Philosophy of Simplicity

It started on a cold winter morning. Sid Chesteburo, PhD, was experimenting in the cramped third-story studio apartment where he lived and worked—having converted his rented space into a functional, even if perhaps primitive,¹ laboratory—when he, quite by accident, synthesized an extraordinary substance. He had on two tattered turtlenecks, a stain-splotched knit-wool sweater, and a red muffler, all of which he wore snug beneath an old, oversized, spill-polka-dotted, unbuttoned lab coat with more than a handful of pens and pencils and gauges and measuring instruments crowded into its overburdened breast pocket's pocket protector. His range of motion was somewhat impeded by the many layers (with his arms at rest, he looked like a man mid-jumping jack), and he was damp with sweat beneath a flop-eared fur hat (though not because he was over-dressed; it was freezing. Sid just constantly perspired).²

But the surplus of clothing, though inhibiting and certainly not contributing to an appearance of scientific legitimacy (not that anyone but the suspicious and irascible landlord was ever around to be impressed), was necessary. See, due to the presence of various, possibly uncontained volatile gases, Sid was both unable to light a fire and obliged to keep the room well ventilated. So the window was always open (there was only one), and the fireplace flue, though there was never any fire, was always open, too. In the summer months, this safety system was almost unnoticeable. For a few days a year it was even downright pleasant. In the winter, however, especially in early February, it became a serious obstacle to protracted research.

So as Sid sat hunched atop his aluminum stool that morning, his legs just long enough to let his toes reach the crossbar where his restless feet were propped, his childlike hands must have been bright red with cold. He must have paused from his work now and then to warm them with his steaming breath. His pale blue eyes were vein-streaked and squinted. His movements were like those of a bird on a branch. He couldn't have changed much since I saw him last. Sid wasn't the type to change much. Loose skin hung under his eyes from lack of sleep. His long black lashes were almost girlish.

But let me stop right there.

Because before we get much deeper into Sid's story, I think a brief word is necessary to defend what I feel has been far too quickly dismissed by those in our community as a lack of professionalism on our eccentric former colleague's part.³ So before you jump to conclusions, know this:

It is not uncommon for a scientific genius, in the midst of his most significant discoveries, to interpret otherwise inexplicable findings based upon an unempirical and perhaps even seemingly illogical flash of intuition—based on something, you might say, in the gut. In fact, one is inclined to imagine this sort of thing is the norm when it comes to matters of profound metaphysical insight. Indeed, it may even be a prerequisite. I'm tempted to use words like divination, epiphany, revelation, and enlightenment—though I understand these sorts of religiously loaded terms only further cloud the issue. In any case, the important thing to acknowledge here is that Sid felt his discovery before anything else: somehow gutturally, somehow viscerally—he just knew.⁴

Now, if my mentioning this strikes some of you as incongruous; if you feel I ought to focus on the aspects lending academic credence to Chesteburo's findings and spell it all out in a lucid unassailable chain of consequence, then please know, I agree. I wish I could. As a scientist myself, I live and breathe cause and effect. Empiricism is essential to establishing facts and categorizing experimental findings; I'll be the first to admit that.

But what you must realize is Sid's discovery was, above all else, mathematic.⁵ Because it wasn't just that Sid lacked the impossibly expensive measuring equipment needed to test his hypothesis further. Even if he'd had access to the most advanced tools in science, he still couldn't have demonstrated what his intuition and calculations had already led him to know. He had only sensation and logic to rely upon. The best measuring device he had was himself. And so the empirical basis of Sid's work vanished along with him. What began as an abstract finding about an incomparable substance, will forever, it seems, remain abstract. Without experiencing the material ourselves, we (and I speak here for the scientific community) can never verify what Sid felt. Having been robbed of its referent, Chesteburo's data (which one could call the narrative of Sid's career) is irreparably suspect. So unless we can somehow seize upon the substance Sid himself tells us only became harder to define the more it grew, the truths of his work will forevermore rank amongst those of fiction.

Yet as those of you versed in theoretical physics must surely know, the loftiest support for the most revolutionary theories is, when you come right down to it, aesthetic. We can only observe so much in the measurable realm. At some point, the truth of what we see is only justified by what we feel. This is why we speak of beautiful equations and elegant theories; and what Sid stumbled upon that morning, which struck him first and foremost in his gut, heart, throat, and as an indescribable tingle drifting up his spine to spread across the back of his scalp, was most certainly, whether or not it was anything else, elegant.

Anyway, the point here is Sid's work had taken him beyond the traditional forms and accepted methodologies of scientific practice. So while the details of Sid's research are perhaps impossible to convey in a non-technical language accessible to readers unversed in the esoteric diction of subatomic particle physics and probabilistic quantum interactions, despite the ostensible convolutions of Sid's strange case, the idea at the heart of all this is remarkably simple.

