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Celia Carter, Distinguished Professor of Philosophy, and Liam Sodre, Prode Chair of Mathematics, seemed to be occupying different universes. Liam, ogling the ladies playing pool, sipped his beer. Celia stared at their usual table’s remaining empty chair as if doubting its reality. She didn’t even blink when Arthur Feynstein, Royal Physics Fellow, plopped down.

 

“You’re late,” she said, noting Arthur's disheveled clothes, unchanged from the faculty meeting three days ago. His eyes drooped like he hadn’t slept since then. Celia expected some comeback about fundamental laws being chrono-symmetric, so time was a mere construct.

 

Instead, Arthur asked, “What if the Pythagorians were right?”

 

“That orbiting the Sun opposite the Earth is a Counter-Earth?” she asked, smiling slyly.

 

“They believed that!?” Arthur asked.

 

“Or transmigration of souls until one becomes pure enough to reside with Apollo?”

 

“No, their view that everything is really numbers.”

 

“I’d go forth and multiply,” Liam said, eyeing the approaching waitress. Celia sighed. He must have finished a particularly challenging proof to be in such a randy mood.

 

Arthur made a show of contemplating the menu, but inevitably ordered the same thing as every other Thursday for the past decade.

 

“The house burger plate with a #6, the Belgian Weiss.” The waitress took the menu, flashed Liam a smile, and sauntered away.

 

“Why the sudden concern with the Pythagorians?” Celia asked. “I thought you were working on measuring the universe’s smallest building blocks.”

 

“I am.” Arthur yawned. “But during Monday’s faculty meeting I dozed off. Dreamed of light pulses shrinking until barely more than Planck-length long. And the schematics for this.”

 

He placed a nondescript black box on the table.

 

“What is it?” Ceilia asked.

 

Arthur flipped two switches. A beam of light emerged from one end striking Liam’s beer stein. “It emits pulses shorter than a yoctosecond long. I expected an image like an electron ptychograph, but got this.” Arthur gestured at a stream of numbers holographically projected above the box. “If we’re seeing the universe’s fundamental nature, then apparently it’s just numbers.”

 

“You’ve cracked the code!” Liam said, “Proof we’re in a computer simulation!”

 

“Wouldn’t that be strings of ones and zeros?” Arthur asked.

 

“Alternative hypothesis: our universe is merely the output of a metaverse monkey randomly banging a calculator,” Celia said.

 

“I like the simulation hypothesis better — it’s cooler,” Liam replied.

 

“If only coolness were a measure of truth,” Celia countered.

 

The waitress returned with Arthur’s beer.

 

Liam, ignoring the waitress, pointed the beam at his paper napkin. A new string of numbers appeared. He tore the napkin in half and pointed the beam at one part. He halved the napkin again and again, eventually focusing on a tiny slip, still oblivious when the waitress reappeared with their orders. She slammed Liam’s plate onto the table and stalked off.

 

This explained why Liam’s relationships lasted just yoctoseconds, Celia mused. Numbers invariably kept Liam’s attention much longer.

 

Liam repeated the halving procedure with one of Arthur’s fries.

 

“Hey, use one of yours!” Arthur scolded.

 

“But you never finish.” Satisfied, Liam popped the fry remains into his mouth. “Definitely compositional — the numbers of the parts are contained within the larger object’s number.”

 

“My experiments over that past forty-eight hours already established that,” Arthur replied tartly. “I narrowed the focus down to different water molecules. Each molecule's number was part of the larger sample’s.”

 

“What would happen if you turned the device on itself — with a mirror, say?” Liam asked.

 

“You’d see the mirror’s number?” Arthur replied.

 

“Ok, I’ll stop worrying your thingy will violate Godel’s Incompleteness Theorem.”

 

“You really think this might show the numbers of everything in the universe?” Arthur asked hopefully.

 

“Well, the Number of the Universe, given compositionality.”

 

“A very large number,” Celia idly murmured.

 

“Or very small,” Liam said.

 

Celia arched an eyebrow.

 

“Just put a .0 after your large number and flip it around. The same digits, but a small number,” Liam said.

 

“Just like the universe’s radius,” Arthur added.

 

Celia and Liam stared blankly.

 

Arthur began lecturing. “Assume the radius of the universe is R, what you expect is a very large number. Turns out no experiment can distinguish between the actual radius being R or 1/R which is a very small number.”

 

“Whatever,” Liam interjected, “This is awesome! The whole universe captured in a single number. Infinities of infinities of universes, the entire multiverse, compactly nestled between one and zero!” Liam paused. “Why aren’t you ecstatic?! You’ll win a Nobel Prize and the Fields Medal!”

 

“The dream is lost. I can’t remember the specs and I’m afraid to take this one apart.”

 

“Ramanujan claimed many of his proofs came in his dreams, the goddess Namagiri writing them on a screen of blood.”

 

“Descartes allegedly dreamed of the principles grounding our current scientific method,” Celia added.

 

“Not good enough for the Nobel Committee. They’ll want to know what’s going on inside the little black box.” Arthur frowned. “Also, there’s a disturbing anomaly. A three digit string keeps appearing and disappearing at random, like junk DNA twined within useful code.”

 

“What string?” Liam asked.

 

“666”

 

Liam crossed himself.

 

Celia laughed. “Descartes’ demon obviously has a sense of humor.”

 

Arthur stared glumly into his beer. “You’re saying, it’s the Devil’s work?”

 

“Or the universe is just undecidable. Pythagorean genius or demonic trickery. Computer simulation or dream of the universe. Large number or small. Like the radius of the universe, we may never be able to distinguish between the two.” Celia paused, finishing off her own beer.

 

“You asked what I would do if everything were numbers. Would that truth change how we perceive and experience the world right now? I think not. To paraphrase David Hume, ‘Since reason is incapable of dispelling these clouds, … I’d let nature obliterate all these chimeras. I’d dine, play a game of backgammon, converse, and be merry with my friends.’”

 

She flagged the waitress, “We’ll have three more Weisses please.”

 

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Universal Compactness

The devil's in the details

Jeff Currier

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