.

  What is the shape of this spacetime? Theory permits a promiscuously infinite choice. Our usual view would be that space is one set of coordinates, and time another. But quantum uncertainty erupts through these intuitive definitions.

  Begin with an image of a remorselessly shrinking space governed by a backward marching time, like a cone racing downward to a sharp point. Time is the length along the axis, space the circular area of a sidewise slice. Customarily, we think of the apex as the beginning of things, where time starts and space is of zero extent.

  Now round off the cone's apex to a curve. There, length and duration smear. This rounded end permits no special time when things began. To see this, imagine the cone tilted. This model universe could be conceptually tilted this way or that, with no unique inclination of the cone seeming to be preferred. Now the "earliest" event is not at the center of the rounded end. It is some spot elsewhere on the rounded nub, a place where space and time blend. No particular spot is special.

  Another way to say this is that in 4D, time and space emerge gradually from an earlier essence for which we have no name. They are ideas we now find quite handy, but they were not forever fundamental.

  In the primordial Big Bang, there is no dear boundary between space and time. Rather than an image of an explosion, perhaps we should call this event the Great Emergence. There we are outside the conceptual space of precisely known space and well defined time. Yet there are still only four dimensions -- just not sharp ones.

  Einstein's cosmology thus begins with a time that is limited in the past, but has no boundary as such. Neither does space. As Stephen Hawking remarked, "The boundary condition of the universe is that it has no boundary."

  Perhaps Edwin Abbott would not like the theological ramifications of these ideas. He was of the straitlaced Church of England. (The American version is the Episcopal faith, which happens to be my own. As an boy I was an acolyte, charged with lighting candles and carrying forth the sacraments of holy communion, in red and white robes. The robes were intolerably hot in our Atlanta church, and once I fainted and collapsed in service -- overcome by the heat, not the ideas. I'm told it provoked a stir.) However, it is notable that members of that faith had a decided dimensionally imaginative bent, at least in the nineteenth century; Lewis Carroll and H.G. Wells come to mind.

  No doubt, psychologically the sharp-cone cosmological picture, with its initial singular point suggests the idea of a unique Creator who sets the whole thing going. How? Physics has no mechanism. For now, it merely describes.

  Here lurks a conceptual gap, for we have no model which tells us a mechanism for making universes, much less one in which such basics as space and time are illusions. We need a "God of the gaps" to explain how the original, defining event happened. These new theories seem to bridge this gap in a fashion, but at the price of abandoning still more of our basic intuitions.

  Much of God's essence comes from our perceived necessity for a creator, since there was a creation. But if there is no sharp beginning, perhaps we need no sharp, clear creator. Without a singular origin in time, or in space for that matter, is there any need to appeal to a supernatural act of creation?

  But does this mean we can regard the universe as entirely self-consistent, its 4D nature emerging with time, from an event which lies a finite time in our past but does not need any sort of infinite Creator? Can the universe be a closed system, containing the reason for its very existence within itself?

  Perhaps -- to put it mildly. Theory stands mute. Yet this latest outcome of our wrestling with dimensions assumes that there are laws to this universe, mathematically expressed in a stew of coordinates and algebra and natural beauties.

  But whence come the laws themselves? Is that where a Creator resides, making not merely spacetime but the laws? Of this mathematics can say nothing -- so far.

  Edwin Abbott would no doubt be astonished at the twists and turns his Lewis Carroll-like narrative has taken us to, only a bit more than a century beyond his initial penning of Flatland. The questions still loom large.

  So such matters progress, sharpening the questions without answering them in final fashion. We can only be sure that the future holds ideas which he, and we, would find stranger still.

  GREGORY BENFORD

  HUMANITY AS CANCER

  " . . . still I have not seen the fabulous city on the Pacific shore. Perhaps I never will. There's something in the prospect southwest from Barstow which makes one hesitate. Although recently, driving my own truck, I did succeed in penetrating as far as San Bernardino. But was hurled back by what appeared to be clouds of mustard gas rolling in from the west on a very broad front. Thus failed again. It may be however that Los Angeles will come to me. Will come to all of us, as it must (they say) to all men."

  Edward Abbey Desert Solitaire

  In 1960 the journal Science published a short paper which is still sending slow-motion shock waves through the soothsayers of our time. Titled "Do
omsday: Friday, 13 November, A.D. 2026," its abstract reads in full, "At this date human population will approach infinity if it grows as it has grown in the last two millennia."

