“An asymptote,” said Menelaus softly. “A change so powerful strange that no man can see beyond it. An event horizon.” More loudly, he continued: “Well, what if we are not smart enough to jump that ditch? Not bright enough to understand the invitation written out for us? The estimate worked out by Dr. Chandrapur.…”
“Nonsense! The established authorities have dismissed his work!”
Menelaus was not surprised by this reaction. He had seen Chandrapur’s estimate of the complexity of the Monument, and it was a fairly simple calculus to show the number of possible combinations of untranslated symbols, and to compare that to the known statistics on human brain use.
There was too much math, a whole little world of it, miles upon miles covering the surface of the Monument, and so little had been cracked: less than thirty square feet of it. If the Mandelbrot fractal structure of the alien glyphs extended, as the primitive tests carried out by Croesus seemed to hint, down into the microscopic, molecular, or even atomic level, the calculus was even more daunting. The number of years estimated even to read the thing, at the human civilization’s current level of computer information storage and cross-referencing ability … and supposing the library of symbols continued inside the volume of the black sphere, not merely a surface inscription … the estimated values fell outside of the likely lifespan of human life on Earth.
Chandrapur was only stating the obvious—but the scientific community did not like an idea so unflattering that their minds would prove unequal to the task, so Chandrapur was ignored, even though he could not be answered.
Dr. Ram Vidura, who was of the Vaisyas caste, descended from craftsmen and commoners, spoke. His work was in the Poincaré Conjecture. Even his brilliance in mathematics could not expunge the shame of his inferior birth. By long habit, his voice was diffident, soothing, placatory. “Sir, let us speak of practicality. I assume you are using a cascade of multireceptors with combinations of binding patches or epitopes that will transport, sort, and bind the lipoproteins to their target areas?”
“Correct,” said Montrose.
“The number of possible interconnections between the neurons in the brain is ten to the eleventh power, or ten to the twelfth. What are the odds that you happened to hit upon the correct combination of nerve paths to augment?”
“I used the Eidgenössisches Polytechnikum computer in Zurich, their famous Denkmalsymbollogik Mainframe, to do the pattern-solving,” Menelaus said. “We may not know what all the alien symbols mean, but we know some of the grammar rules for manipulating them. Well, sir, I assume the logic is just as sound for conclusions the alien grammar laws allow, even if our math cannot confirm the result. Ancient Greeks who did not cotton to the concept of the ‘zero’ would still have reached a correct answer if they multiplied ten times ten using Arabic numerals, wouldn’t they just?”
There was no murmur among the eight men in the punt, but in his helmet, Menelaus could see the text channels light up, as the mathematicians asked each other in silent finger-type about the ramifications of what they were hearing.
Menelaus continued: “Countless millions of designs were filtered through Zurich computer analysis, until the near-infinite possibilities had been narrowed to one. In other words, here in my hand is the output of the Monument’s own math.”
There was a moment of silence. Finally, one voice said, “It is not really a math, but a symbol-system that can apply to any logic set.” This was Dr. Bhuti, the only scholar older than Dr. Ramananda aboard the punt. His caste was the lowest in the caste system: he was a Sudra. His long-dead ancestors had been serfs, and so had his grandparents, when serfdom was reintroduced under theories of genetic work differentiation. Despite that his caste rendered him fit only for manual labor, his work in the extrapolation of Kronecker’s theorem on abelian extensions to base number fields beyond the rational had won him coveted manumission. His findings also had applications in the topology of algebraic surfaces.
He and Menelaus had played long games of chess in the early morning cool, before Reveille, the only two men who woke before cockcrow, back in Africa, where there weren’t any cocks. Bhuti was gentle-souled, thoughtful, the very opposite of Menelaus, and so they had become close.
“Fine. I used the alien’s own symbol-system.”
Dr. Bhuti nodded slowly. The white hair clustered above his ears had been shaved for his helmet, which he unchocked and removed, to allow him to turn his neck and look thoughtfully at Menelaus. His skull was as wrinkled and brown as an apple left out in the sun, and his eyes twinkled like garnets.
Bhuti said carefully, “Please, I urge you to delay your experiment. Wait! Wait until we reach the target star. By that time, new methods of analysis might be discovered back on Earth. They might build the Xypotech, the self-reprogramming artificial mind whose coming has been for so long imagined. Perhaps we do not need a posthuman to translate the Monument for us, no? Let us not explore this avenue unless it becomes needed.”
Montrose had no ready answer for that. He had been planning for so long to augment his intelligence at the first possible opportunity, the idea of waiting had never occurred to him. Menelaus blinked in hesitation.
Father Venture Reyes y Pastor raised his gauntlet. He was the ship’s chaplain for the seventy or so men in the Hispanosphere complement. He and Menelaus had spent many an evening engaging in disputes on every topic under the sun, and Menelaus was surprised to find the man was absolutely wrong on absolutely everything, from politics to religion to art to war. He was an entertaining and thought-provoking debater nonetheless, a ruthlessly logical thinker. His work was in the Poincaré Conjecture.
“This is an incautious dream you cherish, Dr. Montrose,” he said in his somewhat soft and breathless voice. “Consider: If the Monument is too complex for our race, then we are not meant to read it. This must be left for whatever race will walk the earth after mankind is extinct: all in the fullness of time. We are the products of evolution, therefore by definition we cannot be in a position to regard evolution objectively, reflect on it, or question its wisdom.”
Menelaus said, “Says who?”
The young priest answered, “That is what we must assume the Monument says—if it were meant to be read, it would be legible to us. To us as we are, I mean. It is wrong to meddle with nature.”
“I figure that without some amount of meddling, I never would’ve learned to read. Sure as hell that ain’t natural, squinting at squiggly lines on a piece of cloth and all. That Monument holds all the secrets of our future, gentlemen! And if a man h’ain’t got the right to take a few risks with his own brain—a brain I trained into shape without no help from any man in this vessel, I warrant—than what rights has he got?”
Sarmento i Illa d’Or spoke next. He was from the Hispanosphere, and, by the agreed-upon conventions governing in-cabin speech, he had waited until each of the Indosphere members had spoken. He had been a wrestler, a weightlifter, the only person other than Menelaus willing to use the Camp ring in the gym. It was only because Menelaus fought dirty, using illegal blows and holds, that the gym circuits had halted their matches. He and Menelaus, grimacing, smiling, and growling at each other, had privately agreed to finish the match some day, but that day never came. Sarmento i Illa d’Or won his berth for his work in the topology of algebraic curves and surfaces, particularly valuable since topology and knot-theory was the main avenue of approach of most of the Monument symbolism so far translated.