Local Optimism

             Local Optimism

Voltaire mocked Leibnitz (in the guise of Dr. Pangloss) for proposing that this is the ‘best of all possible worlds’. But Leibnitz, co-inventor of the calculus, knew the difference between local and global maxima. A global maximum is the largest value that a function reaches, for any input; whereas a local maximum is the largest value that a function reaches, in some neighborhood of the locally-maximizing input.

I therefore propose this modification of Panglossian optimism; Local Optimism, which states that this is the best of all sufficiently similar possible worlds. Any stable world locally optimizes; it’s the best of all nearby possibilities.

          Local optimism suggests that there may be many stable worlds, some better than ours. There may also be inherently unstable worlds, that are the worst of all sufficiently similar possible worlds.

          Any continuous path from one stable world to another must begin by getting worse.

          Any continuous path from one stable world to a better one must, in between, pass through the worst world on the path.

          A path from one stable world to a better one that never gets worse must be discontinuous.

          Analogs of local optimism are confirmed - and fundamental - in biology and physics; Darwinian evolution for biology and the Law of Least Action for physics. Local Optimism has sufficient scientific support to appeal to the likes of Leibnitz; yet also sufficient satiric undertones to appeal to the likes of Voltaire.

          For why does the universe minimize action? Is it lazy?

Collective Individuality

            Collective Individuality

 

            In my writngs I call into question the existence of money. I call this philosophy ‘aplutism’; it calls money a fiction. Any money system’s reality is at best social; money’s value is determined by a market, which is by definition transpersonal. Therefore there is no such thing as “my” money system; it is by definition “ours”.

            Therefore money is collectivist! It has to be, otherwise it wouldn’t be fungible. The same goes for language. Words have to have shared meanings, or they have no meanings at all. Or take Reason; there is certainly no such thing as “my” rationality, distinct from “ours”. If anyone has Reason, then Reason is the common property of all mankind.

             (Once Calvin, of the comic strip Calvin and Hobbes, was told to answer a test question “in your own words”. A loophole! So he answered in gibberish.)

             A curious political paradox emerges. Money, speech and Reason are the gods of libertarian individualism, but they’re also as collectivist as the fire department! Money, speech, reason and much else (for instance the Rule of Law) is collective by nature. We all have rule of law or none of us do. In such a situation the only rational policy is to build government relating to such things on collective principles.

             The money that you make is yours; but it is denominated in terms that are ours. Your speech is free, you may say whatever you like, but you’d better use English, and not some private language of your own, if you wish to be understood. You have your individual rights under the law; but the law is a creature of the State. And so on.

            The individual and the collective are interdependent; they only make sense in terms of each other. Yin and Yang.

             The paradox works in the other direction as well. Every collectivist movement ends up being run by a powerful individual, usually an alpha male. The army needs a general, the church needs a priest, the commune needs a manager.

             The human dilemma is that we are individual yet social. Monty Python parodied the paradox in this scene from their “Life of Brian”:

            Brian to crowd: “I mean, you’re all individuals!”

            Crowd: “YES, WE’RE ALL INDIVIDUALS!”

            Lone man in crowd: “I’m not!”

             Rudyard Kipling celebrated the paradox with:

            The strength of the pack is the wolf, and the strength of the wolf is the pack.

  

            Signed,

            the illusion of the individual Nathaniel

 

 

Against Uniqueness

             Against Uniqueness

  

          What does it mean, to be unique? To be the best, the exception, the only? It seems a positive thing somehow, but really it has a lot of negativity built in.

          To be unique is to have a certain description – that indeed is the positive part of uniqueness, especially if the description is flattering; but to be unique also means that nothing else has that same description. Nothing else whatsoever is like the unique; hence there is negativity within uniqueness.

          Were a lover to say, “I love my friends and relatives and many others, including you,” well, the one wooed might find his ardor limited, but soothing; but were he to say, “I love only you,” well how thrilling, but stressful. The lover of many needs keeping an eye on; but the lover of only-one is needy, clingy, and potentially dangerous.

