Estimated reading time: 50 minutes
The present piece contains some informal reflections on my novel, Heaven Engine.
I was educated at Gilmour Academy and Santa Clara University and began writing seriously in the 1970’s, eventually writing three books: two novels and a nonfiction book on new information technology and its potential value to strategic analysis in the national security arena.
On the basis of my second novel, Heaven Engine (2004), I have been selected by a Barnes and Noble panel as one of thirty-six featured authors who have written novels of Other Science Fiction (a hybrid genre of traditional novels and science fiction novels) ranging from the medieval period to 2099. Among these featured authors are Austen, Conrad, Joyce, Twain, Forster, Conan Doyle, Wells, Verne, Chesterton, Bradley and Bradbury. Heaven Engine has also been listed as a best-selling science fiction novel by various booksellers such as Amazon UK. I am also one of Barnes & Noble’s Fifty Featured Authors, Science Fiction and Fantasy, High-Tech/Hard Science Fiction, Nineteenth Century to Present.
The judges selecting the Other Science Fiction list have considered/projected Heaven Engine to be a signature book in 2000-2099. Perhaps one way of looking at the novel is to see it as a work of literary fiction, a Quest Story, dramatizing a future in which the progress of technology has led some humans to attempt to transform themselves and seek a secular heaven against enormous odds, an indefinite sublime experience of suspenseful mathological “creatovery” in Ideality by newly formed posthuman beings of great mindfulness, beings made not in the image of any deity, and who are created beyond natural selection with its painful temporality, and whose story departs from both the literary tradition of “cathartic” tragedies in the Vale of Tears and the more modern tradition of epics of heroic defiance by heroes explicitly trapped in bloody mortality, victims of natural selection: which in the former case is to say, the tragic King Lear; and in the latter case, the defiant Captain Ahab.
Heaven Engine has in places departed from some traditional practice in forming fictional narratives, for example, Aristotle’s “Unities.” The novel has multiple points of view, characters who speak in a variety of fonts, lengthy time spans, many settings, a panorama of actions, and other stylistic features not typically considered standard in storytelling. For example, Heaven Engine contains several frames of reference, most notably theoretical mathematics.
Theme begot form. Heaven Engine is structured in ways intended to convey its chief sense of things, most prominently a transition to a possible age of technology which enables a posthuman experience.
The novel appears to have a predominantly younger readership. Is perhaps the “screen-immersed,” “Internet-searching,” “digital generation” more at home with the “idiosyncratic” style of Heaven Engine? With respect to the shift in the readership of Heaven Engine, readers in particular have been obtaining the book through the growing number of media-streaming subscription-based services offering access to millions of books. An example service is Zeusfun which has some 80,000 subscribers. The company first uploaded Heaven Engine in mid 2019 and as of late 2021 there have been over 700 reviews averaging a rating of 4.5/5.0 stars. Certainly the rule stands that more readers on Zeusfun than those who chose to review Heaven Engine have obtained the novel. Other subscription services with similar readership statistics bearing on Heaven Engine are BOOKFORREAD, Maseke and Find-Full eBook.
The basic questions raised in Heaven Engine are these:
1. Is there a mindful, dynamic, progressive, secular heaven beyond the natural human life?
2. If so, can humans transform and transcend themselves to experience it?
Marvin Minsky has written this cover endorsement of Heaven Engine:
A vast, important, and radical vision.
In truth, all that follows here and in the novel itself deals either with the vast entrapment of natural selection, important historical and speculative attempts to escape that trap, and the specific radical solution of a posthuman sublime experience.
That said, before going further, I should highlight two words here: conjecture and plausibility. I am going to present several instances in which I conjecture that there could be signs of both the existence of, and the gaining of, such a secular heaven. And I am going to qualify that thinking by recalling the problem of plausibility, especially turning on the limits of the remarkable human intelligence over and against the matter of the sheer time needed for that achievement that might be granted by History.
Heaven Engine, then, can be considered a Transhuman Novel.
There is at present an early, stirring, multi-disciplinary, far-reaching and international “Transhuman Movement” with various complex viewpoints. There is productive contention–ethical, technical and otherwise–about what its aims should be, including whether achieving some form of posthuman immortality should even be pursued. Some participants such as Nick Bostrum raise important questions about both the favorable and the adverse possibilities of the endeavor. Science fiction writers have dramatized possible ironies of the enterprise such as Neal Stephenson in his novel, Fall. Contesting in all this activity are the ideas “posthuman” and “post-biological,” for considerable and serious debate can ensue over distinctions about these terms as well as over many other aspects of the Movement.
I must plead guilty to the central idea in Heaven Engine–an idea some might call “narcissistic”–of a transcending of the human being and of the natural life in what has been called “a quest for more exquisite ways of being,” namely, in my novel, a Mathematica Dramatica in Ideality.
In that light, my primary interest has been the notion of such principals of artificial intelligence as Marvin Minsky and Douglas B. Lenat, the futurist Hans Moravec, and the science fiction author Vernor Vinge, expressed by the technology infused idea of “the singularity,” a term perhaps suitably defined as that possible future when artificial intelligence surpasses human intelligence. The term, “superintelligence,” also often applies in some forms to ideas of transhumans.
There are various ideas of the problems and prospects of a transition to forms of posthumans. Heaven Engine dramatizes a scenario I have not seen elsewhere:
A distant future of smart machines and protean technology. Our indispensable, radically dwindled descendants, exiled by a global authoritarian government to large space stations after the Eco War, visit Cleansed Earth occasionally for gravity- and sensory-deprivation therapy. Human longevity, at last attained, has ironically created a Great Plague of Suicidal Despair, Disnovelling, an infernal, growing ennui and weariness born of the intruding longer personal prospects of the dead ends of bloody Nature and of the impersonal, unreachable, inscrutable, hurtling cosmic vastitudes. Various attempts to create sophisticated pursuits for the Longevitites, entertainments and activities–tours of Jupiter’s moons, “Knowledgian” Hiking Gear, enhanced sexuality, enlivening and entering the worlds of famous paintings, and others–are created to offset Disnovelling but soon fail. In short, the limitations of Disnovelled Homo sapiens (including the authorities)-–especially the sense of baffled entrapment—not the event horizon but the mental horizon—have become increasingly unbearable, leading to times of widespread suicide. Centwen, a technologically resurrected twentieth century archetype joined by similar resurrected elites and archetypes from other earlier centuries and who are not yet suffering Disnovelling, and all chosen by the superbot, Prodigy, and its outlaw human creator, the great polymath Psychodor, hater of natural selection, tour the disheartening future after their earlier deaths, ultimately learning about a final hope beyond Disnovelling, namely, a last-chance project ultimately founded and managed by Psychodor himself to create not a mythical but a secular, dynamic, intelligent, posthuman Heaven; and, if it succeeds, whether or not these resurrected humans can themselves be transformed, and/or their intelligent machines, and escape to it.
My special gratitude goes to the late John Updike, a very occasional snail mail correspondent, who in the aftermath of my commenting on his novel, Roger’s Version, kindly asked me a crucial question about the Longevitites with whom I was populating Heaven Engine: “How do they keep from being infernally bored, as human consciousnesses would become in any infinitely prolonged situation?”
It took me some time to see his profound precision: human consciousnesses.
The infernal downfall, the impending extinction, of long-lived homo sapiens wearied not only of our deadly Natural Battle lost in the Vastitudes but in any imaginable state in which we remain human, is psychological.
* * *
For most readers, one strongly presumes, such concerns and questions are foolish and/or worse.
To them I say nothing.
* * *
As to the first question, concerning a plausible secular heaven, I think there is an answer: the thrilling, engrossing, beautiful discoveries of mathematics are basic. Call the state, Ideality. Crucial is the idea of infinity. More on this below.
I call the posthuman in this state a Mathite.
Of the second question, the transformation of humans into Mathites, I believe there is today no confident, although a hopeful, answer.
Setting aside hope for a moment: As we think about the all-too-real existential threats to the human species mythically galloping across the skies toward us in our day, and as we recognize that advanced projects of transformation do not yet exist, there may never be enough time needed to create Mathites. Consider this surely partial if dreadful list:
-Massive Cyber attacks, Out-Of-Control Hostile Technology, Other Catastrophic Technology Ironies
-Orwellian Dystopia (Authoritarianism, etc)
-Pandemic (Man Made)
-Solar Storm or Gamma-Ray Burst
Yet we are entering what seems likely to become an age of would-be transformational science and technology. Not simply a transhuman movement per se but a transformational reality. Clues appear: Artificial intelligence. Artificial reality. Augmented human intelligence. Anti-aging research. And so on. A trend here, however precarious, toward the transnatural for Homo sapiens seems clear.
Certainly Minsky and colleagues are right to think about “the singularity.”
But for the transformation question, obviously many considerations arise. It can hardly be forgotten that we are creatures of natural selection. Or perhaps better said, we are captives of natural selection. We might even be likened to drunkards of natural selection. It is almost impossible, it sometimes seems, for us ever to look at, to imagine, our situation as other than natural selectees. We perhaps seldom realize we are thus constrained. After all, as the saying goes, we’re almost always merely “doing and thinking what comes naturally.” No surprise here, for in the Darwinian context commonly described in general as “the survival of the fittest” it is obvious that the human condition–rife with painful struggles–greatly complicates–inherently interrupts–a consistent focus on the transnatural.
Here is one example, perhaps a cruel one: the human social question: Would attaining Ideality mean leaving your family and friends forever? The answer, complex and explored in Heaven Engine, is most probably, Yes.
Immediately, the sense is sadness, perhaps bitterness. This is instinctual, i.e., natural.
Longer term, perhaps the sense arises that new mindful creatures need not be social.
Today where do we see clues of a possible human transformation? As admitted, there are yet no fulsome technological projects. But we can see the chance coming.
We can see hints of it in some works of art. It whispers and sometimes, if very rarely, shouts from the arts.
The arts can be the earliest heralds.
Art scholars historically have liked to show that some art dramatizes at once both an established spirit of times and an aborning spirit of times.
I wrote Heaven Engine with the wish to pursue literary art to contribute in the moment to a change, or at least an intimation of one, in the history of consciousness; namely, the possible appearance of a truly transcendent technology.
I emphasize “contribute.”
Yes, by my reading, there are dramatic clues in art of that change possibly on its way. Indeed, I analyze below the last epic one–the last such epic in my view, anyway–and one which anticipates our own times–embodied in Herman Melville’s usually and massively misunderstood Moby-Dick. As it were, the pivotal Melville both transcends and demolishes a long previous era and literally clears the decks for our own era. Moby-Dick is indeed one of the handful of epochal books.
Here are seven art examples from many, including and starting with Melville, and all of the chosen seven showing at least intimations of the human urge, often nearly buried, for escape from natural selection and the gaining of a heavenly Ideality. Accordingly Melville serves as a foundation for the six other later, much-less-grand works, upon which I reflect for clues–poetry, novels, artful nonfiction, and movies among these works–which may bring in you a kind of dawning in dramatizing that human urge, ill-formed as it still is.
After all, that whispering is usually how the urge manifests itself in our distracted consciousnesses.
