## 20120129

### Review: The Art of the Long View

I've been calling myself a futurist for the past five years, and for five years, I've been lying. But no longer, because I've read this book, which is every bit as a thought-provoking as Science Fiction for Prototyping proved disappointing. Peter Schwartz is one of the founders of the Global Business Network consulting firm, and honed his skills designing scenarios for Shell Oil in the 1980s. In The Art of the Long View, he makes a strong case for the utility of scenario planning, explains how to develop a proper futurist mindset, and how to create your own scenarios.

Scenario planning is not predicting the future. Rather, it is about challenging the official future, and the assumptions that underlie it. Scenarios force you to examine your unspoken beliefs and values, the evidence supporting them, and how you might react in the future. An organization that includes scenario planning in its process is better able to react to rapidly changing conditions, and less likely to be rendered slowly obsolete through technological change.

Scenario planning is inherently interdisciplinary. A scenario plan has to include technological, economic, cultural, and political factors, as well as individual psychology. Broad areas of knowledge rather than deep and narrow research is better suited at picking up on trends. The ideas and forces that most powerfully influence the future originate on the margins of society, among the dispossessed, the utopian, or the just plain weird. Finally, Schwartz includes a detailed, 8 stage guide to using scenarios in your own organization, with a good balance of theories and examples. Perhaps the ultimate success of scenario planning is that it creates a shared language to talk about the future.

Scenario planning might not be about predicting the future, but a futurist who makes no predictions isn't very useful. The book was published in 1991, and some parts feel oddly anachronistic, like the Japanophilia, the groping towards a 'digital global teenager', and the absence of the War on Terror. On the other hand, he offers three scenarios for the world in 2005: New Empires focused on regional militarism, Market World with multicultural entrepreneurialism, and Change Without Progress, where the wealthy hollow out states, and fear of losing what little remains prevents successful action. Change Without Progress is strikingly similar to the world today, with our 1%ers and 99%ers, paralyzed multinational bodies, and collapsing infrastructure.

Scenario planning is not a strict methodology that automatically produces valid results, it's an attitude towards the future that is based on broad understandings of historical forces and skepticism about the status quo. The results will vary on the quality of the questions you can ask, the data available, and the conversation you foster. But as far as crystal balls go, scenario planning is one of the best.

## 20120117

### Why Andrew Sullivan is Wrong About Obama

Andrew Sullivan has been blowing up the internet with an article about how Obama has outsmarted his critics on the Left and on the Right, by playing a long game that has allowed him to achieve meaningful policy advances without grandstanding or drama. Yet while Obama has achieved policy successes, he has failed to establish the government as a credible force for good. Andrew Sullivan misses the cultural forest for the policy trees. I didn’t want Obama to be FDR; I just wanted him to reverse the worst parts of the Reagan revolution. Instead, at this rate Obama is going to wind up looking more like Richard Nixon than Ronald Reagan.

In Sullivan’s words:

Obama was not elected, despite liberal fantasies, to be a left-wing crusader. He was elected as a pragmatic, unifying reformist who would be more responsible than Bush.

And what have we seen? A recurring pattern. To use the terms Obama first employed in his inaugural address: the president begins by extending a hand to his opponents; when they respond by raising a fist, he demonstrates that they are the source of the problem; then, finally, he moves to his preferred position of moderate liberalism and fights for it without being effectively tarred as an ideologue or a divider.

This is essentially correct. Obama has achieved some notable policy successes, and I for one have greatly enjoyed the frothy fury of the Republican primary, but come November, the election will be over, and somebody will have to govern. And the fact is they’ll do so with a population that trusts the government less than ever before. It’s what David Brooks calls the instrument problem; 10% of Americans trust the government to do the right thing, even as they rely on the government to secure the borders, ensure the safety of food and drugs, and provide healthcare, social security, and unemployment insurance. Suzanne Mettler identifies the problem as the submerged state. Most of the government programs that benefit the middle class are either invisible or run so smoothly that more than half the people who use them don’t think they’re using a government program. If you don’t think the government supports you, why would you support the government?