  Period. Its authors, Heinz van Foerster, Patricia Mora and Lawrence Amiot, were members of the staff of the department of electrical engineering at the University of Illinois, Urbana. They were not population experts, but they noted a simple oddity of mathematics. The rise in human numbers was always studied in "doubling times," the measure of how quickly population doubled. But real human numbers don't follow so clean an equation.

  For a species expanding with no natural limitation aside from ordinary deaths, the rate of increase of population is proportional to the population itself. Mathematically, the population N is described by an equation in which the change in N, dN, over a change in time t, dt, obeys dN/dt = b N

  with b usually assumed to be a constant. If b is truly constant, then N will rise exponentially.

  Fair enough. But if people are clever, the proportionality factor b itself will weakly increase as we learn to survive better. This means the rate of increase will rise with the population, so N increases faster than an exponential.

  In fact, it can run away to infinity in a finite time. The equation describing this is a bit more complicated. To find how b changed with N, the authors simply looked at the average increase over the last two thousand years, to iron out bumps and dips, seeking the long-term behavior.

  They found a chilling result. Our recent climb in N in the last few centuries is not an anomaly; instead, it fits the smooth curve of human numbers. Tracking the solution backward "post-diets" that we were a mere 9.00,000 people a million years ago. Of course such great spans aren't well fit by population counts gathered from two millennia, and the equation becomes silly. But it should be good for at least a few centuries more.

  Looking into the near future, it predicts a chilling result: a singularity, with N rising faster and faster,going beyond view on Nov. 13, 2026. "The clever population annihilates itself," they remark laconically. "Our great-great-grandchildren will not starve to death. They will be squeezed to death."

  The paper has never been refuted. Further checks on the growth of the factor b have pushed the singularity date further away, to about 2049. This is comforting, moving the date by about twenty years in the thirty-four years since the paper appeared.

  But the general conclusion stands. As an exercise in statistics it is stimulating, and as far as I know the authors did little with it after their first telling point.

  Of course, nothing grows to the sky. Something will happen before b gets too large; the four horsemen of the apocalypse will ride again. Perhaps they already are. Still, we are not doormats. We are attempting population control, but results are slow, and pressures are mounting.

  I wrote before in this column about the ideas which follow, in a piece titled "The Biological Century." I'd like to revisit an idea I floated there, with some second thoughts.

  The future is coming, and it's ugly.

  Or so many believe. From staid university presidents and scruffy environmentalists alike, a growing consensus holds that humanity has entered a watershed era, a time of vast disasters looming large, just over the horizon of this generation. Their case rests on far more than an equation, too.

  In 1992 1 went on a cross-country hike in Orange County to protest a highway soon to go in. Puffing up a hill, I struck up a conversation with a member of the eco-warrior group Earth First, who wore the signature red shirt with a clenched fist. We mounted a ridge and saw the gray sweep of concrete that lapped against the hills below.

  "Looks like a sea of shit," the Earth Firster said. "Or a disease."

  That same month the National Academy of Sciences and Britain's Royal Society jointly warned of the dangerous links between population and environmental damage. Following this up, the Union of Concerned Scientists mustered 1500 experts to sign a "World Scientists' Warning to Humanity" and published it in leading newspapers. Heavy hitters, these, including the predictable (Linus Pauling, Paul Ehrlich, Carl Sagan), the inexpert but sanctified (Desmond Tutu], but also the heads of many scientific societies, Nobel Laureates, and authorities of many fields. One such Laureate, Henry Kendall of M.I.T., is leading the New Cassandras in a campaign to muse the intelligentsia.

  His case is easy to make. World population grows by 90 million yearly and will double within half a century, maybe less. More people have been born in the last forty years than in the previous three million years. About 8 percent of all human beings ever born live today. We are gaining at about 1.7 percent a year.

  Meanwhile, the Green Revolution is apparently over: world per-capita crops have declined. About ten percent of the Earth's agricultural land area has been damaged by humans. Water may be the first major resource to go; half of all nations now have water shortages. Even in the American midwest and southwest, farmers are sucking "fossil water" laid down in the ice ages, pulling it from aquifers which will deplete within a generation.