1. Moby-Dick by Herman Melville. I was afraid to reread Moby-Dick (1851) because it had seemed so overwhelming when I first read it years ago. Melville seemed intent on characterizing the whaling enterprise of his day in seemingly its every facet; was there not a narrative tension between the pure whaling-adventure scenes and the interruptions of that adventure by all those chapters effectively presenting the full technical and cultural magnitude of the hunting of whales–the massive job descriptions, new technologies of the day, and especially the broad cultural and historical context which Melville gives to the Whaling Story? If anything, Melville would supplant previous grand myths with the Whaling Story, insisting at every point that it is a novel and realistic way to render the human condition.
Yet over the years I had often thought about–indeed, been haunted by–Melville’s epic of the sea–the greatest story of the sea ever written according to such as D.H. Lawrence and John Masefield. And because of those and a few other late discoveries, the obscure and forgotten Melville’s sublime book was redeemed from oblivion in the 1920s. Of course, like most of the handful of truly great epoch-making stories which move storytelling in new directions to dramatize new spirits of place and pivotal times, Moby-Dick is nothing if not strange on first reading. The style and premise are shaped by new compositional challenges arising out of new times. The natural enemies of serious literature–tradition-bound English Departments and distracted “schools” of literary critics stand out here–will seldom recognize truths in such crucial strangeness: poor Melville could not rely on “the shock of recognition.”
But I surprised myself. I devoured Moby-Dick on my second reading. The best I can say here is that looking back from our present day it has become inevitable that Melville’s classic now emerges in all its simple profundity.
Yes, simple profundity.
The wonderful Emily Dickinson wanted to “unname” the male-dominated poetic tradition and reconfigure experience in new ways. Fellow New Worlder Melville wrote Moby-Dick as an interruption of a vast, hoary cultural outlook whose literary paragon is, of course, Shakespeare. Yes, Melville turns away from earlier versions and explanations of the human condition, a vast body of drama epitomized by the Bard. Apropos, there is no hero in all of high literature who is like Ahab. Nor, I would wager, is there one who has been misunderstood more consistently.
Thinking of Melville’s state of mind–really, his inspiration–as he writes Moby-Dick is the key. Such genius eludes us in its wonderful moment-to-moment soaring and diving and just plain staying-the-course, but I think there are three roads which lead to the heart of Moby-Dick: First, a reflection on the final paragraph of the novel; Second, Ahab and the Theodicy Problem; Third, the malevolent beauty of the natural world.
(1) The End of Moby-Dick. Here it is in all its terrible, poetic beauty. The Pequod is sunk by Moby-Dick; all ends thusly:
Now small fowls flew screaming over the yet yawning gulf: a sullen white surf beat against its steep sides; then all collapsed, and the great shroud of the sea rolled on as it rolled five thousand years ago.
Melville tries to fit the absolute essence of human experience as he knew it–the Human Condition–into the story of the White Whale. There is adventure, there are thrills, there is the surface beauty of Nature (though monsters swim below the sun-dappled surface of the sea on a balmy tropical afternoon as noted for an enraptured sailer manning the Crows Nest who forgets the brute physics still holding during his idyllic vista in which in his seductive reverie he loses his footing and plunges to his death). In other words, after the whole stirring and brutal adventure in which EveryHero Ahab, calling himself “Adam, staggering beyond the piled centuries since Paradise” just to make sure we Get It about his enormous symbolic stature, diverts the Pequod and its carefully depicted global crew–Here Comes Everyone–from the lamp-oil mission to a new Story of stories to “strike through the mask” of an “inscrutable malice” in a Nature, the monstrous agent of which is the White Whale, that has it out for us. If Moby-Dick is Melville’s version of the whole world and the essence of human experience–a vast take–humanity ends up sailing on a journey which is–no other words seem as fitting–a Defiant Hero’s (not a Pilgrim’s) progress through a deadly enshrouded Nature: “…the great shroud of the sea.” We must, says Ahab, defy our circumstances. This is our supreme integrity.
(2) Ahab and the Theodicy problem. Theodicy is a centuries-old intellectual pursuit of some explanation of why God permits evil, and a mindful quest finally focussed on the mystery of human suffering. Again, Moby-Dick is the irreligious Melville’s agent of savage nature, and the pursuing Ahab, scarred from nape to sole by the horrific whale in earlier encounters, says that he’d even strike the sun if it offended him. Ahab is “monomaniacal” in his determination to defy Nature; indeed, to punish Nature. (And I imagine Melville to be snickering on those few times he allowed that old psychological term into the narrative in characterizing Ahab). Now, what are the traditional “answers” to the Problem of Evil? Here are some: We humans are guilty sinners and deserve our suffering in this Vale of Tears. We humans show darkness of the intellect and cannot fathom why actually All Is Well: God has things right but we aren’t smart enough to realize it. And further, and even though suffering, we humans can through mysticism transcend that grief. Zen and Theresa of Avila.
And Ahab’s entering into this Great Question? We could review much of his conduct, but the marvelous Melville says it profoundly and simply in one moment in the drama: In a South American church on one of his voyages made before the novel opens, we are told, Ahab is shown a “Holy Chalice of Communion”: Ahab spits in it.
Ahab rejects an entire and pervasive tradition.
So, of course, does Melville himself. Melville’s prophetic Elijah, encountered by Ishmael and Queequeg on the pre-voyage docks, foretells of doom, unlike the Elijah of the bible. Melville here is going about Emily Dickinson’s “unnaming” of things traditional. And here, perhaps, better said: “renaming.”
Another of the many signs of Melville’s anger about Theodicy: Father Mapple’s sermon early in the novel on the Old Testament story of Jonah in the belly of the whale is the inverse of Melville’s vision of reality, Mapple’s harangue being a silly myth from the previous (Biblical) Story of stories before Moby-Dick appears (make no mistake, the “renaming” Melville is supremely ambitious!) and the Jonah story having no referents to the realities of Moby-Dick. In that wintry church in which early in the novel Mapple climbs his little play ladder up to his little play ship of a pulpit, the abiding impression of the scene is those cold marble tombstones mounted on the church walls and listing whalers killed in that endeavor. That imagery complements the mysterious murky painting hanging in the Spouter Inn where Ismael stays before the voyage and which Ishmael sees, as he studies the canvas, that it gradually (as in the manner of an optical illusion–ah, Herman, what a symbolist are you!) resolves into the image of a huge whale emerging from the waves and leaping high to fall upon and crush a whaling ship. (Recall those lectures in English class about “foreshadowing.”)
The worst oversight in reading Melville’s epic is the all-too-frequent diminishing of Ahab as somehow an obsessive who merely wants vengeance on a dumb brute. Perhaps the right explanation here to show why there are such forlorn views by readers is Emerson’s warning about foolish consistency: I’m certain Melville would shrug and admit that the Old Testament Habits of Thought are in many invincible. Of course, he gives wonderful dramatic evidence to the contrary. First, Ahab is no forerunner of Hitler, etc. Ahab is Right About Things in the world of Moby-Dick (and, soon, the Darwinian world), and he rouses the crew to abandon the conventional major business of whaling–obtaining whale oil for lighting lamps–for an epochal quest. Yes, rouses. Stirred, they (even practical-Quaker Starbuck at The End) resoundingly follow Ahab. We see in Moby-Dick that Ahab’s harpooner, Queequeg, former member of the royalty on a South Sea paradise island, forsakes that indolent life for the dangerous, avid whaling adventure as a master harpooner ever ready to strike through the [malevolent] mask. And as the novel opens, Melville pictures Manhattanites gazing out to sea as humans are wont to do when encountering from a coast the inscrutable and vast oceans, the great shroud. Something pulling about it, eh?
3) The Savage Beauty of the Natural World. The symbolist Melville loves life both beautiful and painful and describes it sublimely:
Steering north-eastward from the Crozetts we fell in with vast meadows of brit, the minute, yellow substance upon which the Right Whale largely feeds. For leagues and leagues it undulated round us, so that we seemed to be sailing through boundless herds of ripe and golden wheat. (Right Whales) with open jaws sluggishly swam through the brit…. As moving mowers who, side by side, slowly and soothingly advance their scythes through the long wet grass of the marshy meads; even so these monsters swam, making a strange grassy, cutting sound; and leaving behind the endless swaths blue on the yellow sea.
But finally Melville speaks through Ahab about the malevolent force behind the “mask” of the natural world, a mask we must strike through to attack that “inscrutable malice” savaging us. And indeed Melville leaves us with little else but a shocking, stunning heroism: fierce Ahab, turning his back on an enormous tradition of human thought, becomes a would-be punisher of our omnipresent foe, Nature herself.
Ahab: The Defiant Hero.
Of course, Ahab is a larger-than-life hero. He embodies Melville’s Grand Take. And it is New. After all, the marvelous Herman is of the New World. And for Ahab, and eventually for the others in the global crew, reality, just as depicted in that murky painting hanging in the inn, resolves to the shrouded malevolence of a punishing monstrous whale.
This is not catharsis, not little stories about emotional problems, not metaphysical, not mystical, etc. It is instead a truly grand and pivotal and strange book, and as the great literary theorist Harold Bloom says, the Canon is comprised of strange books.
At the end, after all that magnificent adventure, we honestly do not know much, saith Melville. But we must be heroic in defiance. It seems right. And so: Ahab leaves his young wife and child and the warmth of home and hearth and takes to the sea and finally and fatally sinks his knife into the immortal flesh of the inimical White Whale.
And so here is Moby-Dick, in between the Old World and our new and most dangerous one of sensational and amazing technology. Melville did not know then where we might be now.
But to say it again, he cleared the decks (grimly appropriate in talking about the Pequod) for our period.He would demolish the Mysterian Tradition.
And now there is indeed our period. And herein another enormous story opens up to us, a redemptive one that may offer little hope of success given all the obstacles. Yet: Consider discoveries like Cantor’s Diagonal Argument (an inkling of an edificial Beautiful)–the sheer wonder and thrill of it–Cantor’s great glimpse of varieties of Ever. Recall that in Moby-Dick Melville speaks of the “infinite series of waves” that encircle the Earth: here is not Cantor but an Escher-like sense of being confined to a circling infinity bound to a globe: ultimately a hellish infinity of ennui. But that is not the presumptive direction of our present and future technology: I am presuming that technology portends the ultimate meaning of a transformation into post-biological life in which the New World becomes Ideality and there is a boundlessly happy infinity of a grand Mathematica Dramatica far beyond the impenetrable mask.
2. A Single Line from Noel Coward’s The Vortex (1924)
“How can we help ourselves? We swirl around in a vortex of beastliness.”
3. The Heavy Bear Who Goes With Me, by Delmore Schwartz
“the withness of the body”
The heavy bear who goes with me,
A manifold honey to smear his face,
Clumsy and lumbering here and there,
The central ton of every place,
The hungry beating brutish one
In love with candy, anger, and sleep,
Crazy factotum, dishevelling all,
Climbs the building, kicks the football,
Boxes his brother in the hate-ridden city.
Breathing at my side, that heavy animal,
That heavy bear who sleeps with me,
Howls in his sleep for a world of sugar,
A sweetness intimate as the water’s clasp,
Howls in his sleep because the tight-rope
Trembles and shows the darkness beneath.
—The strutting show-off is terrified,
Dressed in his dress-suit, bulging his pants,
Trembles to think that his quivering meat
Must finally wince to nothing at all.
That inescapable animal walks with me,
Has followed me since the black womb held,
Moves where I move, distorting my gesture,
A caricature, a swollen shadow,
A stupid clown of the spirit’s motive,
Perplexes and affronts with his own darkness,
The secret life of belly and bone,
Opaque, too near, my private, yet unknown,
Stretches to embrace the very dear
With whom I would walk without him near,
Touches her grossly, although a word
Would bare my heart and make me clear,
Stumbles, flounders, and strives to be fed
Dragging me with him in his mouthing care,
Amid the hundred million of his kind,
The scrimmage of appetite everywhere.
