chaos and economy and weather

Economies are multi-variate chaotic systems.

What’s a chaotic system?

A chaotic system is a function. It’s arithmetic. But it’s a function in which its variables future state depends on its current state. For example:

f(z) = z² + C

C is a constant. Every iteration you take the old value of z and square it, then add C and that’s your new value of z. Doesn’t look dangerous, right? Well if z is a complex number (so it’s really two parameters, not one — the real part and the imaginary part) and you map the number of iterations before it explodes to some huge number or to zero, you get this;

File:Mandel zoom 00 mandelbrot set.jpg
Created by Wolfgang Beyer with the program Ultra Fractal 3. – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=321973

And that’s just two variables. Well, one complex one. Which is like two. Even that lovely image doesn’t do justice to the complexity of this result. If you zoom in on the regions that border on the black area of certainty, drilling down into variations in starting conditions at the fifth, tenth, sixteen thousandth decimal place, you will see an explosion of new complexity. Not random, but chaotic. With tiny islands of stability, regions of periodicity, and a whole lot of places that cannot be determined without another decimal place.

Just two variables.

Let’s look at just one. Let’s use f(x) =  + 0.21. Just one variable, no complex math. And let’s use a spreadsheet to see what happens between, say 0.01 and 1.3 or so. I won’t paste in my whole sheet but you can do it for yourself. Here are some features:

Screenshot 2019-09-26 17.02.54
It’s tiny so you can see the convergence patterns. The #NUM! errors is because Excel doesn’t like to work with numbers that have more than around 300 digits. So we’re calling that infinity.

If we start with x less than 0.3, the function trends up towards 0.3.

Between 0.3 and almost 0.7 (in fact infinitely close to 0.7), the function trends down towards 0.3.

At 0.7 the function just always returns 0.7

After 0.7 the function explodes faster and faster towards infinity.

0.3 is clearly some kind of attractor, an orbit in this simple (so very simple) system. And something is magic about 0.7 — it’s perfectly, utterly stable over time and yet it is so very precise. A millionth of a millionth more or less than 0.7 and it either hugs 0.3 eventually or it spins very rapidly indeed off to infinity.

In any chaotic system there may be regions of stability, called “attractors” or “orbits” where state fluctuates around some point on the map, never quite leaving the region (for the period we simulate). You see some perfect attractors in the super simple system above — 0.3 is obviously an attractor. 0.7 isn’t but it’s a stable point. A tiny tiny one. In more complex systems these orbits might not be so reliably convergent — they might diverge suddenly as they approach. Maybe at the fiftieth iteration. Maybe later.

The important thing here is…well there’s two. They are:

Unpredictability. You can’t guess from the current state what the next state will be. You have to crunch the numbers. In simpler systems you can make a guess of course, and even likely be right, but it’s hard (or in more complex systems impossible) to prove your guess analytically.

Sensitivity. You can’t simulate the future state because tiny variations in a variable’s value can have dramatic impact on future state: your simulation has to be perfect to be useful. 0.6999999999999999 converges on 0.3. 0.7000000000000001 goes to infinity. A rounding error can kill you.

Our economy has thousands if not millions of variables. Just three would need a three dimensional image to display, and one we can see inside of. Four variables would need a space we are not equipped to visualize. The economy is mind bogglingly complex. It’s at least as bad as the weather. And while we have all kinds of tricks for predicting the weather they all pretty much boil down to this: tomorrow will be like today only slightly different, with a sprinkling of last time it was like this the next day was like that.

A free market economy (a perfect one — a spherical cow in a vacuum) is a chaotic system in which participants have faith that this algorithm will result in the best possible world for the most people. This algorithm was not, however, designed in any fashion. It was just set loose. No one ever has understood all the variables and it’s intrinsically impossible to predict its behaviour. It has no knowledge nor interest in us or itself. It’s just a huge chunk of arithmetic. This is a weird place to put your faith.

Variations on the free market are an attempt to change key variables to get local effects that are desirable. Experimentally (and even analytically) we can find ways to reduce interdependency, to force certain variable states, and even to make certain variables irrelevant to the calculations. It’s fundamentally an attempt to simplify the chaotic system, to make it less chaotic. Or to push people into stable regions with positive effects.

You are already aware of some of the more stable regions. Being incredibly wealthy is a fairly stable region. Few variables impact you meaningfully and you have to make extreme moves to put you in a position where you won’t just be nudged back into this comfortable orbit no matter what you do.

Being incredibly poor is also a very stable region. There is very little that will shift this orbit short of the random injection of a ton of money. It’s why lotteries are so popular even though the odds are bad. It’s worth being worse off even for the hope of being catapulted out of this region of space, whether or not it comes true. Because it’s pretty much the only game in town once you orbit this dark star.

But without deliberately manipulating the system, without trying to control variables based on past experience, you are at the mercy of the winds. There are no guarantees. No large body of math cares about you. Don’t put your faith in it. Put your faith in people.

orbital mechanics

While tinkering with the technology levels in Diaspora Anabasis, we had an interesting opportunity disguised as a problem.

