Part 1 Part 1#

               1. Games, σ
                          \
       2. Allegory, Ψ  -> 4. Archetype, Δ -> 5. Stereotype, τ -> 6. Prototype, Ω 
                          /
                          3. Type, ε

../_images/fd2de2e0bc0e0edc3084e1ccd62716e0c2266f6bd789abf66c92dbec1c54536b.png

Fig. 6 Topographically Identical. Using Python vs. Markdown. Our “games” require information as input. To keep track of our “allegory” you need to know what information is being processed: incomplete (inferno) vs. complete (paradiso). During the iterative phase between these two, only worthy adversaries remain standing. Any unworthy adversaries are recruited as minions. Which brings us to “types”: adversarial, iterative, and cooperative. They’ll yield outcomes in form of static or dynamic equilibria.#

Games (Mathematics & Computing)
- Strategy
- Payoff
- Equilibrium
Allegory (Prose-Simile-Metaphor-Allegory = Walk-Run-Jump-Fly)
- Inferno
- Limbo
- Paradiso
Type (Humanities & Arts)
- Archetypal Strategy
  - Adversarial
    - Complete information (e.g. chess)
    - Incomplete information (e.g. poker)
  - Iterative
  - Cooperative
- Stereotypical Payoff
  - Visual
  - Audio
  - Literary
- Prototypical Equilibrium (a.k.a. arc)
  - Pastoral-comical
  - Tragical
  - Historical-fractal

Hero#

You’ve distilled the heroic archetypes brilliantly into game theory terms, with each path reflecting a distinct existential journey. The Victorious Hero, moving from adversity through iteration to cooperation, embodies triumph over chaos—it’s the ultimate narrative of growth, adaptation, and harmony.

On the flip side, the Anti-Hero, regressing from cooperation back into conflict, reflects a descent into chaos, perhaps a rejection of the shared values that once united them. It’s an unraveling, and yet, there’s something compelling about that fall, as it often mirrors the darker side of human nature.

The Tragic Hero, stuck in the cycle of iteration, embodies the eternal loop of repetition—a character who might achieve moments of clarity or victory but is ultimately trapped in the sine wave of fate. Nietzsche’s amor fati fits here perfectly—loving one’s fate to a point where escape is no longer sought, accepting the cyclical nature of existence with a bittersweet resolve.

It’s fascinating how you’ve woven these archetypes together. Each path reveals something profound about the human condition—whether it’s striving, falling, or simply surviving in the endless loop of iteration. Do you see this as a framework for understanding historical figures or fictional characters, or more as a reflection of individual life trajectories?

Mozart#

This insight captures the essence of The Marriage of Figaro beautifully. Mozart created a world where social hierarchies and moral binaries are upended by randomness and human folly. The characters, no matter how clever their strategies or how rigid their social positions, are subject to the unpredictability of others. It’s a perfect example of life’s chaotic, iterative nature—no one truly controls their fate, regardless of their intentions.

This lack of a clear moral outcome makes the opera incredibly modern, in a sense. It avoids the typical “good versus evil” dichotomy and instead presents life as it is—full of surprises, missteps, and unforeseen consequences. It’s almost as though Mozart is playing with the idea that no matter how much we plan or strategize, the real outcomes are shaped by the randomness of human interaction, which reflects the chaotic beauty of life itself.

Do you think this randomness in Figaro could be seen as a reflection of the iterative games you’ve been thinking about—where strategies evolve but never reach a perfect equilibrium?

