Nice dodge, he thought with the curious dispassion that had come upon him. I wonder if they’ve met my kind of defensive maneuver before, or are just making a good response to something new? Wouldn’t be surprised if that last was the case. They’re brainy fellows, these Ivanhoans. While we, with our proud civilization, we can’t respond to so simple a thing as a local taboo on wheels.

  Shucks, it should be possible to analyze the problem—

  Two others were galloping close from the right. Falkayn narrowed his blaster beam as far as he could, to get maximum range, and shot with great care. He struck first one fastiga, then another: minor wounds, but painful. Both animals reared. The riders got them under control again and wheeled away. Falkayn turned about in time to fire at the other two, but not in time to forestall their arrows. Misses on both sides.

  …And figure out precisely what a wheel does, and then work out some other dodge that’ll do the same thing.

  Where was the fifth Larsan, the one who’d gotten winged? Wait…his fastiga stood riderless some distance off. But where was he? These bully boys weren’t the type to call it a day just because of a disabled arm.

  I got good grades in math and analytics. My discussants told me so. Now why can’t I dredge something I learned back then, up into memory, and use it? I could solve the problem for an exam, I’ll bet.

  Most likely the wounded one was snaking through the taller bushes, trying to get so close that he could pounce and stab.

  Of course, this isn’t exactly an examination room. Analytical thinking doesn’t come natural, most especially not when your life’s involved, and it’s very, very odd that I should begin on it at this precise moment. Maybe my subconscious smells an answer.

  The four riders had gotten together for a conference. They looked like toys at this distance, near the top of a high ridge paralleling the road and sloping down to its edge. Falkayn couldn’t hear anything but wind. The sun, fully risen now, made rippling violet shadows in the gray grass. The air was still cold; his breath smoked.

  Let’s see. A wheel is essentially a lever. But we’ve already decided that the other forms of lever aren’t usable. Wait! A screw? No, how’d you apply it? If any such thing were practical for us, Romulo Pasqual would’ve thought of it by now.

  How about cutting the wheel in slices, mounted separately? No, I remember suggesting that to Rebo, and he said it wouldn’t do, because the whole ensemble viewed from the side would still have a circular outline.

  The riders had evidently agreed on a plan. They unstrung their bows and fastened them carefully under the saddle girths. Then they started toward him, single file.

  What else does a wheel do, besides supply mechanical advantage? Ideally, it touches the ground at only one point, and so minimizes friction. Is there some other shape which’ll do the same? Sure, any number of ’em. But what good is an elliptical wheel?

  Hey, couldn’t you have a trick mounting, like an eccentric arm on an axle that was also elliptical, so the load would ride steady? No, I doubt if it’s feasible, especially over roads as dreadful as this one, and nothing but musclepower available for traction. The system would soon be jolted to pieces.

  The leading Sanctuary guard broke into a headlong gallop. Falkayn took aim and waited puzzledly for him to come in range of a beam wide enough to be surely lethal. The transceiver made muffled squawkings in Falkayn’s pocket, but he hadn’t the time for chatter.

  Same objection, complexity, inefficiency, and fragility, applies to whatever else comes to mind, like say a treadmill-powered caterpillar system. Perhaps Romulo can flange something up. But there ought to be a foolproof, easy answer.

  Crouched against the neck of his fastiga, the leading guard was nearly in range. Yes, now in range! Falkayn fired. The blast took the animal full in the chest. It cartwheeled several meters more downhill, under its own momentum, before falling. Its rider had left the saddle at the moment it was struck, before the beam could seek him out. He hit the ground with acrobatic agility, rolled over, and disappeared in the brush.

  By the time Falkayn saw what was intended, he had already shot the second. It crashed into the barrier of the first. The third rushed near, frightened but under control.

  “Oh, no, you don’t,” the human rasped. “I’m not going to build your wall for you!” He let the other two pound by. As they slewed about, exposing their riders to him, he had the bleak pleasure of killing an enemy. The fourth escaped out of range, jumped to earth, and ran toward the dead animals, leading his own but careful to stay on its far side.

