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Fiction

No One Bet On Canis Major

by Andrew Fraknoi

From the United Planets Official Wikipedia, last edition before the Catastrophe

When, after years of acrimonious debate, the United Planets Council finally legalized betting on astronomical events, it was natural to exclude professional astronomers from those eligible to place a wager. But many commentators pointed out that astronomers were as likely as the next United Planets citizen to have extended families and close friends. What was to prevent an astronomer, after some productive nights on the Extremely Large Telescope in Chile, from asking a drinking buddy or third cousin to place a bet on the next comet to enter the inner solar system?

Indeed, a number of early payoffs were eventually traced to insider information. Soon, however, astronomical betting became so widespread, that it didn’t much matter. After Asteroid 2045QY2 hit downtown Las Vegas (a random event with which the religious right had a field day), the hobby of astronomy became so popular that astronomical gambling became a major source of revenue for planetary governments around the system.

Early on, astronomers could earn some extra cash by suggesting new phenomena on which bets could be placed. With the solar-system-wide net of repeater stations allowing inexpensive communications between worlds, planetary gambling authorities vied with each other to come up with new games to attract gamblers not only from their own local populations, but from around the system.

At first, bets were placed only on the best-known astronomical phenomena. There were games guessing the direction and arrival time for new comets coming from the Oort Cloud, or the discovery of new asteroids above a certain size that crossed Earth’s orbit. Others involved predicting the Sun’s next coronal mass ejection pointed toward Earth and above a specified energy threshold, new volcanic eruptions on Jupiter’s moon Io, or new geyser eruptions reaching above a certain height on Neptune’s moon Triton, to name just a few top money-makers.

Soon, however, the solar system was just not big enough to contain humanity’s urge to gamble and gaming authorities turned to the wider Milky Way. Suddenly, schools felt the pressure of teaching astronomy to all children before they were done with high school.

Popular longer-term games involved predicting the explosions of massive stars at the end of their lives and the detonation of white dwarfs in binary star systems. To the initial confusion of the betting public, astronomers called both types of explosions supernovae, yet the odds for the two different kinds of stellar blasts were different. Still, both kinds of supernovae were quite rare in the Galaxy. The wait between explosions could be decades or centuries, meaning that, if a lot of people played, a successful prediction offered the chance for a huge payoff.

Stellar explosions remained elusive even when the inauguration of GART, the Gargantuan Array of Radio Telescopes on the far side of the Moon, made their discovery easier. In earlier years, supernovae had been discovered by the light they produced. Unfortunately, there was enough dust filling the disk of our galaxy that only the nearest explosions could be observed with visible-light telescopes; more remote ones were hidden by that curtain of dust. With radio observations, more distant parts of the Galaxy were opened to our view, but the number of supernovae in the Milky Way during any human lifetime remained annoyingly small.

When the Mars gambling authority decided to expand the betting to include supernovae in other galaxies, and to allow bettors to select one galaxy, a group of galaxies, or even a constellation to wager on, the supernova game suddenly got a lot more popular. Scientists were quick to point out that supernovae were random individual events – given the scale of distances between stars, the explosion of a star in any given galaxy would not lead to the explosion of another elsewhere in that galaxy. Nevertheless, when, within a decade, three supernovae were observed in galaxy NGC 3190, lots of people put bets on that galaxy for a fourth explosion. That’s how government budgets grew and people’s electronic wallets shrank.

Other violent astronomical phenomena that eventually lent themselves to wagering included two kinds of gamma-ray bursters, the fast radio bursters, and ordinary novae (stars whose surface explosions brightened them but didn’t destroy them.) Gravity-wave events were too common to bet on, but there were wagers on the largest masses resulting from intermediate black hole mergers. Ingestion events (and even minor burps) by supermassive black holes – in the Milky Way Galaxy and beyond – were soon added to the list.

When a top government official on the Moon was caught trying to get advance information from the director of the Joint Lunar Observatories (whose son had been quietly caught in a compromising sex TriD by the local authorities), new commissions were set up to isolate gambling servers and rule-makers from political influence.

Humanity’s addiction to astronomical gambling only came to an end when a large rogue planet happened to approach a previously unknown, but rather massive, black hole that had been hiding, with no previous sign of its existence, in our section of the Milky Way’s local spiral arm. Once the material of the planet was disrupted and drawn to circle the black hole, as luck would have it, one of the resulting jets of relativistic-speed particles was pointed directly at our solar system. The accompanying gamma-ray energy, coming at us from the constellation of Canis Major, wiped out most of our colonies on worlds that were not protected by a substantial atmosphere. And it damaged the Earth’s ozone layer and changed the composition of our upper atmosphere. Darkened skies, acid rain, and copious ultra-violet radiation made the life of the survivors on Earth miserable for decades to come. No one had placed a bet on that outcome.