Schwartz’s fine poem is a complaint: “A stupid clown of the spirit’s motive…. That inescapable animal (who) walks with me.”
The plight of the natural selectee. After all, for these times, we are animals.
4. Black Swan, A Film by Darren Aronofsky
Black Swan (2010) is a most artful modern retelling of an old story, the conflict in each of us between the angelic and the primordial leading to the distinguishing human transcendent yearning for a perfect state, namely one perfectly beautiful. The movie is in the general tradition of Jekyll and Hyde, Metamorphosis, Equus, Beauty and the Beast, The Wolf in Sheep’s Clothing, The Picture of Dorian Gray, the guardian angel versus the devil, the ego and the id, the civilized primate and the naked ape, and many others.
Nina Sayers (Natalie Portman), the ballerina of a famous New York company, is selected to play both the White and Black Swan in a radically revised Swan Lake stripped down to its essential conflict in these tumultuous times so far from Tchaikovsky’s day. The original score, story and choreography are shaped for our era.
The mistaken interpretation of this intense and haunting movie, one growing in the critics’ echo chamber, can be summed up by Voltaire’s famous observation, “The perfect is the enemy of the good.”
The real question is, which “perfect” is Black Swan about? The perfectly beautiful discoveries of mathematics as a human transcendence seem consonant with dreams of the ultimate engrossment of Strong Artificial Intelligence and its presently vague idea of a new consciousness, a next-stage sentience, “silicon consciousness.” But though Black Swan is contemporary with a vengeance, the “perfection” sought in it is the traditional one which assumes humans are ever to be of natural selection and that to be “perfect” is to war with one’s evolved natural self to sublimate the natural and break free to be supernatural. In that psychological war within Nina, the White Swan must vanquish the Black Swan. The Black Swan is primal, swampish, insistent, unrepressed and irremovable. So, Nina’s balletic vanquishing is strictly sublime suicide.
Yes, to attain the old ideal of human perfection, a most fleeting refuge for these unscriptural and irreligious times, and in the most sublime secular artistic expression of it, the ballet, is to live a grim paradox. To say it again, Nina Sayers must become suicidal for her White Swan to overcome her Black Swan, and crucially she must bravely confront and do in her Black Swan–do in her primal self and, because she is not purely angelic and cannot be, ultimately do in herself wholly, to bring in that very act her dancing to the perfection she supremely consciously wants to reach and may well at most achieve in performance as barely more than an intimation if indeed one which her audience thunderously understands and appreciates in a mysterious recognition that seems most human, happily so.
Black Swan is as deeply paradoxical a movie as you may see for some time.
Its art is superb. Darren Aronofsky, a youngster-director with a short resume, creates a Hitchcockian aura of dark, eerie, canny suspense. The camera stays as close to Nina most of the time as the mythical guardian angel is said to have shadowed Medieval man. Nina is all, everything, finally, in this remarkable movie–in the deepest sense there really isn’t anyone else in the story (nor, given the drama here, does there need to be)–and the most serious things about the human creature take up the story of Nina as we too follow her. (Here Comes Everyone).
Aronofsky adapts several horror movie motifs gracefully and for artistic purposes never imagined by the schlockmeisters who contrived them. For instance, Nina’s ballet-trained legs morph for a horrifying instant into equine legs; and her toes, in another such moment, become webbed after which, horrified, she quickly slips on her long, square-toed ballerina shoes. How’s that for a central metaphor? It’s even better than another one: Nina cuts herself deliberately at times in the manner of the old self-flagellating monks: Beat the Devil, as they say. Here, though, we can and should be modern and substitute “Black Swan.”
5. Close Encounters of the Third Kind, a film by Steven Spielberg
I think a case can be made that Close Encounters of the Third Kind (1977) is Spielberg’s finest. The story, a modern fairy tale about benign and superior visitors to Earth from Somewhere in the universe, shows a Hitchcockian awareness of preserving classes and culture (e.g., the Master’s wonderful movie of the 1940s capturing for history twentieth century British aristocratic ways and means, The Paradine Case). Likewise, Spielberg focuses on the speech, houses, clothes, food, fears, settings and other components of American middle class life in the 1970’s: they are magnificently preserved with an exactness that is remarkable and bespeaks an intense observation and dramatization. And in our fast-moving culture, the world of Encounters has already largely passed into its only remaining reality, memory.
Most importantly, this movie has an interesting small place in what some have called “The History of Consciousness.” The hero, Indiana power company field worker, Roy Neary (Richard Dreyfus), one of the few humans called to a rendezvous by the friendly aliens with their stunningly advanced technology, is far from the usual Hollywood central figure. Why? Because he wants to get Out of Here! He wants to leave the Vale of Tears of human earthly existence, escape the final fate of all its mortal human characters, and all this on an irresistible dare, a faith that simply by departing to another and much advanced world–walking up the ramp of that huge mysterious ship and entering it–you might discover that Hobbes and his observation that human life is poor, nasty, brutish and, above all, short, might be escaped! Indeed, at one point Neary explains that in view of his Close Encounters, “I want to know what is going on!” Neary is pure wonderment!
Yes, few heroes of our art-stories would put down human life. How many of them would do as Roy Neary does, forsake wife and kids without so much as a backward glance?
I’m more than prepared to believe that such was not foremost in the minds of the principals as they created Encounters. It may have been a dawning irony post mortem. My daughter, who worked in production in Hollywood, says word has it that there was indeed a later regret over the chance of emerging disapproving implications to some movie-going sensibilities of wonder-struck Neary’s intense decision to leave his family: What sacrilege have we wrought?
But Roy Neary sees irresistible evidence of a greater technology right in front of him, in the ships and behaviors of the “Alien” Visitors. And he especially senses it when the happy outsiders do a little mind-control on him: especially as shown in his nagging, mysterious urge to sculpt what turns out to be a scale model of Devil’s Tower, the rendezvous point for the event that will change history.
Roy Neary is acting on what in a sense we might call an inhuman faith when he leaves Trauffaut, Balaban and the others behind and boards the Mother Ship. Lots of unknowns before him, welcomed unknowns.
After all, he is turning his back on…well, his Earthly existence.
6. The Children Act, a novel by Ian McEwan
What exactly had troubled her? –Narrator’s Question about Fiona Maye in The Children Act
This question–the Question of questions in McEwan’s novel–is answered most dramatically for his heroine, Fiona Maye, a still-fetching middle-aged High Court judge in today’s London and ruling on child welfare cases, that answer revealed through a superbly understated and controlled narrative which is intended to carry you unerringly and with a dismaying sense to accepting a traditional, brutal literary naturalism updated for our times. McEwan, as always, dramatizes Bad News: we are futile actors of a darkened intellect and a weakness of the flesh whose floundering lives dramatize ironic futility in the face of forces, often invisible, against which actually we have no chance of prevalence. The old saying that we are our own worst enemies is a half-truth: we’re self-defeating but it’s nothing to become egotistical about: we’re merely in a happenstance situation “rigged” against us and in which our behavior itself is ultimately a dooming joke we don’t really get. “Rigged” rather than rigged because, when you get down to it, the forces are impersonal. There is no one beyond us to care about us.
Philosophical and literary Naturalism, pure and simple.
So: The Trouble with Fiona is the trouble with us all. It’s the Trouble with the World. In it redemption is no more real than unicorns. Biology, anthropology and cosmology are all secular and impersonal latter day components of a Grand Surround: by definition, there is no way around it.
The artistic response of McEwan is to fashion beautiful, masterful narratives in which his revenge is a superbly accurate rendering of our hopelessly Bad Fortune: if we can’t overturn the forces, at least we can expose them; we can be aware; we can thus be tragic rather than merely innocent, let alone stumbling around ever as Blind Fools. Says McEwan and out of a demanding, triumphant art created to make us Knowing: Damned if we must be fools!
McEwan’s literary skill is a joy to behold. See how he dramatizes “What exactly had troubled (Fiona)?”
First, he makes her an exemplar, an estimable exponent of the essence of the Enlightenment, that promising miracle of civilization, that brave fortress in savage history. Specifically, the moral and expert Fiona is at home in the world of great jurists of the past who formed principles to rule favorably in cases of child welfare. The problem of child welfare–what could be more central and engaging in Enlightened thinking, especially given modern humanistic ideas about children? And so, now a prominent judge, she must decide the most urgent cases, for example, concerning separation of Siamese twins (named “Matthew” and “Mark” by the artful and rather nasty Ironic, McEwan) in which one will survive and without which both will die, the latter outcome favored by the traditionally religious parents and their community; custody of children in which wealthy care in a traditionally stifling culture must be traded off against somewhat precarious upbringing in which the child enjoys greater freedom in a rapidly changing world; and saving medical operations for otherwise terminally ill children of parents who are Jehova’s Witnesses determined to allow their children to die.
Second, the childless Fiona will be troubled when we first meet her. Something about her Child Welfare cases has begun to disturb her. She is losing her sense of physicality. Her husband, Jack, a fifty-nine-year-old “professor of Ancient History” (mark that well as McEwan’s Naturalistic-theme-reinforcing assignment of a profession), is threatening an extramarital affair with a young stenographer because Fiona seems to have lost interest in sex. Jack is pretty much an ordinary chap. He stays in good shape with daily hoisting of light weights in his office. He likes to ski. Although he and Fiona are childless, he’s great with their visiting neices and nephews–he delights them by goofing off with them without a thought about their psychology and mental stages of growth: he’s a natural.
McEwan is a great compressor of complexities. Here, in a passage that beautifully sends up a poetic Naturalism and goes far in making us feel the Why and What of Fiona’s Trouble, is a superb example similar to several others in The Children Act:
At nights her thoughts returned to that photograph of the (Siamese) twins and the dozens of others she had studied, and to the detailed technical information she had heard from medical specialists on all that was wrong with the babies, on the cutting and breaking, splicing and folding of infant flesh they must perform to give Mark a normal life, reconstructing internal organs, rotating his legs, his genitals and bowels through ninety degrees. In the bedroom darkness, while Jack at her side quietly snored, she seemed to peer over a cliff edge. She saw in the remembered pictures of Matthew and Mark a blind and purposeless nullity. A microscopic egg had failed to divide in time due to a failure somewhere along a chain of chemical events, a tiny disturbance in a cascade of protein reactions. A molecular event ballooned like an exploding universe, out onto the wider scale of human misery. No cruelty, nothing avenged, no ghost moving in mysterious ways. Merely a gene transformed in error, an enzyme recipe skewed, a chemical bond severed. A process of natural wastage as indifferent as it was pointless. Which only brought into relief healthy, perfectly formed life, equally contingent, equally without purpose. Blind luck, to arrive in the world with your properly formed parts in the right place, to be born to parents who were loving, not cruel, or to escape, by geographical or social accident, war or poverty. And therefore to find it so much easier to be virtuous.
The Children Act culminates in Fiona’s intervening in a judicial case to save a seventeen-year-old boy, Henry, from death owing to the denial of medical treatment by the parents, Jehova’s Witnesses, Henry’s certain death being tragically favored as well by the obedient boy. Fiona’s is a triumph of humanistic civilization, an Enlightened response to superstition. She eminently does The Right Thing.
