A mathematician and computer scientist, N., who had been working with Cantor's theories on infinite sets and cardinality and the physics of parallel universes, devised an experiment he felt could vindicate the much-maligned C.
Georg Cantor was often vilified for having produced unprovable, assailable mathematical conjectures regarding the infinite and its interplay with the individual constituents which composed it. The encyclopedias of the day include skeptical notes on Cantor: "These results are highly counterintuitive, because they imply that there exist proper subsets and proper supersets of an infinite set S that have the same size as S, although S contains elements that do not belong to its subsets, and the supersets of S contain elements that are not included in it."
N. wondered how he might definitively prove to the world that Hilbert was indeed correct with his "Paradox of the Grand Hotel": "It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and that this process may be repeated infinitely often."
The experiment N. devised was ingeniously simple. He decided to email himself a simple message whose text would explain that he was exploring the infinity of the set of himself and searching for proof of an alternate version of himself in a parallel universe. If he wrote back to himself, without ever setting his own fingers to his keyboard, he would be vindicated.
He was using a computer of his own design, nearly a supercomputer, but not quite. He began the mailing and ten thousand, one hundred thousand, one million, ten million, one hundred million emails sailed off and returned without a hitch. This was what N. expected to occur. But the computer continued shooting these textual arrows, these emails, into a vast cosmic sea of numbers and soon it was ten billion, one hundred billion, ten trillion, and so on, until a googol of these emails had been sent, and then, arguably, a googolplex of such emails, if computers could be said to "get tired" of appending zeroes to the end of a number, growing that strange abstract creature's infinitely extensible tail.
And then the first few stray emails showed up on N.'s "registry of miscounts." They went out. They did not come back. Still, N. waited. He felt the shudder of the quantum symmetry. But he realized the problems. In how many universes, did N. have the same email but still lack the comprehension to understand the deep meaningfulness of this simple communication written from himself to himself? It would be like a satellite messenger from earth sailing past a planet with a primitive life form that could not even reckon an overture from another world.
How many emails that slipped through and reached their designated N.-other (N.'s preferred term for his alternate selves, with a subscript to indicate number) were disregarded and discarded, disbelieved as pranks or cognitive flukes that came out of some altered state, believed to have been the result of having been drunk or high or having gone without enough sleep. Many emails would be seen but never opened. How many N.-others were capable of understanding the import of the email and knowing the importance of writing back. Most N.-others would be self-absorbed idiots, some even worse. And, of the infinitely small number of emails that N. estimated would "make it through," he knew the process of writing back would be equally fraught. The odds of that email returning to its true sender would be just as astronomically high. There was no guarantee that these slippages opened up a "true conduit" or isomorphic mapping of time. Indeed, N. believed this would not be the case at all. This is why he believed the odds of success in his experiment to be dauntingly slim.
It was on a rainy Thursday afternoon that N. had been writing a paper on the arrays of "slipped emails" which had never returned, which appeared to have made it through to parallel universes, when his textual scanner gave him "The Ding." The Ding was N.'s pet name for the audio signal which allowed N. to know that an email had returned from a different email address or from his "own" email address with text added or the original text altered. Since N. could not physically read these astronomically huge numbers of returning emails, and since he had every reason to suspect the "confirmatory email" would simply return with himself as sender, that it would come from the same email address from which it had been sent, he needed to add this verification procedure to his process.The text-comparison verification was designed to weed out any email text differences that merely denoted server problems and their standard verbiage, which had been authored by N. himself as controls for this experiment. The Ding was actually a sound file of the old seventies song "All by Myself."
N.'s heart was nearly stopped when he heard Eric Carmen's treacly, drawn-out delivery of the lyrics from the schmaltzy, self-pitying pop song of radiophonic yesteryear.
He went to the target email which was highlighted, segregated from the massive body of returns, which was still growing in magnitude in nearly unimaginable leaps and bounds, still attempting to scale that impossible distance between finitude and infinitude.
He opened the email and read:
"Hello? Is this some sort of joke? I don't remember sending this email and I don't see how it is possible that I did so, and I have no idea why I am writing this "reply" (it is preposterous) but we do seem to have some mathematical interests (a faith, no?) in common, and I figured it wouldn't hurt to write you "back". Although, if I am correct, your odds of receiving this "reply" are astronomically against "us," and I don't expect to ever hear back from you. In any case, thanks for thinking of "me" (yourself?) and Farewell."
It was all N. needed to read and know.
