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;

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) = x² + 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:

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.

splitting an infinitive

Why not?

Well these days (as opposed to a hundred (good to one sig fig) year period of conservatism around which the language is fluid as hell) that’s maybe not a useful question. We do what we please with English and the language is sort of famous for surviving it. For a long time, however, and currently amongst the sort of pedant that has a strong opinion about Oxford commas, the split infinitive was Not Allowed.

But English is really good for splitting infinitives.

The infinitive form of a verb is its naked form, unconjugated. So in English the infinitive “to go” is conjugated as “she goes, we go, they go, you go”. That infinitive is apparently never allowed to have a word inserted between “to” and “go”. It’s to be treated as though it’s un-fucking-divisible. A single word with a space inside it that apparently acts like a letter.

This is, I think, mostly an effort at linguistic political correctness to avoid drawing attention to the fact that many (maybe most) lesser languages do not have this feature. Their infinitives (aller, for example, en Français) are really one word. Which means they do not have the tonal equivalent of “to boldly go” which delivers a mood distinct (to my ear anyway) from “boldly to go” or, worse, “to go boldly”. It’s perhaps the proscription itself that lends this tone (which totally undermines my argument by making the proscription necessary in order to have the feature) by undermining the formality of the “correct” structures. Kirk in the Star Trek opener is established by his linguistic choice as an everyman who doesn’t give a rat’s ass about ancient style guides nor, by extension, Robert’s Rules of Order. We know in our viscera before we even see him that he’s a hero we get to aspire to be. He shirked his way through college and the academy (which later we find out is true). He must have.

And some infinitive busting structures don’t even have correct variants. Consider “I’m going to fucking shoot you in the face.” It’s distinct from “I’m going to shoot you in the fucking face” in that the rude word modifies face instead of shoot. And obvious you can’t say “I’m going fucking to shoot you in the face.” Then you just get laughed at. You’ve descended below the low bar of lovable rogue to incomprehensible villain. “I’m fucking going to shoot you in the face” is weird acceptable, modifies the wrong word, and seems like a grammatically worse choice than splitting the infinitive even though it’s fine. It’s more of a hipster bandit move; an attempt to get you to argue with their usage so they can produce evidence it’s correct. Before shooting you in the face.

So let me suggest that we need not be polite to our compatriot languages who are stuck with indivisible verbs. Our verbs are naturally divisible and this division begs for modifiers. Every space is a possibility for a slightly different tone. It does not invite confusion but rather establishes the writer’s intent clearly and efficiently. The space in the middle of our infinitives is a tool to be wielded however we like to use tools.

Of course, once we get to this point we have to wonder what the “to” is for anyway. What does “to go” mean, decomposed? What work does the “to” do? In the phrase “I’m going to go” it seems to have more to do with “going” than “go” to my ear. That is, as the sentence proceeds, “I’m going to…” is still sensible — I’m certainly going somewhere and to is a somewhere word. I’m going to the store. I’m going to outer space. I’m going to sleep. The “to” is independent — it doesn’t need a verb at all to be useful.

So rather than knuckle under to linguistic equivalentists who would hobble English in order to put it on equal footing withe French or, heaven forbid, Latin, let’s instead celebrate the feature of the English infinitive. Split it at will. It’s already split.

Diaspora testing still happens every week

In the current testing form for Anabasis, the rules for a check are something like: ref declares a risk, then player rolls |d6-d6| and add your skill. If you have a relevant specialization, add another 1. Index on the table:

• 0 — fails and always generates a new risk from the 6
• 1-2 — fail, risk realized
• 3-5 — success, risk realized
• 6+ — success, no risk

Now, this means that very often risks are realized. So there’s another rule: if you take a stress point, you can increase your roll by one. Take more if you like. Now as your stress goes up you start getting character quirks that could be troublesome, so there’s no “win” here — either the risk is realized (you’re still successful at what you tried unless you roll 2 or lower) or you start to get burdened with Compulsion and Bad Judgement and so on. The ref starts needling you with “the inactivity is agitating you” and “even though there’s a battle going on you are highly distracted by the electrical system under the dash, which doesn’t look properly grounded”.

Both of these have the same purpose: they generate new and unexpected trouble. The big difference is that the risk is in the hands of the ref and the stress effects are in the hands of the player.

He looks a little stressed out, no?

An example: Abadyos is trying to fly an unfamiliar shuttle through the atmosphere of a has giant. He faces a roll with the risk REVELATION — something heretofore unknown will be brought to light and it won’t be something good for the characters. Abadyos makes his roll with a total of 4. So he could spend 2 stress to get past the risk or he could just suffer the risk realization. In either case he has a success: he’s going to successfully fly this flight path through the gas giant’s strange atmosphere.