But….After masterfully instilling that sense of Fiona as an Eminent Civilized, McEwan stages his crushing final act, the Prevalence of Naturalism over even the Enlightenment. After Fiona imparts to Henry the virtues of Enlightened ideas of the individual–The End in many stories–a dreadful final chapter plays out in which Henry is neither saved nor Fiona allowed to triumph in a cause of the Rational. Neither is at fault. Fiona will, you are certain, be haunted by her awful lesson in the Naturalistic Vale of Tears.
Hence McEwan’s story is honest if not defiant.
7. Dreams of Earth and Sky, by Freeman Dyson
I’m here a little early in the evening at Club Paradise. I’m relaxing in a booth. Place is quiet. Paddy has brought over my first Bombay Sapphire martini. I’m expecting a couple of little known poets and a hermit writer to join me soon for drinks. A few days ago I asked this trio to help me look into some possible implications of Freeman Dyson’s latest collection of book reviews. The books he reviews are mainly vehicles for his own dreams and observations. These always seem worthwhile reading. Dyson looks into the heart of things.
My guests and I have read many of polymath Dyson’s wide-ranging, well-regarded and popular reviews in The New York Review. Now 92, Dyson has been a most prominent professor of physics at the Institute for Advanced Study in Princeton for many years, and he has known and worked with many of the seminal physicists and other scientists and technologists of the times, notably Hans Bethe and Richard Feynman. He writes in a clear, declarative style especially friendly to a public audience and surely welcome to specialists used to strenuous divining of tangled texts.
Dyson is what is sometimes called a “free thinker,” in his case especially signifying someone who (a) can look at both (or many) sides of an ongoing scientific and/or philosophical matter for a broad rather than parochial outlook; and (b) imagine how further related discoveries will take place, discoveries often made in a dialectical process such as a period of brilliant theorizing followed by a period of inspired experimentation. Einstein and Eddington.
Dyson is full of wonder and unquenchable delight in the variety of worldly and unworldly scientific and artistic adventures in History and instinctively seeks to weave them together as Grand Drama. His latest and the subject of our bar meeting is Dreams of Earth and Sky, a conference of invited books which conduct among themselves a sub-conversation about which Freeman the Eavesdropper is not only a Commentator but an awakened Visionary, to include speculations and reflections on: our likely move from the present period of information technology to one of biotech; theory and mathematics versus empirical measurement in the progress of physics and cosmology; “Rocket Man” Wernher von Braun driven at bottom by dreams of interplanetary space travel; Dyson’s sense of insufficient evidence of global warming; the question of whether elegant physics–for example, the idea of processes “accomplished with the least action”–shows ours to be “the best of all possible worlds”; the traditional, Baconian idea that progress in the sciences must benefit humankind, this pondered by Dyson against his youthful work in World War 2 as a strategic designer of the RAF bombing campaign against Germany; the true Oppenheimer; and Churchill’s pursuit of nuclear weapons.The scope of his curiosity shows in the books reviewed in these pieces, including: Thinking, Fast and Slow, by Daniel Kahneman; Physics on the Fringe: Smoke Rings, Circlons, and Alternative Theories of Everything, by Margaret Wertheim; The Fellowship (on The Royal Society of London), by John Gribbin; The Age of Wonder, by Richard Holmes; and Robert Oppenheimer: A Life Inside the Center, by Ray Monk.
Dyson ultimately thinks and writes in a cheerful tone. He is not unrealistic about the shadows in History and the plights of the Human Condition. But death, war, pestilence, folly, farce–in the olden encapsulations “the darkness of the intellect” and “the weakness of the flesh”–are left outside on the stormy heath of History. And as to our Future: After reading Dyson’s Dreams of Earth and Sky, we must say: Dystopia, we hardly knew ye.
In looking for a definitive statement and accompanying major assumptions in Dreams, there are these stirring words:
The vision of the future as an infinite playground, with an unending sequence of mysteries to be understood by an unending sequence of players exploring an unending supply of information, is a glorious vision for scientists.
Apropos: My friend Marvin Minsky, who passed away a few years ago, told me that over his theorizing years he had posed the question of personal immortality to fellow scientists and thinkers and that they had almost all longed for it primarily so they could keep working indefinitely on grand mysteries.
About that I’ve always thought, “Humm.”
Dyson sees for artists and writers and ordinary people, “people who feel alienated from the prevailing scientific culture,” a darker sense of the Human Condition in an “information-dominated universe,” citing Borges’s famous short story, “The Library of Babel” in which, as critic James Gleick says, humans “walk the corridors, searching the shelves and rearranging them, looking for lines of meaning amid leagues of cacophony and incoherence….” Borges wrote his story in 1941; since then, notably Thomas Pynchon in an epic series of novels has massively dramatized the confused epistemology of Homo sapiens.
But here I’m sure Dyson is just being evenhanded. Elsewhere in Dreams of Earth and Sky I discover a passage with which he seems most sympathetic. It is this timeless definition by Francis Bacon:
The true and lawful goal of the sciences is simply this, that human life be endowed with new discoveries and powers.
Bacon’s words, together with Dyson’s in that earlier passage on the vision of the future as an infinite playground, create the general impression that Dyson is essentially cheerfully brave–a stiff upper lip–on the rim of what Pynchon calls “the vortex of history.”
I’ve invited the poets and the hermit writer for drinks because they tend not to be generally cheerful. That’s putting it mildly.
Perhaps a Mercilessly Negative Person could think of a Grand Take on Things as Nightmares of Earth and Sky.
Looked at in a dark way, what are we learning from cosmology? The vastitude, the unimaginably violent scale of which has exceeded our minds except perhaps through colorless and dispiriting probability, seems a less and less inspiring field of discovery. Not so much a matter of the event horizon as of a human mind horizon. If string theory is itself beautiful (and wildly assuming that beauty must equal truth), what it portrays seems Bad News. Meanwhile, natural selection, whatever its “engineering” merits, grips us as per another timeless idea of the Human Condition, Bloody Nature, a realm wherein perhaps not the speed of light but the certainty of Death is the great constant.
Some present mathematicians such as Thomas Harris and Reuben Hersch can make you think of pure mathematics as the Great Refuge. They’re hard to argue with. All that forlorn “philosophy of mathematics”–“foundations” and “existence” and elegant mathematics reflecting a “deity’s mind”–caused by a most understandable confusion of the Natural (including Theology) with Mathematics…we’re getting over it. And notice that you can’t really observe infinity but it’s real. Mathematics is ultimately unto itself.
And apropos new mathematics, here’s a profound cited passage in Dreams of Earth and Sky by the contemporary Noble physicist, Frank Wilczek, which has a telltale duplicity about it, a sense of a fundamental idea on the verge of escaping the Natural for the Pure:
Through patchy clouds, off in the distance, we seem to glimpse a mathematical Paradise, where the elements that build reality shed their dross. Correcting for the distortion of our everyday vision, we create in our minds a vision of what they might really be: pure, ideal, symmetric, equal and perfect.
So: Roy Neary and Nina Sayers and Delmore Schwrtz grasped by his Heavy Bear, and furious Captain Ahab, may not have this vision, just variously a felt need: But for you and yours truly: Imagining the shedding of dross and the correcting for our everyday vision–the two enormous processes must be profoundly related–we may come to consider an outlook of escaping to an endlessly suspenseful Ideal of Mathematics–dynamic and progressive edificial discoveries ever the inverse of a Static Heaven aka the Beatific Vision aka Nirvana–through a non-natural selection in which we re-engineer ourselves into Indefinites. It’s far too soon to analyze this glimpse of a new human history, one surely of a fragile plausibility owing to perhaps an insufficient time to create it not to mention the weaknesses of human intelligence. Best now just to raise it. But the timing doesn’t seem bad.
Yes, the raising of it seems fitting. A duty? Perhaps a fitting intimation?
So, on second thought in my excitement, I’m leaving before those sober poets and the “realistic” hermit writer show up. Knowing them, they’ll imagine they know less than we really already do about all this.
I’ll leave a hundred at the bar as their tab. (I have a trust fund.)Text them after I leave.
Maybe talk to them sometime later.
PS. Here it is the next day and one of the poets, an elderly traditionalist, posted for me a few verses–she won’t call them poetry–about a couple of the many problems in rising to Math Heaven.
I. On Rebuilding Ourselves
I see inward beyond the Natural
A human heaven I might capture all,
A Mathematica Dramatica,
A suspenseful silent sinfonia,
Rising not from physical reality
But only from my own mentality.
I’ve long known this Ideal place
Distractedly, within the Natural place,
Hence interrupting mathematics
To eat, sleep, weep and procreate–basics,
So that I can never see math heaven,
And die dramatizing cruel Ulam:
Unable to build, hold and extend an
Edificial math alive within my ken.
In my natural life, that would bring quick death,
No doubt by accident–yes, my last breath.
Hence Natural Me does not see math heaven,
Though the idea of it does regret deaden.
To escape from my mortal Determine,
To reach my mathematical Heaven,
My psyche saved from accident,
My mental beyond the Natural sent,
I need not superstitious redemption
But immortal non-natural reinvention.
II. On The Endless (?) Engrossment of Mathematics
Now I ask: Math by super numerists
Eventually bores those numerists?
Infinity, basic to the Ideal,
Fosters familiarity too real,
Stealing, say, fun in coin-flipping,
All suspense in supermath then slipping!
But design of superhuman mathite,
And endless drama in infinite flight,
Hopefully sum in happy ratio
For heavenly suspense ever neo
Thrilling: not static but intelligent:
No beatific vision but ascendent.
Mathite’s design aside for the moment,
What in math could make mathlife descendent?
Perhaps math collapsing of its own weight?
Or might internal flooding be math’s fate?
But most profoundly there’s Infinity,
Unobserved in math sublimity.
Yes, a simple example: the coin flip–
Heads or tails? “Chance” in the natural grip,
Those occasional instants of suspense
But with which Infinity will dispense,
By eliminating uncertainty
In unimaginable certainty.
Two issues for designers of Mathite:
Redesigning humans for Ideal flight?
The Infinite as infinite dramas?
The first, Redesign, eschews pajamas.
But the Great Infinite must be unknown;
Could Big Sleep befall us in that unknown?
An Outrageous Summary of Sorts
Now, in this essay on Heaven Engine and its theme of a life in Ideality, the time comes for an outrageous summary of Art History. After all, I am so obligated, for I have claimed that some art is heraldic. At least I can burden the reader with only a brief summary (recalling that we pay little mind to art scholars and professors); and indeed, my insolently outrageous art history–what a satisfaction for me!–can be said simply.
Apropos, psychologists say that a list of three items fits our human minds well; more items might defeat the attention. So: lets be cavalier and divide Art History into three phases.
Shakespeare heads up the first period, his span extending before and after his time. We’ll call this period Traditional. We might call it Hopeless, too. The Bard superbly accepts life in the Vale of Tears. The premise? That’s just the way it is. Every mortal loses at last. There is something alien about the place in which we live. The most an artist can do is create “catharsis”: by facing pain and suffering–“Tragedy”–supposedly “catharsis” soothes us and somehow we calm down about the undeniable prospect, The End. Just about every artist in history and globally lives finally in or near Shakespeare’s creative world and under the Bard’s assumptions. Lear is archetypal as he grows old and destroys the very things he most loves because he is ground under by aging, circumstance, and the rest of it. Moreover, his stormy heath is the place in which we first and last find ourselves. It’s wise to accept it. Best we can do.
