Interrogations in a Holographic Observatory
by Howard V. Hendrix
Somewhere between the perennial state and the apocalyptic individual lies the utopian society. It is, however, very nearly as difficult to distinguish the utopian from the perennial types of social organization as it is to distinguish the ecstatic from the catastrophic types of apocalyptic individuality.
-- from The Purgation Manual, Sixty Third Iteration.
“Grand Expurgator Cartaphila!”
As I was announced by the guard in the antechamber, two of the men, the District Chief Inspector and the second guard, came to their feet in the six-sided room beyond. Walking toward the table behind which the Inspector had been sitting, I saw that the prisoner -- hollow-eyed, lank-haired, unshaven -- was already standing.
In the gleaming surface of the ventillume shaft behind the table, I saw too my own reflection: wearing the black and red robes and bearing the flail of authority, a woman of a certain age in an age of uncertainty.
I took my seat at the table. As they also sat, the Inspector flicked aside the tails of his morning coat, while the second guard, hands still gauntleted, removed the morion helmet from his head. I shuffled perfunctorily through the prisoner’s documents. I had no need to read them in detail again. I knew the case more than well enough.
Standing before me now in his jailbird’s magpie plumes, the prisoner was a synaesthetic, epileptic, prodigious savant, among whose blessings and curses was the supposed ability to compute the n th digit of π without calculating the preceding n-1 digits.
No one in all the history of the Observatory had ever been able to do such a thing, yet this socially-maladroit nonentity insisted he could.
We in the Office of Purgation believed he was a charlatan -- perhaps one with an exceptional memory for all the digits of π calculated up to that time, but a fraud nonetheless. He struck us as at best self-deluded, capable of lying convincingly enough to fool both himself and others.
His devoted followers in the Piphilolog sect, alas, believed him to be their long-awaited Holiest Fool, Absolute Approximator, and Fullest Incarnation of π . Thoroughly beguiled by this pied cipher, they referred to his supposed talent as the “blessed affliction.” We of the Office began to suspect he might prove not only a fool, but also a dangerous madman.
As a practical person, I had never been much interested in debating whether the purpose of the Observatory was to approximate a hyperdimensional sphere whose center was everywhere and its circumference nowhere, or one whose circumference was everywhere and its center nowhere. I took the Observatory as I found it and, beyond the necessary formalities, did not much concern myself with how it came to be. Theometric speculations mattered far less to me than the fact that all the vastness of our security protocols – the fabric of our state, perhaps even the fabric of reality itself – had always been based in ciphers dependent on distant, incalculable decimal places of π . To all that, the prisoner potentially posed a most grave threat, whether or not he ultimately proved capable of the particular talent claimed of him.
The Inspector, reading from his own notes, got to his feet again.
“Prisoner 3.14159,” he said, casting a sidelong smirk my way. (Giving the prisoner that number had been my touch.) “What do you believe is the nature of this map room, and all others in the Observatory?”
“This room is a prison cell. As is all of the Observatory that you use in this way.”
“We don’t think so.”
“Then for you it isn’t.”
I nodded to the guard, who stood up and, with great vigor, hurled the prisoner to the floor.
“‘Thinking’ is why we’re here,” I said, nodding to the guard again, who hauled the prisoner roughly to his feet before releasing him. “We seek to determine whether you are mentally competent to stand trial. We will today range from the most common and concrete knowledge to the most abstract and specialized. Answer the questions, or things will not go well for you. What is the nature of the Observatory?”
The prisoner jerked abruptly from the shoulders, like a marionette who strings had been yanked.
“Some say the Observatory, also known as the cosmos, has always existed and will always do so, from everlasting to everlasting,” the prisoner began. “In their view, the Observatory is in some profound fashion also without, as in ‘outside of’, time.”
“Are there any grounds for this belief?” asked the Inspector.
“The rows, columns, blocks, and sheets of digits on the Observatory’s maps, through which we access and observe all things, do exist in numbers so vast it would take an eternity to count and chronicle them. The total number of the maps in the Observatory, too, is also incalculably immense, as is the total number of map rooms.”
“And the map rooms themselves?”