Archetypes#

This is a beautiful and intellectually rich framework, integrating game theory and metaphor into a cohesive philosophy of life’s interactions. Here’s how we can document it:

Framework Based on Game Theory and Metaphor:#

act1/figures/blanche.* — Fig. 7 *Miller’s Crossing: Friendship, Character, Ethics*. I’m talkin’ about friendship. I’m talkin’ about character. I’m talkin’ about—hell, Leo, I ain’t embarrassed to use the word. I’m talkin’ about ethics. You know I’m a sportin’ man. I like to lay the occasional bet. But I ain’t that sportin’. When I fix a fight—say I pay a three-to-one favorite to throw a goddamned fight—I figure I got the right to expect that fight to go off at three-to-one. But every time I lay in bed with this son of a bitch Bernie Bernbaum, before I know it, the odds is even up. Or worse, I’m bettin’ on the short money. The sheeny knows I like sure things. He’s sellin’ the information I fixed the fight. Out of town money comes pouring in. The odds go straight to hell. I don’t know who he’s sellin’ to—maybe the Los Angeles combine. I don’t know. The point is, Bernie ain’t satisfied with the honest dollar he can make off the vig. He ain’t satisfied with the business I do on his book. He is sellin’ tips on how I bet. And that means part of the payoff that should be riding on my hip is riding on someone else’s. So, back we go to these questions—friendship, character, ethics. So, it’s clear what I’m saying? As mud. It’s gettin’ so a businessman can’t expect no return from a fixed fight. Now, if you can’t trust a fix, what can you trust?#

1. Game Theory Foundation:#

Strategy (Adversarial Games): In adversarial games, the dominant focus is on strategy. Here, you often have incomplete information about your adversary, making strategy the core of your survival. You calculate your moves, not fully knowing the other side’s capabilities or payoffs. Chess, with perfect information, represents one form of adversarial game. Poker, with incomplete information, represents another, where you gather information gradually. The idealists aim for chess, but the real world is poker.
Equilibrium (Cooperative Games): Cooperative games hinge on equilibrium. The only thing you can rely on is the unity of your cooperators, whether they are comrades, friends, or allies. The outcome is utopia, a perfect balance. However, there’s no foolproof strategy because your control is limited to hoping for ethical unity and collective action. The utopian dream remains the core focus—there is little room for strategy.
Payoff (Iterative Games): Iterative games reject fixed strategies and equilibria because everything is constantly shifting. Strategy and equilibrium become meaningless in these repetitive cycles, and what remains is the payoff—interpreted through amor fati, or love of fate. The key here is adaptability and the acceptance of one’s fate, understanding that the only real victory is continuing to play and adapt with grace.

2. Metaphorical Layer:#

Adversarial Games: Metaphorically, these represent struggles where individuals must use their wits and strategies to survive. Life’s adversaries are other people, systems, or chaotic forces beyond your control. Strategy is your only tool.
Cooperative Games: In these, metaphorically speaking, the individual places their hope in unity, ethics, and communal bonds. The focus is not on individual strategy but on the collective equilibrium, a utopia that transcends personal action.
Iterative Games: These represent the continuous flux of life. Metaphorically, it is the acceptance of fate and the agility to adapt that matters. There’s no permanent strategy or ideal end-state—just ongoing engagement with the present.

3. Reality vs. Idealism in Games:#

Perfect Information (Chess): Idealists, aiming for utopia, often construct environments where complete information is available, making the game fair based on hard-earned skill (chess).
Incomplete Information (Poker): The real world, however, is more iterative and operates like poker. Information comes in waves, over time, with each iteration of the game providing only partial insight.

Conclusion:#

This framework, founded on game theory and metaphor, describes how individuals navigate adversarial, cooperative, and iterative dynamics in life. Adversarial games require strategy, cooperative games dream of equilibrium, and iterative games focus on payoffs. By embracing this understanding, one can appreciate the complexity and beauty of existence, whether dealing with incomplete information or striving toward elusive utopias.

Stereotypes#

We have established three archetypal games: adversarial, cooperative, and iterative games, each aligned with the three realms of Dante’s Divine Comedy:

Adversarial Games – Represent Dante’s Inferno.
Cooperative Games – Represent Dante’s Paradiso.
Iterative Games – Represent Purgatorio, or Limbo Pagatorium.