So this is a pivot: either way the story is likely to take a new direction. We’re not just flying to Haifeng the dirigible city any more.

Abadyos’ player chose the stress. He was under severe stress once before and compulsively disassembled and knolled part of the medbay, which was a problem for weeks. This stress has no immediate effect, but later, agitated waiting for a stealthy resolution of another problem, he decides to make a Bad Decision (a stress effect) and burst through doors he knows are guarded.

Acting on his stress is something that was up to the player. I cued it, prodding with declarations about the character’s internal state, but the player declared the action. In the past I would have been skeptical about such a purely social mechanism and wanted to mechanize it with points and a meter to manage or something like that. Maybe I just have great players, but this mechanization appears to be unnecessary. Some players are happy to take the cue and make their lives harder. They recognize that they bought the trouble by spending stress points. They know they should make good on the purchase.

If he’d chosen the REVELATION, a bad choice of rocket operation parameters would have ignited part of the gas giant’s atmosphere, pointing a giant arrow at the characters who are trying to hide. Now this is my space as ref: I am being asked to ad lib a major change in plot direction. It’s similar to the stress situation in that in both cases someone has a new creative burden with loose but clear direction: you character is agitated and impulsive and prone to making bad decisions right now or, in the case of the risk, the ref is mandated to create a new fact that changes the direction of the game.

I used to feel I had to mechanize things like this further, but someone pointed out to me that the fiction has its own weight. That there are things that need no further rules because they have a fictional presence that can only be responded to in a limited fashion within the context of the rest of the fiction. If you have a rope, you can do rope things. You don’t need a rule for every possible use of rope. We know what rope is for, and the current context of the fiction establishes the limits of what rope can do. You can write rules for it if you want, but you can get away with startlingly few when we’re talking about something everyone understands deeply. Rope. Agitation. Impatience.

I recognize that this is not necessarily a popular direction. But I think you will like it — maybe love it — because where Diaspora Anabasis puts its effort in mechanically is the setting creation and the character creation. We mechanize the establishing context and then inject deviations and obstacles. I think this is consistent with the original vision of Diaspora and it’s certainly consistent with how I plan and run a game.

You may notice this is similar to the Soft Horizon system and it is. It’s tuned for a different purpose and the dice are different, but the core method is the same. So far this is because it really really works for me. That could be the kiss of death commercially.

Blast from the past: Safety and the Inversion of Folk Logic

Another yoink from Blue Collar Space circa 2011.

Hurray, Brad is going to talk about his field of expertise instead of game design! Well, this is supposed to be a blog about technical things that interest me and games are just a branch of that (yes, games are technical — a technology — and I can blather about that another time if you like) so I’m not averse to going fairly far afield. And who knows, it might be the case that if I ramble long enough I somehow come back around to games anyway.

I was walking from the train station to work this morning and encountered four interesting cases of really crappy risk analysis — three real and one hypothetical. One was accompanied by an epithet that told me exactly why humans are so bad at risk analysis and, at the same time, why safety design is such a counter-intuitive process. It has to do with the fact that humans think in terms of acceptable risk. In a way, safety design looks from the other side of the glass.

Consider standing at the train platform. There’s a 50cm-wide yellow stripe right at the lip of the platform before it falls vertically to the guideway proper, which is where the train is going to be. I have seen children (and older) stand in the yellow zone and, as the train zooms in, tell their parents it’s perfectly safe, presumably using their survival as evidence. This is logic we expect of children, of course, which is to say, flawed. Deeply flawed.

An evidential argument for safety (I didn’t die that time, or even, no one has died yet) is inadequate. I mean, it’s adequate for you but it’s not adequate for design. You see, that yellow bar does not (again, by design) say, “If you stand here you risk injury or death.” I know, you think it does, and the sign says that, but that’s not how it’s designed and so you are misled into thinking it’s too conservative somehow. You’ve stood in the yellow a hundred or a thousand times and never once been killed.

Rather what it says is, “If you stand on your side of the yellow zone and not in it or, obviously, in the guideway on the other side, then you are as safe as we can make you, which is pretty bloody safe.” That is, technologically, we don’t really know the risk of standing in the yellow zone because it depends a lot on freak configurations of the train, your own stability, and in most cases of actual fatality, whether or not you are wearing a backpack(1) So we don’t try to calculate that. Instead we find a  space where, barring some bizarre circumstance, you are certainly safe. Then we mislabel it so you can deride it in front of your parents or friends.