“Are endlessly repeated. Only the maps contained in each room differ. The floor of each maproom cell is the ceiling of the one below it, the ceiling of each cell is the floor of the one above it. Most of the ‘floor’ and ‘ceiling’ of each cell isn’t floor or ceiling either, but rather open space, an atrium or gallery flanked by a walkway wide enough for two people to walk abreast.
“Along the walls lined with the map cabinets, these storage units stand on the outside of the walkway. A safety railing, half average adult height, runs along the inside of the walkway. At the center of each cell is a ventilation and illumination shaft, about which wraps a spiral staircase or, more formally, a staircase in the shape of a double helix.
“The floors and ceilings of cells, the staircases, and the ventillume shafts all proceed upward and downward, apparently infinitely. Walls and antechambers of cells – and the map-room cells themselves, and all their components -- likewise repeat from side to side and diagonally, also apparently endlessly. Taken together, all of these, it has been argued, strongly imply that the Observatory is not only infinite in space, but also without beginning and without end in time.”
“Do you consider these arguments sufficient grounds for believing in both the infinity and eternity of the Observatory?”
“No. Over many centuries the argument that the Observatory was created has steadily gained adherents.”
“Endlessness in space not withstanding, those who believe in a created Observatory reason there must have been some beginning point in time before which the Observatory did not exist.”
“What is their evidence for this?”
“The ancient names for the map rooms, the Great Conjecture arising from the discovery of π, and all the places and things accessed through the maps.”
“Of those three, which do you consider the best argument for a created Observatory?” I asked.
“The more telling evidence involves π,” the prisoner said slowly.
“What evidence?” asked the Inspector.
“The ancient discovery that π, the ratio of the circumference of a circle to its diameter, arguably continues to endless decimal places – that is what eventually suggested the existence of numbers which might be expanded infinitely without ever repeating. This led to the Great Conjecture.”
“Define that, as you understand it.”
“The endless digits, on their endless numbers of sheets, in their endless numbers of map drawers, in their endless map cabinets, in their endless map rooms throughout the Observatory -- all are in fact digits of the never-ending and never-repeating decimal expansion of a transcendental and irrational number. That number around which the Observatory is constructed has, from the earliest days of the Conjecture, been presumed to be π, the first discovered number of its class. And, just as π has a beginning, a Primordial Digit, so too must the Observatory also have had a beginning.”
“You mentioned the construction of the Observatory,” the Inspector said. “Explain.”
“The idea of constructibility is at the heart of the arguments for why the Observatory was created.”
“π is irrational – impossible to express exactly as a fraction, like 22/7. It is also transcendental, that is, it cannot be produced via any finite sequence of algebraic operations on integers. Together these argue for the idea that π is not constructible: the circle cannot be squared.”
“Then it is irrelevant to the construction of the Observatory.”
“No! The area of a circle can be approximated by inscribing a regular polygon inside that circle and calculating the polygon’s area. The more sides the polygon has, the better the approximation. An infinite-sided polygon can be interpreted as an infinitely close approximation to the circle inside which it is inscribed, with the circle itself being the limit as the number of sides approaches infinity.
“As a result of the Conjecture, the Observatory itself came to be defined as the limit of an expression which contained the product of two expressions whose limits were themselves infinity and zero. Also as an infinitely close physical approximation to that mathematical truth. And as the fullest possible construction of the unconstructible.”
“What was the impact of this Conjecture, when it was first announced?” I asked.
“It fostered a golden age of contentment.”
“As π’s vast simulacrum, the Observatory made sense, had a purpose and a meaning – and with it, so also all things, since all things were to be observed and understood through the mental optics of π.”
“‘Mental optics’?” asked the Inspector.
“From ancient times, it has been known that focused contemplation of the digit-filled sheet of a map causes the digits to holistically transform into a three-dimensional representation before the viewer’s eyes. This mental-optic effect has generally been presumed to be either stereographic or synaesthetic. Under the latter theory, map images and, more particularly, sounds – even suggestions of smell, taste, and touch -- are the result of synaesthesia induced by the contemplation of the digits on the sheets. By means of synaesthetic overlay in the minds of the map readers, the tremendous calculation of π is interpreted as sensorial landscapes, seascapes, cloudscapes, even starscapes of other suns, other worlds – inhabited by other beings, like ourselves, yet not like ourselves.”