          Once I was walking through Harvard Square when someone ran up to me, calling another man’s name. It turned out that there was another mathematician there, one who looked like me, at least from behind. I found this revelation reassuring; if I’m part of a type, then we must be on to something.

I felt the same sense of collective security when I noticed that raccoons have hands. Evidently hands are a good idea; someone else seconded the motion. If we were the only animals with hands, then I might doubt the soundness of the concept; but as is, if there’s something that we ought to do with these hands, but we fail, then there’s a back-up team, to do it in our place. How reassuring!

          Uniqueness is the enemy of positivity just as the best is the enemy of the good. The unique is the least positive of the positives; for irreplacibility equals insecurity. Uneasy rests the One, for fear that there might be another One.

          All could be good but only a few can be best; therefore the good are a better bet than the best.

          Therefore we should all renounce uniqueness. Never sell your soul, not for a treasure, nor even a penny; instead give it away for free.

 

Zurn, Tork and Bobrick Explained

       Zurn, Tork and Bobrick Explained

 

          One BayCon, at the Santa Clara Hyatt Regency, I was in the men’s-room on the first floor. I noticed that all the urinal plumbing bore a corporate logo: ZURN. I thought, “Zurn?!”; then I turned to wash my hands. The towel dispensers had a corporate logo: TORK. And the hot-air hand-dryers bore the name BOBRICK.

Zurn? Tork? Bobrick? Corporate names are weird for some reason; they have a dream-like quality. This, at a science-fiction convention, invited appropriation by imagination. I figured that Zurn has got to be an evil interstellar emperor, and Bobrick the Earthling adventurer who overthrew him, but I wasn’t sure about Tork. Was he Zurn’s minion, or Bobrick’s sidekick?

          Puzzled by this, I proceeded towards the science-fiction convention’s Info desk. Before reaching the escalators, I met a fellow conventioneer; a tall fellow wearing a fez. I told him about Zurn, Bobrick and Tork, and asked about Tork. He said, “I could tell you, but then I’d have to wipe your memory.” I replied, “Maybe we’ve had this conversation before.”

          I went up the escalator, to the science-fiction con’s Info desk. I told them about Zurn, Bobrick and Tork, and asked about Tork. They handled this absurd question with aplomb, and between them and me, we figured out that Tork started out as one of Zurn’s minions, but ended up as Bobrick’s sidekick.

          Later I met the fez fan again. I said, “Your attempts to suppress the truth have failed.” Then I told  him about Tork’s switching sides.

          And that is how much sense corporate names make.

Against Uniqueness

             Against Uniqueness

 

 

          What does it mean, to be unique? To be the best, the exception, the only? It seems a positive thing somehow, but really it has a lot of negativity built in.

          To be unique is to have a certain description – that indeed is the positive part of uniqueness, especially if the description is flattering; but to be unique also means that nothing else has that same description. Nothing else whatsoever is like the unique; hence there is negativity within uniqueness.

          Were a lover to say, “I love my friends and relatives and many others, including you,” well, the one wooed might find his ardor limited, but soothing; but were he to say, “I love only you,” well how thrilling, but stressful. The lover of many needs keeping an eye on; but the lover of only-one is needy, clingy, and potentially dangerous.

          Once I was walking through Harvard Square when someone ran up to me, calling another man’s name. It turned out that there was another mathematician there, one who looked like me, at least from behind. I found this revelation reassuring; if I’m part of a type, then we must be on to something.

I felt the same sense of collective security when I noticed that raccoons have hands. Evidently hands are a good idea; someone else seconded the motion. If we were the only animals with hands, then I might doubt the soundness of the concept; but as is, if there’s something that we ought to do with these hands, but we fail, then there’s a back-up team, to do it in our place. How reassuring!