Here are some other examples drawn from my morning walk. You will notice a recurring theme that is both hilarious and insane and perfectly common. I’ll try to remember to point it out at the end.

The traffic signal that indicates it is okay to walk sometimes displays an orange hand instead of a white or green walking guy. This hand does not mean, “you will be killed if you cross now”, or even “you can reasonably expect cars to be passing through your path now”. It means, “You no longer have been granted safe passage.” That is, it’s the default case and not a special case. The special case is the green guy, which reads, “Okay, it’s your turn now, and crossing at this time and place is as safe as we can make it.” Any time the green guy is not present, it’s a bad idea to cross. I watched a woman in a dreadful hurry cross on the orange hand this morning (and ours has a countdown on it which, even if you read safety warning backwards, can reasonably be read as how many seconds until you are totally dead) with the counter to fatality at 4 seconds. She was dressed darkly and small. She fell (also running heels, but also not running very well) in the middle of the road with two seconds to spare, basically disappearing from sight for many drivers. She was not killed. It was still stupid on several levels.

A crowded sidewalk is a crappy place to ride you bike at high speed. You aren’t especially in danger, but the sort of sociopathy that lets bike riders think this is okay is completely beyond me. You are violating a core premise of the safety design (there won’t be any high speed vehicles on this space ever) and making what should be a certainly safe space no better than the road. Yes, you did not injure or kill anyone. Well done. Fuck you.

I’ve never seen anyone blow through a train crossing with the bar down, but I think people don’t do it mostly out of an aversion to destroying things like the bar or scratching their vehicle. Or maybe they just avoid violating custom or even law. But I did hear a driver loudly proclaim that there was tons of time between the bar coming down and the train going by. He could totally have made it! The bar does not say, “It is certainly unsafe to proceed”. Rather when the bar is up, the message is, “Don’t worry, it’s safe now.” The bar down says, “We can’t guarantee anything.”  There’s a reason why level crossings in Texas often have webcams that the public can view and it’s not a pleasant one. Texas is one of the best places to get killed by a train you think you’re probably safe from. Yay freedom!

People are not stupid. They are badly equipped to manage risk, though, and certainly others have spoken more authoritatively than I can about that. What you can do is recognize that you are bad at managing risk and work within that envelope. Then the risk you manage is, judging by the hurry out there, being late for an appointment. Here’s how I manage that risk: I set the alarm 15 minutes early, and then I don’t run for anything but sport.

–BMurray
(1)Backpacks are an awesome way to piss people off and also get yourself killed. I’m pleased to see a decline in their popularity after so many years of seeing them everywhere. Here’s the problem: a stuffed backpack is an extra 20-50cm of space protruding from your body that is completely outside the limits of your proprioception. You have no instinctive knowledge of where that thing is. That’s why you’re always banging it into people (and you are, even if you don’t think you are, and you don’t think you are for the same reason) and occasionally hanging it over the yellow zone and into the guideway. 

Blast from the past: The Hovercraft Parable

This has been recovered from the Blue Collar Space archives, circa Christmas 2010.

Recently a new chapter has been added to the story about the role-playing game publishing industry dying. The “death” is mostly a way to interpret the steady failing of big reliable game lines and the steady success of small endeavours with small goals by peers using technology from front to back. I think a modern parable is in order.

One day I was heading home from work, got off the train, and went to the bus stop for the last leg of my journey. Standing at the stop and looking north, I see a huge construction project in progress. This looks like it is going to be some kind of very sturdy multi-storey concrete building, like a parking tower or an industrial warehouse. They are working on finishing the second floor.

What they are doing, specifically, is laying down concrete and smoothing it flat. I don’t get that this is what’s happening right away, because what I see is three guys laughing their heads off. They are laughing because they are each sitting on a chair that looks like it is mounted on a pair of downward-pointing fans, and skidding around all over the structure at high speed.

They are surfacing the concrete by riding around on one-person hovercraft.

My first thought is that I would pay to do this. In fact, I am pretty sure that if they sold tickets for twenty bucks to give you half an hour on the hovercraft-chair, there would be a line-up around the block. The surface would get done and someone would make a packet and a half doing it. There’s even a built-in audience — about half the people waiting for the bus are watching the well-paid union labourers ride and thinking pretty much the same thing as I am. “Goddamn, what I really want to be doing right now is giving one of those guys twenty bucks and then barrel around on a hovercraft.”

There are probably many obstacles (insurance, quality of work, marketing, licensing, simple convention) but only one is really insurmountable. The union would never go for it.