I’d like to compare two Republican presidents, not on their conservative credentials, but on their legacy. By conventional measures, Nixon is a far better president. He founded the EPA, opened relations with China, unilaterally renounced the development of biological weapons, negotiated the first arms control treaty with the USSR, ended the Vietnam War (eventually), got American off the gold standard, reduced inflation, launched the War on Cancer, and saw American land on the moon. Reagan presided over ballooning budget deficits, used government power to crush the unions, cut taxes only to raise them, ignored AIDS for several years, supervised the Iran-Contra affair, presided over a massive arms race, slashed anti-poverty programs, pushed the war on drugs, and saw the Challenger explode.

Yet for all this, Nixon’s legacy is “I am not a crook,” and Reagan’s legacy is “The nine most terrifying words in the English language are: ‘I'm from the government and I'm here to help.’” Sure, Nixon was a paranoid lowlife with the moral instincts of a hammerhead shark, but he led many initiatives which America is rightfully proud of. Reagan’s accomplishments are far thinner, but he was the Great Communicator, and he established a political dialogue that is with us today, an undead ideology that flows through the Tea Party and cripples the ability to govern.

Sullivan thinks that Obama’s opponents will be punished for their carelessness with the truth, but I’m not so sure. Paul Krugman believes that Mitt Romney is running a post-truth campaign, and he’s the most reasonable of the Republican candidates, or at least the least insane. Being elected today requires that you believe a dozen contradictory things before breakfast (to link to Krugman again). I’ve not seen any backlash towards public figures for spouting obvious falsehoods, and even the New York Times is wondering if it should challenge people who lie in its articles.

I supported Obama because I believed that he could articulate a vision for American democracy in the 21st century. I thought that the author of Dreams from my Father, the 2004 Democratic Convention Keynote, and the speech on Reverend Wright, would be somebody who could inspire America in the same way that Kennedy and Reagan did. We needed, and still need, inspiration more than any specific policy solution. I believed that roused to action, the American people would find their own solutions to major problems, like healthcare, energy, education, and the war.

Instead, Barack Obama has presided over an ugly and secretive government. It is a government that uses drones to kill terrorists on the other side of the world, while making the absurd claim that “There hasn’t been a single collateral death because of the exceptional proficiency, precision of the capabilities we’ve been able to develop,” (according to senior counter-terrorism official John O. Brennan) despite ample evidence to the contrary. It is a government that has failed to address basic concerns about hidden risks and ‘shadow banks’ in the financial system. And while the rancor and insanity of the 112th Congress is not Obama’s fault, the White House is little better. On the Keystone XL pipeline, and Plan B birth control pill, the Obama administration has given the impression that it does not make decisions based on evidence, or what he believes would be right for the country, but what is most politically expedient. It is a short-sighted tactic that reduces his own credibility.

David Brooks, at the end of his editorial on the instrument problem, says:

“If Democrats can’t restore Americans’ trust in government, it really doesn’t matter what problems they identify and what plans they propose. No one will believe in the instrument they rely on for solutions.”

I do not want people to uncritically trust Big Government, but American has passed the point of reasonable skepticism to the point of political solipsism. Congress is less popular than polygamy, the BP oil spill and Maoism. If Obama cannot restore some basic faith in government, then he will be a failure, no matter how many policy successes he manages.

## 20120116

### Equivalence of Statistics on a Pair of Gaussian Channels

This post is a departure from our usual discussions. It relates to statistics and information theory, as applied to a somewhat limited model of communication. In this model, we have two variables with normally distributed amplitudes. One variable is the "true" signal, and the other contains the "true" signal mixed in with some noise. This is a model of a noisy Guassian communication channel. The main purpose is to show that, under these conditions, correlation, squared error, mutual information, and signal-to-noise ratio all become equally good and interconvertible measurements of how related the two signals are. This topic was of interest because many people apply all of these statistics separately to the same data. These notes are not written for a general audience, I'm just putting this out here in case someone, somewhere, finds it interesting.