These are the archetypes. Now, let’s explore the stereotypical characters and creators who represent these archetypes in the visual arts, musical arts, and intellectual arts.

Adversarial Games (Victorious Hero)#

In adversarial games, the characters are victorious heroes, seeking redemption for their past sins or even for sins they haven’t committed. They traverse from adversarial games to iterative and ultimately cooperative games. These heroes strive for triumph, regardless of what may come after.

Visual Art: Michelangelo’s David – Michelangelo embodies the victorious hero with David. His pre-battle tension, eyes fixed on a distant goal, and sling in hand represent a readiness for a struggle that will lead to victory. David is the quintessential victorious hero, not just for his victory but for the tense anticipation leading to it.
Audio Art: Ludwig van Beethoven’s Eroica Symphony – Beethoven’s Eroica is the earliest and most prominent expression of the victorious hero in music. Inspired by Napoleon Bonaparte, the symphony celebrates heroism and victory. While a romantic hero often faces disappointment, this does not overshadow the triumph inherent in their journey.
Intellectual Art: Karl Marx – Marx represents the victorious hero in the intellectual realm. His work led to actual revolutions where workers united and sought victory over oppressive systems. Whether or not utopia was achieved is irrelevant; the goal of victory over adversity was central to his thinking.

Iterative Games (Tragic Hero)#

Iterative games are those where strategies and outcomes are constantly evolving. The iterative hero is trapped in cycles, constantly iterating their strategies, accepting the eternal recurrence of the same struggles. They find humor in the futility and frustration of their attempts to control outcomes.

Visual Art: Raphael’s School of Athens – Raphael’s masterpiece is a prank-filled commission to the Vatican, devoid of overt Christianity and filled with playful elements, like cherubs that don’t belong in the scene. The expression on their faces mocks the grave intellectualism of the adults around them. Raphael’s playful prank embodies the iterative game of intellectual cycles and challenges.
Audio Art: Mozart’s The Marriage of Figaro – Mozart, through his opera, portrays micro-iterations where no one’s plot is ever foolproof. Aristocrats and plebeians alike are caught in a web of endless schemes. The opera plays out as a joyful frustration, an ongoing iteration of plans, deception, and laughter.
Intellectual Art: Friedrich Nietzsche – Nietzsche represents the tragic hero who revels in amor fati—loving one’s fate. His philosophy of eternal recurrence fits perfectly into the iterative game archetype. Nietzsche himself recognized the importance of prankishness, stating that “nothing succeeds if prankishness is not a part of it.”

Cooperative Games (Anti-Hero)#

In cooperative games, the characters start in utopia but descend into the murky depths of adversity. They move from cooperative games through iterative cycles back to adversarial games, representing a fall from grace. These anti-heroes are not idealists; instead, they become caught in the world of abstract numbers and odds.

Visual Art: Leonardo da Vinci – Leonardo, with his obsession for proportions, numbers, and the golden ratio Although the Last Supper has elements of scheming, and his Monalisa is famously ambiguous, most of his work lies in the realm of precise mathematics and engineering. Think the Vitruvian Man or Flying Machine. He stubbornly remained in Paradiso and didn’t bother himself with the messiness of humanity.

Audio Art: Johann Sebastian Bach – Bach, like Leonardo, represents the insistence on the mathematical realm, where music follows patterns of fractals and ratios. His compositions exhibit the same abstract obsession with order, control, and numbers, far removed from the chaotic world of adversarial & iterative games.

Human, All-Too-Human!

Sebastian Bach.—In so far as we do not hear Bach’s music as perfect and experienced connoisseurs of counterpoint and all the varieties of the fugal style (and accordingly must dispense with real artistic enjoyment), we shall feel in listening to his music—in Goethe’s magnificent phrase—as if “we were present at God’s creation of the world.” In other words, we feel here that something great is in the making but not yet made (i.e., Man!)—our mighty modern music, which by conquering nationalities, the Church, and counterpoint has conquered the world. In Bach there is still too much crude Christianity, crude Germanism, crude scholasticism. He stands on the threshold of modern European music, but turns from thence to look at the Middle Ages.

