by Joan Brady (1974)
ALEXANDER SIMPSON WAS the youngest of five children; his parents had not expected him. With the fourth child, Alexander’s father had fulfilled his plan for a balanced dinner table—himself at the top, a boy and a girl on either side, and his loyal wife at the end—and Alexander’s appearance struck him as evidence of discord in the order of things. But Mr. Simpson knew the world to be administered according to scientific law; he was a teacher and, from time to time, he submitted articles to learned journals. When Alexander was old enough to eat with the rest of the family, Mr. Simpson instructed his wife to buy a circular table.
Although he never became reconciled to it, Mr. Simpson grew used to the round table; it was several years before he could find it in himself to forgive Alexander. Perhaps on this account alone, Mrs. Simpson preferred her fifth child above the others; she gave him the roundest apples from the basket and the tenderest cuts from the roast, and she watched him fondly as he ate. As for the other children, they accepted Alexander without thought, and he grew up as happily as most.
He was a drowsy, somewhat sluggish child, dreamy and overweight from the first, but affectionate and uncomplaining. He shared his toys readily, partly out of good temper and partly because he didn’t much care about them; and, while he provided his sisters and brothers an appreciative audience, he rarely interrupted their games. Until he grew into an unwieldy six or so, his chief pleasure was to be swathed in an approximation of a christening gown and pushed about in a wagon by one of his sisters, clucking softly to himself.
When he started school his mother took him there, holding him by the hand that first day and kissing his cheek before she left. The schoolboys gathered as soon as she was out of sight, forming a circle and dancing hand in hand around him, laughing and hooting, darting in and out one by one to kiss him with loud, wet sounds. Alexander responded with delight. He laughed and danced too, as gaily and as sincerely as they; and before the week was out they were accepting him into their games without reservation.
Just as his father had predicted, he was a poor scholar. He had no gift for sport, either, although he did come to enjoy cards as he grew older. Most of all, he enjoyed hearing people talk; he didn’t talk much himself—the effort seemed greater than the reward of being heard—but he listened happily to other voices, content to give in to the intensity of one, the resonance of a second, the monotony of a third.
It was to this trait that his father succumbed in the end. It caused Mr. Simpson pain to look around the table during a pause in the discussion of some important matter and see the bored faces of four of his children. Only Alexander, his dreamy eyes fixed on his father, showed interest; or so it seemed to Mr. Simpson. And the fact is, Alexander did absorb some of what his father said, enough certainly to realize that it was to his father he should go for advice when the time for advice came.
As a young adult Alexander proved to be much as he had been as a child, a nondemanding companion and a sympathetic listener. In the filing department of the local newspaper, where at length he was installed, he proved to be no worse at his job than anyone else. He spent his spare time at a gathering place for young people, a place for poker at low stakes and beer at low prices. Alexander was a poor poker player; if his hand was good or bad he was delighted or unhappy in visible proportion. He played because his companions played and because, no matter what his hand, the scrambled colors and shapes aroused in him an agreeable sense of excitement. So it was with him that Wednesday evening—an evening much like any other at the start—when the first step in the direction of his conversion took place.
ALEXANDER SAT AT a table with his friend Peter, and while they waited together for the others, Peter embarked on a tale about a distant uncle, idly shuffling and reshuffling the cards as he spoke.
“. . . on my father’s side. Uncle Homer was born into a big farm family—the last one—and he was kind of slow when it came to
Peter beckoned to two young men, who came over to join them, and then set the deck down on the table ready for play. The deal fell to him, and he shuffled the cards, shoved them to Alexander for cutting, and dealt them out as he continned with his story.
“He didn’t say ‘da-da’ or ‘ma-ma’ when he was supposed to, and he didn’t say them a year after, either,” Peter paused a moment to examine his cards, “or the year after
Alexander, off to his right, hiccuped loudly; the two of them had drunk a fair proportion of beer already.
“Well, I don’t know what I can make of this mess, but I’ll open for two.”
“. . . it wasn’t that Uncle Homer couldn’t understand things. You could say ‘do
“. . . or ‘do that’ and he’d do it. They took him to all kinds of doctors, and they all said there wasn’t anything wrong they could find. Maybe just a little
“Hey, Sandy, come on. Come on, it isn’t all that hard.”
Alexander lifted his head from what appeared to be an intense concentration on his cards and looked vaguely around at his companions.
“Well, well, well, got something, have you, Sandy?”
“Come on, come on, what are you doing? Are you raising him ten?”
“Well, I don’t
“Are you raising him ten or aren’t you?”
Alexander looked down at his hand again, his face vacant for a minute, then he giggled a little and the giggle rippled throughout his bulky form.
