Poincaré

By 1900, the educated world had become familiar with Newton's Laws of Gravitational Mechanics. The Copernican Model of the Solar System had become accepted. The Calculus was in place, and scientists now had the tools to compute the orbits of the planets around the sun. In this climate, a question arose.

Can it be shown that the Solar System is stable, under the assumption of Newtonian Gravitational Mechanics? If you run a model of the Solar System (such models are called Orreries), can you show that the orbits of the planets are forever stable, or does the Solar System "blow up" by flying apart or spiraling into the sun?

The King of Sweden was sufficiently intrigued by this question that he offered a handsome cash prize to anyone who could rigorously prove that the Solar System was stable, under the assumption that the motions of the heavenly bodies is indeed governed by Newton's Laws.

Enter Henri Poincaré, who decided to take a crack at this problem and the prize.

Computing the orbits of all the planets and their satellites is a daunting task, so Poincaré began his work with a much simpler model. He began with a trivial solar system that contained one large Sun at the center and but one Planet, in a nice circular orbit. It was fairly easy for Poincaré to show that after one orbit, the Planet returned to exactly the same position. This Two-Body Solar System was Periodic, hence stable.

Then Poincaré added a Third Body. But he didn't just add another Planet in a different orbit. Nope nope nope. He did something you might not have expected. He added a Comet in an elongated elliptical orbit -- one that swung way out to the outer reaches, far from the Sun, and then swooped in close to the Sun, crossing the orbit of the Planet along the way.

And then Poincaré discovered something astounding.

For the longest time, the Planet, in its Circular Orbit, and the Comet, in its elongated elliptical orbit, remained in their original orbits. But then, on one pass, something different happened.

Eventually, as the Comet crossed the orbit of the Planet, it did so while the Planet was nearby. When the Comet passed close to the Planet, the gravitational attraction between them kicked into action, and the orbit of the Comet was bent. Thereafter, it assumed a new and different elliptical orbit. And the Planet was affected, too. It was deflected a tiny amount from its circular orbit, which now became slightly elliptical, too.

Nothing much interesting happened after that for a very long time, until the Comet made another close pass to the Planet. And then, once again, its path was bent, sending it into yet another orbit. And the Planet's orbit was perturbed again, as well.

So the first thing that Poincaré found was that a Three-Body Solar System isn't periodic. The orbits are not permanent, but change due to the interactions between the bodies.

But wait. There's more...

Poincaré discovered something even more unexpected.

He went back to his Three-Body Solar System and ran the Orrery again. Only this time, he started the Comet in just a slightly different orbit than the first time. And what he found amazed him. While the same basic phenomenon happened, the history of the Solar System was markedly different. After a few close passes, the two versions differed wildly from each other. Even the tiniest, most infinitesimal change eventually leads to dramatically different histories.

Poincaré had discovered what we today call "exquisite sensitivity to initial conditions." What that meant was that the future of the Solar System was not predictable, because the tiniest error in specifying the initial conditions eventually leads to completely different outcomes.

But wait. There's more.

Eventually, the Comet, when it crossed the orbit of the Planet doesn't have a close call. Nope. Eventually it collides with the Planet. Not unlike the Asteroid that plummeted into the Yucatan some 65 million years ago, thereby killing off the Dinosaurs.

So the Solar System, is not stable, but chaotic, unpredictable, and doomed.

And all the objects -- in this case just three of them -- are religiously obeying Newton's Laws of Celestial Mechanics -- the Inverse Square Law of Gravity, and F = ma.

What Poincaré had discovered, in the early years of the Twentieth Century, were the roots of Chaos Theory. But it would take another 50 years before that branch of mathematics came of age.

Poincaré presented his results to the King of Sweden, who was so astonished that he awarded Poincaré the prize. Of course Poincaré had proven the opposite of what the King had anticipated. The Solar System was not inherently stable under the assumption of Newtonian Gravitational Mechanics, but unpredictable, chaotic, and doomed.

Poincaré's most astonishing result was that a Rule-Based System, in which the rules were rigorously followed, was not an Orderly System as everyone imagined, but a Chaotic System.

Is there no hope? Are we hopelessly trapped in a Rule-Based System, hopelessly trapped in an unpredictable, chaotic, and doomed system?

Is there is a solution? We turn now to CNN Headline News...

