Russell’s Paradox: A Cinderella Story

Lunar Awards Submission October 2023

The town of Didderdither was agog with the news of the imminent arrival of her Eminence Princess Ptolemy Tulip. The trumpets sounded, and Zanzibar was the first one to jump haphazardly into the road in his pajamas to witness the calamity of her arrival. As a retired astronomer and the eldest citizen of Didderdither, he felt it was his duty to observe—and vigorously comment on—the depravity of youth as exemplified by the most regal caste of society.  

Zanzibar shielded his eyes with one hand and protected his beard with the grip of his other hand. Her Eminence was arriving in a pumpkin-shaped space pod, and he could smell the ozone her ship had dragged with it into his atmosphere. Once the engines stopped, Zanzibar could resume hiking up his trousers with one hand and slogging forward with his third leg—that is, his trusted friend the wooden stick cane—gripped tightly with his other hand.

“It’s up to us now,” Zanzibar said to his cane.

“Zanzibar! Back down, man!” some well-dressed onlookers shouted.

“Quiet you, obstreperous youth!” Zanzibar replied.

The Pumpkin Pod opened its hatch with a zoosh like a bridge descending over a moat. Guards poured forth from the aperture. They created a perimeter around the space pod and pushed Zanzibar and his cane back three steps. Zanzibar was understandably enraged, but his shouts were drowned out by the applause as her Eminence Princess Ptolemy Tulip appeared in the walkway. She was dressed in a shimmering silver gown, made of the finest silk spun from the Worms of Wubb. Wubb was the star she called home. But it had not always been her home.

“Welcome home, Princess,” the crowds shouted. For indeed, the town of Didderdither laid claim to being the birthplace of the famed Princess. Every century or so, the Worms of Wubb would demand a peace-offering. They would requisition the most intelligent inhabitant of their town in exchange for vague terms of protection and dubious if not spurious promises of friendship. You see, Princess Ptolemy Tulip had been chosen, and not Zanzibar. And for that, Zanzibar would never forgive her.

“Noble People of Didderdither,” the Princess began.

“I hope this isn’t a long speech,” said Zanzibar to his cane.

“The Worms of Wubb send their warmest and wrigglingest of greetings,” she continued.

“Get to the point!” Zanzibar yelled. A guard gave him a fierce look of warning.

“They sent me here to report back that the human colony on their planet is thriving and our symbiotic relationship is even more symbiotic than they had ever imagined,” she said with a blank look on her face.

Zanzibar gripped his cane. “I knew her mother. Slatternly woman, that. How could anything with a wisp of intelligence come from her?”

“And therefore, they would like me to personally escort one new candidate back to Wubb to be incorporated into the royal colony. They have brought me here to present you with a paradox to solve. The first person to solve it will be joining me on my return trip,” the Princess curtseyed and regressed into the Pumpkin Pod, as waves of applause ricocheted off the seamless metal of the 3D-printed spaceship.  

At this, Zanzibar raised one bushy eyebrow and stroked his beard with his thumb. I have another chance? he thought to himself. “Maybe I won’t be having to use you this moment to knock out any guards, my friend,” Zanzibar said to his cane.

A slim, well-armored lad holding a scroll stood before the people and slowly unrolled what appeared to be the announcement of the paradox problem. He grunted and cleared his throat and then began to read: “Hear ye, hear ye, people of Didderdither, the paradox problem of Wubb:

Weaving silk we never tire
of seeing beauty we desire
Woven webs of civ’lization
Peace, Order, Retaliation
Curséd be the one to let in
Plague or pestilence that threaten
But what if our own employ
Modalities we must destroy?

Axiom One: The Worms of Wubb protect their own species.
Axiom Two: The Worms of Wubb destroy species who are threatening to their civilization.
Axiom Three: Some Worms of Wubb are threatening to their own civilization.
Solve this paradox problem, and you will be awarded a place on her Eminence Princess Ptolemy Tulip’s space pod back to the star of Wubb. Finally, if you refuse to solve this paradox, the Worms of Wubb hearby declare that your planet will be annihilated.”

A youthful fool blurted out his answer in a reckless attempt to be first: “Just kill off the worms who kill off worms!”

The guards surrounding the Pumpkin Pod began to beat him mercilessly. Zanzibar quickly joined the kerfuffle, grabbed his cane, and began beating the youthful fool. “You would have to kill the worm who killed the worm who killed the worm, then, you idiot!” he said while beating the fool with his cane.

Another, somewhat more cautious youth stepped forward and gave it a go: “Why are the Worms of Wubb asking us this question? Our species has the same conundrum. Unlike most other animals on our planet, we destroy ourselves. I propose considering this paradox through a philosophical and sociological lens rather than a mathematical lens.” This youth avoided any beatings, because he sounded wise compared to the first fool, who was presently weeping in the street.

A third youth pushed the second one aside with a clever, though equally naïve, supposition: “This is a paradox because if the Worms of Wubb protect their own species, they would not kill their own species. But if their own species threatens their own species in some way, they would be bound to kill them, which is to say that the first axiom cannot be true. A contradiction. I propose changing the language of the axiom to preclude any contradictions.”

Zanzibar guffawed at the answers. “They avoid solving the paradox by restructuring it so it is no longer a paradox. I’ve never seen such sissies in my life.”

 “Alright, you grumpy gaffer! Let’s hear your answer, then!” the riotous youths shouted at Zanzibar and his cane.

“The way I see it,” Zanzibar began, “is that some infinities are greater than other infinities, as old gramps Georg used to say. Infinity plus one! Ha!”

The crowd gasped and hushed.

He went on: “Some things cannot be solved. Some things cannot be decided. Some things are incomplete in themselves, as old uncle Gödel used to say. The answer to the paradox is that it is unsolvable. And I can write the proof to prove it. That is why the Worms of Wubb come here for us. We are the variables that can change their fate. And maybe they are the variables that can change ours.”

Her Eminence Princess Ptolemy Tulip listened clandestinely from the inside of her Pumpkin Pod and wept at hearing such a beautiful answer to the paradox, for she knew that the winner of the paradox problem would become her husband.

The guards gathered around Zanzibar and fitted him with a silk robe. They escorted him onto the Pumpkin Pod walkway. “Say farewell to Didderdither, Prince-elect Zanzibar.”

“P-Prince?” Zanzibar stuttered.

“Yes, you have been chosen,” the guards replied.

The crowds cheered and applauded. The youth snickered. Zanzibar’s cane fell to the ground in defeat.

In his farewell speech, Zanzibar, a humbled man, uttered these words: “I, Zanzibar, will destroy the fool who marries Princess Ptolemy Tulip. But this statement is not true. But if it is true, then it isn't. If it isn't true, then it is! A paradox!”

As the Pumpkin Pod started its engines and blasted off into the sky, Zanzibar’s haunting words could be heard reverberating in the skies, “A paradox, my lads! Never underestimate a paradox!”