Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction

by Adler, Charles L.

  The stability issue is rather subtle. To begin with we need to look at why planetary orbits around the sun are stable. A planet, as it orbits its star, seems to feel two forces acting on it: the force of gravity pulling it in and a “centrifugal force” pushing it away. For a circular orbit, the two forces balance out at all times. For an elliptical orbit, as the planet approaches the star, the centrifugal force is stronger than the gravitational force, resulting in it being pushed away. As the planet gets farther from the star than its average distance, the force of gravity is stronger than the centrifugal force. This results in a net force toward the star. The final result is that the planetary orbit is stable: when the planet is too close, it is pushed away; when it is too far, it is pulled in.

  This isn’t true for a Ringworld structure. Here the centrifugal force pushing outward is much stronger than the gravitational force pulling inward. The total force is balanced out by one that doesn’t exist for a planet: the tension in the ring structure. The Ringworld is a lot like a rapidly spinning gyroscope. If the structure slides off-center, it’ll start to wobble. The wobble will couple into the motion of the ring, sliding it further off center, and soon. This will eventually crash the structure into the star, but it will not be a smooth motion at all. The wobble may get so strong that it tears the structure apart before it hits the sun.

  19.5.3 Deformation

  The final issue is deformation of the structure. If the ring deforms a little bit from a perfect circle, does the structure tend to “bounce back” to a circle or does it tend to collapse itself out into a line? I don’t know the answer to this question. It probably depends on the material properties of scrith. Such stability problems tend to be highly nonlinear, and therefore difficult. My suspicion is that the extremely high centrifugal force will complicate the problem a lot.

  19.5.4 Other Large Structures

  In the recent novel Bowl of Heaven, Gregory Benford and Larry Niven write about another type of large structure. Essentially it is a half Dyson sphere. The structure looks like a parachute being dragged behind a racing car, with the Sun functioning as the car and the world-bowl as the parachute [37]. It is being used as some sort of very large starship. The structure was built for mysterious purposes; humans stumble across it during the course of the first interstellar exploration. One of the characters says of the structure:

  The shell should fall into the star—it’s not orbiting. There’s some sort of force balance at play…. Just spinning it isn’t enough, either—the stress would vary with the curvature. You’d need internal support. [37, p. 33]

  I have no idea whether Benford and Niven did a stability analysis for this structure. To give them credit, they mention in the book the misconception that Dyson’s original idea was a solid structure:

  Only—the old texts reveal quite clearly that Dyson did not dream of a rigid structure at all. Rather, he imagined a spherical zone filled with orbiting habitats, enough of them to capture all of the radiant energy of a star. [37, p. 33]

  In the 1970s Larry Niven wrote an essay “Bigger Than Worlds,” in which he discussed different structures from the size of large space stations to the galaxy [180]. I think they are all implausible for reasons that were brought up when Dyson published his original paper.

  19.6 GETTING THERE FROM HERE—AND DO WE NEED TO?

  Dyson originally proposed these structures as a cure for overpopulation. However, Dyson’s assumption was that the world population would continue to increase exponentially in a Malthusian fashion. Exponential increase is characteristic of populations that have plenty of resources. This can be seen in bacterial populations; given sufficient resources, they double every generation until the food available to them is exhausted. Human population has increased at an average rate of about 1% per year since around 1800 CE, that is, since the beginning of the Industrial Revolution [69]. However, this rate of increase was made possible by the enormous increase in resources available.

  The growth of a bacterial or animal population doesn’t follow an exponential curve indefinitely. It follows the same sigmoidal curve that we investigated when looking at the Hubbert peak for oil use. It is characteristic of an expanding use of a finite resource. Dyson’s point was that the expansion of human population is limited by the resources, chiefly energy, available to it. The question is whether the human race will expand to this point if such resources are available to it. After Dyson’s original article was published, John Maddox, Eugene Sloane, and Poul Anderson published rebuttals to his thesis in Science magazine [156]. Anderson made the rather cogent point that unrestrained population growth would make the structure nearly impossible to build because, at the growth rates postulated by Dyson, the structure would take much longer to build than the time it would be needed in. To quote Anderson:

  Even Dyson intimates that the project would take several thousand years to complete. In short, uncontrolled population growth will make the construction of artificial biospheres such as Dyson spheres impossible, and birth control will make them unnecessary. [156, p. 257]

  It is a truism that First World civilizations have lower birth rates than Second or Third World ones. This is due to easy access to birth control and (probably) to other social factors, equality of rights for women being chief among them. If this trend holds for the developing world as in the developed, overall world birth rates would be expected to drop. (It’s interesting to note that one predicts the same result if one assumes resource depletion and the Four Horsemen.) In this optimistic scenario, world population should level off or possibly even decrease in the future. In any event, birth control seems easier in the long run. However, this still doesn’t rule out highly advanced civilizations.

  Note

  1. For the same weight/strength ratio, structures in Earth’s orbit are limited to about 100 km in size because of the higher value of g and lower value of r. This is another reason why it is difficult to build a space elevator.