You see, Dr. Chesteburo was a materials man. His life's work was synthesis. He tweaked, bonded, and manipulated molecules. Sid was an expert in crack propagation, a specialist in organic polymers (which his research rendered inorganic), and one of the few scientists in the world at that time actively developing biomaterials. Actually, it was ironic he happened upon the substance in question while pursuing the line of inquiry he was immersed in, because before all this started, Sid's goal was to create a more versatile substance than has ever existed. He was aiming for unprecedented elasticity, malleability, and tensile strength—something resembling a rubberized alloy gel: a material for which we don't even have a category. And Sid was making considerable progress that winter, even despite Christmas.⁶

He had become so optimistic, in fact, he was already working up an outline of the findings he hoped to publish in the coming months. He even sent me an email at the end of January (apparently just a week or so before the discovery) asking if I would edit a paper for him before he sent it out to the university journals. He gave a brief account of the substance he was in the final stages of perfecting, and it sounded remarkable. It was the first I'd heard from him in years. Of course, I said yes. But I never heard back.⁷

After the investigation, I had the opportunity to review that early outline (and still have it now, I should mention), and in light of the circumstances, found myself moved by several of the key metaphysical insights he felt the existence of his new material would make implicit. The similarities between his expectations for the substance he was looking for and the realities of the utterly unexpected material he found are uncanny.

So when I eventually typed up and circulated selections of Sid's work, I included some excerpts from that prescient outline. I was hoping to generate interest in the case and perhaps enlist some help in my efforts to discover what Sid was up to, with the final goal of trying to recreate his groundbreaking substance. Instead, it seems I only managed to provoke derision. At first, Sid's claims were met by his cynical colleagues (and there are many) as aggrandized and over-enthusiastic. Later, as more details started to get out, and a few people actually turned up to have a look at the notebooks, words like unhinged and farce began flying around. It became a joke. It even came to the point where my own reputation was being called into question. Apparently, it is just easier to deride whatever violates common sense than to recognize the potential truth of an idea threatening to upset the basis of a rationality you cling to.

As for me, I not only believe Sid's story, I feel his discovery was the single most profound scientific breakthrough since Copernicus described the movement of our planet. So the thought his work might just be laughed at and forgotten disgusts and deflates me in ways I can't begin to describe. I am thus far alone in that sentiment, however—alone in what more than a few colleagues have tactfully undertaken to remind me is an emotional reaction: an illogical, sentimental response to the death of a friend.

 

So let's focus on the facts. At approximately 0520 hours on February 6th, Dr. Sid Chesteboro sent a 1.5-volt electric pulse through his experimental colloid sample (we have all this from his own extensive account, which—though often digressive and at times illegible—fills 14 well-worn notebooks).⁸ When it received the two-second shock, the sample was a hue of diaphanous sallow-pink. It had slight irregularities of color saturation—probably indicating density inconsistencies—and was 3.26 mm thick. Spread evenly in the base of a 100mm diameter petri dish, its volume (as Sid correctly calculated) was 25614.285714285692 cubic millimeters. Chesteboro notes the sample displayed an almost negligible, though nonetheless visible, concave meniscus, indicating its slight adhesion to the glass.

That shock changed Sid's life. Its incredible affect on his experimental substance catapulted him into a state from which, it seems, he never recovered. The disk-shaped gelatinous sample...

...contorted in on itself, gathered, densified, drew itself uniformly toward some spontaneous nascent core—there are hardly words. A substance overwhelmed by cohesion. It became a sudden spheroid. Sudden, though not instantaneous: that seems unutterably significant. The transition was fast, it was efficient. But it didn't happen all at once...

For hours, Chesteboro observed. I see him in my mind's eye with his elbows propped on the desk, petrified of breathing too hard, afraid even his heartbeat might dislodge the miracle on the table before him. He was convinced it would fall apart at the slightest tremor. How could it be anything but unstable? How could it be? How?

We can't know how long Sid sat frozen there. He only spends a few cursory lines describing his initial reactions. But I'm sure it was a good long while; Sid was a patient man. Finally, though, unable to control himself any longer, Sid climbed off the stool and stepped back from the desk. He kept his unwavering gaze fixed on the sphere, vigilant for even the most miniscule change. He worried the slight gravitational displacement of his body retreating might unbalance the epiphanic object. It didn't. He worried that by withdrawing his body heat, he might bring the material crashing back down into liquid. But it kept its form as Sid inched back. Still, he feared a too heavy footfall might generate an obliterating tremor. He agonized. Sweat dripped from his forehead onto the floor. Finally, after an unbearable duration of slow-motion groping, he found his camera. His whole body ached.

He took the first photo (wincing at the shutter) from right where he stood when the found the old SLR.⁹ He snapped another shot with each tentative step forward. When he had taken several close-ups from all sides of the sphere, he put the camera down on the computer desk behind him, not wanting to disturb the surface his sample was on. In the photos (there is a full roll of 25 from that first day)¹⁰ it looks like a marble. It's not spectacular, surprising, or unnatural in any way. It looks like a small shiny marble.

And for all I know, it was a marble in the petri dish that day. They could be right, you know. I'll be the first to admit that. The questions linger.