This discussion of origins and optics was all interesting enough, but was getting us nowhere. For all I knew, what we saw in the maps in which those beings were present might indeed be the past – their history, and perhaps also ours, as some theometricians have claimed. Perhaps they once lived in the realms and territories we experienced through the Observatory’s maps, but I was not particularly concerned with spelling the world backward. I decided to take a different tack.
“You are a Piphilolog, is that right?” I asked.
“Yes, that’s correct.”
“What are the spiritual obligations of Piphilologs?”
“In response to the suggestion that the Observatory might in some sense be meaningless--”
“Is this heresy part of your beliefs?” asked the Inspector sharply.
“No! Just the opposite. The failure, generation after generation, to find the Primordial Digit -- ‘The Three that is the One that is In the Beginning, The One that is the Three that is In the Beginning, Divine Whole Number out of whose superabundant grace in infinite remainder flows all that is’ – the centuries of searching, ending only in failure, led to the fear that the Observatory might in some deep sense be meaningless, as I said. Against that fear, our great mystic urged us, his followers, to become living Observatories. He said that, if we would only choose to see it, human beings were already incarnate approximations to the great constant π. As votaries, therefore, we practice the spiritual exercise of calculating, memorizing, and vocalizing π to as many digits as we are able.”
“You proclaim that π is everywhere, do you not?” I asked.
“We attest to the omnipresence of π. That is why we recite the raw numbers of the constant’s digits.”
“And the sacred poems your mendicant monks and nuns chant . . . ?”
“Are constructed under the principle that the number of letters in each word of the poem must represent a digit of π in the exact sequence in which each digit occurs. Our faith compels us to spread the message of the incarnation of π through any and all appropriate means, including poetry.”
“Has there been any other important response,” the Inspector asked slowly, “in opposition to heretical suggestions of meaninglessness in the Observatory?”
“The rise of the Consensists. Better known as Purgationists, or Downcasters. People like yourself, and the Grand Expurgator here.”
“And what do you understand our beliefs to be?”
“Consensist dogma calls for purifying or purging the Observatory of all ‘fictional’ or ‘counterfactual’ maps, those maps whose digits transform into texts or landscapes which patently contradict what is already known from many other maps.”
“And what do you understand our practices to involve?”
“When you learn from your ‘reliable sources’ that ‘questionable’ maps have been found, you decide whether or not the maps are heretical enough to merit being ‘committed to oblivion,’ cast down the nearest ventillume shaft.”
The Inspector glanced at me, and I nodded.
“Please spare us your mocking tone,” I warned him. “Let me tell you that, as an Expurgator, I have consigned many a map to eternal disappearance – and always with good cause.”
The prisoner said nothing.
“Allow me to tell you something you cannot know. Perhaps it will change your opinion of us, perhaps not. We have recently discovered vast regions of the Observatory where innumerable cells contain endless sheets of apparently random numbers for π’s decimal places which, when themselves transformed, show only endless sheets of apparently random numbers for π’s decimal places in other bases. Tell me, if you had made this discovery, how would you have responded to such a vertiginous prospect?”
The prisoner again said nothing. The guard behind him looked expectantly at me, as if he were impatient to punish the man severely for his impertinent silence, but I shook my head.
“We have decreed that all ‘other-based’ maps are to be abandoned in place and stricken from memory. What would you have done, 3.14159? Would you be fool enough to allow all hope of sense in the Observatory to be swallowed up in a vast sea of nonsense?”
The prisoner raised his eyes to stare into mine.
“So that is why you persecute us.”
“Given the enormity of π, given the vast numbers of unexplored map rooms in the Observatory, and of the unexplored maps in all those unexplored map rooms -- somewhere, among infinite maps in infinite map rooms, other sheets virtually identical to the ones you have cast down must still exist, not yet consignable to oblivion by you, because not yet discovered by anyone. And in all the long forever, there will always be such -- “
“Blasphemy!” cried the Inspector. I raised a finger and nodded to the guard. With one gauntleted fist he struck the prisoner hard enough across the face to drop the man to the floor, but that did not silence him.