For a pair of Gaussian channels ( continuous random variables who's values follow a normal distribution ), the mutual information, correlation, root mean squared error, correlation, and signal to noise ratio, are all equivalent and can be computed from each-other. Without loss of generality we restrict this discussion to zero-mean unit variance channels. This discussion elaborates on the discussion of mutual information between Gaussian channels presented in the third chapter of Spikes.

Correlation & Mutual Information

Consider a single gaussian channel $y = g x + n$, where $x$ is the input, $y$ is the output, $g$ is the gain, and $n$ is addative gaussian noise. Without loss of generality, assume that $x$, $n$ and $y$ have been converted to z-scores. Reconstructed z-scores can always be mapped back to the original gaussian variable by multiplying by the original standard deviations and adding in the original means. This means that all random variables have zero mean and unit variance. If we do this, we will need a separate gain for the signal and noise, say, $a$ and $b$.
$y = a x + b n$
Since ths signal and noise are independent, their variances add:
$\sigma^2_{y} = \sigma^2_{a x} + \sigma^2_{b n}$ and the gain parameters can be factored out
$\sigma^2_{y} = a^2 \sigma^2_{x} + b^2 \sigma^2_{n}.$
Since $\sigma^2_{y}=\sigma^2_{x}=\sigma^2_{n}=1$,
$a^2+b^2=1$
This can be parameterized as
$\sigma^2_{y} = \alpha \sigma^2_{x} + (1-\alpha) \sigma^2_{n},\,\,\alpha=a^2\in[0,1]$
and
$y = x\sqrt{\alpha} + n\sqrt{1-\alpha}$

The relationships between mutual information $I$ and signal-to-noise ration $SNR$ come from Spikes, chapter 3.
$I=\frac{1}{2}lg(1+\frac{\sigma^2_{a x}}{\sigma^2_{b n}})=\frac{1}{2}lg(1+SNR)$
Where $lg(\dots)$ is the base-2 logarithm.
The $SNR$ simplifies as :
$SNR=\frac{\sigma^2_{a x}}{\sigma^2_{b n}}=\frac{\alpha \sigma^2_x}{(1-\alpha) \sigma^2_n}=\frac{\alpha}{1-\alpha}$
Mutual information simplifies as :
$I=\frac{1}{2}lg(1+SNR)=\frac{1}{2}lg{\frac{\sigma^2_y}{\sigma^2_{b n}}}=\frac{1}{2}lg{\frac{\sigma^2_y}{(1-\alpha)\sigma^2_n}}=\frac{1}{2}lg{\frac{1}{1-\alpha}}$
The correlation $\rho$ is the standard definition of Pearson's product-moment correlation coefficient, which can be viewed as the angle $\theta$ between vectors defined by the samples of random variables $x$ and $y$.
$\rho=cos(\theta)=\frac{x y}{|x||y|}$