~

Bio:

Andrew Fraknoi is a retired astronomer, college instructor, and the lead author for “Astronomy,” the free, online introductory textbook from the nonprofit OpenStax project, which has now been used by more than 1.1 million students. He has also written two children’s books, edited or written a number of books for science teachers, and published seven other science-fiction stories so far. His colleagues have named Asteroid 4859 Asteroid Fraknoi to honor his contributions to the public understanding of science.

Philosophy Note:

Many studies have shown that, in making bets on unlikely events, we humans tend to overestimate our chances of winning, sometimes by huge amounts. Why do people bet? The anticipation of a big win gives us a shot of endorphins in our brain which allows us to associate betting with feelings of pleasure. Psychologists have come to understand the “Gambler’s Fallacy” – a cognitive bias in which we think prior outcomes of an independently determined wager will influence the next outcome. So, if you flip a coin and it comes up tails three times, you convince yourself that it now must come up heads the next time. For some people, gambling can become an addiction, very much like becoming dependent on the pleasure of alcohol or drugs. Many state governments in the US have taken shameful advantage of this addiction to fund services to their citizens, even including such vital things as education, through state-sponsored lotteries. In this story, I tried to imagine a future in which governments – always looking for new sources of funds that have few political costs to elected officials – allow and encourage people to bet on astronomical events.

Fiction

The Right Answer

by Cliff Gale

Other professors liked to say that Victor Mancuso the mathematician and set theorist “was lost in the labyrinths of infinity.” His entire adult life, both his profession and his hobbies, had been centered in The Concepts of Time, the title of his eight-hundred-page magnum opus. Mancuso attempted to analyze time from every available perspective, and then springboard from them to his own original theories. He availed himself of every known analysis from ancient Greece, India and China, to the most current journals of physics and cosmology. He studied from every angle: potential, actual, multi-functional, physical, astronomical, and even religio-philosophico.

Legend had it that he had spent years studying the vague mathematics of extinct cultures and that, though he didn’t get his answer, he had “gained certain mysterious powers.”

When he was in a religious mood he would tell the class, “The probability of life existing at all is only 1 in 10 to the 215^th, which might as well be zero, except it isn’t and there is life. This is considered by some to be a strong argument for the existence of God.” He refused to say whether he agreed or disagreed.

Mancuso worked within the framework of certain recurring words: absolute, limitless, continuum, endless, complexity, order, disorder, indefiniteness. These words often, more often than he wished, led him to words like inconceivable, incomprehensible, overwhelming, and, as he would tell a good listening ear, “even terror.” This in turn forced him to be caught up, for years, in distinctions and paradoxes, and he found that no matter how deeply he cut into his subjects, he could not get to a hard bottom, the type of hard bottom that Thoreau recommended as a place to stand. Mancuso could find no such place to stand. Time was a non-linear flow without beginning point or end, and he couldn’t escape it, or go backward, or forward. The future did not exist, except as an idea, and the past was unrepeatable and generally unknowable. You can never step into the same river twice. No, Mancuso could find no solid place to stand.

So, he sat instead. He sat in his gray fake-leather office chair over his brown walnut-veneered desk with its polished brass study lamp. His posture worsened over the years, hunched over the crowded workspace under a single low-watt bulb, looking at papers, hundreds, thousands of them. His neck was bent forward enough to make a seasoned chiropractor squirm. “There is no end to these papers,” he would shout in dismay at times, when a student interrupted him for a good or bad reason. Sometimes he would take a stack or two and throw them up into the air in front of his visitor, making his exasperation demonstrable, and then quietly request the aid of the shocked or embarrassed student in retrieving them into a workable order. “The research must go on,” he would say, “We must never give up. Churchill was right about that.”

Mancuso’s favorite word was the Greek word apeiron, which allegedly meant “unbounded, infinite, indefinite, undefined, the original chaos of the universe, and a crooked line.” His favored symbols were the sideways figure eight, 00, which is the mathematical symbol for infinite, and the Hebrew letter alef, the alef-null. His favorite phrase from the Bible was, of course, “The alpha and the omega, the beginning and the end.”