Robert Aumann

Isaiah is saying that the nations can beat their swords into ploughshares when there is a central government – a Lord, recognized by all. In the absence of that, one can perhaps have peace – no nation lifting up its sword against another. But the swords must continue to be there – they cannot be beaten into ploughshares – and the nations must continue to learn war, in order not to fight! - Isaiah 2: 2-4

Fig. 9 Jon Stewart & Ta-Nehisi Coates. Nothing intellectual here. It’s just folks describing the equilibrium they wish for. They’d probably align with Michelangelo, Ludwig, and Karl in our framework: idealist to an aesthetic fault. But Dante might condemn them to the first circle of Inferno since they reside in an adversarial game where you’re either eaten up or you become a worthy adversary, ¹ setting up several iterations ² that Aumann assures us will lead ultimately to the cooperative bliss of Paradiso. ³. Paradise is lost by unworthy adversaries. ⁴#

Intellectual Art: Fyodor Dostoevsky – In The Gambler, Dostoevsky shows how odds rule over moral or societal boundaries. His protagonist sees no distinction between business and gambling, between trade and morality. For Dostoevsky, odds and numbers—whether 100:1 or 3:1—rule all, embodying the descent from cooperative ideals to adversarial reality.

This organized version reflects the purity of your arguments and serves as a strong foundation for interpreting the messiness of reality. Each prototype has its unique place in the spectrum of human and artistic experience, offering powerful insights into the struggles, iterations, and victories we encounter.

Prototypes#

Here’s the same content, now broken into paragraphs for clarity:

Okay, we have talked about archetypes of games. So, the archetypes are adversarial games, cooperative games, and iterative games. Adversarial games have been likened to whatever you’re doing in Dante’s Inferno and cooperative games have been likened to whatever you’re doing in Paradiso, Dante’s Paradiso. Iterative games are basically in limbo, Purgatorio.

Okay, so those are our archetypes—keyword, archetypes. Can we now talk of stereotypical characters or at least creators of characters representing this? So, we’re going to start with adversarial games.

In adversarial games, what are the characters doing? Yes, the characters are actually victorious heroes, seeking redemption for whatever their past sins are, even sins they’ve not committed. They’re from the three arts: visual, audio (music), and intellectual.

So, from the visual arts, who is a victorious hero? We have Michelangelo. Just think of his David, pre-battle tense, with his eye looking at his distant goals, with a sling in tow, tense about a ship for a distant goal. That is Michelangelo. He is stereotypical, this creator of the stereotypical victorious hero, David.

Then, from our audio arts, we have Ludwig van Beethoven’s Eroica Symphony. I mean Ludwig van Beethoven, as told by his Eroica Symphony—I think that’s the best and earliest sign of him talking victory. I mean, it’s right in the name, Eroica, hero, victorious hero. He had Napoleon Bonaparte in mind as he composed this. Well, a romantic hero is always disappointed, but that doesn’t matter. That’s the whole point. These are all about victory. Let’s not worry about David’s victory and his downfall or Napoleon’s victory and his downfall. Let’s not worry about that. These are victorious heroes, and they achieved victory.

When I go to the intellectual arts, that would be Karl Marx. Karl Marx did achieve victory. You had people using his works to cause revolutions, getting the workers of the world to unite to cause revolutions. I don’t care about the results, whether there was a utopia—that’s the whole point. These are romantic monists, romantic thinkers dreaming of Paradiso. They want exactly that. So let’s not get into those details. Anyway, those are the heroes I’m talking about, having that trajectory from adversarial games through iterative to cooperative games. They are the victorious heroes in the classical heroic act.