Imagine there is a traveler aboard that ill-fated Comet -- a trenchant CNN news reporter who is going to keep us informed of the unfolding drama. And who better to do that but our favorite CNN field reporter, Christianne Amanpour.

So here is Christianne, decked out in her flak jacket and fly-away hair, gripping her microphone and breathlessly reporting the trajectory of the ill-fated comet from the depths of space.

In between live reports, Christianne is chatting offline with her colleague and occasional news rival, Wolf Blitzer, safely stationed (as usual) at the Pentagon in his well-pressed suit. Wolf is envious of Christianne's plum assignment -- clearly the capstone of her fabulous career. But Christianne is troubled, since this story has a disturbing (if predictable) ending.

"I hope you have your make-up kit so you can look good for your final transmission," says Blitzer.

"Very funny," retorts Christianne, "but I really wish there were some way to change the ending. I can't imagine you having to don a flak jacket and take over for me after I meet my maker."

But Wolf has pity for young Christianne, so he offers a glimmer of hope. "Let me call up this guy at Jet Propulsion Laboratory and see if he has any bright ideas." Wolf places the call and explains the situation to his buddy in Rocket Science.

"What resources does Christianne have?" inquires the space jock?

"She has her flak jacket, her microphone, her makeup kit that she never uses..."

"What's in the makeup kit, Wolf?" asks the guy at Jet Propulsion Lab.

"Oh, the usual... Face powder, eye shadow, and the aerosol can of hair spray that she never uses."

"Did you just say that Christianne has an aerosol can of hair spray she never uses?"

"Well yeah," says Wolf, "haven't you ever seen her, with her fly-away hair?"

"She's saved," announces the rocket guy.

How is Christianne saved?

The rocket scientist advises Christianne to fire her aerosol can sideways to her direction of travel. Yes, sideways. Christianne does this, thus producing a reactionary thrust, in accordance with Newton's Second Law of Motion. She's got the Force with her, now. By changing the direction of her trajectory, she can steer around the looming earth and avoid a direct collision.

Our CNN news crew has discovered the Joys of Rocket Science.

Christianne lives to report another day, and Wolf can continue to wear his suit at the Pentagon.

The solution involved an understanding of the Model of the System in which Christianne is embedded. And then she had to solve that model (with the aid of some Rocket Scientists at JPL who know how to solve system models). By solving the model, they supplied her with the Best Practice that was concordant with the Laws of Celestial Mechanics, to change her fate from doom to victorious survival.

Note that the solution did not involve adding more laws to the Books of Celestial Mechanics. It did not involve any legislative or political or judicial acts. It just involved comprehending and solving a System Model.

And that is the moral of my story. Rule-based systems are unpredictable, chaotic, and doomed. But the solution is to advance to Model-Based Reasoning, and to learn to solve System Models for the Best Practice to avoid the Apocalypse.

So... How does this help us understand the error in the architecture of human culture?

Our culture is Rule-Based. Most people believe, without question, that rule-based systems are orderly and predictable.

But that belief appears to be in question. The entire branch of mathematics known as Chaos Theory studies the production of chaotic and disorderly systems from the repeated application of a few simple rules. Scientists now know perfectly well that repeated application of rules generates chaos. It's a mathematical fact.

Just as the heavenly bodies obey the discoverable laws of Celestial Mechanics (which have only been known since the time of Kepler, Copernicus, Galileo, and Newton), the earthly bodies also obey the discoverable laws of human socio-cultural mechanics.

At the time of Copernicus, few souls knew of his work. Indeed, he did not publish his tome until after his death. And I can understand why. Systems Thinkers have not been well received by the Powers That Be.

Today there is a new Copernican Revolution afoot. Today there are emerging models of Human Socio-Cultural Dynamics that apply to the motions (and emotions) of the earthly bodies. If you run these models forward, the way Poincaré did with Newton's Laws, you find the system is chaotic, unpredictable, and doomed.

But if you solve the System Models for Best Practices, you find a computable solution. But the solution is not Rule-Based.

Rule-Based systems are too weak to compute the "Rocket Science" needed to avoid the Apocalyptic Doom of Rule-Based Cultures.

The first Systems Thinkers who gained any insight into the Models of Human Socio-Cultural Mechanics, and who solved them for Best Practices ended up founding all the world's major religions. But their followers only got the solution, not the model itself, or the method of reasoning to solve it.

Now we are getting the model itself. And thanks to a handful of brilliant thinkers, we also have the associated methods of reasoning.