He was troubled by the ideas of foreknowledge, predestination, and fate, but dismissed them to the realm of metaphysics, which he considered a circular trap. It was a trap he felt he had spent too much time in already.

The sign on his office door said, in his own bold calligraphy (his only other hobby), “What is an infinite thought?” Whenever a student came for some varied counseling appointment, he asked every single one of them this question, even if they had visited five times in a single day. Most of the students found this entertaining once or twice, but it quickly became irritating to most, an interference in their own mission, and a big time-waster. Mancuso never seemed to tire of it, and wouldn’t let them leave without answering, even when they had no idea what to say and had used up all their clever comebacks, and were forced to say something trivial. “That is stupid,” he would say. It was surprising he was never punched in the mouth. Probably the only reason he wasn’t was because he looked so frail one strike might kill him.

Forewarned by other weary students, I prepared an answer for my initial introduction, for showing off my own mathematical prowess, hoping to gain favor that might prove useful sometime along the road of my own education or career. I was determined to avoid getting trapped in one of the frustrating circular discussions the others complained of, and somehow escape the clutches of simple logic also. I needed something beyond a tricky Zen koan to put him off, that had been tried before and nobody ever won. Mancuso liked to watch students squirm in the chair after a few attempts at parrying with him; then he would finish them off with some version of, “If you are going to be a student of mathematics, or physics, or astronomy, etc. (for him mathematics was in every subject, somewhere at the foundation), you are going to have to think much harder.” If they were lucky, they would only get a short lecture on brain functions, which Mancuso still believed to be: Left Brain: Logic, reasoning, mathematics, words, time, linear thinking, and Right Brain: Intuition, creativity, images, dreams, spatial relationships, non-linear, and most important (for him), timelessness. He would say to each student, “Somewhere residing in your little-used brain is the answer to eternal thought.”

I bandied various words and phrases about with other students in the cafeteria and Student Union, preparing for our face-off. The most common suggestions were variations on: mystery, power, ultimate, god (only small g), Nirvana, things like that, attempting to be deep. All the fancy ideas had been tried before, more than once, and Mancuso was always unimpressed, so they whined. I was certain that was the wrong approach. I suspected it was better to say something more along the lines of “the speed of light surpassed,” or “ultimate elementary particle than cannot be further divided,” or even, possibly “the basic thought process at the heart of the universe,” or maybe even, “a mathematical Platonic Form from which all arithmetic sprung.” In my mind I could hear his voice – “That’s stupid.” I sweated over this for a week before making my appointment. But it was in a typical college town bar, drinking shots with my roommate, that the answer came to me. I would make the whole thing a joke, said with a very straight face.

#

When I walked through his hallowed mahogany door and stood before his small but intimidating desk, Mancuso immediately looked up at me with his crooked neck and, seeing that I was a new victim, asked, “Well, what is an infinite thought?”

I was ready, and here is what I said: “Emptiness does not, and cannot, resolve the linear/cyclical conundrum of time. The first set of thoughts, consisting of ultimate elementary particles, so to speak, being (in reality- consciousness) which surpasses the speed of light and is undetectable by any natural methods and can never be quantified in less than five dimensions, and unfortunately, we are trapped in four.”

I expected him to smile or laugh or say something like, “Where did you come up with all that bull manure?” (Mancuso was said to abhor bad language, calling it “a sign of a lazy mind.”)

Instead, he looked at me wild-eyed, as though he had been attacked, and asked me, “Does time end then?” and as I prepared to answer facetiously, but keeping my poker face, he went on to, “Does space end even if it is curved?” and next, “So you are claiming that subdividing does end in infinity so that infinity is then an illusion and not infinite at all and we’ve been chasing the wrong dog for centuries and I have wasted years of my life. I have to start over again. That’s what you’re implying! The problem is simply the limitations of four dimensions. But it can still be solved with math!”

At that moment I found myself sitting at his desk, and looking at myself. But I immediately saw that my hands were his, my clothes were his, and when I hobbled over to the mirror, I saw that my face was his. I had become Professor Mancuso – and I as quickly saw and realized that he was now me.

“I’m sorry for this, dear boy, but it has to be this way. You must understand, and listen to me very carefully now – if you run out of this room telling people I have switched bodies with you, no one will believe you, you will spend the rest of your life in an asylum, which you wouldn’t want. You must realize by your answer that you have changed my life, and your own, irrevocably. You have just handed me the keys to discovering the solutions to my lifelong quest, my lifelong questions, but I was old and my bent body wouldn’t last long enough to work out the proofs. I had to do this, have waited decades for this opportunity, thinking it would never come, but here it is. So now I, in your younger body, can continue my work, and you, in my body, can be grateful for the opportunity to sacrifice your life for such a greater cause. Not many students can say such a thing, though millions of people sacrifice themselves for the stupidest of causes.”