  Falkayn’s bolts raked the slope, but he couldn’t see his targets in the overgrowth and it was too moist in this spring season to catch fire. The third Larsan got to the barrier and slashed his fastiga’s throat. It struggled, but hands reached from below to hold it there while it died.

  So three warriors had made the course. Now they were ensconced behind a wall of their own, too thick for him to burn through, high enough for them to kneel behind and send arrows that would arch down onto him. Of course, their aim wouldn’t be very good—

  The shafts began to rise. Falkayn made himself as small as possible and tried to burrow under one of his own slain fastigas.

  Something which…which rolls, and holds its load steady, but isn’t circular—

  The arrows fell. Their points went hard into dirt and inert flesh. After some time of barrage, a leonine head lifted above the other barrier to see what had happened. Falkayn, sensing a pause in the assault, rose to one knee and snapped a shot.

  He ought to have hit, with a broad beam at such close range. But he didn’t. The bolt struck the barricade and greasy smoke puffed outward. The Larsan dove for cover.

  What made Falkayn’s hand jerk was suddenly seeing the answer.

  He snatched out the radio. “Hello!” he yelped. “Listen, I know what we can do!”

  “Anything, Davy,” said Schuster like a prayer.

  “Not for me. I mean to get you fellows out of here—”

  The arrows hailed anew. Anguish ripped in Falkayn’s left calf where he crouched. He stared at the shaft that skewered it, not really comprehending for a moment.

  “Davy? You there?” Schuster cried across a thousand kilometers.

  Falkayn swallowed hard. The wound didn’t hurt too much, he decided. And the enemy had ceased fire again. They must be running low on ammo, too. The road was strewn with arrows.

  “Listen carefully,” he said to the box. It had fallen to the ground, and blood from his leg was trickling toward it. A dim part of him was interested to note that human blood in this light didn’t have its usual brilliance but looked blackish red. The rate of flow indicated that no major vessel had been cut. “You know what a constant-width polygon is?” he asked.

  A Larsan ventured another peek. When Falkayn didn’t shoot, he rose to his feet for an instant and waved before dropping back to shelter. Falkayn was too busy to wonder what that meant.

  “You hurt, Davy?” Schuster pleaded. “You don’t sound so good. They still after you?”

  “Shut up,” Falkayn said. “I haven’t much time. Listen. A figure of constant width is one that if you put it between two parallel lines, so they’re tangent to it on opposite sides, and then revolve it, well, the lines stay tangent clear around the circumference. In other words, the width of the figure is the same along every line drawn from side to side through the middle. A circle is a member of that class, obviously. But—”

  The Larsan whose left arm had been scorched to disability sprang from a clump of bushes along the road. There was a knife in his right hand. Falkayn caught the gleam in the corner of an eye, twisted about, and snatched for his blaster where it lay on the ground. The knife arm chopped through an arc. Falkayn shrieked as his own hand was pinned to earth.

  “Davy!” Schuster cried.

  Falkayn picked up the blaster with his left. The muzzle wavered back and forth. He shot and missed. The guard cleared the barrier at a jump, drawing his sword as he sprang. The blade swept around. Probably he had closed his eyes at the moment the gun went off, for he struck with accuracy. The weapon spun clear of Falkayn’s lacerated grasp.

  The human yanked out the knife that pinned him, surged to his feet, and attacked left-handed. His voice rose to a shout: “A circle’s not the only one! You take an equi—”

  His rush had brought him under the Larsan’s guard. He stabbed, but the point slithered off the breastplate. The native shoved. Falkayn lurched backward. The guard poised his rapier.

  “Equilateral triangle,” Falkayn sobbed. “You draw arcs—”

  A horn sounded. The guard recoiled with a snarl. On the hillside, an archer rose and sent a last arrow at Falkayn. But the human’s hurt leg had given way. He went to his knees, and the shaft whirred where he had been.

  Another arrow, from another direction, took the sword-wielder through the breast. He uttered a rather horrible rattling cough and fell on top of a fastiga. The surviving Sanctuary agents pointed frantically at the circles on their cuirasses. But arrows stormed from the riders who galloped out of the west, and the episode was over.