“Sandy, my boy, the odds against filling an inside straight are pretty high. Did you know that?”
Peter looked at his cards for a moment, then at Alexander, and then again at his cards; he shrugged his shoulders slightly and said, “You know, I don’t think Sandy knows a good hand from a bad one, but I think I gotta see what he thinks he’s got. Anyone want any cards? State your needs.” Peter looked around the table, pausing a moment to study Alexander’s face.
“After a while,” Peter began again, “they about gave up on
“God help me, Peter, give me two.”
“. . . and they let him alone a
“One, and make it a good one.”
“Then one day his father was working out in the fields late and his mother said, ‘Here, Homer, here’s your father’s coat. You take it to him.’ So Homer took the coat and went out to find his father, and when he found him
“Come on, Sandy, come on. We’re going to be here all night at this rate.”
Alexander glanced up from his cards, giggled again, and shook his head from side to side.
“No what? You standing?”
“No. I mean yes. I mean no cards.”
The three other players studied Alexander, who looked around at them, his face puzzled and pleased by turns; but finally he settled himself into his chair and resolved his face back into its usual dreamy expression. The others continued looking at him for a moment, then each with a sigh or a shrug or a shake of the head turned his attention to his own hand.
After a further pause and another glance at Alexander, Peter said, “Oh, well, I’ll try two.”
“That idiot uncle of yours,” the second young man said abruptly, “what’d he do then?”
“Well, like I was saying,” Peter went on, “when he found his father he walked right up to him and he just said, ‘Here, Charlie, here’s your coat.’” Peter looked to his left. “What’s your bet?” he said.
“Well, I’m damned if I know. But I been playing poker with Sandy for more than two years now and I just gotta see him too.”
“Anyhow, that’s what he said. ‘Here, Charlie, here’s your coat.’ Those were his first words ever. The very
There was a sudden loud snort from Alexander, and his large body began to jiggle up and down. He pressed his hands against his moon face in a vain attempt to stop the foamy jets of beer spurting out of his mouth, and as his companions stared at him in silence he rocked and jogged and bounced out of all control. Recovering himself, he spread out his cards face up in front of him. There on the table lay a royal flush.
ALEXANDER PLAYED NO more poker that evening, nor did he play the next evening, nor the evening after that. In fact, he found he didn’t want to see Peter or his poker friends again, not because they continued to tease him about his royal flush—he enjoyed being teased—but because they distracted him. He wasn’t sure just what it was they distracted him from, though he knew it had something to do with the royal flush; he knew that something vitally important to him flickered now on the dark inside wall of his head and that its light escaped him when he was with them.
He looked up poker in a book of his father’s and found that a royal flush occurs only once in 649,740 hands, and this statistic intrigued him beyond anything he had ever encountered before. He turned it over and over in his mind, and at length he decided that probably if every man, woman, and child of the 20,000 or so in his hometown were to play thirty-three poker hands each, a royal flush would have to appear. The thought alarmed him slightly.
As he considered further, he began to wonder why it had happened that he was dealt that 649,740th hand. Why hadn’t Peter got it? Why hadn’t one of the others got it? Why himself in preference to one of the other three? In fact, anyone in town might have got it; wasn’t there some meaning—some special meaning—in the fact that he, Alexander, was the one that gave so huge a number its meaning?
Such thoughts as these bothered his sleep and interrupted his appetite but failed to give any form to the flickering in his mind. He decided that the time had come to consult his father, whose learning, he was sure, would help him to bring things into focus.
“If you’ve got one fact it doesn’t mean anything under the theory of probability,” Mr. Simpson said, looking abstractedly at his son, “—that’s what you’re talking about, you know, probability—and two facts aren’t much better, and neither are three. Or four, for that matter. But if you’ve got all kinds of facts—thousands are better than hundreds and millions are better than thousands—you can make almost anything you like out of them. And all of it’s as infallible as the Pope.”
Mr. Simpson sighed. “There’s an army of clerks about, you see,” he continued after a pause, “and they go and gather up facts—facts about everything: how many children are born and when, who dies how young of what, who eats what and who buys what and who wants what, and on and on like that. Then they write it all down and make it into patterns—it’s all very precise. And then they know everything, since everything everybody does ends up as some part of a curve or a chart or a table. Everything. And if you want to know everything, all you’ve got to do is gather up whatever you can find, calculate a bit, and lo! a pattern will emerge. Then you’ll know everything, too, just like the clerks.” Mr. Simpson sighed again. “Everything,” he said. “Everything.”