He went ranting on and on while I sat, weak and stunned, in his desk, unable to think anything clearly, but knowing that he had the upper hand. There was no place for me to appeal, no one would believe me; after all, I now had his face and body. I also heard him threaten me quite clearly: “Please do not make much of this. Be content to live my life for awhile. If you do try to upset the situation, remember, your body is as weak as mine was, and mine is as strong as you were. I only do all this for the greater interests of science, which you as a scholar should be able to appreciate. You know science requires sacrifice.”

Then I realized something else was happening to me rapidly, and I as suddenly understood that Mancuso knew it would happen. I was forgetting who I had been; I was becoming him, gaining his memories, and losing my own.

#

My name is Victor Mancuso. In my office is a perpetual fountain, only twelve inches high, and a perpetual waterfall, and a set of mirrors facing one another to provide an illusion (or reality) of infinity. I am a professor of Mathematics at a prestigious university in Europe, but I spend most of my time dissecting diagrams of geometrical shapes, or describing non-random fractals decipherable only to those able to grasp my explanations. I am a brilliant teacher, they say, but I know that somewhere along the line I have gone astray. I know that somewhere, sometime before now, I was on to something big, something that would have won me the Nobel Prize. Instead, that prize will be going to one of my former students, Alan Wintersen, who has found ways of explaining and describing infinity so that it has affected all other sciences and is filtering down into religions and philosophies. Good for him. He has invited me to attend the award ceremony as his guest of honor, since he says my work has influenced him. I am honored to go.

~

Bio:

Cliff Gale’s journey saw him in foster homes till age 18, various cults till age 42, as college kid from age 42-53, then he finished MFA Writing, retired lost, and adrift now.

Fiction

No Room At The Infinity Inn

by Richard Lau

Joseph had never seen Bethlehem so crowded. It seemed like an endless number of people was packed in the streets and surrounding structures.

But he had more important things on his mind. His pregnant wife Mary was about to give birth, and he could not find a place of sufficient space and privacy.

“I’m sorry, sir,” apologized the front desk clerk, “as I said, we have no rooms available. They are all filled.”

“How can they all be filled?” demanded the expectant father-to-be. “This is the Infinity Inn! It’s known for having an infinite number of rooms!”

“That’s true,” admitted the clerk. “Unfortunately, at this time of year, especially during the census, we have an infinite number of guests!”

“But…” started Joseph, struggling to picture that many people in a head whose capacity was twenty.

Beside him, Mary took a deep breath and released a slow, smooth sigh. She was well-aware of her husband’s penchant for stubborn argument and unnecessary discourse, particularly when he was tired and under pressure.

Joseph continued. “Doesn’t having so many guests make taking a census impossible?”

The clerk thought for a moment and then nodded. “That does make it more difficult. And the task does seem to take a while. But who can say when one census ends and the next one begins?”

Joseph was about to argue the point when his wife’s elbow nudged a familiar area in his ribcage.

Joseph leaned forward. “Well, we don’t have an infinite amount of time. Can’t you see my wife is pregnant?”

“Yes,” acknowledged the clerk. “Congratulations.”

“So, we really need a room.”

“I am not disagreeing with your need, sir. I am just unable to fulfill your request.”

Joseph tried another approach. “Wait a minute. In order to have an infinite amount of rooms, you have to be adding rooms constantly, otherwise you’d just end up with a finite number, isn’t that correct? It would be a rather large finite number but still finite!”

“True,” agreed the clerk, nodding his head. “We do have the continuous construction of new rooms. Fortunately, the guests don’t seem to mind the noise.”

“So, give us one of those rooms,” insisted Joseph. “One of the new additional rooms you’re adding.” He gave a “know-it-all” and “I-told-you-so” look at his wife.

She frowned, holding her protruding belly. Of all the inopportune times for her headstrong husband to get into a one-upmanship contest!

“I have to apologize again, sir,” said the clerk. “We have a waiting list for those rooms, and it is infinitely long. We can add you to the list, but it could take a while before we can get you a room, and, as you say, I’m not sure if your wife has that much time.”

