Jafar's Math Curriculum Proposal to the Sixth Slawkenberg Council on Education (Lesson 3)

Chaos is fundamentally about playing with the rules that create our universe.

So let us play!

Instead of a hab, like last lesson, let us return to an even simpler shape, the same triagnle we made last lesson. Serpinski's gasket.

Let us see how, by rolling a dice, and moving a single point around like a messanger boy randomly delivering mail to various addresses in a Hab, we can sketch out the shape of Serpinksi's Triangle.

Remember Serpinski's gasket? Here's how we made it last time.

What if, instead of shapes, I started with numbers?

If I do that, then, just like every room in my home hab, every piece of this triangle is numbered.

Just like I, as a messanger boy, could find any room in my hab by knowing it's address. I can go to block 14, complex 8, and room 3. and find the people within it...I can find any point in this triangle.

Let's look at address 21322

Just like finding an adress in a hab, I start with the biggest aread first. Let's imagine this triangle serpinski's triangle is the size of a city. a ruthless imperial city built by a governer obsessed with the mind-numbing, excessively triangluar simplicity of the Imperium. This city is split into 3 zones. To get to address 2, I fly my aircar to city sector two. Within it, there are three triangluar habs. I fly to hab 1. Within that hab, I need block 3- so I land my aircar in the central landing pad of hab 1, get out, and walk to block 3. Once inside block 3, I walk to plex two. And in plex 2, I find a human-size room, large enough, barely, for my tall bones to stand without my hat brushing the ceiling. I have found room two.

So in this hideous triangluar capital, I've found city sector 2, hab 1, block 3, complex 2, room 2- a room of human size that humans can live in, although again excessively triangular.

While the room can be subdivided furhter, there isn't a practial need. The study of spaces is a study of humanity, and human brains are meant to toy with ideas on a human scale. A room is an excellent place to start. If i subdivide this further, smaller, only dogs can fit, in the next level. or even smaller, only roaches. Smaller still, bacteria. It can go down until infinity, but as humans with a human perspective, as a practical matter we can stop short with a human sized room.

Finding the address is backwards from how I learned my place in the world in the first place. In the beginning, my room was my world, Then it expanded to the plex. Then the block. Then the hab. Then the world. And then...the galaxy.

But every time my knowledge expanded, my world appeared to shrink, until my room was the size of a dot. Initially, this made me feel very small. But then I learned to accept the glory of being human, and of operating on a human scale.

Let's picture the address 21322, starting from the biggest number, all the way down to the smallest- overlayed onto our Imperial city.

An address locates a point in space, and as you can see, we're just finding a small dot- the boundary of our address, the boundary of our knowledge.

Now that I've found room 21322, and sit down in the bare, brutal, Imperial triangle, I decide I wish a change. I wish to go to a different room, in a completely different zone of the city. So I'm going to go visit a new address. a new address. I decide to throw out number two, the one that tells me which room I will choose.

I decide to keep four of the numbers, and simply, move them right one space. I still have the four numbers of an adress- a new room number, a new complex number, a new block number, and a new hab number. But that means I haven't decided which subsector of the city I am going to locate the rest of this address.

I let the Lord of Fate decide, and roll the dice. It comes up 1. I'm headed to subsector 1 of the city, and in it, I will travel to find hab 2, block 1, plex 3, room 3.

If I do this again, and again, and again...as we all know, when rolling the dice of fate, eventually every number will come up. The rules of fate demand it.

This means that, eventually, I will roll every address. And explore every room in this benighted triangle of an imperial city.

So I can explore the whole shape, find every room, and see the city mapped out in my minds eye.

However, long before I visit every room- long before I banish my ignorance about what they contain, I will still start seeing a visceral sense of the shape of the city. The parts I know will become faimiliar, and the more I visit, the more it's overall pattern becomes clear.

This is why the chaos game is fast.

This is why the chaos game is valuable.

One does not need to know every step of the fated path to use chaos to map the underlying order of the universe. One need not know the universe in every particular in order to be able to make use of it's structure, and it's rules.

And so, by walking a fated path, a path determined by nothing more elaborate than the roll of a dice, and doing it over and over...I can map out the city with exactly the same precision of the the godlike, top-down construction of the copy machine method.

!

And you know the most important difference between the copy machine method of buildinga city, and the chaos game method of randomly exploring it?

It's humanity.

The Copy Machine method demands that you start big. It demands that you start with the end in mind, with tools and machines and ideas already given. It demands you starton an inhumanly large scale. Start with Gods, and Galaxies, and forces far too large for the human mind to hold in hand.

We humans don't think on a galactic scale. We think from ourselves outward. Starting as children, we explore the world within reach of our grasping hands. Then we crawl outward, expanding our thoughts to what we can crawl towards. We grow up, stand up, and think in terms of where we can walk or run. We build wings, and think where we can fly. But our explorations are not the systematic imaginings of a machine. Ours is the explorations of desire, and fear, and pain, and pleasure. We learn the world based on both our wants and our needs, our limitation and ambitions- so many of which are as chaotic as a roll of the dice.

But with the Chaos game, you can start anywhere. Any room. And like a child, stepping out of the room, armed with only a spell, a hope for home, and a few simple rules- you can step out and explore a whole fractal world.

So, young Slawkenberger...why is it important to know things like the chaos game?

Not just because it liberates us from the rigid brutality of imperial architecture. It liberates us from the brutal simplicity of Imperial *thinking.*

This can be seen in the new construction of Cainville, as the habs come down and more livable, varied, and diverse human spaces arise in their place.

Instead of building a city all at once by dropping a square cube on a piece of land and shoving every person into their own assigned room...we can build as we need, at a human scale, addressing each problem as it comes, with an eye to the needs of the larger system but always honoring our changing nature. Always allowing the individuals to be individuals. Making space and honoring those who create the enticing and delightlly fractal detail of our world the privilage of running around in ever-evolving, ever supporting sandboxes, and learning the new and ever changing sets of rules. It allows us to become architects of our own fate.

We can run around, building and learning the way the best of humanity learns...from our size on up.

We can rewrite the rules to make our own game.