Is all this just the wreckage of a schizophrenic delusion? Maybe. Was it the prank of an unstable man who spent too much time alone? I don't know. Was Sid playing an elaborate condescending hoax on the community that for years had ignored his accomplishments? Perhaps. Or was it an obsessive, off-balanced scheme of life-insurance fraud perpetuated by a suicidal insomniac scientist as a departing declaration of devotion to the woman he drove away, but never stopped loving? We can't rule anything out.

Yet I, for one, remain convinced.

In any case, the subsequent investigation never turned up any shiny marbles. After two years of grumbling, the insurance company paid Mildred what they owed. If it was a prank, Sid left no loose ends to tug at. The whole account remains airtight.

 

The sun had long since set when Sid worked up the courage to touch it. He decided, after much deliberation, to do so with his finger. If something so beautiful was about to come to pieces, he wanted to know what it felt like as it did. So he used the ungloved pad of his pinkie, deeming it the least callused digit.

Sid watched the sphere over his shoulder as he washed his hands. He knew he would need to touch the material at its highest point to keep it from rolling to the edge of the dish. It had formed in the exact center, and, so far as Sid could tell, hadn't moved since. He took a moment to slow his breath and calm his hand. Then Dr. Chesteburo reached out and touched it.

After so much trepid preparation, the moment must have been anti-climactic. "It feels as it looks," he wrote. "Like a hard, smooth marble; like glass." Sid didn't say much more about how the material felt. But in the days after his discovery, he dedicated long sections of his notes to the appearance of its particular, ponderous surface. It was a mirror. It was a mirror unlike any Sid had ever seen. He called it a "perfect reflector," devoid of impurity. Though Sid couldn't measure down to the nanometer, he felt certain the sphere was geometrically true: proportionate in each dimension.

As he points out several times in his notes, the substance seemed almost like glass. Yet rather than seeing through it, Sid saw himself when he gazed into the sphere. His tiny face, shrunken in the convex surface, stared back at him in a clarity he had never before witnessed.

Sid spent hours contemplating his face in the miraculous sphere. He said it reflected light with "absolute integrity." Though he had no instrument for measuring such a thing, he claimed each photon touched the sphere and reflected with perfect mathematic consistency, sending the unaltered image it carried back out in a new (exactly predictable) direction. The sphere's smooth, uniform, and uninterrupted surface encompassed a 360-degree view of everything around it.

Sid prodded the orb three times with his smallest finger. Then he gave it a tentative pinch between his forefinger and thumb. It felt solid. So he nudged it with the nail of his middle digit. It rolled, and clinked against the edge of the shallow glass dish. Nothing happened.

Emboldened, Sid spent the next half-dozen hours examining the sphere: rolling it, weighing it (it was incongruously heavy), measuring it, submersing it in water, scraping its exterior, testing its reactivity against chemicals of wide-ranging PH, introducing it to powerful magnets, and even heating it over a blue Bunsen flame (which, out of respect for those aforementioned gases, Sid lit on the windowsill). His astonishment grew as his tests grew more vigorous. So at last, sometime in the early morning after yet another sleepless night, Sid raised the marble-sized sphere above his head and dropped it to the floor—just to see what might happen.

It cracked the tile. It didn't bounce. It didn't tremble. Sid was incredulous. He couldn't believe it. He needed sleep. He picked up the heavy sphere (it seemed heavier), placed it back in the petri dish where it formed, collapsed fully clothed into bed, and slept for the next 12 hours.

 

It was dark when Sid woke with a sudden realization. It was obvious! How had he missed it before? He rushed to his desk. His thoughts had coalesced in sleep, revealing everything. He sat down and uncapped his pen. One, he thought. One...

Sid was groggy. He groped for the next idea: for the language and logic of an understanding that had reached him without either. He flipped through his data, scanning the pages, trying to settle back into the truth he felt with such certainty upon waking. He stopped. His eyes fixated on (C). He ignored the equation it was involved in, and studied the symbol: (C). Carbon. Sid flipped to a blank page. He stopped at the first empty line. His smoky intuitions began to condense. He wrote down the atomic mass, 12.0107 amu, stared at it for a few thoughtless moments, and began to write, fast and fluid.

The notes he took that evening (and late into the next morning) are erratic, often circular in their apparent reasoning, remarkably dense, and almost unreadable. They span some 16 pages and are webbed in an intricate maze of arrows, underlines, circlings, crossing-outs, and obscure technical diagrams. So I will save myself the embarrassment (and you the confusion) of trying to sketch even a vague linear progression of Sid's logic, and instead just focus on a few of his most incredible conclusions.¹¹

So far as we can discern, Chesteburo was able to calculate—based on known atomic masses, approximate nuclei diameters, and the initial properties of his already meticulously examined experimental solution—the approximate number of atoms in his original sample. The colloid—being more or less amorphous, unstable, and given over to easy state change—consisted of bonds that were, to put it rather simply, loose. The atoms were in flux, leaving the material free to shift and sprawl as the molecules arranged themselves in whatever form was most congenial to gravity and the shape of their container.