  CHAPTER TWENTY

  ADVANCED CIVILIZATIONS AND THE KARDASHEV SCALE

  20.1 THE KARDASHEV SCALE

  Any sufficiently advanced technology is indistinguishable from magic.

  —ARTHUR C. CLARKE, PROFILES OF THE FUTURE

  In the 1950s, Isaac Asimov envisioned a great “Galactic Empire” as the stage for his Foundation novels, a civilization set thousands of years in the future that encompassed every star in the Milky Way Galaxy. The sweep of this vision proved popular: Asimov followed his initial three novels, focused on the collapse of the first empire, with three more that both chronicled the rise of the second empire and also deconstructed the background of the first novels. Not only have several more Foundation novels been written posthumously (a neat trick, that), but his vision has been shared by many other science fiction writers since his time. Galactic civilizations have featured in the stories of Cordwainer Smith, with his “Instrumentality of Mankind”; in Larry Niven and Jerry Pournelle’s Codominium and Empire of Man stories and novels, including The Mote in God’s Eye; and in the various Star Trek series, novels, cartoons, and films and the Star Wars films and novels. The combination of Napoleonic era intrigue with ships popping in and out of hyperspace is almost irresistible.

  We’ve devoted two previous chapters to discussing the problems inherent in interstellar travel. The issues of cost, time, and energy consumption effectively nix travel between the stars for a civilization like ours. However, our technological civilization is historically extremely young, and technological developments have shown explosive exponential growth. Maybe humanity can eventually develop some sort of galactic empire (or at least some kind of galactic civilization) if given sufficient time to grow and sufficient development.

  In 1964, in a paper on the detection of advanced alien civilizations, Nikolai Kardashev, a Soviet astronomer, proposed a typology of advanced civilizations:

  Type I—A civilization that could harness the energy resources available to the entire planet.

  Type II—A civilization that cou
ld harness all the energy produced by its planet’s star.

  Type III—A civilization that could harness all the energy produced by its galaxy.

  Actually, in the original paper, a Type I civilization was defined as being like the technological civilization we have today; no mention was made of being able to harness all of the resources available to the planet. However, since the original publication, the term has taken on that meaning.

  20.2 OUR TYPE 0.7 CIVILIZATION

  World energy usage rate is currently about 1013 W. This is the average amount of energy used by everyone in the world every second of every day. The United States is the largest energy consumer, accounting for about 25% of the total amount, although China and India may surpass the U.S. share within the next half century. Carl Sagan took Kardashev’s original loose classification and wrote out a mathematical formula to place the different civilizations into these categories:

  Here, K is the Kardashev scale rating; the “log10” refers to taking the logarithm, base 10, of the average power used by the civilization. Usage of the logarithm compresses the scale; for example, log10 10 = 1, while log10 100 = 2. Because of the division by 10 in the formula, to increase by one unit on the Sagan-Kardashev scale, a civilization must increase its power usage by a factor of 10 billion. Putting in the numbers, our own current world civilization uses 1013 W; log10 1013 = 13, and (13 − 6)/10 = 7/10 = 0.7. Our civilization thus stands at 0.7 on the Kardashev scale.

  I want to consider what it will take for us to become a Type I civilization, but let’s first take a look at preindustrial civilization on the same scale. The big thing that separates pre- from postindustrial civilization is energy usage rates. Before the Industrial Revolution, people were limited in their power usage to the amount of power that a human body (or in select cases, draft animals) can exert—roughly 250 W. In a hypothetical civilization of 10 million people, this implies a power usage of roughly 2.5×109 W. The Kardashev rating can be found easily: log10 2.5 × 109 = 9.4; (9.4 − 6)/10 = 0.34. This gives some idea of the relative ratings of the world civilizations; even though world civilizations are very different from one another, they occupy a fairly small range on the Sagan-Kardashev scale. We can reverse the formula to find the energy usage for a given value of K:

  A Type I civilization has an average power usage of 1010×1+6 watts = 1016 W, or 1,000 times the amount of power consumed by the world today.

  If we guess that energy usage in the world increases at an average rate of about 3% per year, then energy usage doubles roughly every 23 years. If we take a number and double it, then double it again, then repeat that again, after ten doubling periods the original number will have increased by a factor of just about 1,000 (really, 1,024, but we’re rounding off). So, ten doubling periods = 10 × 23 years = 230 years until we become a Type I civilization. This makes some sense: by the calculation I did earlier, we are about as far away from a Type I civilization as a preindustrial civilization is from us (i.e., a distance of about 0.3 or so on the Sagan-Kardashev scale). It took roughly 250 years of industrialization to bring us to the civilization we have today, so we can imagine that it will take about the same amount of time to bring us to the next stage of civilization.

  20.3 TYPE I CIVILIZATIONS

  A Type I civilization has come to mean one that has complete control over all of the resources available to the planet. Resources is a big concept and could mean a lot of different things; for example, should a Type I civilization be able to control the planet’s weather? However, if we just pay attention to energy usage, things become simpler.

  The most valuable resource on Earth is sunlight. Don’t believe me? Agriculture is impossible without it. Without sunlight, everyone dies; actually, all life on Earth dies, because it is completely dependent on the energy we receive from the Sun. Earth is not a closed system: without an input of energy from the Sun, life can’t work. So, in principle, in controlling all of a planet’s resources, a Type I civilization will control (harvest, use, whatever) all of the sunlight that intercepts the Earth.