Mary tugged on her husband’s sleeve, but Joseph had thought of yet another angle.

“All we need is one room,” Joseph said. “I’m sure with the infinite number of guests here, you’ll be able to find two guests willing to share a room for the good of a woman about to be in labor.”

The clerk at least tried to look sympathetic. “That may be so, but we’d have to speak with each guest until we find one who wants to move and then we’d have to continue contacting guests until we find one who wants to share their room. It is already too late to disturb our guests. And even if we tried, it could take quite a while until we found a compatible pairing. Plus, most of the guests might figure like you that with an infinite number of guests, some other guest might be more agreeable to moving or sharing, so why should they?”

Joseph had one last idea. “Look, with an infinite number of guests, you must have an infinite number checking out, right? Why can’t we have one of those recently vacated rooms?”

“My apologies again, Mr. Joseph,” said the desk clerk, “but along with an infinite number of departures, we also have an infinite reservation list for those vacated rooms.”

Joseph had a sudden epiphany: that at the Infinite Inn, the desk clerk also had an infinite number of rebuttals to whatever Joseph proposed.

Sullenly, the tired and worn-down husband turned to his wife and sadly confessed, “The manger it will have to be.”

An exasperated Mary, thrilled that her husband had finally had a change of heart and had seen the light, cried “Thank God!”

“Good luck getting there,” said the desk clerk rather snappishly.

Joseph had reached the end of his rope and was spoiling for a fight. “What is that supposed to mean? The manger is just down the street from your so-called infinite establishment!”

“Yes,” admitted the clerk. “But before you reach the manger, you must first go half the distance to the manger. And before you even reach that point, you must first traverse the halfway point between here and the halfway point to the manger. And go half that distance. And half that distance. And so on and so on. Each step covering an infinitely smaller distance.

“You have quite a journey ahead of you, sir. Good luck and good night.”

However, Mary and Joseph did manage to make it to the manger, where their baby was born.

It was indeed a time for miracles.

~

Bio:

Richard Lau is an award-winning writer who has been published in newspapers, magazines, anthologies, the high-tech industry, and online.

Philosophy Note:

Can one fully grasp the concept of infinity and wield it into a practical, understandable framework? And can the same be said of God? Or are both knowingly unknowable? This piece of speculative philosophy combines perhaps the most popular Christmas story ever told with The Grand Hotel Paradox of mathematician David Hilbert, with a bonus paradox thrown in for good measure!

Fiction

Nothing Could Be Something: A Parable of Sorts

by Robert L. Jones III

G. K. Chesterton once wrote that materialists address the easier questions posed by the universe, ignore the more difficult ones, and then retire to their tea. Accordingly, a particular individual of this persuasion discovered a problem inherent to his materialism. His conceptual universe consisted solely of matter, energy, and the forces that governed their operation, and it followed that his thoughts and his personality were nothing more than patterns of electrochemical impulses coursing along randomly evolved neural circuits. These explanations begged the questions of what all this really meant and from what it had originated. Accepted chemical and physical theory presented much for consideration.

#

Electromagnetic energy was made of photons which had no mass. Matter was composed of atoms which contained protons, neutrons, and electrons within spherical, mostly empty volumes. Protons and neutrons were combinations of quarks held together by gluons. Evidence existed that electrons, once thought fundamental, were divisible into spinions, orbitrons, and holons.

So everything consisted of particles of one kind or another arrayed in motion through empty space. Quantum effects allegedly produced the simplest of these from nothing, and this raised the disturbing possibility that everything had arisen from and was reducible to the same. Even the faithful have their doubts. Prone to introspection, the materialist examined his.

Mind was indistinguishable from body. Mentally as well as physically, he was a finite but ever-changing association of matter and energy, and this implied that he might be a manifestation of nothing. In arriving at this conclusion, he confronted his chief complaint against his materialism: nothingness was not enough.

Impenitent but searching for answers, he grasped for salvation through geometry. Euclid’s Elements became his nightly panacea, his “now I lay me down to sleep” before turning out the lights. The logic of this ancient work reassured him, for it reminded him of what he needed to believe, an inference both elegant and pure: nothing could be something. In light of this revelation, he considered the nature of pure geometric forms.

#

A point had no height, width, or depth. Being of no dimension, it was a position without volume or mass. It was the most elemental of geometric concepts.

A line was made of an infinite number of points. With length but not width, it occupied only one dimension.