But in our day such seems less and less acceptable. “Catharsis”? Wow. Who says big ideas don’t get old and embarrassing? Or (especially) “ironical”?
As we have seen, the second phase–Heroic Defiance–has a lonely but noble champion, seemingly someone for whom we have been waiting. Captain Ahab hasn’t any metaphysical answers, and he conducts Heroic Defiance against all those malevolent forces, those diseases and those storms and winds and floods and stormy, forsaken heaths and, really, the even worse demons such as the leviathan Moby-Dick (an agent of inimical Nature to top all such agents) which prey seemingly inscrutably on us. Again: scarred from nape to sole by the metaphorical monster, Ahab goes with exhilaration to his death in the futile attack on Moby-Dick. It’s the most heroic thing that can be done then, at that historical point. The marvelous Melville creates his evil swell, the “infinite series of waves” over “the great shroud of the sea,” seas that Escher-like (in the eventual nightmare sense) endlessly circle the globe, a hellishly boring Infinity.Ergo:
Most importantly: Heroic Defiance is the plausibility for Ahab and crew. There was no technology then to rival today’s. No such hope, however tenuous. Longevity, enhanced intelligence, modern cosmology–largely not present and barely hinted.
So: What is the third phase of Art in this admittedly glib account? What would be an escape from ours and Ahab’s malevolent world? Well, here’s a conjecture:
Quest for the Transcendent.
Indeed, the Age of Personal Technological Quest.
Imagine the intent of a new posthuman experience is uninterrupted mathological wonder–a transnatural Mathematica Dramatica. It is a Quest of quests! Imagine an indefinite life in which there are mindful beings, shorn of Natural Selection and its cruel, irresistible and impersonal grip on each of us in a mindless experimentation to find the “fittest,” with us now as well no longer corporeal humans but Mathites–new beings who live in a Forever typified by such as Cantorian discoveries of a variety of infinities. In short, the mindful Beautiful. If shorn of Natural Selection, the postbiological Mathite has no cares about reproduction, self-defense, nourishment and those imperatives of naturally selected Homo sapiens. Now it is one narrative of ecstatic discovery; Hawking’s later doubts he can really be sure of what he earlier seemed to be sure of: that is because finally physical reality is ever knowable only through some remarkable but painfully impermanent models–well, a predicament to be sure!
But that beauty that is won in the suspense of discoveries in the Platonic mindscape of the Mathematica Dramatica–and always entailing wondrous “tricks” such as the Great Diagonal in Cantor’s exposing of varieties of infinity–does not go away. It does not vanish in a maelstrom of competing new imperfect models. It prevails. It portends.
After all, can you blame Roy Neary for taking a chance and walking up the ramp into that unprecedented ship? He is on a quest. We might want to keep a look-out for him.
Given what physicists and other scientists have discovered about the universe(s?), namely, that invoked here is a humanly unimaginable and overwhelming scale and violence whose time is measured in billions of years and within which the “Goldilocks” happenstance of humanity on the mere pebble of Earth is but a blink of temporality; and further given that the natural order of human existence–the Darwinian strife, stress, pain and brevity whose rectifying would only bring the grand irony, Updike’s “infernally bored” human immortals and/or Disnovelling, my Prevailing Plague of Suicidal Boredom for Human Longevitites in Heaven Engine, this question seems to arise:
What superintelligence, what far advanced post-singularity mind, aided by such presently incomprehensible power as distant future quantum computing and other advancements, would think it intelligent to remake mindful life strictly according to the natural order of things, that is, engulfed in physical reality?
As Homo sapiens, we cannot begin fully to imagine, let alone experience, the sublime mindful life of the Mathites I am postulating. But in the epiphanies we sometimes do experience through our human psychology, especially in advanced mathematics, such an experience can be sensed, glimpsed, intimated. Suffice to make an apology now and note that in the course of this essay, especially what follows below, hopefully the sustained and edificial nature of what ideally Mathites may experience will become more imaginable.
(Through his revolutionary incompleteness theorems) Godel proved that mathematics is inexhaustible.
(The goal of mathematics is) the symbolic comprehension of the infinite with human, that is finite, means.
I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our “creations,” are simply the notes of our observations.
–G. H. Hardy
[T]he infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to. Can thought about things be so much different from things? Can thinking processes be so unlike the actual process of things? In short, can thought be so far removed from reality?
But what accounts for this limbic-mediated thrill (of elegant mathematics in Euler’s e)? I think it springs from a combination of things, including Euhler’s equation’s seriousness, generality, depth, unexpectedness, inevitability and economy–qualities that prominent twentieth-century English mathematician G. H. Hardy singled out as key ingredients of mathematical beauty.
…there is nothing more abstract than infinity….It’s sort of the ultimate in drawing away from actual experience. Take the single most ubiquitous and oppressive feature of the concrete world–namely that everything ends, is limited, passes away–and then conceive, abstractly, of something without this feature. Analogies to certain ideas of God are obvious; abstraction from all limitation is one way to account for the religious impulse in secular terms. …the exact same sort of explanation can be given for where we get the concept of infinity and what we ultimately mean by all forms of the word ‘infinite’ we toss around.
–David Foster Wallace
… the mysterious and fantastic world of infinity and beyond…. (You can) revel in the power of mathematics…and head toward the horizon of human thinking without that horizon ever getting any closer.
It is impossible to think about Ideality without also considering the Mathites I’m imagining to be the mindful posthumans who themselves think and discover there. After all, the imagined vision of Ideality at present is merely a human one. The Ideality of a presumptive Mathite would, of course, be the Ideality available to Mathites to know. Certainly a Mathite’s mindful heavenly experience would mean discovery. A process. A story. Pursuit. Suspense. Epiphany.
Or as I prefer to call it, “Creatovery.” For example, Cantor creatively uses a matrix format and its diagonal to help discover that there are varieties of infinity (see below).
Yes, the presumption here is that knowing Ideality, discovering it, would be happily eternal. Infinite.
An endless story.
The best I can do now, and sought to do in Heaven Engine, is to dramatize intimations of the experience in a heavenly Ideality. Further, I’ll emphasize here a Mathite’s experience involving not all possibly foreseeable excursions in math in Ideality but essentially (if hardly completely) that involving the theme of infinity.
If I can hardly exhaust the theme of the human pursuit of infinity in these pages, perhaps it is possible to convey in an exemplary way something of the ecstatic discovery of aspects of infinity by some of the great mathematicians. After all, as David Foster Wallace points out, infinity is the ultimate counter to the brief experience of us humans, natural selectees all.
Here are some examples:
* * *
The inspired finding of ingenious mathematical ways to grasp and use the beauties of infinity is a telltale story in the long, progressive history of mathematicians’ determined excursions into what I’m calling, Ideality.
We may start with the simple. Again, call them, and later examples below, at best glimmerings of the Mathite’s experience.
Early in mathematics, it became evident that the Number Line–the natural, familiar and fundamental line employed throughout history for linearly counting from left to right the natural numbers 1, 2, 3 …–helps solve certain kinds of problems in dealing with magnitudes. Now pause and actually form a picture of that same Number Line displaying natural numbers. Note the gaps, the inevitable spaces on the Line, between the natural numbers. The significance of these gaps? It is stupendous. For obviously the Line itself is larger than any row of natural numbers on it, no matter how long that row. Indeed, as we shall discuss shortly, we have learned that the Line is infinitely larger than any count of natural numbers arrayed on it. Of course, each natural number on the Line can always have yet another natural number added to it–1 + 2 + 3 …–and hence the natural numbers themselves are infinite. Yet between the gapped natural numbers the Number Line itself evokes infinity.
And so, regarding infinity, what about further, progressive “creatovery” thereof? Hence: Lets resume thinking of the Line itself as continuous, that is, the more powerful realization also promoted by the Number Line that in mathematical reality there is the fractional all along the Number Line which more powerfully embodies the infinite. Again: The Line itself is infinite. The exploratory significance?
In his excellent book, Infinity and the Mind, Rudy Rucker observes:
For the Greeks there were two kinds of magnitude: discrete and continuous. Discrete magnitudes could be counted, set into correspondence with natural numbers that were sometimes visualized as patterns of dots. But continuous magnitudes simply did not correspond to any number at all. Just as we can add and multiply numbers, we can manipulate continuous magnitudes by means of the techniques called geometrical algebra. The Greeks developed these techniques to the point where they could, in effect, solve most quadratic equations involving continuous magnitudes.
In short, the Greeks, after searching very hard, found a new and no doubt counterintuitive way–geometrical algebra–beyond natural numbers to deal with a daunting manifestation of infinity, one that until then had defeated their time-honored (if early) number-crunching derived from the dawn of a human mathematics that must have began with a counting by fingers! Herewith the Greeks resorted to an entirely different mathematics in which finally they could both begin to understand and make actionable a sophisticated infinity.
What a beautiful triumph! And yet only one among the many that signify the drama of the mind and infinity. It serves as a prelude to far more thrilling triumphs.
* * *
We can see from various developments in pure mathematics a deep desire to grasp a true, robust, even torrential infinity coursing onward endlessly. But our constrained psychology as creatures of natural selection–as personally confronting an experience of Beginnings and Endings–has led us psychologically to an ironic paradox. The capturing of infinity by us finite humans has sometimes led us–unwittingly?–to a remarkably provincial symbology of hellish infinity. The basic symbol of infinity in our mathematics, the lemniscate, depicts a graceful form reminiscent of the famous “lazy figure eight.”
As Rudy Rucker notes about the lemniscate in Infinity and the Mind:
The appropriateness of the symbol ∞ for infinity lies in the fact that one can travel endlessly around such a curve…. Endlessness is, after all, a principal component of one’s concept of infinity.
But imagine an intolerable eternity of traveling that closed track! Rita Mae Bown, the novelist, once defined Hell as doing the same thing over and over. Is the lemniscate not an ironic symbol? Is it not surpassingly human?
Three dots, more prosaic, seem immensely more visionary, humbler, and certainly more hopeful.
Similarly, in his epochal Moby-Dick, Melville writes of the Pequod sailing “the infinite waves”: In Ahab’s heroically defiant rousing of his crew to pursue globally, in all the oceans if needed, the White Whale and destroy it as the agent of that inscrutable, malevolent, affronting force of Nature which has it in for each and every one of us suffering naturals and hence mortals, not sinners in Melville’s modernity but undeserving innocents, Melville appropriately dramatizes in the 1800s the great watery grandeur of the Earth, its infinity of waves, in encircling it in pursuit of the Whale; but not too many decades after Ahab and his crew are lost we have images of the Blue Planet taken from space in which, given that Earth is a mere pebble lost in the inscrutable vastitudes which terrified Pascal, one can see that to ride the infinite waves of the oceans endlessly in circling that flighty Goldilocks speck known as Earth, poetically if not plausibly, and most perfectly by combining sailing routes with airline routes that cross both land and water, would be to embark forever on what then might be called an evil swell of Melville’s: yet another hellish experience of infinity. And to what end? Indeed, as Melville’s magnificent novel ends: “…and the great shroud of the sea rolled on as it rolled five thousand years ago.”