  But such policy-wonk numbers, the ecologists remind us, are too human-centered. Our swelling numbers have their greatest impact on defenseless species in rain forests, savannahs and coral reefs. Biologist E.O. Wilson of Harvard warns that we could lose thirty percent of all species within half a century, and that might be only the beginning.

  Humans exert selective pressures on the biological world. North Atlantic waters show a clear pattern of over-fishing, and ever-shrewd nature has filled these new niches with "trash fish" like skates and spiny dogfish which we cannot eat and thus do not take out.

  Monoculture crops worldwide gain efficiency by growing the same staple-wheat, rice, corn, trees-over a large area, but this is inherently more fragile. Diseases and predators prey easily and already erosion is a major threat in many such areas.

  Environmental damage grows not merely because our numbers rise, but because our expectations do, too. The masses jammed into Buenos Aires want a better life -- which means more consumer goods. The chain between such ambitions and the clearing of distant forests is, though long, quite clear.

  Most environmentalists are technophobic, reluctant to admit that the greatest enemy of the rain forests is not Dow Chemical but rather sunburned, ambitious men newly armed with chain saws, eager to better their lot in life.

  Still, hand-wringing is not new and skepticism about it is well earned. Paul Ehrlich's alarmist "The Population Bomb" has yet to explode, twenty-five years after publication, though some demographers feel that Ehrlich may simply be a few decades off.

  And there are counter-trends. Many are laboring to see that the factor b does not increase.

  The "developing world" -- to use the latest evasive tag attempting to cover societies as diverse as Singapore and Somalia-- is the great engine of population growth, but its pattern is not an exponential runaway. Taken all together, the poorer nations' growth rates seem to have reached a plateau.

  This may echo the industrial world, whose net growth curve broadly peaked around 1900 at a rate of about one percent a year, and is now a fourth of that. The poor countries may have entered just such a transition era. Some nations began peaking in the 1970s and others join them. Still, the plateau average rate is 2.5 percent per year, so they have a long way to fall.

  Will they decline? Environmentalists and professors alike fear they won't.

  Our numbers respond to both feedback loops and to feed-forward anticipations. Gloom, doom- well known intellectual commodities, finding a perpetual market. The 1960 paper is still the firmest basis for hand-wringing. Few experts believe the planet can sustain a population doubling in parallel with rising economic desires. This is how the Earth Firsters merge with the academics -- a profoundly pessimistic view of our collective future, shared from the hushed halls of Harvard to the jerky hip-hop images of MTV.

  This sea change we already see in severe cultural collision, such as immigration. MIT's Kendall predicts a doubling of Mexico's immigration into the USA within a decade.
Shantytowns along the USA southwestern border recall the slums of Rio. Last year the USA added 970,000 new legal immigrants, plus 132,000 refugees and the INS estimates that slightly over a million illegal immigrants came to stay. Our growth rate is nearly at one percent per year. Since our native population is near the Zero Population Growth level so publicized in the 1970s, this means immigration is virtually the sole cause of US growth, and places us far ahead of other industrial nations.

  Immigration-driven cultural strife is growing both here and in Europe. Anti-immigration forces typically fix myopically upon their local rise, Kendall says, but the only true solution must be global. "Until masses of people stop wanting to emigrate, you still have a basic problem." He is careful to shy away from the immigration issue, pitching his cool Cassandra tone to a lofty moral plane. His arguments seem far from the fever-eyed cries of the eco-warriors.

  But Garrett Hardin, emeritus professor from UC Santa Barbara and Kendall ally, argues for an America-saving cut in immigration. Target: eventually, less than 200 million Americans, since this is the sustainable level. "Sustainable" is the consensus watchword, including some unsettling ideas.

  To me the most significant one is Hardin's opposition to sending food aid to overpopulated areas such as Somalia. "Every time we send food to save lives in the present, we are destroying lives in the future." He invokes a cycle now well known-- aid fuels birth rates, then leads to famine within a generation. Human "die-backs" are now a routine feature of worldwide news, with "compassion fatigue" already evident in the media.

  Robert Malthus, the original population prophet, thought that civilization would hit the wall in the late nineteenth century. Economists like Julian Simon of the University of Maryland dismiss the doomsayers, noting that they've been around since the Bible. "The only difference is that Ezekiel and Jeremiah were much better writers."