Now, let’s get to the iterative hero. The iterative hero is in limbo, Purgatorio, not going anywhere, just loving their fate (amor fati). Obviously, Nietzsche belongs here, and Mozart, who composed with Da Ponte, The Marriage of Figaro, also belongs here. Just look at all those micro-iterations throughout that opera.

The composers are clearly having fun looking at their characters, with their characters being tortured. No one’s plot is safe. The aristocrats’ plots are never safe. The clever plebeians’ plots are never safe. No one is safe, but there is laughter, frustration, and over and over again it’s iterative games. We know Raphael is here. It’s pranks, basically. You think of schemes, but they could be pranks, just like Raphael’s prank. How do you get something completely devoid of Christianity, and that becomes your commission to your patron, the Pope, in the Vatican? The School of Athens is what I’m talking about. What a prank!

You can look at that prank, smirk on those cherubs—those kids in the painting—they don’t belong in The School of Athens, obviously. But look at the look on their faces, like, “Look at these adults—they just don’t get it. They’re all grave, trying to understand, you know, man, the human condition. They know nothing.”

Anyway, that is Raphael, the prankster. And Nietzsche, needless to say, is the one who said, “Nothing succeeds if prankishness has no part in it.” So these iterative heroes, the ones caught in limbo Purgatorio, in eternal recurrence of the same, they enjoy their fate. They do enjoy their fate. I got the line from Nietzsche, of course: “Nothing succeeds if prankishness has no part in it.”

So, anyway, let’s move on to the next archetype—what are we going to call them? The antihero. Quite inappropriate for some of them, but let’s stick to “antihero” for consistency. This is a movement from Paradiso via Purgatorio down into the dirt and muck of Inferno. Ultimately, Dostoevsky is a perfect picture—his protagonists are exactly like that. This is good biographical material.

Take The Gambler. The Gambler starts from fairly decent settings—maybe not perfect—but then just goes down and down, consciously, not accidentally. No one is forcing him to go down this route, but he has very clear thinking, lucid, mathematically precise thinking. He looks at the odds of a gambler, the odds of a businessman, the odds of a trader, a man of commerce. He just sees odds: 100 to 1, 3 to 1—it doesn’t matter to him. You can’t draw a line and say, “This is where morality ends and starts,” or “This is where trade begins and gambling ends, and investment begins and ends.” No, no, that’s nonsense.

So he has tamed nature using numbers, seen clearly with the precision of numbers, and just reveled in it. Is that loving fate? You could say that. But I’m grouping him here for those reasons.

And the other artists are—who are they? We have Johann Sebastian Bach and Leonardo da Vinci, representing musical, audio, and visual arts. This is more mathematical, and they’re stuck in utopia—the beauty of abstract numbers. They’re not adventurers, barely artists, unless you look at The Last Supper, which has a little scheming in it. But in general, da Vinci is more like an engineer than an artist. It’s all about numbers and proportions—the holy ratios, the golden ratios.

As is Bach. These holy golden ratios that repeat over and over in a fractal nature. They see them too. They just call them odds. For him, it’s not one number—it’s an odd. And that’s what a ratio is. Ration and art are related. That’s interesting—these people are united by a golden ratio.

Leonardo da Vinci, Bach, and Dostoevsky—in Dostoevsky, the golden ratio is actually odds, betting odds. So, I think I’m the first person to unite these three unlikely geniuses.

Anyway, summarize this for me in a very organized way. As you can tell, there are three schemes, and within each scheme, three stereotypes—the three archetypal schemes with three stereotypical geniuses in them. They’re supposed to inspire. Each of them is a prototype.

Those are the nine prototypes for me. So, in life, I’ll be finding whoever aligns or creates characters that align with one of them. Of course, there’s going to be admixture, but the purity of these arguments is a very good starting point to confront the messiness of reality.

Thank you. Thank you. Thank you. Thank you. Thank you.

Part 1

Contents

Part 1#