A further example, if ironic, of the infernal human conception of infinity can be seen in M. C. Escher’s lauded depiction, Ascending and Descending:
* * *
However, rather than represent infinity via certain shortcuts devised by us mortals, ways that truncate it, we deeply wish and need to appreciate it robustly, and even if indirectly to grasp it better, in its ongoing and endless magnificence. And even though infinity “radiates” from our finite settings, we can, as some of you know, nevertheless simplify and use the Number Line to aid us here. And from mathematics we’ll use the example of Euler’s Number, e, one of various mathematical dramas serving our vision of infinity. Specifically, in a great case of finite humans searching infinity, we’ll dramatize the very earthly role of e in representing no less than compound interest in finance, an old magic dating back to the 1600s. The symbol, e, is a mathematical constant that paradoxically serves to represent change. Its value is about 2.7.
In his wonderful book on the appreciation of Euler’s famous formula, A Most Elegant Equation, Charles Stipp reminds us that e “is uniquely valuable for mathematically representing growth or shrinkage” and is “one of math’s most versatile superheroes.” Stipp proceeds as follows to exemplify:
Imagine a (fantastical!) bank offers 100% annual interest on savings accounts for a year. An idle billionaire in a jocular mood invests $1. In a year she would have $2. This total is calculated by multiplying her original deposit times “1+ r,” where r stands as the interest rate expressed as a decimal number. (That is, 1 = her principal and r = the interest she’ll add to the principal.)
Next, a sharp but arrogant Harvard graduate, a finance major and new hire at the bank and whose grandfather is bank president, is promoted to Head of Investments and insists on attracting new customers by splitting the 100% into two 50% pieces to be paid respectively after the first and second six months of the year. The billionaire again deposits $1. Doing the math, we can readily see that she now realizes an annual ROI of $2.25.
So: When compounding periods are added within the twelve months there is repeated multiplication by 1 + r. Let’s say that the whiz kid from Harvard wants to buy a yacht, his grandfather has suffered amnesia, and the kid, unchallenged heir apparent and usurping power, demands that the bank should divide its 100% annual interest into lots of equal interest payments.
If we make the number of compoundings extremely large, won’t it be possible to cash in with only a modest investment? If she got serious, even our billionaire could truly enrich herself!
As they say, there’s no free lunch.
Apropos, here are some annual ROIs for those $1 investments:
$2.25 50% and 50%
In short, even with boundless compounding periods, only a comparatively modest ROI is obtained!
Why is it that as compoundings grow in size toward the infinite, our investor’s twelve-month total will move ever nearer to a number that is merely 2.718? Which is to say, the approximate value of Euler’s e described as the number that is approached as n gets bigger on its way to reaching the infinite.
Indeed: if e is rounded to the nearest hundred-billionth, its value becomes only 2.71828182846.
In A Most Elegant Equation, David Stipp reacts to this seeming paradox:
I find all this lovely and unexpected. Pondering the value of a ridiculously tiny bank account leads directly to one of the grandest conundrums of all time: how to conceptualize infinity without making the brain explode. (Or, as twentieth century mathematician Hermann Weyl put it with greater gravitas, the goal of mathematics is ‘the symbolic comprehension of the infinite with human, that is, finite, means.’)
Elsewhere, Stipp exclaims, “e effectively encapsulates the infinite.”
Herewith is a profound lesson about finite humans comprehending the infinite: the imposing of limits is crucial. In the bank example, it is a twelve-month period in which the compounding occurs, whether that compounding is once yearly or effectively boundless yearly, so that as the compounding increases, the compounding periods within the twelve-month period shrink. The torrents of wondrous infinity, its unimaginable scale, are channeled on the occasion into increasingly constrained situations and hence intriguingly and beautifully revealed.
As Stipp implies, here is a lovely and enormous magic.
Another similar case cited by Stipp is the well-known scenario in mathematics of the hat-check problem. Each male guest at a posh party wears a top hat. When the guests depart at the end of the party, a butler who covertly helped himself to the Rothschild champagne during the party ignores the owner-identification notes he’d carefully placed on each hat and, now tipsy, randomly hands the hats out to the departing guests. Stipp writes:
“What’s the chance that not a single guest gets the right hat? ….It turns out that this probability gets ever closer to 1 divided by e as the number of guests gets ever larger. Using 2.718 as an approximation for e, my calculator shows that 1/e equals roughly 0.37, which means there’s about a 37% chance that every guest walks out with the wrong hat. ….Strangely, the probability is about 37% regardless of whether there are 50 or 50,000 guests. ….I don’t know about you, but this isn’t what I expected when I first encountered the problem.”
Here the imposed limit that “encapsulates” infinity is our single focus of looking solely for a percentage, a proportionality, no matter how large the number of entities, i.e.,the number of guests wearing hats: 50, 50,000, much larger, boundless.
I indicated above that in the case of e, the Number Line can once again be used to enhance the understanding of the beautiful capture of infinity. Indeed, the “encapsulation” of infinity by e is further dramatized when we recall that e is an irrational number. An irrational number is a real number that cannot be written as a simple fraction. For example, the square root of 4 is a rational number because 4 is a perfect square; but clearly the square root of three is not so. The numbers between rational numbers on the Number Line invoke e: the digits of an irrational number go on forever (also termed “decimal expansion”) without repeating. Summoning the Number Line, we should note that hence there is an infinity of irrational numbers between any two real numbers such as 4 and 9. (Note that 3 is the perfect square of 9 but it is the first perfect square to appear on the Number Line since 4).
* * *
Another more astonishing and thrillingly beautiful capture of infinity by a great but finite human mind was accomplished by the German mathematician, Georg Cantor (1845-1918) even as he battled serious emotional problems. Let’s begin with a common perception: Infinity is just infinity, right? Yes, there is infinity and it is endless. Isn’t that ordinary knowledge? Well, Cantor showed that there are multiple sizes (or “levels”) of infinity, a stunning breakthrough discovery which took a long time in human history to appear, given that early thinkers including Greek and Roman philosophers, wrestling with the idea of infinity, had nevertheless not fathomed it. Cantor showed that besides the natural or counting numbers (1, 2, 3, 4…), which as we’ve seen above are infinite, there are actually many sizes of infinity, and that some infinite sets are immensely larger than others. Set theory became crucial. You can think of a set as a collection of many (e.g. natural numbers) that seems one; moreover, sets are fundamental in allowing tractability in exploring the complexities of infinity. Cantor showed how to set forth the sizes of such infinities. In doing so, a simple, profound and revolutionary discovery is that some infinite sets can be countable and are also of the same size if a one-to-one correspondence or pairing up can be established between two such sets. In mathematics, such a pairing is known as a “bijection.” As it has turned out, there are many countable infinite sets. Here is an example showing the correspondence between integers and the natural numbers; note that a common impression might well be that the naturals are the smaller infinity. But:
Integers: 0 1 -1 2 -2 3 -3
Naturals: 1 2 3 4 5 6 7
Cantor also determined the countability or lack of it of certain additional infinite sets. For example, he considered the countability of real numbers: a collection of numbers that can be written out with some form of decimal expansion, for example, 1/3 = 0.3333 (with the decimal 3’s going on infinitely). And there are indeed far more real numbers than natural numbers. To explore whether the infinite real numbers are countable, Cantor brilliantly developed what is called the Diagonal Proof. It proves the inability to set up the needed one-to-one correspondence between real numbers and natural numbers.
However, as was done by Cantor himself, one should begin by imagining that the real numbers in the real number set can in fact be counted. As a test case, assume we would be able to list all real numbers whose decimals are 0’s and 1’s.
Remembering that although we could not actually count an infinity of all real numbers whose decimals are 0’s and 1’s, we can imagine (falsely) that the matrix below shows in principle that there is a form in which the requirements to show countability are met: first, the matrix format might appear to allow a systematic listing of all the numbers; and second, the S1, S2 … progression would seemingly enable the necessary one-to-one correlation (bijection) with the counting numbers.
S1 = 0 0 0 0 0 0 0 0 0 0 0
S2 = 1 1 1 1 1 1 1 1 1 1 1
S3 = 1 0 1 0 1 0 1 0 1 0 1
S4 = 0 1 0 1 1 1 0 1 0 1 0
S5 = 1 1 0 1 0 1 1 0 1 0 1
S6 = 0 0 1 1 0 1 1 0 1 1 0
S7 = 1 0 0 0 1 0 0 0 1 00
S8 = 0 0 1 1 0 0 1 1 0 00
S9 = 1 1 0 0 1 1 0 0 1 1 0
S10=1 1 0 1 0 1 0 0 1 0 0
S11=0 1 0 1 0 1 0 0 1 0 0
But look at what Cantor has done! Look at the diagonal numbers which appear in a heavier font. Cutting through the matrix diagonally, Cantor shows that valid real numbers could be generated beyond those from the careful listing, thereby invalidating any possibility of bijection.
Here is the proof: Using the diagonal cut, simply construct a new number by taking the first decimal of S (see immediately below) to be the complement of the first decimal of the first number on the list; and proceed to do so for the rest of the diagonal:
S = 1 0 0 0 1 0 1 0 0 1 1
In short: If the first number in S1 is 0, it will in the diagonal cut be a 1; and so on. Clearly S, which is a valid real number!, cannot be on the original list, for it cannot be the first number since it would differ in the first decimal. Moreover, this impossibility would hold for any and all diagonally-obtained real numbers. Cantor’s demonstration of the uncountability of real numbers would hold endlessly.
For the infinity of real numbers, then, no bijection can be established and countability is impossible.
* * *
Given that envisioning infinity is central to it, can there be for Mathites an endless as well as endlessly engrossing Mathematica Dramatica? An important thinker on both questions is Logician-Philosopher Kurt Godel, rightly considered among the giants of human thought owing to his profound breakthroughs about mathematics in his incompleteness theorems. I am not so interested in rendering a scrupulously academic treatment of his important but complex ideas bearing on both questions as I am in conveying a dramatic, essentially true, one. In short: An entertaining one in which I take some fictional liberties but hopefully not serious technical ones. So I invite readers to look into the official, formal details of Godel’s thought for themselves.
I will, however, note here, and primarily as a framing comment, two points in a piece on Godel by the physicist, Mark Buchanan, that are especially salient. Buchanan points out that the polymath, Freeman Dyson, writing about Godel’s incompleteness theorems and echoing other observers, informs: “Godel proved that the world of mathematics is inexhaustible.” And Buchanan goes on to cite the prominent British mathematician, John Barrow, who has written: “Godel suggested…that the loss of logical foundations (as entailed by his incompleteness theorems) might actually be liberating…that mathematical intuition will one day be restored as a reliable means for finding truth….”
Dyson’s observation applies to the issue of mathematics as endlessly engrossing. Barrow’s hints at aspects of the general design questions concerning what the mind of a Mathite might entail.
Those points noted, I take the following representation directly from Heaven Engine. Toward the end of the narrative, well into the future, the polymath, Psychodor, the all-time greatest of human geniuses, is explaining the increasing relevance of Godel’s insights to our stand-in for ourselves, a character named Centwen who has been resurrected to learn in that far future, so far dismayingly, whether humans might be transformed to become happy Mathites in a heaven of a Mathematica Dramatica. Centwen is one of a small number of resurrected humans, elites and ordinary folks, from all eras and who simultaneously but individually (thanks to advanced technology) tour the distant future in the company of Psychodor and his created, superintelligent bot, Prodigy, well beyond the human tourists’ natural deaths (Centwen’s at the end of the twentieth century) to learn of future wars, technology, and many other historical developments bearing on the quest for Ideality. In fact, the drama may also be thought of as the attempt to discover whether there is an escape from the terminal boredom arising from the advanced longevity medicine of the era, the ironic plague known as Disnovelling. At the narrative point in question, Centwen is visiting the distant future time of Wylan “Why” Bell, human mathematician extraordinaire and a true visionary, a genuine and lonely exponent of the possibility of a heavenly math in Ideality.