Now, for the sake of referencing a familiar touchstone, recall water expands and crystallizes when frozen. It becomes less dense as the H2O molecules arrange themselves into a grid, so that each molecule is held in firm place, while empty spaces form in the gaps between columns and rows. And although most materials become more dense when transitioning from liquid to solid, every known material nonetheless manifests cavities as its molecules "snap to grid."

But Sid's material was different. It condensed in a way no known substance ever has. There is simply no precedent for that type of bonding: one that could form a spherical solid like Sid's. First of all, though many materials densify as they solidify, even in the most extreme cases they only do so by about seven percent. Yet one of Sid's earliest measurements shows his material's volume contracted by almost 89 percent! What's more, his calculations go on to conclude the molecular arrangement (regardless of how it might have been revised by the electric shock) must have been devoid of cavities to fit into such a small space. Because the object's mass remained unchanged, Sid felt confident no atoms had been ejected during the phase change. Yet as he quite well knew, an absence of molecular interstices is not even conceptually possible, because molecules and the substances they combine to form—being compounds of many atoms, no two of which can occupy the same space at the same time—necessarily manifest divisions in the very connections allowing us to define them as compounds.

So in a final test (which I must admit seems to have been more symbolic than empirical), Sid removed the diamond from Mildred's wedding ring¹² and attempted to score the surface of the sphere. When he chipped the diamond, he dismissed the notion altogether his material was molecular.¹³

This is quite a claim,¹⁴ and certainly not one to be taken lightly. But with neither an x-ray photoelectron spectrometer nor an ultrasonic density sensor with which to conduct further testing, Sid could go no further with established empirical methods. So even if we do take his word for it (and we'll have to), we must admit beyond this point he was going on little more than abstract math and his own intuition.

Yet his assertion—made with such confidence, despite a lack of empirical support—not only implies all the molecules had disappeared from his material; it also means all the atoms had vanished, too. It means whatever force was strong enough to form the sphere in the first place had also been strong enough to fuse together the atoms into a single, homologous, sub-atomic substance. It means the protons and electrons were driven together by such a tremendously overpowering combinatory pressure, they canceled each other's opposing charges, obliterated the disparities defining them as disparate entities, and became a contiguous, neutrally charged body. Sid felt the object in his petri dish was the densest stable material to ever exist on Earth.

But although it was a first for our planet, Chesteburo also knew such a substance was not unprecedented in our universe. In fact, when stars collapse, they sometimes do about what Sid describes having happened on his desk. When the core of a star "runs out of fuel" and can no longer generate sufficient radiation, its tremendous gravity overcomes the quantum degeneracy pressure holding its particles apart, and it implodes. In some cases, this implosion creates a phenomenally dense ball of neutron matter, something we call a neutron star.

For the present discussion, it's not necessary to know much about quantum degeneracy pressure or neutron stars. But you must understand there are countless reasons a neutron star, no matter how small, could never form on Earth—the most relevant being a teaspoon of neutron matter would weigh about the same as a mountain range in our atmosphere. It would likely be so dense it would drop like a rock through air, straight down to the molten core of the planet. Not to mention the gravity of such a staggeringly massive object would absorb the whole city block and presumably alter the Earth's orbit as it fell.

Sid knew all this. So he also knew he didn't have a marble-sized lump of solid neutron matter. But he did still think he had neutron matter.

Sid claimed his substance was wrapped around nothing. He felt the sphere was empty inside. He felt the shell of his sphere was so thin, its component parts wouldn't be visible even under the most powerful microscopes in the world today. Though he didn't have one, Sid was confident even an electron microscope would have revealed nothing but a smooth, uninterrupted surface. He said his substance was the closest thing to a singular object to be touched by a human hand or seen by a human eye.¹⁵ He didn't need an electron microscope or an x-ray spectrometer to tell him what his calculations had already shown him was true. There were days when he held the proof in the palm of his hand. The neutron matter composing his sphere was a unity enveloping an emptiness. It formed in the shape of a shell so thin, it was no more than two neutrons thick at any given point.

So although I've always felt numbers like these are too small to be given form by imagination, except in the most basic comparative sense, the crust of Sid's sphere was about 4.4 x 10^-15 meters thick.¹⁶ The wall of an ordinary soap bubble is somewhere in the neighborhood of 5 x 10^-7 meters. And yet, even with such astounding thinness, the marble still weighed about a kilogram more than a proportionately sized lump of solid lead. Furthermore, whereas Sid's early calculations showed about 89 percent densification when the material changed state, if the sphere was indeed hollow, it meant the shrinkage was well in excess of 99.9 percent.

But let's turn our attention now (having deciphered what Sid felt his substance was made of) to the more important question of how such an object could possibly be stable, because the only thing more extraordinary than the material's existence is the thought of its persistence: its ability to endure through hours and days and weeks.

Apart from Chesteburo's work, science can only name two forces capable of compressing matter into the density Sid describes: the gravity of a collapsing star and the violently collided kinetic energies of accelerated subatomic particles. Experiments in hadron colliders have produced similarly dense material, but it always diffuses within a fraction of a second. When stars collapse, the by-product is a supernova.