Since $x$ and $n$ are independent, the samples of $x$ and $n$ can be viewed as an orthonormal basis for the samples of $y$, where the weights of the components are just previously defined $a$ and $b$, respectively. This relates our gain parameters to the correlation coefficient: the tangent of the angle between $y$ and $x$ is just the ratio of the noise gain to the signal gain
$tan(\theta)=\frac{b}{a}=\frac{\sqrt{1-\alpha}}{\sqrt{\alpha}}$
Then $tan(\theta)$ can be expressed in terms of the correlation coefficient $\rho$ :
$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}=\frac{\sqrt{1-cos(\theta)^2}}{cos(\theta)}=\frac{\sqrt{1-\rho^2}}{\rho}$
This gives the relationship $\sqrt{1-\alpha}/\sqrt{\alpha}=\sqrt{1-\rho^2}/\rho$, which implies that that $\alpha=\rho^2$, or $a=\rho$. (There is a slight problem here in that correlation can be negative, but it is the magnitude of the correlation that really matters. As a temporary fix, correlation now means "absolute value of the correlation".) This can be used to relate $\rho$ to $SNR$ and mutual informtaion:
$SNR=\frac{\rho^2}{1-\rho^2}$
$I=\frac{1}{2}lg{\frac{1}{1-\rho^2}}=-\frac{1}{2}lg(1-\rho^2)$
As a corollary, if $\phi=\sqrt{1-\rho^2}$ is the correlation of $y$ and the noise $n$, then information is simply $I=-lg(\phi)$. Mean squared error ($MSE$) is also related :
$MSE=(1-\rho)^2+(1-\rho^2)=1-2\rho+1=2(1-\rho)$
which implies that
$\rho=1-\frac{1}{2}MSE$
and gives a relationship between mutual information and mean squared error:
$I=-\frac{1}{2}lg(1-\rho^2)=-\frac{1}{2}lg(1-(1-MSE/2)^2)$

The relationships between correlation $\rho$, root mean squared error $RMSE$, information $I$, and signal to noise ratio $SNR$, all increase monotonically, implying that correlation, SNR, and mutual information, all give the same quality ranking for a collection of channels.

Further Speculation

This can be generalized (as in chapter 3 of Spikes) to vector-valued Gaussian variables by transforming into a space where $Y=AX+BN$ is diagonal, treating each component independently, and then transforming back into the original space.

Similarly to how chapter 3 of Spikes generalizes mutual information of a Gaussian channel into a bound on mutual information for possibly non-gaussian, vector valued, channels, these relationships can be generalized to inequalities for non-Gaussian channels :

$I\geq-lg(\Phi)=-\frac{1}{2}lg(1-\Sigma^2)=-\frac{1}{2}lg(1-(1-MSE/2)^2)$
Where, for vector valued variables, $\phi$, $\rho$, and $MSE$ become matrices $\Phi$, $\Sigma$, and $MSE$.

## 20120110

### D&D: Working the Rules

Last time, I wrote about how gameplay is enacted as a negotiation at the table, with the rules serving as one component of the common grounding for negotiation, a means of abstracting tedious or low-player knowledge negotiations, and furthermore as a wagering game that is fun in and of itself. I was planning to write a follow-up about that last part, but before I could, Wizards of the Coast announced the next Dungeons and Dragons, with generally favorable articles in The New York Times and Forbes. Most interestingly, they’re inviting participation from the community to design and playtest the new edition. While I haven’t yet decided if I want to formally be part of the process, it seems like a good time to throw in my two cents.

The last edition change, from 3.5 to 4e, was a little bit of a disaster. While I thought it was a major step forward, many players didn’t like the how all the classes in the new edition had the same core structure (at-will, encounter, daily, and utility powers) compared to simple fighters and complex spellcasters, the mandatory use of a battlemat, the length of combat, or just the aesthetics of the books and character sheets. While some of the complaints were fundamentally off-base, D&D4e is not an MMO, it is not ‘dumbed down’, and it is just as viable to roleplay in as any other edition of D&D, and other complaints were corrected by Essentials classes and new math for monsters, the damage had been done. The D&D community split into 4e players, a solid core of 3.5/Pathfinder fans, and the new Old School Rules movement, which leveraged digital distribution and a vibrant community to create cleaned up versions of the first editions of D&D.

Wizards claims that 5e will reunite the scattered fans and become the One Edition to Rule Them All. Personally, I’m doubtful. People have diverse tastes, and the only common ground is that they like what they already know. I’m also not sure how much participation the community will have, or even if the community actually knows what it wants (A common joke in the RPG industry is that to make a successful game, you should look at what RPG.net says and then do the exact opposite). All I know is that right now the geekier corners of the internet are exploding with speculation, demands, and manifestos. So without further delay, this is what I think about rules, and how to write good ones for D&D.