As a brief preface to Psychodor’s explanations, we will consider the following.
In very simple terms, note that Godel used a version and refinement of the Liar’s Paradox in proving grave and fundamental and eternal limitations in mathematics, limitations happily (!) bearing on both questions above. The Liar’s Paradox: A notorious Liar declares: “I am lying (about such and such).” If the liar is in fact lying, the liar is in fact telling the truth. If the liar is in fact telling the truth, the liar is in fact lying.
Lets versify a la Heaven Engine for a while.
Well, it (the Liar’s Paradox) is a Benign Destroyer!
Just ask Bertie Russell, Dapper Dave Hilbert & Math Friends,
and by this time maybe even Roy Neary and Freeman Dyson,
now awakened in a
It means that the Mathematical Edifice-System itself must essentially be contradictory!
(Or call it incomplete.)
I.e., there can certainly be ONE statement in the Mathematical Edifice-System (and that’s enough), this true-if-false and false-if-true paradox,
which perversely can’t be proved within the maxims of the Edifice-System!
This unprovable will ever dangle at a weird angle!
Making the whole Edifice messily asymmetrical!
the axioms of the Edifice can never be assumed entirely self-sufficient, i.e., complete!
Which brings us to some irrelevant, mistaken fun:
Whereupon “Why” Bell, smiling broadly and sipping champagne, at once
Even though it isn’t really apt, Godel makes me want to declare:
“This is not a sentence!”
Whereupon Why further cackles:
In the spirit of Godel
I cannot resist adding the following
but indubitably suitable
clever non sequitur:
“Don’t read this sentence.”
But now back to Kurt: Godel’s news is truly great news!
Godel’s shown there must ever be
not stasis but dynamism:
ever more to explore.
Godel, a Hardy Hurdler,
ran and ran the hurdles out to the horizon and then observed,
the hurdles are an incomplete test.
So please listen closely: For according to Why, sated Hurdler Godel now does a second great thing!
For Why then declares that few recall versatile Godel, that Hardy Hurdler, likewise ran the only other running contest known then: the Mile!
(Now, Dear Reader, play along here with Professor Bell and his damned metaphors and pretend that in Godel’s day and despite the sweaty history of the Olympiad, we humans didn’t yet know about the other events Track and Field routinely had.) Bell goes on to say: Our Hardy Hurdler/Smiling Miler made another portentously important declaration; i.e., Mr. Incompleteness, once he had added to the Hurdles the Mile, championed in a different sense a new and higher (to use the popular misnomer) Completeness;
the Hurdles and the Mile are fundamentally consistent
with each other as belonging to some larger class of
foot-race tests, and so we must presume they’re valid
single tests within a larger test collection!
Yes, dear reader, they are little members
of a great collection!
My, my–how Platonic.
And how exciting, eh?
That’s right, Dear Reader, we’re pretending here about a postulated big structure–that super test collection–we haven’t even yet fully creatovered, containing fundamentally similar (“noncontradictory”) foot-race tests and other such physical tests (only two which in this hypothetical case, I stress again, we’re pretending we know at the moment–“Mile” and “Hurdles”).
In short, the conclusion is:
There’s an unseen edifice–in this case (and as we “later” name it),“Track and Field”–which in a special sense is already in existence!
Without resistance, please envision it to have a sort of avid availability.
Now let us join the Heaven Engine narrative at a point both late and hopeful in the future history dramatized in the novel. It is the twenty-fifth century, the time of mathematician Wylan “Why” Bell, the pioneer cited above who is crucially wrestling with the issue of a mathematical secular heaven. In his time, Bell referred to the problem as “The Narrative Conjecture.”
Bell’s life is dramatically telescoped to Centwen by his two tour guides. In sum there are three main characters in the excerpt.
Great Psychodor, Prodigy, and Centwen.
Great Psychodor is an overbearing, shouting genius, the greatest polymath in human history.
Prodigy is a super intelligent bot created by Great Psychodor and who has returned after being sent forth to search out the conjoined questions about Ideality and Mathites.
Centwen is a stand-in for us humans. He is being guided suspensefully on a tour of the future leading up to discovering the answers already sought by Prodigy.
Centwen: Hold it!
Prodigy: What is it, Centwen?
Psychodor: You’re confused, aren’t you, Centwen?
What the hell is this mathematics all about?
Don’t get it, huh Centwen?
Psychodor, I told you not–
Well, Centwen, it’s pretty simple stuff!
Sure! Godel did a couple of crucial things Old Why absolutely loves. First, he identified a confounding paradox that appears to keep mathematics from ever becoming a purely self-contained system able to prove everything within its own axioms! In other words, he cast doubt on it ever becoming a Stand-Alone Realm. Think of this as meaning mathematics is never going to be complete! Never closed. Never perfect unto itself. Never rooted securely in its own unshakeable foundation of truths. It’s analogous to saying: there is not now and never will be some veritable Rock of Ages for mathematics! No! It will always eventually confront an unresolvable contradiction, a dilemma in Logic it can’t take care of by its own powers! And hooray! For then mathematics may never finally stratify but always newly ratify. And all this thanks to Godel’s paradox! A paradox in which true is true when it’s false and false when it’s true! Yes, a Diabolical but Fruitful Trap of Logic! The Long Subversive Serpent all along twisting and turning finally to swallow its own tail! Or if you prefer, Centwen, think of this not as a riddler snake’s sarcastic hiss but as the scary Begotten Sense of a Mathematics Acrobat forced ever to dare jumps and leaps and somersaults over a Bottomless Abyss. And obviously for all the Anal-Retentive Mathematicians with Fearfully Blinking Sphincters, this trapeze unease becomes the ultimate disease. But to Why, it is all Great News! He goes wee-wee all over himself, because he thinks of this as support for suspecting you don’t ever have to worry about a mathematical deadend! He takes it as a clue that mathematics will never (to use one of your quaint sayings) die on the soil-ensnared vine, which is to say, it’ll never reach dry, arid stasis but always be alive, adrift, happily unsatisfied, and suspensefully floating along in search of the new! And this, if you think about it, is what makes Bell want someone–the great me, it turns out to be!–to engineer a new, dynamic psychology of Mathematica! See, Centwen, you have to understand that Old Why thinks we’re not standing still in the Garden of Beatific Eden but forever soaring through a Space of Creatific Bein’! In short, according to Why we’ve arrived at quite a radical shift in how we need to think, because now the seductive knowledge-serpent’s become the hero! Yes, that’s the way Old Why sees it all. He’s a true new mathematician, one who thinks, “Bless this mess!” Since he’s chasing after The Narrative Conjecture, the Never-Ending Story, he mightily wants mathematics never to become closed! Right? Of course! Happily we don’t even hazard the slightest thought of mathematical stasis leading to collapses! For that calamity would be Why’s Hades!
But that’s only the half of it, Centwen. The second thing that Godel does which Old Why salivates over–
Psychodor, I’m your Prodigy but I’m certainly glad you were never an official professor!
–is to get us to the logical reality–the actual necessity!–of Mathematical Edifices which we have yet to construct! Or discover. Actually a little of both. Because Old Why not only wants edifices to be open-ended. He wants more than that. In fact, he wants something which precedes that! He wants assurances that coherent Edifices not yet creatovered are in some sense out there! Awaiting us! In short, Godel wants those Edifices to be inherently plausible! If you will, he wants them to be ever-pending.
Hence all this metaphorical Track-and-Field stuff where we eventually create the pending marathon and dashes and sprints and add them to the already known hurdles and miles, perhaps someday ending up even with the Decathlon and then even more thrillingly entire Olympiads and who knows what wonderful else beyond, and which has been there for the creatovering all along! Orbit Billiards, maybe.
One tried-and-true way to glimpse the point, Centwen, is to imagine that you, the New Immortal Intrepid Creatoverer happily wandering the Forever, are setting sail for unmapped new worlds. Lets say you’re pacing the decks of your ship in a state of high anxiety as you sail uncertainly across a great expanse. Imagine, however, that one day in the Doldrums you realize something Absolutely Saving, Supremely Vital: you come to see that you can be confident that those New Worlds are out there in the first place! They are there, awaiting you! About their sheer existence you no longer need have any terrible doubts! You are not sailing across a temporary Flatness in which sea monsters lurk, a measurable plane whose edge you will eventually tumble off! Instead, you are always going somewhere novel and beautiful! The voyage is eternally valid!
But now we’re talking about a New New World, Ideality. And when you refer to Ideality, you must start thinking a little differently. As I’ve implied, mainly you have to start thinking neither solely of discovery nor solely of construction. Think both! Think of “creatovery”! Think of yourself not as a mere Explorer but as a Creatoverer. And then, to borrow from your own culture of Century Twenty, go buy yourself a stiff drink because you’re encountering the insights of mystical mathematicians. Hunchful ontologists. Which all the great ones have been anyway.
I think so. And yes, you’re right, Psychodor–I definitely could use a Bombay Sapphire martini straight up with two olives!
Coming right up!
Prodigy, why are you simply acting the bartender, while letting Psychodor explain things?
They call him Great, don’t they? Besides, I appreciate natural humor even more than you humans do! Here’s your Marty.
Just ignore him, Centwen! Who cares what smart-ass Prodigy is thinking? Besides, before you start chomping on those skewered olives, you should realize that Old Why has now gotten himself into a couple of even worse messes! Lets see if he continues to like messes!
What do you mean? (Chomp, chomp.)
Obviously, the present weak-minded Homo sapiens–that’s you!–isn’t up to the task of attaining Ideality. And of course Old Why knows this better than anyone in human history. Yes, as you Centwens used to say, Old Why’s learned about this human failing the hard way! And, oh, does he take it personally! Indeed! As if the earlier two challenges I just described–the ones Godel helped resolve–weren’t enough, poor Why now sees that he’s got to worry about two enormous further problems. And he hasn’t got Godel to help him!
First, he has to worry about whether this endless Edifice he’s trying to creatover can be accommodated by a new, more powerful mental creature–either an organic extension of Homo sapiens–a transformation of the original Accident into a self-made new superhuman (you should hope!)–or some separate intelligent creature–not Homo sapiens–which has to be engineered from the ground up and which somebody, some great psyengineer–namely and to say it again, me!, as it turns out to be–must find a way to build, and which creature you now see embodied in bartender Prodigy!
And as if that anxiety weren’t enough, Old Why must now worry about this second problem: No matter which form of the new, improved creature comes onto the scene and succeeds, including the grand possibility they both do, Why still must continue to worry as to whether the endlessly engrossing experience the creature or creatures would creatover would indeed remain endlessly engrossing! I mean, with all due respect to Godel, we’re not absolutely sure about this eternal edifice! Seeing is believing!
