The judge pressed the piece of paper near his nose and cleared his throat. "Citizen number 40-231-37, will you please present yourself to the court?"
A thin woman with hands aged at least 10 years beyond her own 20, a common symptom of the Vrahos class, stepped forward. With her eyes lowered to the sand-filled floor of the stadium, she shuffled her feet towards the three judges – the most powerful citizens of the Sphere. The crowd began to howl at the sight of her as they filed into the colossal stadium large enough to hold the entire population of the Sphere.
The middle judge, a member of the Novas class, knocked on the table three times with a gavel. The crowd returned to silence once more, as the middle judge began to speak.
"Citizens of the Sphere, the accused who stands before you is on trial for crimes against our people." He turned his head towards the woman. "Citizen 40-231-37, you are being tried for seditious activities, specifically of an intent to spread dissent among the populace of the Sphere. These crimes are heretical in nature against the Great Articles of the Sphere. How do you plead to these charges, Ms..." He took another glance at the paper. "Galois?"
The accused hesitated before whispering her plea.
The crowd erupted. The judge on the right, a member of the Ganymedes class, began to knock violently on the table with her gavel. "Quiet! I will have quiet!" She took a moment to recompose herself before speaking in a high-pitched voice that carried easily throughout the stadium.
"We hear that you have spread lies among the populace that the lottery has been corrupted. This is a grave offence, Ms. Galois. For nearly 90 years since the start of the great divide, there have been dozens of people," she sneered as she spoke the next two words, "like you who have questioned the fairness of the lottery. Yet, no one has moved the populace to unrest quite so... aggressively with this talk of," She turned to the judge in the middle. "What is it, again?"
"Abnormality in curves," he answered.
"Ah, yes." She went on. "These mysterious curves. You do not deny these allegations, Ms. Galois?"
"No, your honor, I do not. But not all of the populace has been moved, as you say. It is only the members of the Vrahos class that are unhappy with what I have found."
The middle judge leaned forward, resting on his forearms before him. "But how could the words of an admitted criminal move anyone?" Appearing satisfied with his question, he reached into a bowl and removed a grape from a stem before placing it delicately into his mouth. "Our divisions are deep, I grant you. The Vrahos class has always had a much... simpler life, it is true. Yet, it was written in the Great Articles of the Sphere long ago that ten percent of our citizens would be chosen in a lottery overlooked by the three judges, one from each class, whereupon all of the chosen's possessions would be taken and spread among the population, so that we may all prosper more than before. It is the greatest sacrifice a citizen of the Sphere can make, as well as the most honorable. The honor of being chosen is spread among all of the classes equally. What is this abnormality you speak of, Ms. Galois?"
Gabrielle Galois looked at each of the judges in turn as she spoke, but she lingered a bit longer on the judge on the left, a member of the Vrahos class and a man who had seen many years. "It is the oddities of the numbers, your honors. You say that the lottery is equal, but it does not seem to be so equal for everyone. You say that the lottery is fair, that the Novas and the Ganymedes classes give as much as the Vrahos class, yet every time the lottery is called it is the Vrahos class who gives the most. If the lottery is truly fair, then citizens of each class should be called, on average, the same number of times."
The middle judge nodded. "And so it is."
"I must disagree, your honor. The last lottery spread the wealth of each chosen's sacrifice among the remaining 15,489 citizens, as the ledgers show. If the lottery is truly fair, 516 citizens would be expected to be chosen from each class. Yet, 891 were chosen from the Vrahos class, far more than either of the other two classes."
The judge on the right shook her head. "There's an element of chance among the lotteries. Surely, you know it will rarely come out perfectly even, Ms. Galois."
"Yes, your honor, but there's more. I looked through the recordings of the Sphere for the last several decades to find the percentage that are chosen from the Vrahos class. I then put all of those numbers together and made drawings of what you would expect to see and what the ledgers show. The numbers should follow a shape like this," Gabrielle traced an outline resembling a half-moon tilted to the side and squeezed in on the edges into the sand with her foot. "This is the curve you would expect. Yet, the average of the citizens belonging to the Vrahos class was much higher than expected. The shape instead looked like this," Gabrielle drew a shape into the sand that resembled the extended wing of a bird. "I looked in the recordings of the Sphere and found that it has been nearly forty years since a lottery took place where the number chosen from the Vrahos class was even close to the expected number. " Gabrielle looked towards the old judge on the left before saying, "The lottery, it seems, is rigged against the Vrahos class, your honor."
The members of the Vrahos class in the crowd stared intently at the outlines on the ground. The old judge, silent as of yet, shifted uncomfortably in his seat.
"The middle judge glared at the young woman before him. "Outrageous! Abnormalities in curves? These are only shapes and numbers! Abnormalities, you say? What is even normal when it comes to curves?"
Gabrielle carefully extended one arm and pointed at the symmetric outline in the ground. "This curve is normal, your honor."
A whisper began to rise through the crowd that was crammed into the vast structure in the middle of the Sphere. The middle judge seemed to speak more to the crowd than the accused. "This is proof of nothing! Only shapes and numbers! Shapes and numbers!"
Gabrielle could sense the rising tension in the stadium. Her voice was barely audible over the noise of the crowd before she smiled and, directing her attention to the aged judge on the left representing the Vrahos class said, "Do you deny these allegations, your honor?"
The judge she addressed, the elder of the other two by several decades and the most lavishly dressed with gold rings on what appeared to be each of his fingers, spoke for the first time as fear seemed to animate him to life. "Of course we deny it! We have always treated my class fairly. If the Vrahos class believes it has given more, it is only because I know my people prefer a life of simplicity. We have only ever given the classes what they want!"
Gabrielle gazed at the gold rings worn on each of the old judge's fingers. "You were once one of us, with hands worn like mine. When did you exchange calluses for rings? Was it nearly forty years ago, your honor?"
The noise in the crowd increased in volume until the pounding of the judges' gavels could no longer be heard. The tension reached a breaking point. One by one the members of the Vrahos class began to stand up. The guards posted around the stadium could only watch as over 5,000 people entered the lower bowl of the stadium to stand alongside Gabrielle Galois.
The old judge on the left looked alarmed at what was happening around him. "I have only ever wanted what is best for my class! You are all committing treason! These shapes mean nothing! Nothing! Please, I am only an old man!"
The judges froze in terror as the members of the Vrahos class in the crowd slowly encircled the table where all three judges sat, the outlines of the two curves at their feet – one normal and one abnormal. The accused, Gabrielle Galois, became lost in the gathering crowd, her presence indistinguishable among the thousands of citizens that filled the stadium of the Sphere. Two simple shapes had been the judges' undoing. Shapes and numbers were all it took.