          Uniqueness is the enemy of positivity just as the best is the enemy of the good. The unique is the least positive of the positives; for irreplacibility equals insecurity. Uneasy rests the One, for fear that there might be another One.

          All could be good but only a few can be best; therefore the good are a better bet than the best.

          Therefore we should all renounce uniqueness. Never sell your soul, not for a treasure, nor even a penny; instead give it away for free.

Stalked by a Bot

Stalked by a Bot

 

 

 

The phone rang. I picked up on the third ring and said, “Hello, who is there?”

A robot voice said, “Good-bye.”

 

Several days later, the phone rang, I picked up on the third ring, “Hello, who is there?”

A robot voice said, “I’m sorry, that is not a valid extension.”

 

After that I picked up on the third ring every time, in the hope of getting a third creepy robot. Finally: Ring, ring, ring, I pick up, “Hello, who is there?”

Silence.

 

And that’s a trifecta! Have I been rejected by a bot?

Inoculating my Daughter

          Inoculating my Daughter

 

I once had the honor of giving my daughter Hannah an inoculation against a common teenage ailment. I refer to Objectivism; for she asked me about Ayn Rand, and I gave her my informed opinion.

Specifically I told Hannah about the infamous railroad scene in “Atlas Shrugged”. I detailed the set-up; the dangerous tunnel, the idiotic bureaucrat’s suicidal demand, the chain of buck-passing, the fatal go-ahead, the complaisent workers, the train’s doom... all of which I described with admiration for Rand’s meticulousness (for once not tiresome) and her passion. A death machine of incompetence and spinelessness, clickety-clicking right there before your eyes! A masterpiece of eldritch horror! That scene was this close to Literature!

But the moment the train entered the tunnel, her writing all went horribly wrong! For Rand then focused on the passengers; a risky move if you do it wrong, and she did. For what if (I asked Hannah) that train had been full of good people? Or perhaps even a few of them super-virtuous by Rand’s elitist Objectivist standards? For them to die alongside the idiot bureaucrat would been supreme injustice; a raw red wound, an affront against humanity! What if Rand had raged and wailed against the sick cruelty of the idiot world? That (I told Hannah) would have been writing!

But no! By the way Rand told it, everyone on the train was an idiot moocher, as bad as the bureaucrat, and so everyone got what they deserved! (Hannah rolled her eyes upon hearing this.) Instant justice, automatic karma, all’s well with the world! Rand got that close to Literature, but at the last moment she turned it into Propaganda!

        The trainwreck scene was itself a trainwreck!  And that (I told Hannah) is Ayn Rand.

At Half-Mast for Roadkill

At Half-Mast for Roadkill

 

 

        I was driving past Colma on December 26, 2006, to find the flag at half-mast there; though it was officially there in honor of Gerald Ford, former unelected President of the United States, I announced to my daughter that, as far as I am concerned, it was really at half-mast in honor of James Brown, the Godfather of Soul; for that is the world in which I prefer to live.

        Later I was driving on the same road. I passed two roadkills; a cat and an opossum. This saddened me; but then I passed Colma, with the big flagpole there, and guess what, it was at half-mast.

        Right away I felt better. I thought, “How considerate of them.”

        Now again, I am well aware that officially the flag was at half-mast for a human, specifically someone prominent in business or government. Nonetheless I insist, just as before, that as far as I am concerned, that flag was at half-mast in honor of the roadkill; and any human being also honored that way is benefiting from a coincidence. That is my story, and I am sticking to it.

 

Welcome to my world.

 

        Since then I have evolved a ritual. Every time I drive past Colma, and the flag there is at half-mast, I take off my hat, I hold it over my heart, and I intone:

 

        Honor the heroes,

        Honor the V.I.P.s,

        And honor the roadkill.

 

        For we are all heroes,

        And we are all V.I.P.s

        And we are all roadkill.

        Amen!     