Alexander was impressed. After all, he worked in a place where many facts were collected already and he liked calculations. The next day at work he found a folder entitled “Miscellaneous Statistical Material.” He chose at random.
The very first article he came across concerned a family by the name of Pitofsky, which in more than seven generations had produced no daughters. The occasion for the article was the birth of the forty-seventh male Pitofsky; and, as the reporter pointed out, the chances against such a run of boys were one in 136 trillion. The reporter went on to say, by way of illustrating the peculiarity of such figures, that whatever the pattern of the last forty-seven boys and girls in a family—any family at all—that pattern, too, would occur only once in 136 trillion times on the average.
Alexander made a copy of this article and pasted it in a scrapbook.
Then, reaching into the file again, he retrieved an interview with a certain Dr. Williams, who was distressed by the tendency to prescribe vitamins according to the needs of “the average man.” One must keep in mind, Dr. Williams urged, that bodily organs vary in size from individual to individual; the stomach, for example, varies on a scale beginning with one and ascending to fifteen and the heart on a scale from one to five. If a researcher were to consider organs in the middle third of their respective ranges as “middle-sized organs” and if he were to select only eight from the many available, he could find only one average man in every 6,500 he tested.
Alexander pasted this article in his scrapbook too. He felt around his ample middle with his hands and thumped his chest but found he could not in any way estimate the size of his stomach or his heart. He made an appointment with Dr. Drude, who had delivered him and treated him for chicken pox when he was six.
Dr. Drude was not a patient man. “Well, well, Alexander,” he said. “I haven’t seen you for many years. Not since chicken pox. You’ve grown up. You’re overweight. What can I do for you?”
Alexander pondered a moment, wishing to phrase his question precisely. “I want to know,” he said, “how big my organs are.”
Dr. Drude stared. “Your what?”
“My organs,” said Alexander politely.
“What organs?” Dr. Drude’s temper had failed him already. “How in hell do I know how big your organs are? Why don’t you look? What a damn fool question. You always were a foolish boy—too many puddings—I told your mother so. Now what’s the matter with you? I’m busy.”
“I must know how big my organs are,” Alexander persisted gently. “It is very important to me to know.”
He paused a moment. “I want to know particularly if I have a medium-sized stomach and a medium-sized heart. I have tried to find out myself and I can’t.”
Dr. Drude sighed angrily. “Do you feel sick?”
“Then you’ve got a medium-sized stomach.”
“Ah,” said Alexander, much pleased. “And my heart?”
“Are you short of breath?”
“Then you’ve got a medium-sized heart. Now go away.”
“Ah,” said Alexander again. “And what other organs have I got?”
“Oh, my God! Kidneys, liver, lungs, pancreas, intestines,
Alexander returned home in a happy state of mind. In his scrapbook he wrote: “I have eight medium-sized organs.”
IT WAS AT this point that Alexander became aware of the pattern in his researches; he now knew what sort of information brought order to his thoughts although the order as yet escaped him. He continued to search through the newspaper files and he spent many long hours among his father’s books—he even began visiting the public library one or two evenings a week—and the entries in his scrapbook grew in number as the days went on. He listed the chances against being born into a family of five, against being born to a member of the teaching profession, against being born on any given weekday in any given month; and he listed the chances against receiving any given Social Security number, any given telephone number, any given driver’s license number. Soon he was able—by steady reference to tables of calculation with which he was now becoming familiar—to enter into his book the chances against being named Simpson and those against being named Alexander; those against living in the town he lived in and those against living in his house on his street.
The area of his search widened steadily. He carefully noted down in his book the chances against the sperm that had carried half his genes ever reaching its goal the night of his conception, against that sperm being the one to have done so, and against his conception on that particular night coming about at all. He collected figures on overweight and beer consumption and, indeed, everything he could think of.
At the end of two months he was ready for the final step, the grand multiplication of all his many individual chances into the one great chance. He wrote down the figures he had culled in a long, neat list in order of size, beginning with the smallest. For two days he reviewed these and thus cautiously prepared the way for the calculation that at last would reveal just what were the odds against the existence and activity of himself, this many-faceted Alexander, just what was the probability against himself with all of his characteristics coming to be at all.
And so it was that early one morning Alexander sat down to his multiplications. For the occasion he took out his newly purchased copy of the table of rare events drawn up by Emile Borel, the eminent French mathematician. Referring to it, he had hardly begun his task before he found that the chances against his being what he was were in excess of 106, which, according to Borel, constituted an impossibility on a human scale.