Pretty much every RPG relies on some random element, usually dice, for a core task resolution mechanic. The exact details of this resolution mechanic aren’t particularly important, you can use XdY+modifier vs a target number, percentile roll under, dice pools, or pretty much anything that can be imagined, but at the end of the day the player will declare some action, with probability P between 0 and 1 of success.

Finding the right P is an important part of game design. Too low, and plays will miss frequently, leading to a high whiff factor. Too high, and players will be rolling simply to see if they fail, which is irritating. Casinos are the experts in balancing probabilities and payoffs, ensuring enough winning to keep players hooked, while the law of averages drains their pockets. Personally, I find a chance of success at p=0.6 for an average task is most satisfying (coincidentally, this is what D&D 4e uses). Easy tasks can go up to about p=0.85, and hard task should be p=0.4, with extremely difficult or desperate tasks at p=0.2.

But rolling and trying to get above an 8 isn’t a game that’s likely to hold a person’s attention for long. So what else is there? I’m going to refer to Greg Costikyan classic essay, “I have no words and I must design”, which you really should read in full.

The thing that makes a game a game is the need to make decisions. Consider Chess: it has few of the aspects that make games appealing -- no simulation elements, no roleplaying, and damn little color. What it's got is the need to make decisions. The rules are tightly constrained, the objectives clear, and victory requires you to think several moves ahead. Excellence in decision making is what brings success.

Negotiation is fun, but decision making is also fun. The rules tell us what kind of decisions can be made, what the option space is, and what outcomes are. And to describe what makes rules fun, or good, I’m going to have to pull in a couple of other theories.

The first one is the Paradox of Choice, which I’ll use to talk about building a character. Having too few options makes us unhappy for obvious reasons-we are constrained from doing what we want to do. Having too many options also makes us unhappy, as the energy involved in coming to a decision outweighs the benefits gain by making the best decision. We become obsessed with alternatives and missed opportunities. In a competitive environment, like a game, the feeling like you’re not making good choices is equivalent to feeling like you’re lost, like you’re losing. It’s not fun.

With that in mind, D&D4e (and 3.5 before it) simply has too many options. At first level, the player has 44 classes, 50 races, hundreds of backgrounds, themes, feats, and powers. In play, every turn a player has a choice of the two At-Will powers, one encounter, one daily, and perhaps a power or two gained from class or background. This is about the limit of most people’s working memories (conventional wisdom is that most people can remember about seven things, so that’s your powers, your HP, and the general state of the game).

At 30th level, this elegant structure has totally imploded. A character has 20 feats, selected out of a list of over 2300, 12 core attack powers select from a list of hundreds, and perhaps a couple dozen more miscellaneous class abilities and magic items chosen from a list of thousands. If you’ve grown organically into that 30th level character, you might understand its full capabilities, but most players are overwhelmed.

And worst of all, there’s not much too clearly evaluate many of these choices. Powers can play very differently, but there are lots of powers of the form “deal 2[weapon]+stat damage and push 1 square”, or the like. Now, I like the power system introduced in 4e, I think it goes a long way towards distinguishing different characters of the same class, and one class from another, but the power system needs to be toned down so that even a high level character doesn’t have more than 12 total. As for feats and magic items, they need to be seriously curtailed. Group similar feats into Themes, or Packages, or Kits, and give each character a choice of one. Magic items that simply fix the game’s math should be combined with the character’s intrinsic skill. Instead, magic items should be singular, rare, and synergize with the characters. A warrior will have a weapon of legend, a mage might have a staff that defends the user on its own, a rogue might have a Ring of Invisibility. Either way, I’d like it if even top level characters have no more than three magic items, and each one was a significant part of the character.