* * *
This brings us to the experience. Obviously we are able now only to intimate an experience by a Mathite in Ideality. We have to draw an analogy to a human experience. This is obviously fraught. Accordingly, the following, taken verbatim from Heaven Engine, is simply a metaphor–and only a metaphor–drawing on one of a variety of prospective archetypal human experiences, a variety because they must be individually tailored to be suitable for giving a sense of Ideality respectively for ancient, recent, or contemporary humans, in this case for my character, Centwen, from the twentieth century, and which indirectly perhaps suggest some design issues for a Mathite’s experiences in Ideality. In the narrative of Heaven Engine, the author of the following drastically metaphorical account of an epiphanic discovery–a sudden bright burst of a grand discovery and not the exciting sleuthing that led to it–by a Mathite, is composed by that great future mathematician, Wylan “Why” Bell, who is desperately trying to conjure a sense of Ideality for humans–here Centwen–who have little knowledge or experience of advanced mathematics.
One design question in early thinking about the experiencing of ideality and the possible engineering of such is intensity. Another is suspense, this latter raising the design issue of creating searches by mindful posthuman Mathites which necessitate delayed (but still happy) gratification–explorations leading up to the truth–and similar problems in the ever narrative experience of discovery in Ideality. But there is, after all, in mindful searches for understanding by such earthly heroes as PI’s the exhilaration of the hard cognitive and other work to uncover truths. As cloistered, theistic/mystic Theresa of Avila said: Heaven is getting to heaven.
There are, of course, many other stupendous considerations to be dealt with by the designers of the psychology of the Mathites questing after epiphanies. (More below.)
First, the New Testament has four Gospels and Heaven Engine has (as Bell refers to them below) eight Cogspells, most of the latter being rather formalized, brief histories of important future Historical changes.
Second, Bell also refers to “Disnovelling,” that ironic, terminal boredom of the longevitites in the future as opposed to the “Novelling” Bell’s “Noveltyhumans” (Bell hasn’t heard of “Mathites”) would archieve in Ideality.
So: herewith Bell’s metaphorical foray for Centwen, one that became memorialized and spoken by others as well:
HEAVEN — VERSION C-20
When (and if!) You, Dear Friend Centwen, Become Noveltyhuman, You will thus become ever the lucky creature who in its multiselved uniself sits at once in sweetly anxious anticipation in many gaily decorated trestle cars which slowly climb in unison up and up in the pull of clanking chains to position for The (Latest) Greatest Coherence Rollercoaster Ride, all the cars reaching zenith all at once to pause momentarily on the many towering trestle tops of the Current Edifice, there to let the myriad representations of you view from all these cars the Grand Surround and integrate all versions in your Meta Mind,
then simultaneously rush,
in ubiquitous-yet-integrated thrilling joy around the structure of the Edifice in complex uncolliding schedules, a Scintillating Grand Scenario of Near Misses, this living Edificial Structure reshaping Itself in real time, everywhere throughout The (Latest) Greatest Coherence Rollercoaster Ride the multiple selves of you, Lucky Noveltyhuman, speeding down living serpentine sidewinding rails which sever themselves into shorter lengths leaving gaps, empty space no less! and always just in front of the whirring wheels of the speeding trestle cars!!!, yet always managing just in time!!! to reconnect anew to other disconnected rails springing forward in precise strikes to connect in nanosecond perfection to reroute exactly correctly in the perfect precision of massively coordinated myriad inferential consequences, all summing to an elegantly lovely formation of an
oh yes gloriously entailed
new architecture of the Entire Grand Structure of Rails,
each new thrill ride an unprecedented episode of beautiful gripping surprises-cum-inevitabilities unfolding gracefully!
Yet each ride as it ends instantly becomes Jaded Thrills, Old News, Faded Beauty, Punched Coupons, Used Tickets,
thereby raising new questions!
uncovering newly seen contradictions !
revealing subtle omissions!
impugning illusory unity!
rediscovering unfailing fallibility!
Yes! Get ready, Noveltyhuman, for your next and
even greater ride!
Apparent Coherence not only was, is, and always
will be the illusory absence of contrariance;
Apparent Coherence is ever dispelled in disillusion
at the Latest Ride’s conclusion,
followed by delicious crisis meetings to resolve
anew a new, and this time perfect (hah!), Rollercoaster architecture.
Which in turn initiates new rides.
Onward to the next newly novel rollercoaster ride
on the self-transforming trestled Edifice!
Thereby rounding out Soclar’s Fifth Cogspell,
and also fulfilling all the linked transcendent
prophecies of the First, Second and Third
while transcending dread Disnovelling
as rendered in the Fourth Cogspell.
This is 6C!
This is This novelling.
Our Prodigious Child’s new game of
* * *
“Yes,” Why thinks to himself: “Even if some parts of the Meta-Ediface — whole specialties — do not change, or change very seldom, no matter!: for in the act of extending the overall Edifice into truly novel areas, the heightening contextual value of these re-used parts, their function as dependable and mobile connecting bridges, will only create for them a renewed importance, which means our sense of their value and beauty even as we traverse those bridges again and again will with each new-purposed crossing spring forth anew and bring new joy, and hence not be a psychological drag on the meantime purely novel extensions of the Edifice, all of which is downright: “Novelling.“
Indeed, Eternally Novelling!”
Why tells himself: “Hence Endless Novelling, not Disnovelling, now becomes the rule.
“Grand Novelty: new problems to solve and ensuing new thrill rides created in the very act of solving those new problems:
“which is to say:
“suspenseful new problems throughout the newly disturbed (torn) web followed after their exciting solutions (repairs to the web) by (hopefully) web-wide thrill rides (appreciations of the new wholeness of the web) to experience the thrilling new coherence in the Meta-Edifice:
“which is to say:
“The two major, linked varieties of:
“The greatest possible ride?
“The Ride of Rides? It would always be penultimate!
“It would ever ensue from the penultimate New Problem of All New Problems/the Newest Solution of All New Solutions which would ramify back to change the whole Meta-Ediface, testimony to its Grand Coherence, in turn raising new Edifice-Wide questions.
“And why not forever!”
Elsewhere in Heaven Engine, there comes this question: Will we…
become an arrested population of Immortal Idealists?
Free at last of imperatives of “natural selection” such as
—and especially Reproduction,
—so as each to start Living Anew in Beatific Privacy.
Hence ever to be:
—in a Psycho (and Physiological) Anarchy!
—An Aesthetic State of Self
But only to be Lonely?
—For each of you Self-Sufficient will be eternally self-entertaining, happily vaudevillian-knacked, topping yourselves with each new personal “godthrilling” act, on your private stage in your personal theater.
—You’ll not unravel in the Plague of Disnovel.
—You’ll not opt for Oblivion over Living.
—Instead of going extinct, you’ll have fled in soloing instinct!
But (I jest but most seriously) there are just a few minor design problems suggested by the above. I don’t imagine I have thought of anything like most of them; nor do I imagine I might. However, by weak light:
1. The Mathites will be material in pursuit of infinity and other abstractions. I think Minsky is right that biology and immortality are mutually opposed. (And I certainly don’t want to raise here the long, long dialog in Philosophy about Being and Epistemology, i.e., about how “To be or not to be” and “How do we know things?” are pondered there, e.g., How does a unicorn “Be”?) But the Mathite, that mindful creature, will need to be a “machine” that is not corporeal in our human sense and yet ever Cosmically survives.
As Prodigy puts it:
“Getting Out Of Here, i.e., far away from doomed Earth, each of you (Mathites) separately to lift and drift through perilous hurtling Vastitude in safe navigational shift…. Specifically, you’ll be a newfangled nananium psyche, hungering only for an Abstract Inspired Condition, your innovative idealizing form (perhaps) designed to live inside a tiny floating space capsule, not Noah’s crude wooden-roofed “flood Ark” but your own minuscule Cosmos-proofed “rainy-day cart,” suffering not Rene Descartes Unfactual Duplicity but enjoying an actual beneficial duality: a truly new psychology: a split personality: a pair of two mutually unaware kin: a pair of fly-in-ease twins….
“Namely, you will now be: (1) An Inner Creator (I. C.) innovating freely in the beautifully engaging Eternal Higher Ideal; and at the same time (2) an Outer Navigator (O. N.) safekeeping this lucky I. C. in the stupidly dangerous External Dire Real. …In short: no longer will your life be Dust to Dust! And neither, either, must you rust! Instead for the new happily divorced you, AKA the benignly schizoid you, two old adages will now ensue: (1) Never again the twain shall meet; (2) Age before beauty.”
2. Stephen Hawking has written the following:
There is no time to wait for Darwinian evolution to make us more intelligent…. (For) we are now entering a new phase of what might be called self-designed evolution, in which we will be able to change and improve our DNA, which means we have read ‘the book of life’, so we can start writing in corrections. …some people won’t be able to resist the temptation to improve human characteristics, such as size of memory…and length of life.
3. Obviously the Mathites must have immense minds. Enormous Vision plus enormous Power. As the futurist Hans Moravec instructs, a being able to think beyond even human thinking must at least accomplish trillions of calculations every second. The physicist, entrepreneur and art-painter, William Hogan, early and long involved in development of supercomputers, has educated me on the tremendous progress and remarkable promise of quantum computing; and apropos, the science writer, Stephen Witt, has written: “A quantum computer could open new frontiers in mathematics, revolutionizing our idea of what it means to compute.” I keep the faith in progress, subject to the plausibility inherent in Time.
4. The possible nascent technological enablers, here a few familiar examples out of the many imagined these days–not all promising suitability for the premise of Heaven Engine–include: simulated reality, mind uploading, strong artificial intelligence, digital life, and superintelligence. For certain the experience intimated in the novel must be mathological and take place in Ideality, and so Mathites must spring from a technology allowing them to access that world, not our present natural one or some mirrored version thereof, and must reach beyond humanity with its attendant limitations, the pain and suffering and confinements afflicting natural selectees. It is, simply and profoundly enough, and among many other things, a staggering new design problem.
5. Speaking very superficially: Such issues as these must be worked out in the design of the posthuman Mathite: visual sense; language; memory; consciousness; inferencing; emotions (e.g., epiphanic, joys of searching, and others [but these emotions not sourced in bio/chem]); and social (possibly). Will any human be able to become a Mathite? Will other senses than that of sight be required? It is presumed that there will be a continuing mathematical edificial splendor to be creatovered; and that the Mathite will be pleased in the pursuit of same just as in the actual epiphanic discoveries themselves. In short, the Mathite will be designed and engineered to be happy. What will be the aesthetic of mathematical edificial grandeur? (Hopefully no latterday comedian will be able to ask, “Are there only a finite number of infinities?”) How would Mathite memory be configured and operate? Won’t the Mathite design need to be right “the first time”? For it seems doubtful a Mathite Enterprise would carry on over many years. Would there be one Master Mind for all individual Mathites or would there be individual minds? And obviously many more issues! To say the least!
6. Alexander Grothendieck, the mathematician some call the greatest of the second half of the twentieth century, is for me an exemplar. He lends optimism to me about my theme in Heaven Engine through his ingenious use of abstraction to lay the foundations for new vistas in mathematics. Among other things, he was a revolutionary in algebraic geometry by (in the words of the editors of the Encyclopedia Britannica) “generalizing varieties (of algebraic geometry) to schemas and extending the Riemann-Roch theorem.” His work was also fundamentally valuable in the legendary solving of Fermat’s Last Theorem. I’ve no doubt he embodies the spirit of mathological discovery.
7. As a science fiction writer, albeit Other Science Fiction (that inevitable hybrid with Traditional Fiction), it’s best for me to stop here. I confront the pessimism-optimism problem in Heaven Engine and confidently leave the miraculous realization up to those Princes and Princesses of the human mind, the mathematicians, scientists and technologists. May they prevail.