Alexander was delighted, although he didn’t know what to make of the figure, and the flickering in the back of his mind flared with a new light. Multiplying in more data, working more and more doggedly, Alexander soon carried his calculations to a total reaching out beyond one chance in 1015, an impossibility on the terrestrial scale. By lunchtime he had exceeded one chance in 1050, an impossibility on the cosmic scale, and before dinner his calculations had passed 10500, the number Borel had set for absolute zero as a possibility.
In the following days Alexander went over his figures again and again, weighing them in his mind, trying to extract some meaning from them; but that elusive thought that had come to him after his royal flush remained as formless as ever despite its new light. He had never been good at theorizing—his father had often said so—but the lack of a pattern to his researches distressed him greatly. Moreover, he lost weight, which bothered him further since it seemed to require an adjustment in his calculations. Occasionally the figures came to him with such a sudden jolt that they shunted everything else out of his mind; even so his thoughts remained patternless, and their patternlessness seemed to him punishment for failure or bungling, although what he had failed in or bungled he did not know.
It was after a month or so of this, in an hour of relative calm, that Alexander’s conversion took place. He was in his bedroom at the time; it was three o’clock on a hot July Sunday. His father had given him a copy of an article he intended to submit to a learned journal, asking him to check some of the figures against the tables of calculations that Alexander kept in his room. Alexander was not particularly interested in the article, which dealt with the genealogy of someone he had never heard of, but it was as agreeable a way of spending an afternoon as any.
The article began in his father’s scholarly style with a discussion of some of the difficulties a genealogist faced; not the least of these, Mr. Simpson wrote, was that a modern individual must calculate the number of his ancestors of Roman times on the order of 1020. Alexander had not encountered this particular statistic before. Did this not mean, he asked himself, that the chances against any one modern individual—himself, for example—having arisen from a given combination of Roman ancestors constituted an impossibility on the terrestrial scale (although not on the cosmic)? The thought sharpened his mind. And at once he abandoned the article to follow an airy pattern of chances through the generations responsible for his being, watching the pattern widen faster and faster.
He knew that he could not continue with the article—or with anything else—until he understood completely what that figure and that widening meant. It was plain to him that together they crowned his studies and held the key that still eluded him, and he stared at the figure and strained to follow the pattern until he felt his head would burst. Then, quite suddenly, pattern and figure seemed to break loose from him altogether, and he felt almost as though he were floating free in the stillness of the room. He had never been so delightfully happy. The familiar things around him—his unmade bed, his tables of calculation, his father’s article—all but disappeared, and he hardly knew where he was. The Alexander who played poker and drank beer and used to get the roundest apple from the basket drifted across his mind and out of sight; that Alexander was gone forever.
Near him, almost next to him, he now sensed a new being, a strange presence somehow intimately connected with him but stronger than he; and at the same moment he became aware of something else too. That once elusive flickering had taken on shape. Alexander saw the truth; he knew everything. Everything. He and the presence were one and had always been one, for all that he had not known it. He was in fact—and he marveled that it had taken him so long to see it—he was his Statistical Self.
He was the embodiment of his relation to all the data in the world, past, present, and future; he was himself that aggregate of facts that imposed order on the disparate elements of the universe, that body of infinitely calculable probabilities that constituted his extraordinary uniqueness. He moved his arm slightly and shivered with the chances against doing so at just that moment and in just that place; he trembled before the enormity of the probabilities from the beginning of time against the chance that he, Alexander, in this room, here, now, with his bed unmade and his father’s manuscript in front of him, should have done such a thing. All but exhausted by elation, he wanted to close his eyes, but the astronomical chances against his doing so seemed bodily to hold back his eyelids and pinion him, wide-eyed forever, in the position in which he sat.
Numbers grew around him, circumscribing every aspect of his being, trailing off from him into their own immensity, wrapping him in their immeasurably long tails and holding him there, Alexander Simpson, the object and source of all those calculations, himself, the one chance in a billion, the one in a quadrillion, a duodecillion, a vigintillion, the one chance in trillions of octillions, the one in quintillions of septendecillions, and on and on and on, larger and larger and larger, numbers reaching out to outer galaxies and disappearing through black holes in the universe to be continued in universes beyond. To all of them, he, Alexander Simpson, was the unique figure, the nexus wherein all these numbers met, who gave meaning to them individually and severally; he alone filled the position against which the probabilities reached out in calculations to the very eternal itself.
FROM THAT HOUR Alexander lived his life untroubled and in peace, although he often wept as he caught a glimpse of the mediocrity from which he had been saved by infinite probability; he shuddered at the sight of his earlier ignorance and was overwhelmed with wonder and gratitude for his present faith and knowledge, for seeing at last as men were meant to see. He walked with new dignity among his fellow citizens, and they in turn came to view him with respect and even to seek out his advice in matters of the spirit.