So it seems rather improbable a jolt from Sid's AA alkaline battery was enough to do the trick. It also seems a bit far-fetched Sid's tiny shock could have condensed the matter so cleanly.¹⁷ Yet even despite all this, the material's shape remains the most improbable aspect of all. The notion of a hollowness at the core of a material that must have been compressed by forces of a magnitude strong enough to collapse stars is almost unthinkable.

Yet, for this, too, Chesteburo had an explanation. He wrote in shorthand, in small print, in the margin of one of his pages, that compression played no role in compacting his substance. Rather, he posits (or not even posits, really—asserts is what he does, avers) an implosive force, an infolding force—"a power of singular attraction," he calls it at one point. He felt the only reasonable conclusion was every neutron was accelerating at every moment toward a single central point at the core of the material. Sid claimed the gravitational appeal of whatever was (or wasn't!) at the core of his sphere was infinitely more powerful than any known force ever encountered on Earth. The neutrons were drawn irresistibly toward each other, and thus bound to each other, by neither mutual pull nor external pressure. Instead, they were brought together by a shared attraction to a singularity outside them (or if you consider the sphere as a unity, inside it). In one of the many apparent contradictions central to Chesteburo's work, he seems to claim the emptiness at the sphere's core predicated the solid substance of its crust. He felt nothingness had the power to define substance.

So by virtue of this "overwhelming attractive force of emptiness," each neutron of the tight-packed substance was accelerating along a unique vector, while corresponding to another neutron moving in the opposite direction along an inverse vector. Each particle was drawn along a different path toward a single, unfixed (recall the sphere could be moved) point: an infinity of vectors converging into singularity.

And yet the hollow sphere had not collapsed. The particles had not collided and recoiled. There was no explosion, no implosion, no apparent justification for the unfathomable suspension preventing the sphere from scattering sub-atomic shrapnel throughout the lab in a disastrous, irradiating blast. The Earth went on orbiting the sun. Sid went on writing his notes. He went on with his bold experiments, confident in an inexplicable force constant enough to counter the inexplicable attraction giving shape to his miraculous substance.

He felt a repulsive force was at work inside the sphere. He felt alongside an attraction forceful enough to bind neutrons into a density that could only be increased by the obliteration of neutrons themselves, there was a proportionate force exerting itself in opposition.

As the sun peaked above the rooftop of the building across the street and morning poured in through his lab's sole window, Sid began limning an idea whose simplicity seems far out of proportion to the seeming complexity of the sphere. In the last of those long, uninterrupted hours spent buried in analysis and postulation, as his labyrinthine math trickled out into a stream of philosophical musings, Chesteburo turned his attention to the repulsive force preventing the material from further collapse and introduced a dichotomy central to his later theories.

In the header of the last page he wrote that day, Sid scrawled, "Opposites are complements." I have the impression his handwriting shows relief. I imagine him sitting back in his chair and taking his first deep breath all day. Anyway, the notes become lucid—so perhaps the sigh was my own—and midway down the page, Sid veers into unexpected poeticism. "Emptiness is the root of repulsion," he writes, "substance is the bloom."

Just as he claimed the opposition of matter and emptiness created an attraction strong enough to fuse protons and electrons,¹⁸ so too, did he feel the continuity of matter and emptiness gave birth to repulsion. Because the sphere's shell was not perfectly dense, Sid knew it contained emptiness. When the hollowness inside each neutron drew close enough to glimpse itself in the sphere's vacant core, it recoiled.

The last thing Sid wrote in his notebook that day was:

ONLY CONTINUITY ALLOWS ATTRACTION TO BEAR SEPARATION.

He drew a thick box around these words, put a string of asterisks beside it in both margins, climbed back into bed (still fully clothed), and slept. Apart from his test with Mildred's diamond, Sid hadn't touched the material that second day. He took no measurements, conducted no formal examinations, and made no other experiments. He only glanced at it now and then, there on his desk in its petri dish, whenever he paused from writing to stretch a cramped hand or collect the words of his next thought.

 

Hours later, Sid woke in high spirits. He was hungry. He couldn't remember when he had last eaten. He sauntered to his desk, wondering what he would order at the diner down the street. It was late, but they were open. They were open all night. Sid yawned and sat on the foot of the bed to lace his tattered sneakers.

Then he glanced up at the desk, and the blood drained from his face. He sat frozen in a cold wash of fear, with his fingers gripping the laces of his left shoe, for what he later wrote were the 20 longest minutes of his life. The sphere had doubled in size. It was about to explode.

But as Sid waited for The End, which moment after moment never came, his poised fear subsided. His curiosity grew. If it were going to explode, it would have exploded already, he reasoned—and things would be worse if it shrunk. So Sid picked up his calipers and measured the sphere. Its diameter had more than doubled. Its color had changed. It was a tinge darker now, and less reflective. Some of the crisp color had seeped out of the image shining back at him from its smooth surface. Its clarity had faded. Sid looked at his face, looking back at him from the convex surface. He seemed less defined than he once had.