 

 

 

Cadaeic

        Cadaeic

 

          A “cadaeic” is a mnemonic for the number pi. “Cadaeic” itself is a cadaeic, if you use the letter-code A=1, B=2, and so on; then ‘cadaeic’ spells out 3-1-4-1-5-9-3; whereas pi’s expansion is 3.1415926…; so cadaeic is good to seven places if you round to the nearest digit.

          Most cadaeics use word-length coding, for instance:

          “How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.”

          Counting out word lengths, that’s 3-1-4-1-5-9-2-6-5-3-5-8-9-7-9; pi to fifteen digits. Here are others, some submitted by my Trigonometry students:

 

          How I, even I, adore campfires in August, while the bears scavenge.

 

          “Can I have a merry Christmas at Santa’s house?” she asked.

 

          Pie, I want a piece, blueberry or cherry peach pie helps maniacal cipherers conjure fantasies for an apt mnemonic that brings to faulty mind all the thougts for an apropos, memorable image.

 

          “Hah!”  I roar. “I never calculate pi, having known the shady, half-cute, contrived antique mnemonics!”

 

          Now I need a super difficult pi puzzle, afore our human capacity retaining numbers dissolves and we get mnemonic work.

          Can I have a small container of coffee? These are tough concepts, demanding nightly examining for me.

 

          Now I, with a small packhorse

          Go toward those low hills

          Constant beckoning

          Driving endlessly

          For in the distance

          Days beyond my memory

          Lies the one sleeping eye.

         

          Now I will a rhyme construct

          By chosen words the young instruct

Cunningly devised endeavor

Con it and remember ever

Widths of circles here you see

Sketched out in strange obscurity.

 

Sir, I bear a rhyme excelling
in mystic truth and magic spelling;
Numerical sprites elucidate
and to the circular form relate;
If Nature gain, who can complain
yet my critics fulminate. Finis.

 

            Here are some e mnemonics:

 

 

            To compute a quantity to multiply, a treasure to increase, just apply exponents.

 

It enables a numskull to memorize a quantity of numerals.

To destroy a building we detonate a quantity of hydrogen bombs.

I’m forming a mnemonic to memorize a function in analysis.

In Florida, a kangaroo is escaping a teenager by bounding over gates.

We wrecked a building on Thursday, a hospital on Saturday, with eight engineers.

He repeats; I shouldn’t be tippling, I shouldn’t be toppling here!

He laughed, I screamed. We embraced a paradise of squeezes. ‘Twas love’s grandiose remarkable gift, silly to die madly for people. Faithfully be juvenile, embrace with passion. I was crazy to forget, stupid to fall, weakening quickly, holding love’s embrace.

 

On Creative Defeat

           On Creative Defeat

      Or, Three Little Words

 

 

          There comes a moment in any married man’s life when he learns – or is carefully taught – a strange magic spell which, when properly used, turns night into day, storms into rainbows, and misery into joy. Unmarried men will scoff, but I am not exaggerating in the least.

          You learn this incantation, as you do all true magic, in the midst of crisis. You and your spouse have reached an impasse, and the pressure and heat is rising. At the verge of mutual defeat, you suddenly experience an instant of searing insight, and a joyous recognition of the perfect solution. Thus spiritually prepared (for only thus can one even utter the spell) you speak three little words.

          Three little words, and that’s enough. The quarrel ends,  and all is peace and joy. And what are these three little words?

          “I love you,” perhaps?  So think unmarried men and other romanticists! No, any married person of experience knows full well that the Three Magic Words are:

          “You are right!”

         

 

Coping Strategy

          Coping Strategy

 

          I have given up on immortality and will settle for reproducibility.

A Philosophical Disagreement

          A Philosophical Disagreement

 

           I was at the gas station, paying for a tankful of gasoline, when Gina, the owner, asked me how my wife Sherri is. I said, “Well enough,” and then added that ‘well enough’ is my stock answer to how-are-you.

          Gina, as ever an optimistic extravert, said, “You can do better than that. If you say ‘I feel fantastic’ all day, then by the end of the day you’ll feel fantastic.”

