He stopped as the door behind him opened. Corrie and Senta stood together on the threshold. Senta was in one of her withdrawal spells, bewildered and terrified. She was clinging to Corrie’s arm, eyes nervous and wild. The younger woman was trembling, her face oddly pale. The resemblance between the two was striking. Howard Anson went forward to help Corrie.
“ `Thou art thy mother’s glass,’ “ he said softly. “ `And she in thee calls back the lovely April of her prime.’ Here, let me take Senta. I know what to do.”
It was probably imagination, but in the younger woman’s face he could see the first shadow, the hint of coming disease. He took Senta’s arm.
“We checked it out,” Corrie said. “There’s no truth to it. The group in Chryse have a new treatment for drug addiction, but it won’t do anything for taliza. It was just bad reporting.”
Anson nodded. “I was afraid of that. It sounded too good to be true. Give me ten minutes while I do something for Senta. Until there’s a breakthrough, we’ll just have to struggle along with what we have.”
He grasped Senta tenderly and began to lead her through to the bedroom where a supply of the drug was stored.
“Howard.” Anson paused as Corrie called to him. He turned in the doorway.
“Howard, do you think there will — do you think somebody will find a cure? In time? A real cure?” Corrie’s voice faded to a whisper on the final words.
As she spoke, Rob rose from his couch and moved to her side. He placed his hand on her shoulder, as much for his support as for hers. Anson examined the two of them. Rob was exhausted but full of determination, with a look in his eyes that told Anson how he must answer.
“I’m quite sure of it, Corrie,” he said. “It won’t come tomorrow, and maybe it won’t come next year. But we’ll keep working, and we’ll find it. We’ll find you both a cure.”
APPENDIX 1: Notes on Quotes
When this book first appeared, I received lots of questions about beanstalks. I expected those. What I did not expect was the number of people who came up to me and said, “Were those all quotes at the beginning of chapters? I’ve tried to look them up, and I can’t find half of them.”
They were not all quotes, but many were. Here, for the curious, are their origins.
Chapter 1. “Praise, my soul, the King of Heaven, to His feet thy tribute bring.” — from the hymn beginning with these words, by Reginald Heber.
Chapter 3. “Go and catch a falling star…” — from the poem beginning with these words, by John Donne.
Chapter 4. “Busy old fool, unruly Sun…” — from the poem beginning with these words, by John Donne.
Chapter 5. “The light of other days…” — from the poem beginning, “Oft, in the still night, ere slumber’s chain has bound me…” by Thomas Moore.
Chapter 8. “To meet with Caliban…” — from William Shakespeare’s The Tempest.
Chapter 9. “Pluck from the memory a rooted sorrow, raze out the written troubles of the brain…” — from William Shakespeare’s Macbeth.
Chapter 11. “What seest thou else, in the dark backward and abysm of time?” — from William Shakespeare’s The Tempest.
Chapter 12. “…at the quiet limit of the world, a white-haired shadow roaming like a dream…” — from Tennyson’s “Tithonus.”
Chapter 15. “I do begin to have bloody thoughts…” — from William Shakespeare’s The Tempest.
Chapter 16. “Then I saw that there was a way to Hell, even from the gates of Heaven…” — from John Bunyan’s A Pilgrim’s Progress.
Chapter 18. “Cor contritum quasi cinis, gere curam mei finis.” — from the Dies Irae in the Latin Mass for the Dead; these lines are often translated as, “See like ashes my contrition, help me in my last condition.”
APPENDIX 2: Beanstalks in Fact and Fiction
Beanstalk basics
The scientific literature about beanstalks, in all its different versions (we’ll get to those later), has grown steadily over the past twenty years. Now there exist many varieties of proposed forms, for use in a variety of places, ranging from Earth to Mars to the Lagrange points of the Earth-Moon system. This book uses what I will term the “standard beanstalk,” a structure which extends from the surface of the Earth up into space, and stands in static equilibrium.
To understand how any beanstalk is possible, even in principle, we begin with a few facts of orbital mechanics. A spacecraft that circles the Earth around the equator, just high enough to avoid the main effects of atmospheric drag, makes a complete revolution in about an hour and a half. A spacecraft in a higher orbit takes longer, so for example if the spacecraft is 1,000 kilometers above the surface, it will take about 106 minutes for a complete revolution about the Earth.
If a spacecraft circles at a height of 35,770 kilometers above the Earth’s equator, its period of revolution will be 24 hours. Since the Earth takes 24 hours to rotate on its axis (I am ignoring the difference between sidereal and solar days), the spacecraft will seem always to hover over the same point on the equator. Such an orbit is said to be geostationary. A satellite in such an orbit does not seem to move relative to the Earth. It is clearly a splendid place for a communications satellite, since a ground antenna can point always to the same place in the sky; most of our communications satellites in fact inhabit such geostationary orbits.
A 24-hour circular orbit does not have to be geostationary. If the plane of its orbit is at an angle to the equator, it will be geosynchronous, with a 24-hour orbital period, but it will move up and down in latitude and oscillate in longitude during the course of one day. The class of geosynchronous orbits includes all geostationary orbits.
All geostationary orbits share the property that the gravitational and centrifugal forces on an orbiting object there are exactly equal. If by some means we could erect a long, thin pole vertically on the equator, stretching all the way to geostationary orbit and beyond, then every part of the pole below the height of 35,770 kilometers would feel a net downward force because it would be moving too slowly for centrifugal acceleration to balance gravitational acceleration. Similarly, every element of the pole higher than 35,770 kilometers would feel a net upward force, since these parts of the pole are traveling fast enough that centrifugal force exceeds gravitational pull.
The higher that a section of the pole is above geostationary height, the greater the total upward pull on it. So if we make the pole just the right length, the total downward pull from all parts of the pole below geostationary height will exactly balance the total upward pull from the parts above that height. The pole will then hang free in space, touching the Earth at the equator but not exerting any downward push on it.
How long does such a pole have to be? If we were to make it of uniform material along its length, and of uniform cross section, it would have to extend upward for 143,700 kilometers, in order for the upward and downward forces to balance exactly. This result does not depend on the cross-sectional area of the pole, nor on the material of which the pole is made. However, it is clear that in practice we should not make the pole of uniform cross section. The downward pull the pole must withstand is far greater up near geosynchronous height than it is near the surface of the Earth. At the higher points, the pole must support the weight of more than 35,000 kilometers of itself, whereas near Earth it supports only the weight hanging below it. Thus the logical design will be tapered, with the thickest part at geostationary altitude where the pull is greatest, and the thinnest part down at the surface of the Earth.