A plane contained an infinite number of lines. Being flat, it possessed length, width, and area but no depth. From its infinite points, any two-dimensional geometric figure could be constructed. A circle, for example, consisted of infinite points, all at equal distances from a central point and all in the same plane. It had a radius, a diameter, and a circumference, and it encircled an area which was not intrinsic to its nature.

A sphere consisted of an infinite number of points at equal distances from a central point and all in an infinite number of planes, making it three-dimensional. It completely surrounded a volume but had no volume in itself.

Whether in one, two, or three dimensions, all of these forms and countless others were made of nothing and had no mass or energy, but they were real.

#

These considerations offered hope, and they culminated in a series of appearances.

#

At fifteen minutes before midnight, the materialist looked up from Euclid’s Elements. He rubbed his eyes, and there it was: a minute distortion in his field of vision. It reminded him of light passing through an imperfection in a pane of glass, and it appeared to be in the center of the room. He glanced in multiple directions. The visual distortion remained stationary, so it wasn’t in either eye. He blinked. The spot remained. He stood up, took a few steps forward, and passed his hand through it, but it was still there.

Geometric definitions flickered in his mind, and he suddenly realized what he was seeing: visual evidence of a perfect, geometric point. Because it had no dimension, only position, he wasn’t seeing the actual point. He was seeing an indication of where it was, somewhere within the tiny volume of altered wavelengths. This implied a disturbance of air molecules, a refraction of light, and it resurrected the spectre of nonmaterial causation.

The point began to move erratically but in a way that implied intelligence. Something had emerged into the air, and it evidently was assessing its environment. From whence had it come? Was it from an unknown universe, or had it arisen spontaneously, nothing from nothing but still something?

The point widened its apparent search. When it reached the far wall, it disappeared. The materialist sprang from his chair and ran into the next room to follow the peregrinations of his visitor. It had passed through the wall, which was not surprising given its absence of volume and mass. After careening about briefly, it disappeared through the ceiling.

#

Another visitation occurred the next night. Initially, the point didn’t move. Then it grew rapidly into a line resembling the seam between two fused pieces of glass. Reaching to and presumably through the walls, the line remained stationary and then shrank back to a point. Whatever was behind this activity seemed to be learning, and it had achieved extension and contraction in one dimension. Having completed this operation, the point vanished.

#

On the third night, the point reappeared, and it extended into a curved arc which quickly formed a complete circle. Motionless and resembling the margin of a lens without any housing, this figure hovered vertically in the approximate center of the room. The materialist stood up from his desk and walked slowly around the circle.

As he did so, the circle appeared to change into an oval, then a vertical line, and back to an oval. It was a circle again when he reached the back side, so it was stationary. The different shapes depended on his angle of observation. Again, he wasn’t seeing the circle directly. He was seeing only where it was, and the pure figure was invisible within that space. The entity behind its construction had achieved two dimensions.

The materialist moved back to view it from the side, but now it rotated on an invisible axis to follow him. This gave it a more ominous aspect. The roles of observer and subject ostensibly had been switched, and the circle reminded him of a hollow eye. He couldn’t explain why this bothered him as much as it did. Perhaps it was the sheer emptiness of the figure mixed with a sense of intent.

The circle didn’t collapse back into a point after this. Rather, it flattened into a horizontal line as if winking, and then it disappeared.

#

On the fourth night, the materialist woke with a start. It was not yet midnight. His room was dark and silent, but he knew he was not alone. Reluctant to turn on the light and afraid to leave it off, he wrestled with these options for several minutes. In a spasm of decision, he reached for the lamp on his nightstand and flipped the switch. Wavering on one elbow, he slowly turned his head.

The geometric eye was back, but it was larger. More than two meters across, the optical distortion filled the zone defined by its margin. It had become a circular plane with radius, diameter, circumference, and area. It reminded him of a colorless bicycle reflector, and its bottom was mere inches from the level of his bedroom floor. He abruptly pushed himself up into a sitting position and kicked off his covers.

The disk moved toward him and encompassed the foot of his bed. It moved across the mattress, reached his feet, and slowly began to pass through him. He slid backward but was stopped by the headboard of his bed. The bottom of the disk was obscured by his mattress, but he could see the top half moving up his legs and into his upright torso. It caused no pain, produced no pleasure. It neither injured nor invigorated, and its product was the absence of sensory effect.

Something unseen, something without a body, was experimenting. Beginning with none, it had achieved one and then two dimensions, and it had just finished examining a third. The next logical step would be for this nonmaterial intelligence to assume a three-dimensional form.