Sid inspected the sphere under the microscope. He weighed it on the scale. He found no other changes. The substance was as stable and impervious as ever. So Sid went out to eat.

He was gone an hour, he writes. When he returned, he conducted another battery of measurements and documented another slight increase. Every hour, on the hour, for the next 20, Chesteburo took a new set of measurements. The sphere grew and grew. It expanded erratically: sometimes growing fast in short bursts, other times passing hours almost unchanged. Sid's diameter graph from that fourth day weaves along a jagged upward slope.

An hour after the sun set at the edge of another long day immersed in work, in a rare mood, Sid spent an hour listening to Brahms. He sipped a few fingers of cheap scotch from a chipped mug and watched the sphere. It was gorgeous, he writes. He rolled it in his palm. He tossed it up and caught it. He tapped it with his pen, put it up close to the pulsing speakers, and even balanced it on the back of his hand. He would have loved to be deft enough to spin it on his finger. And though he doesn't mention it in his meticulous notes, for some reason I can't help but think Sid spoke to the sphere that night. I imagine he said more in that hour than he'd said aloud in months—telling it things he'd never told anyone.

When Sid finished the scotch, he turned off the symphony, switched off the lights, and went to sleep.

 

Over the course of the next week, Sid charted the orb's inconstant growth. It was changing every minute. He found it grew faster when he played music, faster still when he contrived ways to keep it moving.¹⁹ Yet, despite the growth, Sid measured no change in mass, and thus no change in volume. So the material was getting denser. The walls were thinning. This made Sid uneasy. The hollow space was growing all the time. The sphere had become an expanding emptiness, surrounded by impermeable walls—walls that, by the tenth day after its spectacular formation, had thinned to less than a neutron thick.

It meant the neutrons had fused. They had vanished into a substance more basic than neutron matter—a substance with one less level of division, one less level of definition. Repulsion was overwhelming attraction. Neutron matter was quark matter now. Density approached its limit.

Dr. Chesteburo saw himself reflected in the sphere. He made pages and pages of sedulous calculations. He knew the walls could only get so thin. The sphere could only grow so wide. He estimated the expansion would reach its limit when the diameter swelled to somewhere just past eight feet. Beyond that Sid couldn't say what might happen. The sphere might pop like a bubble and diffuse into non-existence. Or its end might mean something worse.

As the days passed, compounding Sid's fear, the sphere got darker. At first, it took on a tinge of lucid pale blue, like a windowpane seen from an angle. But it soon turned a blue unmistakable, even at a glance. It was almost as if light itself was somehow changing the sphere. Perhaps, thought Sid, the more light touched its surface, the less light it gave back. "Daily it becomes more unique," he wrote, "more alone in its individuality, as the image it gives back looks less and less like the one it received."

The sphere's color changed in proportion to its expansion. The blue got deeper, richer, and harder to ignore. It imposed itself on whatever glinted in the face of the substance. It saturated whites, gave yellows a hint of green, and purpled reds. Sid looked into the sphere and reveled in the colors of the lab changing, the hue of his own skin different each day, and his eyes becoming an ever more brilliant azure. Yet all the while the substance was drifting toward black. It wasn't long before Sid could hardly see his own distorted reflection in its surface, where once he had seen himself so clearly.

He agonized over what might happen when the substance went completely black. "Darkness is the end of density," Sid wrote, "when each of the innumerable points comprising the sphere's surface becomes so dense its volume vanishes to nothing." Sid knew the material's particles would finally fuse to such an extent, reach such a degree of closeness, that the term "dense" would be stripped of meaning. He knew at its limit, density reaches a razor's edge, an apogee straddling the line of density and something like anti-density, beyond which the signification of dense inverts. It turns inside out. Science calls this singularity. Sid wasn't so sure. He tried to imagine standing outside something infinitely dense. He tried to imagine an infinity of miniature black holes in the shape of a hollow sphere in his apartment, each so close to the next, the concept of contact was rendered irrelevant by the continuity of an infinity and the disappearance of a surface capable of touch. Only weight would remain. Only attraction's darkness.

So Sid stopped playing Brahms. He stopped touching the sphere. He put the calipers away, and his quantified data disappeared into pages and pages of visual observations. His science became prose. As the days wore on, and the sphere grew, Sid stopped experimenting altogether. He watched the sphere; and as he did, he saw himself fading into blue obscurity. Sid worried. He waited.

And though eight feet was still a long way off, the evidence of its approach was harder to ignore each day. The sphere took up more and more of Sid's space—both inside his mind, it seems, and out. He woke each day to a bit more darkness. Every instant a few more photons touched the sphere's shell, and refused to shine back. It was this feeding Chesteburo's fear most of all. It was the sole aspect of the substance he felt at a complete loss to explain. He had no theories. It was simply happening. That was all Sid knew. The sphere was giving back blue light—though a fraction less with each passing second—while it swallowed up the rest of the visible spectrum with a hunger that, as Sid watched, only increased. The sphere was changing color. Sid sat upright on his stool and looked around the room. His lab, his apartment, his home, seemed dim.