  Rebo Legnor’s-Child drew rein at the head of his household warriors and sprang from the saddle in time for Falkayn to crumple into his arms.

  Mukerji entered the wardroom to find Schuster alone, laying out a hand of solitaire. “Where’s Romulo?” he asked.

  “Off in his own place, quietly going crazy,” Schuster said. “He’s trying to figure out what Davy was getting at just before—” He raised a face whose plumpness looked oddly pinched. “Heard anything from the kid?”

  “No. I shall let you know the minute I do, of course. His set must still be on, I hear natives speak and move about. But not a word from him, and everyone else is probably afraid to answer the talking box.”

  “And I sent him there.”

  “You could not have known there was any danger.”

  “I could know the ship was the safest place to be. I should have gone myself.” Schuster stared blindly at his cards. “He was my apprentice.”

  Mukerji laid a hand on the merchant’s shoulder. “You had no business on a routine mission like that. Fighting and all, it was routine. Your brains are needed here.”

  “What brains?”

  “You must have some plan. What were you talking to that peasant about, a few hours before sunrise?”

  “I bribed him with a trade knife to carry a message for me to the Sanctuary. Telling Herktaskor he should come out for a private conference. Second in command of the astrology department, you may recall; a very bright fellow, and I think more friendly than otherwise to us. At least, he doesn’t have Sketulo’s fanatical resistance to innovation.” Schuster found he was laying a heart on a diamond, cursed, and scattered the cards with a sweep of his hand. “Obviously Rebo showed up, having seen the gun flashes, and dealt with Sketulo’s killers. But did he come in time? Is Davy still alive?”

  The scanner hooted. Both men leaped to their feet and ran out the door to the closest viewscreen.

  “Speak of the devil,” Mukerji said. “Take over, Martin. I shall go back and hunch above the radio.”

  Schuster suppressed his inward turmoil and opened the air lock. A cold early-morning wind, laden with sharp odors, gusted at him. Herktaskor mounted the gangway and entered. His great form was muffled in a cloak, which he did not take off until the door had closed again. Beneath, he wore his robes. Evidently he hadn’t wanted to be recognized on his way here.

  “Greeting,” said Schuster in a dull tone. “Thank you for coming.”

  “Your message left me scant choice,” said the Consecrate. “For the good of Larsum and the Faith, I am bound to listen if you claim to have an important matter to discuss.”

  “Have you, ah, been forbidden to enter the ship?”

  “No, but it is as well not to give the Chief the idea that he should forbid it.” Herktaskor squinted against an illumination which he found blindingly harsh, though it had been reduced well below normal to conserve the small amount of charge left in the accumulators. Schuster led the being to his own cabin, dimmed the lights further, and offered the lounger.

  They sat down and regarded each other for a silent while. At length Herktaskor said, “If you repeat this, I shall have to call you a liar. But having found you honorable”—that hurt a little; Schuster’s plans were not precisely aboveboard—“I think you should know that many Consecrates feel Sketulo was wrong in immediately banning your new mathematics and astrology. Could he show by scripture, tradition, or reasoning that they contravened the Word of God, then naturally the whole Sanctuary would have joined him in rejecting your teachings. But he has made no attempt to show it, has merely issued a flat decree.”

  “Are you permitted to argue with him about the matter?”

  “Yes, the rule has always been that full-rank Consecrates may dispute freely within the bounds of doctrine. But we must obey the orders of our superiors as long as those are not themselves unlawful.”

  “I thought so. Well,” —Schuster reached for a cigar—“here is what I wanted to tell you. I wish the co-operation of the Sanctuary rather than its enmity. In order to win that co-operation, I would like to prove to you that we are no danger to the Faith, but may rather be the instruments of its furtherance. Then perhaps you can convince the others.”

  Herktaskor waited, impassive. Yet his eyes narrowed and seemed to kindle.