#

On the fifth night, the point grew into an arc and then a circle. The circle extended into a sphere. As the materialist walked around this newly created figure, the perfection of its form remained constant from multiple angles of observation.

#

On the sixth night, the point grew into a variety of two and three-dimensional figures, disappearing and reappearing between each new formation. These constructions became increasingly complex, and an idea occurred to the materialist as he watched. Was he being instructed? He wondered if ancient philosophers had invented geometry or if they simply had been shown.

#

On the seventh night, the point rested.

#

There were no further visitations. In their aftermath, the materialist often considered the phenomena he had observed, but the question of origins remained intractable to satisfying analysis. His interpretations repeatedly snagged on Plato’s ideal forms and Aristotle’s unmoved mover. This prompted him to wonder whether he was good enough for nothing, and whenever he engaged in these deliberations, he experienced a persistent craving for tea.

~

Bio:

Robert L. Jones III holds a doctorate in molecular biology from Indiana University, and he is Professor Emeritus of Biology at Cottey College in southwestern Missouri. His work has appeared in The Magazine of Fantasy and Science Fiction, Star*Line, Heart of Flesh Literary Journal, and previously in Sci Phi Journal. Samples may be viewed at concentricity.org.

Philosophy Note:

Since the age of fifteen, I have been intrigued by the philosophical underpinnings of geometry. In this story, I have mixed this interest with the concepts of nonmaterial existence, nonmaterial causation, and the logical consequences of materialism.

Fiction

Euler’s Equation

by Neil James Hudson

e

When I first met Euler’s equation, I thought it was proof of the existence of God. e, the base of natural logarithms, underpinning the whole of mathematics. i, the square root of minus one, the unit of complex numbers. π, the relationship of a circumference to a diameter, from which geometry is made. 1, unity, the foundation of all numbers. And we all know about 0.

e i π+1=0, said God, and there was light.

So when Euler’s equation fell apart, I knew we were in trouble. We held an emergency meeting at the maths department at the university, which was fast approaching a 0 of its own. But as long as we were still there and were still being paid, there was work to be done.

Professor Hazlitt chaired the meeting, the only one of us who had actually done any work of real note. “It seems to have happened at about 10:30 this morning,” he said. “Before then, the equation seemed to hold. But now, no matter how hard we try, we just can’t get the terms to fit together.”

“Could we just have missed a flaw in the proof all these years?” I asked.

Hazlitt shook his head. “The equation definitely worked yesterday: it was holding everything else together. But now something’s changed. Mathematics has changed.”

“Euler’s equation was the proof,” I said. “It was God’s covenant with mankind, like the rainbow after the flood. It said, the universe isn’t just chance, it’s designed. All the basic elements of reality fit together like a jigsaw. The equation is God’s signature, just to let us know he’s still here. But now the equation doesn’t hold; God has left the building.”

“Frankly, Dr Carlton, I had hoped for something more helpful,” said Hazlitt. “If we can identify the change, we may be able to rescue mathematics.”

“It’s not given to us to mend the universe,” I said, and indeed the meeting agreed to do no more than to monitor the situation.

#

i

But by the next morning, -1 had a real square root. It was its own square root, like 1. Multiply -1 by -1 and you got -1. This hadn’t happened before. Complex mathematics was wiped out at a stroke.

“This can’t be happening,” said Hazlitt, and I felt pity for him. Complex numbers had been his speciality, and now there weren’t any.

“Mathematics is our best description of the universe,” I said. “The universe is getting simpler. We’re winding down.”

“But isn’t there something we can be doing? Shouldn’t we be praying, or trying to, I don’t know, get our souls in order?”

“The game’s over,” I said. “It’s as if the exam’s just finished, and we’ve handed in our papers. You can carry on working through the problem if you want, but it won’t affect your grade any more. It’s too late to be good..”

“I don’t suppose you’re upset. This is what you’ve been waiting for.”

I allowed myself a small smile. “I didn’t expect it to be like this. Frankly, I don’t know what’s going on. I expected God to finish it, not wind things up. I think there may be another entity at large in the universe. If God can make an equation, I can only think of one being who could unmake it.”

Professor Hazlitt left angrily, leaving me to my thoughts. At least I now understood something that had been puzzling me. For centuries, people had been obsessed with the number of the Beast. Everyone tried to understand the number itself, but no one understood the real significance.

Before long, the Beast would be the only thing left with a number.