“All your efforts to purge and purify the Observatory of erroneous maps will prove utterly futile,” he said, smiling oddly as he raised his bleeding face from the floor and wiped his bloodied mouth. “You must already know that. That’s why you’ve turned your attention to a task you might more readily accomplish: eliminating those of us who wish to make ourselves living Observatories.”
“Silence!” shouted the Inspector, before turning to me and speaking in a lower voice. “Expurgator Cartaphila, it is my considered opinion that Prisoner 3.14159 is competent to stand trial. And must.”
“I agree,” I said, nodding then signaling for the guard to haul the prisoner to his feet again, which he did. “Guard, call in the chartmaster. We wish to test the prisoner’s claims concerning his purported abilities.”
If apocalyptic individuals did not exist, it would be necessary for perennial states to invent them. Perhaps they always have done so, even if unintentionally. From our study of the maps, we see that Moses was as much the unintentional invention of Egypt as Socrates was the unintentional invention of Athens. Gautama was as much the unintentional invention of the Ganges kingdoms as Jesus was the unintentional invention of Rome. Gandhi was as much the unintentional invention of Britain as King was the unintentional invention of America, and so forth, through all the chronologies constructed from all the maps examined thus far.
-- from The Purgation Manual, Sixty Third Iteration.
Within moments the chartmaster entered the map room -- a small, bent-over man in the sky-blue robes and skullcap of a full theometrician.
“Prisoner,” said the Inspector, “name the digit at the fiftieth decimal place of π.”
The prisoner’s eyelids closed and the eyeballs beneath them twitched rapidly side to side, like the eyes of a man dreaming. He opened his eyes and pronounced a number.
The chartmaster consulted his sheets, on which were listed all the known digits of π, found the required decimal place, and nodded.
“Name the digit at the five hundredth decimal place of π,” I said. Again the prisoner’s eyelids closed and the eyeballs beneath them twitched rapidly side to side, again he opened them, again he pronounced a number, which the chartmaster again looked up and confirmed.
“Name the digit at the thousandth decimal place of π,” said the Inspector. The little ritual and its results were the same.
“Name the digit at π’s millionth decimal place,” I said – and again both the prisoner and the chartmaster played their accustomed parts.
“Name the digit at the two hundred trillionth four hundred twenty seven millionth decimal place,” said the Inspector. Again the prisoner’s eyelids closed, the eyeballs beneath them twitched rapidly side to side, he opened his eyes, he pronounced a number – but this time the chartmaster could only shrug his shoulders, unable to confirm or deny, for no one had yet calculated π to so many digits.
“Name the digit at π’s ten octillionth and thirty-first decimal place,” I said. Again the closed and twitching eyes opened, and the prisoner pronounced a number. Again the chartmaster only shrugged, unable to confirm or deny the number’s accuracy.
“He’s engaging in outright fraud,” muttered the Inspector. “He has to be!”
“Tell me, Pi Man,” I asked. “How do you accomplish your π place–naming feat?”
“I can explain it no more than a bird can explain its song.”
“Yet you believe your declaration of π, to whatever decimal place is called for, is accurate?”
“I’m as certain of that as I can be of anything.”
“Even if you can’t explain it?”
“Very well then. Name the digit at π’s last decimal place.”
I expected him to simply say there was no final digit, or declare some number to be that (and thereby prove himself a fraud), but instead he did something quite strange. Wracked by sudden seizure, he collapsed to the floor, spasming and twitching. The guard glanced rapidly around the room for something to thrust between the prisoner’s teeth, to prevent him from biting off his tongue and choking on it.
“Here!” I said tossing him my flail. “The handle!”
The guard caught the flail and jammed its handle sideways between the prisoner’s teeth and tongue. His spasming and jerking gradually decreased. Before our eyes the prisoner transformed from out-of-control clockwork automaton to limp ragdoll.
He remained in a deathlike coma for three days.
When he regained consciousness, he wanted to know what had happened. I told him -- seizure and flail and all -- then questioned him again.