 

At the end of the sphere's first month, when Sid took the last of his quantified data, the substance had thinned to quark matter. And though we know little about quark matter, we know it can't absorb light. Only a black hole's attraction is strong enough for that. Otherwise, we have to revise all we know about ultra-dense matter. And Sid flatly rejected the notion his material contained black holes. He was confident it was uniform at every point. He was sure it was so dense, light could not pass through and get trapped inside.

Yet Sid watched his reflection fade little by little each day. He found less and less light in his lab—and more darkness. He couldn't imagine why.

 

On the morning of the 33rd day after the sphere's astounding formation, when the substance had swollen to roughly the size of a baseball, things took a turn for the bizarre. For the sake of convenience, cleanliness, consistency, and perhaps a little superstition; Sid kept the sphere in the petri dish, even as it grew. The material wasn't getting any more massive, so there was little risk the dish would break. Besides, the petri dish kept the sphere from rolling off the table. Anyway, Sid was sure the orb was in the dish when he went to sleep that 32nd night. He was positive. He remembered.

Yet when he woke, the dish was gone. The material was on the desk in the same spot, but the dish was gone. There was no broken glass. No movement. No trace.

The front door was locked. No one could have climbed in through the third story window. Nothing else was missing. The petri dish had simply vanished.

Sid was flustered. He examined the material, but found "nothing unusual." His notes tell us he sat on his stool with his chin in his palm in a sort of exasperated depression for two and a half hours, watching the sphere and contemplating his sanity. Then he went to the diner across the street for breakfast. It was 9:00 a.m., March 11th. He left the sphere on the tabletop, untouched. It hadn't stopped growing.

When Sid returned, he couldn't find his favorite pen. He looked everywhere. Finally, he used his second favorite pen to report in his notebook his favorite pen had gone missing. He rarely misplaced things. It was 11:45.

Over the course of the next two weeks, more went missing. At first, it was just small things. Paperclips, pens, test tubes, Erlenmeyer flasks, and a pair of digital calipers. Then an empty pad of paper. One sock. The fridge magnets.

If handwriting is any indication, Sid was agitated. He stopped sleeping again. He took photos of each object in his lab, trying to ascertain whether or not they were moving, trying to document each vanished item. The list is extensive. He searched the sidewalks and gutters around his building. Neighbors saw him sifting through trash. He put down strips of tape to mark the outlines of things on his desk. The tape disappeared. He made meticulous, obsessive charts of the times and relative positions of each vanished object: spent ten pages trying and retrying to find patterns. Most of the math is incomprehensible. The diagrams spiderweb into all corners of the page. He kept his notebooks with him constantly. Some part of his body was touching them at all times.

Sid was convinced the substance was absorbing its environment. Internalizing it. But without getting more massive. He spent hours staring at inanimate objects, fighting sleep, tortured by trying to keep his dry eyes open. And yet the instant he blinked or nodded off, another coffee cup went missing—another rubber band.

I asked the waitress at the diner one day if she had noticed Sid acting odd in the weeks before his disappearance. She said she'd already told it to the cops: she might have worried if he'd ever acted normal.

It was a Tuesday, the sphere's 49th day, when Sid's bed disappeared. The desks went several days prior. He woke from a rare nap, shivering (though fully dressed), on the cold floor. The sheets and mattress and comforter were all gone, too. The sphere's diameter was about three feet. It had taken on a deep shade of blackish blue: the color of sky on a moonless night.

 

But even as the contents of Sid's life vanished around him, it seems the disappearances were the least of his worries. Each day the hollow space at the heart of the sphere grew wider. Each day the walls got thinner. Sid treated the sphere with more and more care, almost as he had in the beginning, terrified by the thought it might finally spread itself too thin and break. Even with the lights on, the lab was dim. So Sid kept them off. He pulled the shade down over the window, not wanting the substance to swallow up any more light than it already had. It was consuming everything around it. Sid knew it couldn't be long before the sphere took in one piece of the outside world too many, and shattered itself into non-existence.

In the last filled pages of his 14th notebook, Sid sets science altogether aside. His writing takes a spiritual turn. He saw the sphere nearly touching the ceiling of his almost empty room and felt the end. Sid felt the emptiness at the sphere's core was pure. Sacred. He called it "a space unlike any other in the physical realm." He was tortured by the thought of its violation, by its impending exposure to everything still outside it.

In the last days, there was nothing left in the apartment but Sid and his sphere. The pictures on the wall had long since vanished. The wallpaper was disappearing in long, sudden strips. The last light left was blue. One day Sid looked into the sphere and couldn't see even the shadow of himself in its cold dark surface. The substance had grown so big, Sid had to turn sideways to tiptoe past on his way to the toilet. Its diameter had passed eight feet.

Sid kept all 14 notebooks inside his lab coat, under his sweater, tucked in the waist of pants three sizes too big and cinched to his pale flesh with an old leather belt. As his clothes dwindled, the cold crept in. Sid shivered. His teeth chattered. He reassured himself spring had just arrived, and warmth was soon to follow. He went out four times in the last six days to buy new pens. It was finally so dark, Sid couldn't see the words he wrote. They stray off the ruled lines and crowd in upon each other.