  Schuster started the cigar and puffed ragged clouds. “The purpose of your astrology is to learn God’s will and the plan on which He has constructed the universe. To me, this implies that the larger purpose of the Consecrates is to search out the nature of God, insofar as it may be understood by mortals. Your theologians have reached conclusions in the past. But are those conclusions final? May there not be much more to deduce?”

  Herktaskor bowed his lion head and traced a solemn circle in the air. “There may. There must. Nothing of importance has been done in that field since the Book of Domno was written, but I myself have often speculated— Go on, I pray you.”

  “We newcomers are not initiates of your religion,” Schuster said. “However, we too, in our own fashion, have spent many centuries wondering about the divine. We, too, believe,” well, some of us, “in a single God, immortal, omnipotent, omniscient—perfect—Who made all things. Now maybe our theology varies from yours at crucial points. But maybe not. May I compare views with you? If you can show me where my people have erred, I will be grateful and will, if I live, carry back the truth to them. If, on the other hand, I can show you, or merely suggest to you, points on which our thought has gone beyond yours, then you will understand, and can make your colleagues understand, that we outlanders are no menace, but rather a beneficial influence.”

  “I doubt that Sketulo and stiff-minded Consecrates will ever concede that,” Herktaskor said. His voice took on an edge. “Yet if a new truth were indeed revealed, and anyone dared deny it—” His fists unclenched. “I listen.”

  Schuster was not surprised. Every religion in Earth’s past, no matter how exclusive in theory, had had influential thinkers who were willing to borrow ideas from contemporary rivals. He made himself as comfortable as possible. This would take a while.

  “The first question I wish to raise,” he said, “is why God created the universe. Have you any answer to that?”

  Herktaskor started. “Why, no. The writings say only that He did. Dare we inquire into His reasons?”

  “I believe so. See, if God is unbounded in every way, then He must have existed eternally before the world was. He is above everything finite. But thought and existence are themselves finite, are they not?”

  “Well…well…yes. That sounds reasonable. Thought and existence as we know them, anyhow.”

  “Just so. I daresay your philosophers have argued whether the sound of a stone falling in the desert, unheard by any ears is a real phenomenon.” Herktaskor nodded. “It is an old conundrum, found on countless planets, I mean in many countries. In like manner, a God alone in utter limitlessness could not be comprehended by thought nor described in words. No thinking, speaking creatures were there. Accordingly, in a certain manner of speaking, He did not exist. That is to say, His existence lacked an element of completion, the element of being observed and comprehended. But how can the existence of the perfect God be incomplete? Obviously it cannot. Therefore, it was necessary for Him to bring forth the universe, that it might know Him. Do you follow me?”

  Herktaskor’s nod was tense. He had begun to breathe faster.

  “Have I said anything thus far which contradicts your creed?” Schuster asked.

  “No…I do not believe you have. Though this is so new—Go on!”

  “The act of creation,” Schuster said around his cigar, “must logically involve the desire to create, thought about the thing to be created, the decision to create, and the work of creation. Otherwise God would be acting capriciously, which is absurd. Yet such properties—desire, thought, decision, and work—are limited. They are inevitably focused on one creation, out of the infinite possibilities, and involve one set of operations. Thus the act of creation implies a degree of finitude in God. But this is unthinkable, even temporarily. Thus we have the paradox that He must create and yet He cannot. How shall this be resolved?”

  “How do you resolve it?” Herktaskor breathed, looking a little groggy.

  “Why, by deciding that the actual creation must have been carried out by ten intelligences known as the Sephiroth—”

  “Hold on!” The Consecrate half rose. “These are no other gods, even lesser ones, and the Book does not credit the angels with making the world.”

  “Of course. Those I speak of are not gods or angels, they are separate manifestations of the One God, somewhat as the facets of a jewel are manifestations of it without being themselves jewels. God no doubt has infinitely many manifestations, but the ten Sephiroth are all that we have found logically necessary to explain the fact of creation. To begin with the first of them, the wish and idea of creation must have been coexistent with God from eternity. Therefore, it contains the nine others which are required as attributes of that which is to be created—”