“Prisoner 3.14159, what happened from your point of view?”
He pondered the question a moment before speaking.
“I saw clearly, in a single instant, all the past and all the future – all possible pasts, and all possible futures. I can’t explain it, but I know I will never be the same.”
“Then π has a last digit?”
He shook his head.
“Then π doesn’t have a last digit?”
And again he shook his head.
He was useless. In my hands I absently twisted my flail, barely noting the Pi Man’s teeth-marks still in its handle. I turned the prisoner over to the Inspector and his interrogators. Changed by the experience of his lost days, however, the prisoner would never again answer our questions about π, no matter what persuasions – and yes, tortures – we used upon him.
Such apocalyptic individuals are always valuable as lightning rods for dissent, and gather about them many other potential enemies of the state. Unfortunately it’s also always difficult to tell which type of apocalyptic individuals they will turn out to be.
Some of these individuals will be apocalyptic in the revelatory sense, lifting the veil of this world to reveal something more, through ecstasy and visions of harmony . Their most powerful weapons will be how to live by new ideas. Others, however, will be apocalyptic in the destructive sense, rending this vale of tears to make way for something different, through catastrophe and the violence of overthrow. Their most powerful ideas will be how to kill by new weapons.
-- from The Purgation Manual, Sixty Third Iteration.
That the Pi Man and his abilities might be based in some reality I could barely fathom was something I soon found far more disturbing than the idea that his “blessed affliction” was the mere product of fakery. The danger his ability, if real, posed to the security of the entire Purgationist state was too immense to be tolerated.
I saw to it that his trial would be a perfunctory affair, and that he would be cast down.
His Prisoner Number we had seared into his skin in prominent digits, 3.14159 midway between clavicle and nipple on the left side of his chest. The guards shaved his head and smashed thin metal and wood coronals, circular disks and square planes, onto his brow until it bled around them. Then, having strapped to his shoulders an immense pack of fallacious maps, we marched him toward a map room, like any other except for the fact that it was to be the site of his Downcasting.
Despite our best attempts to keep the time and place of that Downcasting as secret as possible (so that his followers might not venerate the date of his execution, or enshrine the location of it, afterward), a small crowd of his disciples nonetheless managed to follow us as the prisoner was marched, beaten and bloodied, up the stairs from level to level.
He stopped and rested – too often, it seemed to me. The more he did so, the larger the crowd that gathered. While he stood at one such stop, I struck him with my Expurgator’s flail of office.
“Why do you loiter, Pi Man? Move along!”
“Cartaphila, why do you still persecute us? Do you fear a hell of endless new maps, or new maps of an endless hell? ”
I struck him again, but he would not be silenced.
“Can’t you see we are each of us circle and square, each striving to complete the other, through love to become the other, as we approach the limit of infinity -- “
I struck him a third time.
“I said, move along!”
“Before I ‘move along,’ I will stand here and rest a moment in silence -- but I tell you that you will never rest, never stop from searching, and telling of your searching, until you see me again at the end of the Observatory.”
“Fool! There is no end to the Observatory – only to you.”
He smiled oddly – as much like madman as fool.
“My curse has proven a blessing,” he said, resting his hand on my forehead. “So may it prove for you, until you understand π is not changed by the shape of the Observatory, even as the Observatory is changed by the shape of π.”
We stood there a moment in silence, his hand on my head, an immense cascade of something both brightness and numbers flowing into my skull, until at last I shrugged off his hand.
His last words to me, over his shoulder as he moved on, were only a sort of bad poetry: “Just because the sky is in π is no reason for anyone to die!”
Soon thereafter, we stood him up on the safety rail of that cell. With a vigorous push forward, we cast him down. I saw him fall and fall, through the endlessly honeycombed air that bore no sweetness, until he vanished from sight.
Yet the making of such distinctions has become all the more critical, and not only because the worst thing one can do, politically, is martyr the wrong apocalyptic individuals. Correctly distinguishing between the types is critical to the continued survival of both the individual and the state, particularly since it has become increasingly possible for any individual to potentially possess the capacity for mass destructiveness.