  The average insolation for the Earth is about 250 W/m2 at sea level. The total power of sunlight reaching the Earth is just this number multiplied by the total (projected) area of the Earth, 1.3×1014 m2. So the total power available from sunlight is 250 W × 1.3×1014 m2 = 3.2×1016 W. Give or take, this is the energy usage of a Type I civilization on the Sagan-Kardashev scale. But we have to ask whether it is even possible for our world civilization to reach this level of power use, or, if possible, whether it is wise to do so.

  First, there are many reasons why we might not be able to harvest all the power the Sun sends us. One obvious reason is that about 70% of the Earth’s surface is water. While all things are possible for those who believe, it’s hard for me to think that our descendants will want to plate over the surface of the oceans with solar cells. Solar cells are also not perfectly efficient—the best that exist today run at about 20% conversion efficiency of light into electricity. I suspect also that not more than 10% of the land surface could be effectively covered with solar cells before there would be extreme consequences to Earth’s ecology. All three factors would reduce the amount of available power from sunlight by about two orders of magnitude from the value given above, to a level roughly ten times greater than world energy consumption today. Not bad, but far from the godlike beings we want to ascend to.

  Of course, there are other power sources available. At the present time, the only plausible alternative power source is controlled thermonuclear fusion. In principle, the world’s supply of deuterium could furnish us with unlimited energy, enough to make everyone rich. There is an issue with generating that much power, however: ultimately, any energy generated for running our complex civilization is turned into heat. If we use sunlight for power, it isn’t that bad, as the sunlight hitting the Earth heats it anyhow. But generating an enormous amount of power using fusion has the potential to directly heat the Earth by quite a bit. How much? Well, the Earth is maintained at about 300 K simply from heat from the sun. If we generated the same amount of heat using another power source, the temperature of the Earth would increase by a factor of roughly 21/4, or to about 360 K (86.5°C or 188° F), much too hot to sustain life. This is disregarding any other pollution such energy generation would create. Solar power doesn’t have this problem, mostly: the sunlight absorbed by the Earth turns into heat anyhow, so it doesn’t matter if it takes an extra step to generate electricity. (The “mostly” has to do with the fact that if extensive solar cells change the Earth’s effective albedo, the Earth’s mean temperature will change.)

  If you want that much energy, you must pay the price for it. Ultimately, a Type I civilization requires a completely controlled ecology: it would require enormous changes in the Earth’s biosphere, to the point that most animals (including humans) would need to be extensively changed in order to survive. Like many science fiction ideas, this concept seems to have originated with Olaf Stapledon in his novels Last and First Men and Star Maker [225]. In Star Maker, the galactic civilizations genetically engineer their citizens into energy-efficient hyperintelligent insect-like beings in order to make the most effective use of the energy given out by dying stars at the end of time. As many authors have suggested, there are other ways this scenario could play out: humans could all “download” themselves into computers so that we could make whatever changes we wanted to the corporeal world without worrying about consequences (a theme pursued in several of Chris Egan’s novels, among others); the computers could wipe us out (or try to), as in the Terminator movies, and do the same thing (this is explored in detail in the novel Hyperion); we could genetically engineer ourselves to live in the extremely changed environments resulting from our advanced technology, as in Bruce Stirling’s Schismatrix novels; we could accidentally do it to ourselves, and end up with a Type 1 civilization by default (this is more or less the plot of Greg Bear’s novel Blood Music), or some combination thereof. An excellent article by Hans Joachin Schell
nhuber and colleagues addresses these issues in a very readable manner [211].

  20.4 MOVING UPWARD

  If we get a good start,

  We can take Mars apart,

  If we just find a big enough wrench …

  —“HOME ON LAGRANGE,” TRADITIONAL FILKSONG

  So now we control the resources of an entire planet. What do we do now? We ascend higher, that’s what!

  Human colonies in space or on other planets is the next logical step. We’ve discussed such colonies in other chapters, although of course one can imagine creating such colonies even before the planet reaches a Type I civilization. However, there is a next step: the terraforming of a world. The idea is to take a (presumably) lifeless planet such as Mars and make it habitable for people. What “habitable” implies exactly is a little loose, but generally speaking, the idea is that a human could live out in the open on such a world. Of course, one can imagine modifying humans through genetic engineering or creating a cyborg or some such so that they could survive there, instead of modifying the entire planet. Or perhaps some sort of combined approach, in which we changed both the people and the planet, would work.

  It’s hard to imagine what such large-scale changes would mean, or if such a civilization could control them. We are currently conducting an uncontrolled experiment in which we are increasing the average temperature of our planet by increasing the atmospheric retention of heat from the Sun, and it has already had a measurable effect on our ecology. Paul J. Crutzen and Eugene F. Stoermer coined the term “anthropocene” to describe the current epoch, which humans entered when the Industrial Revolution began to change the world’s ecology and weather patterns [61]. Some even extend the term back to the beginning of the invention of farming, about 20,000 years ago.