          I, as ever an introverted pessimist, replied, “Ohh no no no no no, that’s not how my so-called mind works. If I say I feel fantastic all day then by the end of the day I’ll feel awful for not feeling fantastic!”

 

 

Sunblocks Ranked

         From the Annals of “The National Liar”:

       Sunblocks Ranked

 

 

          Ranking types of sunblock, in increasing order of effectiveness:

 

          rating 0:  A bottle full of chemical goop.

          rating 1:  loose-fitting, cool, all-covering clothes

          rating 2:  shade tree or shade forest

          rating 3:  overcast weather

          rating 4:  a floor, 4 walls, and a ceiling

          rating 5:  winter

          rating 6:  night

 

 

Mome Declares Himself Fallible

Mome Declares Himself Fallible

 

 

          Nome, Alaska  -  In a surprise announcement yesterday, J.R.”Bob” Dobbs, Mome of the Noman Particular Church, proclaimed the doctrine of Momal Fallibility.

          “What, me infallible?” the Mome snarked. “Of course Momes can make mistakes. In fact we’ve made some big ones. Just judge for yourself.”

          Sources high in the Noman Particular Church said that they adopted this doctrine because they needed more wiggle room. “We’ve painted ourselves into a corner. It’s high time we ‘fessed up,” said Ordinal Maustinger, the Mome’s most trusted advisor. “His Holiness has made a bad call lately, and he needs a face-saving way to back out of the mess.”

          The ‘bad call’ referred to is the infamous Elvis Clone debacle. “His Holiness sure dropped the ball there,” Maustinger confided. “We never made sure that that hanky was really one of Elvis’s; or if the genetic material found there was his; or even how that genetic material got there in the first place. But ‘Bob’ insisted on cloning, so we went ahead; after all, he’s the Mome. And the result? Well, let’s just say that the clone we grew didn’t see things our way. Put it all together, and it spells M-I-S-T-A-K-E.”

          “I am a man, mortal and therefore sinful,” the Mome confessed to the world. “I say I am fallible, and I say so ex cathedra. My judgement is not perfect; to claim otherwise is the sin of intellectual pride. Only God is free from all error – and sometimes I wonder about Him.”

 

         

"Alternate Jesus"

      Review of Imaginary Book:

     “Alternate Jesus”

 

 

          Every so often there comes along a book which shakes the world. Such books incite revolutions, topple empires, destroy religions, spread mass insanity, and spark genocidal wars. Fortunately, “Alternate Jesus” is not such a book.

          In “Alternate Jesus”, the author asks, what if Jesus of Nazareth had never been crucified?  How would history have been different? The author gives us two answers; two “alternate worlds” in which Jesus lived. Unfortunately, only one of those answers is convincing to this reviewer.

          The book has two parts: “In This Sign Conquer”, and “What is Truth?” In Part One, Jesus seizes control of his environment by secular means; in Part Two, Jesus takes a more spiritual approach. Part One is all too convincing, for its message is “power corrupts”. Part Two is mystical, not dramatic. It teaches that “truth shall set you free”, but it deliberately does not tell us what truth is.

          “In This Sign Conquer” starts in the city of Rome, where King Jesus had just successfully concluded his Crusade Against Empire. With the defeated Roman Empire at the mercy of his Zealots, he proclaims himself Prophet, Messiah, and God-Emperor of the World. “That was his high point,” the chronicler wryly comments. We then see Emperor Jesus play out, within his reign, the entire history of the medieval Church, including censorship, repression, fanaticism, fraud, corruption, witch-hunts, wars and genocides. It ends with Emperor Jesus’s death and the collapse of his tyrannical theocracy.

          “What is Truth?” shows Jesus as an old man, teaching Torah to his students – among whom we find the Roman Ambassador to Judea. The story is a dialog between the old Rabbi and his students, friends and rivals; they ask each other what truth is. In a style similar to Plato’s dialogs, Jesus draws from all participants their own ideas as to the nature of truth; and in return the students draw out his own views. This part of the book is lyrical, philosophical and mystical – and for those reasons lacks the spectacular drama of Part One.