Technology level 0 means no space travel. There are six different oracles to explain this (and of course you can invent your own) but only the space travel bit is interesting here.

Technology level 1 is early space travel requiring huge resources if there’s a gravity well. Chemical rockets.

Technology level 2 is commercial space travel, more advanced rockets.

Technology level 3 introduces the slip drive but not much more.

Technology level 4 is even better drives but so what?

Technology level 5 is magical tech. Crazy off the wall unpredictable tech. It’s peak technology just before a civilization disappears.

So the problem with this is that level 4 is not actually differentiated much from 3. So here’s my idea. From tech level 1-3 rockets have efficiencies such that you can only practically travel most places inside a system using orbital mechanics. At tech level 4 you get so efficient that you can just do a Traveller-style constant burn, turn over, constant burn pattern to anywhere you want to go.

I’m pretty sure most of my audience knows what this means but let’s spell it out.

Right now in the real world we are bound by orbital mechanics when we go into space because we don’t have rockets efficient enough to just point at our destination and burn. Instead we steal energy from the orbits of planets and pay for it in time.

you orbiting home
Orbiting your home, A, you are moving really fast along A’s orbit and also pretty fast around A to stay in orbit.

Any body in orbit is travelling at some huge velocity at right angles to the sun at any given time. It’s basically falling on a ballistic trajectory forever, continuously missing the sun. So as soon as you get out of the gravity well and into orbit around your starting point, you’re already travelling super fast with respect to the sun.

you orbiting the sun
Escaping A and now just in orbit around the sun. Relatively cheap on fuel.

If you accelerate a bit in the direction of orbit or away from the direction of orbit, you’ll escape from your planet and be orbiting the sun instead of the world. You’ll be pretty much travelling alongside the world, but you’re now revolving the sun alone instead of the world and the sun. This is a relatively cheap burn.

Now you can spend energy to slow down or speed up. If you speed up, your orbit will descend towards the sun, allowing you to intersect (if you time it well) with an inner planet and be captured by its gravity. If you slow down, your orbit will ascend outwards from the sun, allowing you to intersect with an outer planet and be captured by its gravity.

you slowing down
Speeding up to go visit B in a closer orbit. Your new orbit is elliptical.
you later
So you wait until you get around here. Notice everything else is moving too.
Canvas 5
Then you burn a little here, slowing a little, to make your orbit closer to circular.
Canvas 6
Then you coast a little, burning no fuel, until you get inside B’s capture radius.
Canvas 7
And make another little burn to start orbiting B. Now you can launch your interface vessels!

 

This is a cheap way to travel but since you are coasting most of the time the following things are true:

  • Your travel times are much longer than if you can burn directly
  • You are at the mercy of the orbits — if you orbit doesn’t intersect your target right away you might have to go around the sun a couple of times. This could get old fast. So could you (though at the usual rate).
  • Most of your time is spent in micro-gravity

This is the sense in which you buy energy for time: you don’t need a whole lot of delta-v (your capacity to change your velocity, mostly measured in how much reaction mass you have to spend) to use orbital mechanics, but you do need to spend some time in transit and you have to plan if you want to minimize that time. Of course what I’m thinking about now is how to mechanize this so that it’s at least roughly realistic but also simple and fun. It’s a bonus for me that this introduces a lot of meaningful downtime — this can then be a phase of play, introducing projects and healing opportunities as a feature of simply travelling from A to B.

Generally your pattern is this: you decide you want to go to B from A. You sit around at A and check your charts and computers and determine when the best time to leave is in order to minimize your total wait time (sitting around before launch + coasting between the planets) and also get a course that’s within your ship’s delta-v limits. Then you wait your WAIT TIME (a downtime period that takes place on planet). Then you launch and do your initial burns. Then you wait your COAST TIME (another downtime period but it takes place on your ship). Then you do your terminal burns and arrive at B.

And now that we have a pattern, we can start to dream up ways to mechanize it and keep it fun. Well I can anyway, in a vague sort of way. Watch this space and look for actual rules to start showing up at our Patreon page.

Now this also implies that using slipknots is pretty expensive and maybe requiring very specific ship designs at T3 — you just don’t get any benefit from orbital velocities when you need to stop at a stationary point in space 2500 light seconds above the star. You are going to have to pretty much cancel your orbital velocity by the time you hit the slipknot and also accelerate there and decelerate before arrival — I think you’ll be taking a kind of rising spiral to the knot (please correct me if I’m wrong) and it’s going to chew up a lot of delta-v. Tech level 3 might be really very interesting indeed as it deviates from tech level 4! Slip capable ships might be defined as having very high delta-v capabilities, sacrificing other capabilities. If you want to blockade a slipknot at T3, your optimum strategy might be to build warships at the slipknot and jump them through where they stay, not having enough delta-v to endanger the system proper but rather just able to station-keep and act as a massive weapons platform. This introduces a whole new set of stories — the old Diaspora stories were all the same when slip is introduced but now we have two distinct narratives around slipknot travel, the orbital mechanics story (T3) and the direct burn story (T4+). I think that’s pretty cool.