On April 8th, the 61st day after he discovered the sphere, Sid made his last notebook entry:

Perfect density—which is absolute unity, too—is pure attraction. Pure attraction is instability. Need: something like loneliness. That which becomes singular can no longer be. Therefore, need gives matter shape. Loneliness is why the universe expands beyond a point. We draw in whatever we can cling to. We cling to whatever we can.

If one reaches out and finds nothing left, one vanishes.

The night waitress said Sid must have slipped out when she wasn't looking. She never saw him leave. He left his notebooks in a pile on the diner counter, along with what he owed for the coffee and a $23 tip. It was the last money Sid had left. In her statement, the waitress remembers thinking it was the least he could do after coming in two nights in three days with no shirt. But Sid was a regular, and the waitress knew how he was. So she hadn't said a thing. She'd just smiled at him like she always did when she refilled his cup. That night, he even smiled back.

 

¹ Unlicensed and in gross violation of what Sid called "innumerable superfluous, elitist, research-staunching municipal statutes."

² He told me once his heart rate was so much higher than the average adult male's, his somatic systems were forced to work overtime to expend the extra energy produced—an anomaly he also felt explained the myokymia, his incessant foot-tapping, and the pen-chewing propensity.

³ Which, after all, is why I'm reaching out beyond science to this wider audience. I suspect you have more in common with Sid than his own peers ever did.

⁴ And while it certainly is, as so many have rushed to point out, convenient that Sid's sensational hypothesis agreed exactly with his incredible and now unverifiable conclusion; that is no reason to dismiss the man out-of-hand as a fraud. If his work hadn't been so unprecedented, it wouldn't be so important.

⁵ Unfortunately, though, Sid never had time to organize his equations in a way even remotely accessible. So amidst hundreds of pages dense with erratic calculations in sloppy print and cryptic notation, the only moments of true lucidity are those when Sid's notes periodically give way to the prose of his remarkable conclusions, which, though cogent, reference a material now lost to the world.

⁶ An occasion he spent alone. His work in recent years, particularly since Mildred left, had been consuming; and he had allowed it to (or rather, had gone out of his way to ensure it would) cut him off from friends, family, and acquaintances. He worked best in isolation. He resented interruptions, distractions and noise; and could only socialize with a constant sense of oppressive guilt about the research time he was wasting. So that year Sid spent Christmas alone, working; and in the evening he became so intoxicated he accidentally overturned a workstation laden with titration tubes, beakers, and irreplaceable samples on his way to the toilet. Though he didn't destroy any of the expensive computer equipment he had been able to purchase a few years prior with the help of the last grant he would ever get—which would have been an utter catastrophe for Sid's work—the debacle caused considerable setbacks (not to mention a good deal of uncontained hazardous debris). It was one of the rare instances in Sid's life when he either engaged in dissipation or consciously experienced debilitating loneliness.

⁷ The detective later told me, apart from the waitress, that email was probably the closest thing he'd had to human contact in half a year.

⁸ After being given over to investigators by the night waitress, the notebooks were eventually released to Sid's younger sister, Celeste, who, remembering me as Sid's former university roommate and only friend (and not knowing what to do with them herself) passed the notes into my possession.

⁹ The fact it was a film camera in a poorly lit room hasn't exactly helped corroborate Sid's account.

¹⁰ He tells us he also shot several more rolls in the following weeks, but never got them developed. The film vanished before he could.

¹¹ Which appear sporadically in the last five pages, fleshed out in relative lucidity, underlined, and bordered in thick boxes emphasized with exclamation marks and emphatic arrows in the margins.

¹² She mailed it back to him in a plain white envelope without a note three days after she left, and Sid never sold it.

¹³ Though density and hardness are by no means correlated, Chesteburo's (somewhat suspect) reasoning was the only substance impervious to the most rigid molecular bonds (i.e. diamond's) was one with no molecules at all.

¹⁴ The sheer hubris and apparent absurdity of which was enough to lead the few scientists who actually took the time to review the documents I sent out to discount Sid's work as preposterous.

¹⁵ Yet although it was close, Sid knew his substance was not truly singular, because true singularity can only exist as a black hole: a mass condensed into the indivisibility of a single spacetime point. Black holes form when stars (much larger than those that condense into neutron matter), overwhelmed by the force of their own gravity, collapse to such a density, their volume is erased. They appear black because even light, if it gets close enough, can't run fast enough to escape their gravitational attraction.

¹⁶ But because the concept of fixed diameter doesn't quite have traction when we enter the strange realm of quantum particles, note this figure is based on an oversimplified classical model, and is intended for illustrative purposes only.

¹⁷ I.e., the lab was not obliterated, the neighborhood remains intact, and Sid went on writing his enigmatic notes.

¹⁸ Remember, opposites attract.

¹⁹ His rare moods were becoming common.