          The book, as a whole, lacks balance. “In This Sign Conquer” is a critique of the historic Christian Church; and as such, all too effective. After such an indictment one would expect praise of equal power, but “What is Truth?” seems thin in comparison. It is more for poets, priests and philosophers than for the rest of us.

          The difficulty is partly due to the nature of the subject. It is easy to write political protest for the masses, but far less easy to present ecstatic mystical liberation theology in terms that relate to the average reader’s everyday life. Neither Dante nor Milton could describe their Heavens as vividly as their Hells. This difficulty is compounded in a secular age such as ours.

          Another difficulty is due to the nature of history. “Alternate Jesus” is an alternate-worlds story, subject to the epistemological limits of such a narrative. We of this world-line can visualize the world-line of “In This Sign Conquer” because it is a lesser line than ours; it contains less information. The opposite is true for the world-line of “What is Truth?”; it is a greater world than our own, one of higher content, and for this reason we cannot know it fully.

          God-emperors have risen and fallen many times; there is nothing new in that old story. But in our world, Jesus died young, so we do not know what he would have taught, had he lived to old age. For this reason, “What is Truth?” falls short; it ends with mystery; one must fill in details for oneself. It ends with silence, as “In This Sign Conquer” ends with noise; and in both cases we see reflected the tragedy of our own world-line’s Jesus, who died before he could tell us all that he had to say.

 

 

 

“Both Sides Now: An Afterlife Exposé”

      Review of Imaginary Book:

     “Both Sides Now: An Afterlife Exposé”

 

          What are we to make of this strange yet familiar book? Surely no-one has ever taken so odd a stance; yet even first-time readers feel as if they had heard this story before. Could it be that this satire tells the true nature of Eternity?

          But that would be too simple, too “linear” a way of thinking. The author is an ironist; he delights in reducing ideologies to the absurd. The bigger they are, the harder they fall; what bigger pratfall, what wilder reversal, could you imagine than for Heaven and Hell to swap places?

          For that is the author’s heretical jest. In this paradoxical morality play, we see the Paradise and the Inferno of medieval Christian theology set into circular motion. Heaven falls, becoming a Hell, and Hell rises, becoming a new Heaven; and by book’s end it is clear that the cycle will repeat forever.

          For this is no accident, but inherent in the nature of the situation. The blessed are corrupted by their pride in being blessed; the damned are reformed by their humility in being damned. We see the all-too-familiar class privilege rationalizing power abuse, in parallel with the inspiring sight of suffering souls redeeming each other through mutual aid. No wonder this book’s subtitle is “An Afterlife Exposé”!

          Shall we call this book’s author a cynic? An idealist? Both? Neither? Surely the term “realist” doesn’t apply; yet this admittedly fantastic fable has a compelling inner logic. Small details help, such as the slightly orange tint to Heaven’s golden clouds that deepens as the decline from the peak progresses. It was inevitable that St. Francis prefer Hell to Heaven, as would Mark Twain, Gotthold Lessing, and D. T. Suzuki; and just as inevitable that Heaven’s theocratic bureaucracy have personnel such as St. Torquemada and the Archangel Goebbels.

          In the book’s first chapter “Summer of our Discontent”, we see Heaven reaching – and passing – its peak, in alternation with Hell bottoming out. In Heaven, the coronation of the Godling is completed; the new deity’s first command is to declare war on Evil. (The clouds turned slightly orange.) Meanwhile in Hell, a temporary cease-fire is declared.

          The book’s second chapter is “The Purge”. In Heaven, St. Torquemada and the Archangel Goebbels start expelling suspect blessed; meanwhile in Hell, the cease-fire holds and peace burgeons.