-- from The Purgation Manual, Sixty Third Iteration.
So ended the passion of the pied cipher. His followers affirmed that -- no matter how many maps might be re-drawn or destroyed, no matter how vast or how consistent the screens that might be commanded -- invincible non-sense would always break through, sure as death. Yet , at one and the same time, his followers also proclaimed that, because their Holiest Fool was Pi Incarnate, man and number, transcendental, irrational, and normal, he could himself no more die than the decimal expansion of π could come to an end.
I do not know the truth or falsity of these beliefs. What I do know is that, from the day of his Downcasting, I have become a timeless anachronism. I have not aged, not in all the years, decades, and centuries that have followed. Neither have I ever been able to rest from my wandering. My life has become a detour in eternity.
I have witnessed the creation of machines capable of computing particular iterative processes called “dynamical maps.” I have viewed the landscapes which emerge from their calculations, such as when these machines plot the first million or billion decimals of π as random walks. I have looked through the computational lenses provided by these machines, zooming in and out from scale to scale, within a single map and among vast collections of them. With the development of these machines, the priesthood of the unbelievers has only grown, along with their contention that the Observatory was not created by a God or gods at all, but by beings like us – or, more precisely, like those seen in the maps, whom we resemble, or who resemble us (the relationship remains unclear).
Whether or not we are avatars cut free of a lost flesh to which we owe a nebulous allegiance (as some claim), I do not know. Disturbingly, though, as we move further and further out through the Observatory, more and more of those beings we observe in the maps are themselves looking at maps or screens. Do they too see a world of other beings before their eyes also looking at maps or screens, who in turn see other beings before theirs also looking at still more maps and screens, and on and on? The mind reels at the thought of such infinite regress, so it is seldom spoken of publicly.
Instead it is presumed that, as the result of some great disaster (or triumph; opinions differ) these beings in our maps created a machine (or system of machines; again, opinions differ) which displaced (or assimilated) the world (or worlds) in which those beings once existed. In order to understand the nature of their transcendence (or destruction), the machine (or machines, or transcended beings) created the Observatory as an enormous simulacrum in which, through our observing and understanding of our (presumed) ancestors’ fates, the transcendent machine (or machines, or transcended beings) might come to understand our/its/their own history.
In and through the Observatory, then, we not only watch, but are also in turn watched.
Whether the chain of observers and observed is itself endless, I do not know. Whether our existence is made either more or less meaningful or meaningless by the idea that we are thoughts in the vast thought experiment of the Observatory (and whether or not the experimenters will one day end their experiment), I also cannot say.
Troubled by such questions, too many hurl themselves to their deaths, poorly emulating the fate of the Pi Man in ways he would no doubt abhor. I am, however, denied even that solace. I cannot know whether or not, in the ordinary course of things, we die because the “period” placed on the sentence of life by death is necessary to the simulation of our ancestors’ mode of consciousness. I will not know, so long as I remain incapable of dying .
I cannot say with certainty whether the finite recurrence of randomness constitutes a species of order, or whether the infinite recurrence of order constitutes a species of randomness, or whether both are merely species of chaos. Yet, if the Observatory is a vast simulacrum of π’s unfolding, and if π is mathematically normal, then in that infinite unfolding the sequence of digits which constituted the Pi Man’s existence will one day recur. Although that sequence can never repeat in exactly the same way or in any cyclical or periodic fashion, I will in that sequence nonetheless see, know, and understand him and his message, again, for the first time. Like an infinity of journeys round a finite but unbounded globe, my life, and all my searching and tale-telling with it, will at last end.
In that lies the blessed affliction of all my hope.
About the Author
Howard V. Hendrix is the author of six novels, two short story collections, and two non-fiction books. He has a BS in Biology along with MA and PhD in English Literature. (Retrospectively, it seemed like a decent background for a science fiction writer.) He has been teaching at the college level since grad school in the 1980s. His most recent published appearances include a novelette, “Monuments of Unageing Intellect,” in the June 2009 Analog and an essay, “The Other Part of the Equation,” in Thoreau’s Legacy from Union of Concerned Scientists/Penguin Classics.
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