The second theory is the OODA loop, developed by fighter pilot John Boyd. OODA (observe, orient, decide, act) is the process by which people make decisions in a strategic or tactical game. You observe the enemy and try and figure out what their capabilities are, using your past experience you orient yourself, make a decision, and execute. In warfare, the trick is to get inside the enemy’s OODA loop, to move with the chaos of combat and direct it at your enemy until they make a mistake that can be capitalized on.

What a player observes is what the DM shows and tells them: A description of the monsters, where they are on the battlefield, how they move and act. But in D&D 4e, and other grid based systems, this description has two parts, the verbal side of what the GM says, and the visual side of what the map looks like. And if the rules and GM are not well coordinate, the descriptions will begin to diverge. Players will be constantly switching from a verbal-negotiation cognitive frame to a visual-puzzle solving cognitive frame.

There are good reasons to represent combat on a grid with some kind of figurines. People are usually fairly skilled in visual puzzle solving. It allows decisions to be very finely grained-precisely how far to move, where to drop that fireball, which rewards players that are using tactical maneuvers to their advantage. Without a map, players have to hold the entire encounter in their heads, and with about 10 combatants on the board (the player, 4 allies, 5 enemies) that can get tricky, especially when people begin to disagree about who was where.

But the downside of using a map is that it focuses attention on this visual puzzle, diminishing attention on the verbal aspect of the game, or to use the phrase of gamers, “immersive roleplaying”. I used to think that this was a silly complaint, but thinking about players having to switch between cognitive systems, it makes sense. Most of us are lousy multitaskers. WotC design Mike Mearls has indicated the next edition will be grid-optional. “The new edition is being conceived of as a modular, flexible system, easily customized to individual preferences. Just like a player makes his character, the Dungeon Master can make his ruleset. He might say ‘I’m going to run a military campaign, it’s going to be a lot of fighting’… so he’d use the combat chapter, drop in miniatures rules, and include the martial arts optional rules.” It’ll be interesting to see how this modularity works out in practice.

Finally, there’s one other issue I want to bring up: pacing and flow. Flow, in games studies, is the sensation of full immersion in the activity, and of playful challenge. One of the major complaints against D&D 4e is that the fights take too long, a critique which I agree with. The length of a fight depends on the total number of rounds, and the time it takes each player to take their action. In my experience, a fight in 4e lasts about 5 rounds. On the one hand, this seems like a good number—it prevents fights from being decided in the opening action, and gives the players time to recover from bad luck.

The problem is that it’s slow. I haven’t taken a stopwatch to my group, but it seems to take about two minutes for a person to take their turn. Multiply by six people (five players + GM) and five rounds, and you have an hour long fight. I think turns could be speeded up by reducing the complexity of the decisions that people have to make, even in 4e there’s too much referring to the character sheet for rarely used powers, and reducing the number of dice rolls. It takes about 10 seconds to find, roll, and do the math on a single die. Powers with multiple attacks and multiple damage dice, which are pretty common, can easily take two minutes just to crank through. Thinking and remembering also add time, every situational modifier bestowed by a power or position adds another few seconds to the turn, and few minutes to the fight. Interrupt actions are even worse. I like big set-piece battles, and the interactivity of 4e turns, but they’re not suited for every situation. It’ll be interesting to see what the designers come up with to speed up play. This is really my biggest open question.

I’ll close with a quote from John Boyd, “The second O, orientation –the repository of our genetic heritage, cultural tradition, and previous experiences –is the most important part of the O-O-D-A loop since it shapes the way we observe, the way we decide, the way we act.” D&D has nearly 40 years of history. Pretending to be elves and casting magic missile on the darkness and unearthing horrors and then running away are part of our gaming DNA. The biggest reason why 4e failed was not that it was poorly marketed, but that it required a different orientation from gamers, one that they didn’t want to learn. Hopefully, people wiser than me are figuring out what the D&D player’s orientation is, and designing rules that work with it, instead of fighting against it. If they can do that, everything else from the modular rules, to tactical depth, to combat speed, will fall into place.