          In chapter three, “Zeroth Circle”, falling Heaven and rising Hell meet and pass each other. Separated souls exchange messages; some choose this point to escape the Wheel.

          In chapter four, “Fallen Spring”, fallen Heaven turns into veritable Hell, and rising Hell becomes truly Heavenly.

          The last chapter, “Looking Up” sees attain – and pass – Heavenly perfection, just as the former Heaven bottoms out.

          And that completes the cycle!

 

 

 

 

Rivendell on Trantor

        Rivendell on Trantor

 

             Call a settlement of limited size but of great duration a “Time colony”, or a “Rivendell”; and call a civilization of great size but of limited duration a “Space civilization”, or a “Trantor”. The names “Rivendell” and “Trantor” refer to, respectively, the Elvish town in J.R.R. Tolkien’s “Lord of the Rings” trilogy; and to the planet-spanning galactic capital city in Isaac Asimov’s “Foundation” trilogy .

             I propose this census:

             Rivendell: a million people, for a million generations.

            Trantor: a billion people, for a thousand generations.

             The first is a fair-sized colony, lasting for tens of megayears, a

longish species lifetime. So this is a Local Range; the Home of a Kind.

The second is a world civilization, lasting for tens of kiloyears,

about the length of history. This is a World Culture with a History.

             Rivendell colonizes time, and Trantor colonizes space.

             To keep Rivendell fresh, let’s make it a college town, home of Rivendell University, in its new location. They had to leave the old place and build a new campus here, due to mega-volcano eruption. They’ve still settling in, it’s been only 1.7 million years. But despite Rivendell’s traditionalism, it manages to keep up with the times; for they accept students from all across space, especially Trantor. How’s that for a happening place?

             And as for Trantor… there is no boredom on Trantor, and no shortage of rebels. Trantor is always up to something big; a war, a revolution, a reformation, a renaissance; political decay, cultural flowering, religious crises and scientific breakthroughs; and whatever Trantor does, it does it.

             Trantor never sleeps. So of course people will want to go to Rivendell  just for a bit of rest. But sorry, no uninvited visitors.

             So which would you prefer? Rivendell or Trantor? Rivendell is at least a somewhat happening place; and Trantor has respectable longevity chops; and it’s a fair trade-off. The elvish city is to the techno-world as deep time is to history.

             I see an SF novel in this, with a single world inhabited by both a Trantor and a Rivendell. (Almost everywhere, from Trantor’s point of view; temporarily, from Rivendell’s.) To Trantor,  a thousand years is a long time; to Rivendell, a thousand people is a big crowd.

             Rivendell has changed locations several times, to keep up with the geography. There are abandoned fossil Rivendells, which other peoples dug up for treasure and technology; notably the precursors to the Trantor world-civilization. The word “Trantor”, to the Trantorians, means the name of their planet; and also mankind; and also ‘culture’, ‘peace’, ‘order’, and many other soothing ideals; with predictable tragicomic consequences.

             A spacelike civilization meets a timelike civilization; temporarily, locally; yet everyone in Trantor is affected by Rivendell, all over the planet; and Rivendell never forgot Trantor, even after mountains wore down.

             For one thing, they stole a lot of tech from each other. There may even be a tendency for Trantor to re-create another Rivendell, on a distant world; and a reciprocal tendency for Rivendell to recreate another Trantor, in the distant future.

             Rivendell’s rebels will leave, and will either vanish into obscurity, or find a Trantor to influence. Rivendell’s influence on galactic culture is slow but cumulative; a trickle of exiled geniuses; Trantor’s influence is all at once.

             Perhaps a rebel Rivendellian will leave, mix with Trantor society,

collect a cadre of likeminded malcontents, and then leave for a distant

world, to found New Rivendell. (Where they will offer modern boredom!)

             Trantor’s rebels will go out, in waves after waves, each to form their own utopian Rivendells. Some of those Rivendells will remain static until they go extinct, others will mutate into new Trantors.

             Rivendell is to Trantor as spore is to redwood.