#

π

There seemed little left for me to do but to go home. I was depressed: I didn’t think I’d scored well enough in my own personal exam, and in any case I wasn’t sure who was in charge here. God, I felt, may have broken his own covenant, and if you couldn’t trust God, who could you trust?

Numbers were falling apart everywhere. Things that were supposed to be equal were greater than each other. The basic relationships that underpinned the universe had become exes.

Wearily I got in my car and started the engine. As I tried to reverse out of the car park though, the car juddered as if it were moving over a pile of rocks rather than the flat tarmac surface. I got out, knowing already what I would find.

The wheels were out of shape. It took me a while to see it, but the circumferences were completely out of proportion to the diameters.

Well, that’s geometry buggered, I thought. I could see no choice but to return to the maths department. Every shape I looked at seemed wrong, and I wondered how long it would take before the Moon fell down.

We had failed humanity. We were mathematicians; people should have looked to us for answers. Instead we just described everything, and expected it to work as it should. We had never looked at how to keep the system going.

I was interrupted by Professor Hazlitt, bursting into the room with panic on his face. “Dr Carlton, how many of us are there in this room?”

“Well, there’s me, that’s one,” I said. “And there’s you. That’s another one. So….that’s more than one.”

“But how many more?”

“Let me think,” I said. “There’s at least one more than one, but….how many ones are there?”

And then there was only one anyway.

#

1

Because everything was one. I’d been right, there were no other numbers left. There were no distinctions to be made between me and anything else: it was all one.

Before now, I’d often thought of the differences between myself and Jasmine. But now there no such differences. We were no longer separate, discrete, countable. We weren’t even we: we were I. Every atom that had ever joined with another was now the same atom. The molecules were just one atom. I myself was that same atom, and far from being a small part in a large universe, I was the universe.

Was I God then? All I knew was, there was no God other than me. That would imply a separate entity, another number. Another universe, in fact, to house another atom.

God could not exist to create the universe: God was the universe. The distinction could not apply. No distinction could apply. Could I see? I didn’t know. I couldn’t draw the line between what I was looking at, and the person looking.

I was total and complete existence. I stretched across the universe, engulfing all.

I had a bad thought.

Euler’s equation was collapsing, coming apart at the seams. Term by term, the universe had been unpicked until there was only 1 left.

But there wasn’t only 1 left. Even when 1 was all there was, there was still something other, something not 1. Even God had a Devil. And 1 had its

#

0

e i π +1=0, someone had written on the blackboard. “You’d better believe it,” I wrote underneath.

The numbers healed. From our non-existence we were returned to unity, then discreteness. Geometry returned to its standards, real numbers realised that they weren’t the only option, and finally logarithms returned to their natural ways, and Euler’s equation, the key to the universe, fitted together once again.

And I realised what had happened.

I was quite wrong to view the equation as a covenant. It was a warning. Everything was there: logarithms, complex numbers, geometry, real numbers.

And there, right on the other side of the equation for all to see, was a big zero.

When we had been non-existent, when everything had been zero, nothing had actually changed. We were still equal to all the terms on the other side of the equals sign. Those terms contained the universe. Which means:

The universe isn’t real.

In the beginning, God created the Heavens and the Earth. And this isn’t it. So to warn us, He gave us Euler’s equation. He fitted the terms of the universe together to show us that it all added up to nothing.

It’s easy to see our mistake now. The equation is three-dimensional. We can see the terms lying flat, but there are other equations at right angles to the equals sign. We can’t see them because they’re edge-on. What we have to do is tilt the equation so we can see the other three-dimensional terms.

These terms define the real universe. If we can unravel them, we can find out what the real universe is like. And if we can describe it, we may work out to get there.

Professor Hazlitt retired, dreading the challenge of the new mathematics. It doesn’t matter; ultimately, neither of us exists anyway. I have a new team, and we’re working to find the equations that describe the real universe. Somewhere, there is a world with a God, where real people can work and love. Where Euler’s equation doesn’t make 0.

And this time, we won’t just describe it. People look to us for answers now, and we will find them. With our constants and our mathematical relationships, we will find God.

~

Bio

Neil James Hudson is the author of around fifty short stories and the novel “On Wings of Pity”. His story collection “The End of the World: A User’s Guide” can be ordered from his website at neiljameshudson.net. He is currently working on a long series of vignettes under the title “One Hundred Pieces of Millia Maslowa”, some of which should be published in the coming months. He lives in the middle of nowhere on the North York moors, and works as a charity shop manager in York.

mathematics

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