Now began the work of convincing the world. He anticipated the odds of his going insane during this attempt were very high. He anticipated failure. Why wouldn't he? He knew the odds.
Georg Cantor was often vilified for having produced unprovable, assailable mathematical conjectures regarding the infinite and its interplay with the individual constituents which composed it. The encyclopedias of the day include skeptical notes on Cantor: "These results are highly counterintuitive, because they imply that there exist proper subsets and proper supersets of an infinite set S that have the same size as S, although S contains elements that do not belong to its subsets, and the supersets of S contain elements that are not included in it."
N. wondered how he might definitively prove to the world that Hilbert was indeed correct with his "Paradox of the Grand Hotel": "It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and that this process may be repeated infinitely often."
The experiment N. devised was ingeniously simple. He decided to email himself a simple message whose text would explain that he was exploring the infinity of the set of himself and searching for proof of an alternate version of himself in a parallel universe. If he wrote back to himself, without ever setting his own fingers to his keyboard, he would be vindicated.
He was using a computer of his own design, nearly a supercomputer, but not quite. He began the mailing and ten thousand, one hundred thousand, one million, ten million, one hundred million emails sailed off and returned without a hitch. This was what N. expected to occur. But the computer continued shooting these textual arrows, these emails, into a vast cosmic sea of numbers and soon it was ten billion, one hundred billion, ten trillion, and so on, until a googol of these emails had been sent, and then, arguably, a googolplex of such emails, if computers could be said to "get tired" of appending zeroes to the end of a number, growing that strange abstract creature's infinitely extensible tail.
And then the first few stray emails showed up on N.'s "registry of miscounts." They went out. They did not come back. Still, N. waited. He felt the shudder of the quantum symmetry. But he realized the problems. In how many universes, did N. have the same email but still lack the comprehension to understand the deep meaningfulness of this simple communication written from himself to himself? It would be like a satellite messenger from earth sailing past a planet with a primitive life form that could not even reckon an overture from another world.
How many emails that slipped through and reached their designated N.-other (N.'s preferred term for his alternate selves, with a subscript to indicate number) were disregarded and discarded, disbelieved as pranks or cognitive flukes that came out of some altered state, believed to have been the result of having been drunk or high or having gone without enough sleep. Many emails would be seen but never opened. How many N.-others were capable of understanding the import of the email and knowing the importance of writing back. Most N.-others would be self-absorbed idiots, some even worse. And, of the infinitely small number of emails that N. estimated would "make it through," he knew the process of writing back would be equally fraught. The odds of that email returning to its true sender would be just as astronomically high. There was no guarantee that these slippages opened up a "true conduit" or isomorphic mapping of time. Indeed, N. believed this would not be the case at all. This is why he believed the odds of success in his experiment to be dauntingly slim.
It was on a rainy Thursday afternoon that N. had been writing a paper on the arrays of "slipped emails" which had never returned, which appeared to have made it through to parallel universes, when his textual scanner gave him "The Ding." The Ding was N.'s pet name for the audio signal which allowed N. to know that an email had returned from a different email address or from his "own" email address with text added or the original text altered. Since N. could not physically read these astronomically huge numbers of returning emails, and since he had every reason to suspect the "confirmatory email" would simply return with himself as sender, that it would come from the same email address from which it had been sent, he needed to add this verification procedure to his process.The text-comparison verification was designed to weed out any email text differences that merely denoted server problems and their standard verbiage, which had been authored by N. himself as controls for this experiment. The Ding was actually a sound file of the old seventies song "All by Myself."
N.'s heart was nearly stopped when he heard Eric Carmen's treacly, drawn-out delivery of the lyrics from the schmaltzy, self-pitying pop song of radiophonic yesteryear.
He went to the target email which was highlighted, segregated from the massive body of returns, which was still growing in magnitude in nearly unimaginable leaps and bounds, still attempting to scale that impossible distance between finitude and infinitude.
He opened the email and read:
"Hello? Is this some sort of joke? I don't remember sending this email and I don't see how it is possible that I did so, and I have no idea why I am writing this "reply" (it is preposterous) but we do seem to have some mathematical interests (a faith, no?) in common, and I figured it wouldn't hurt to write you "back". Although, if I am correct, your odds of receiving this "reply" are astronomically against "us," and I don't expect to ever hear back from you. In any case, thanks for thinking of "me" (yourself?) and Farewell."
It was all N. needed to read and know.
Now began the work of convincing the world. He anticipated the odds of his going insane during this attempt were very high. He anticipated failure. Why wouldn't he? He knew the odds.
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