Organizing and connecting knowledge

Last Thursday I went to a talk by Stone Librande, lead designer for the new SimCity. He worked on the game for the past 3.5 years. His team revamped the whole system; in his own words,

Previous versions of SimCity used statistics to determine the state of the city; in essence the entire simulation was like a spreadsheet that could be analyzed by simply looking at the stored data. In contrast, the upcoming SimCity game relies on thousands of agents carrying information from one building to the next as they travel along player-created road networks. This makes it next to impossible to understand the simulation by looking at a static data set. In fact, the only way to truly understand the simulation is to keep the agents in motion.

In other words, information is not stored statically, but in the agents (people, water, sewage, crime alert) that travel between different parts of the city. This post summarizes key ideas in the talk.

How did Librande build something as complex as SimCity knowing nothing about the game when he started? His team spent the first month making the master plan for entire game: diagrams/flowcharts for how the residential, commercial, and industrial zones worked. For instance, here is a quick summary of the diagram for the residential zones: start with potential lower-class, middle-class, and upper-class residents. They filter through the availability of transportation to get into the city (roads for lower-class, ships and airplane for upper-class) and availability of cheap/luxury housing, and like in a pachinko machine, find one of 9 possible housing types to settle down ({low, medium, high density}x{low, middle, upper class} housing); if they can’t find housing they don’t come in the city. Parks and shops give people happiness, and lots of things give people unhappiness (cf. Anna Karenina). When Sims are unhappy, they put their house on sale; if no one replaces them the house becomes abandoned, increases crime, and decreases neighborhood desirability. If they can’t find a job, they become homeless.

There are also diagrams for commerce, industry, production, and a day in the life of a Sim. If you can’t draw the diagram in a nice way, then it is probably too complicated, Librande said. They simplified the day of a Sim diagram until every day a Sim woke up as either a worker or a shopper (or sick).

The people in charge thought we were getting nothing done the first month, he added—they were drawing diagrams instead of making “visible” progress in programming.

After that month, every staff member received a huge poster—replete with iconal artwork—of the diagram to hang on the wall, and Librande still refers to it. This way, he said, no one would trip over abstractions in their head. The month of organization made the (iterative) process of game development a lot more efficient.

If you take away just one thing from the talk, he said, let it be this: to be a game designer you have to establish clear communication with the team from the start.

But this is an important skill not just for game designers, but anyone who wants to transmit information—especially people working in education and research. Below the fold I’ll discuss why it is so important to organize and connect up knowledge like Librande’s team did in planning SimCity, why traditional classes and books fail to follow this paradigm, and what we can do about it.

Organizing and crystallizing knowledge saves time down the road—both for you and others.

In the book How Students Learn, the authors propose three basic principles of learning. Here is one of them.

2. To develop competence in an area of inquiry, students must (a) have a deep foundation of factual knowledge, (b) understand facts and ideas in the context of a conceptual framework, and (c) organize knowledge in ways that facilitate retrieval and application.

I.e.,

2. Facts must be organized in a conceptual framework.

Here I’ll just convince you of one step in organizing knowledge: making a diagram. Although this is not the only way, this is an obvious and easy way, and (oddly enough) an underused way.

How many classes/textbooks actually make explicit a conceptual framework: this is how all the different concepts you learn in this course connect? Most courses, after giving you a syllabus (which is a list of topics), marches down the list of topics in a linear fashion. The task of connecting these different pieces of knowledge, and relating them to other subjects, is entirely left up to the student. It’s often assumed that the student will automatically do so after being fed all the knowledge.

Compare this with how a statistics teacher at Harvard starts each class with a huge diagram: this is the road map for the entire course, and this is where you are now. (See the 6th slide here, http://isites.harvard.edu/fs/docs/icb.topic1210565.files/Unit%201a%20-%20Class%2001.pdf) My education professor, Justin Reich, says “Whenever I see something like this, it fills me with awe.”

By creating a road map for students, a teacher allows students to know where to place each new piece of knowledge they learn into their minds, and speeds up the process of learning.

Often the amount of technical content that has to be covered prevents the teacher or student from “roadmapping.” We often think a course is complete when all of the content is there (and this maybe takes 80% of the work), when the 20% of the teacher’s effort that makes the most effect is organizing that content (which should really be done at the beginning, rather than the end). (Focus on content is one of the “two big sins” of curriculum constructions according to Wiggins and McTighe.)

On the flip side,

If you’re learning by yourself, organizing the knowledge you learn into such a roadmap helps you retain the material and know what each piece of knowledge is for.

For instance, here is a roadmap I made of the prime number theorem a while ago (the blanks are meant to be filled in). But really, I think this should be fitted into a larger roadmap for analytic number theory which I hope to make, dividing it into the essential questions that we ask (for instance, distribution of primes, subdivided into what kind of distribution), and what techniques or objects can be used for each type of estimate (L-functions? Sieve methods?). Here is a great diagram showing the connections between L-functions, algebraic varieties, and automorphic forms (the thrust of much research in current number theory).

Another reason preventing roadmapping is the following: When you are organizing knowledge, it seems on the outside that you are not making any progress! You’re not “learning new things.” This is exactly analogous to Librande making a diagram at the start of making SimCity, and the boss thinking, they’re not making any progress on the game! But if Librande’s team hadn’t so carefully planned out the entire system, they would waste time later tripping over a basic game framework they never made clear. When you don’t stop to organize knowledge, you forget it.

I think it is a serious misconception that the main ingredient of becoming smarter is gaining more knowledge. The main ingredient of becoming smarter is making connections between knowledge you already have.

This idea has been substantiated by child psychologists, and given a name.

Papert’s Principle: Some of the most crucial steps in mental growth are based not simply on acquiring new skills, but on acquiring new administrative ways to use what one already knows.

In other words, knowledge is stored in isolated facts, but in the connections between them, just like in the new SimCity the state of the system is not stored in the buildings like numbers in a spreadsheet, but rather in the agents that move between them. A piece of math becomes “easy” for me once I see the facts connected in multiple ways. If I forget one connection, another one is still there to help me remember. Everything can be derived from simpler things.

As an example of Papert’s Principle, Piaget made the following experiment: pour water from a cup into a taller and thinner beaker and ask, was there more water before or after? The 7-year olds said the same; the 5-year-olds said more. Both 5-year olds and 7-year olds understood that taller means more, wider means more, and “conservation of water” when explained. It wasn’t exactly knowledge 7-year-olds lacked, but the right organization of knowledge about space: they had “tall/short” as a priority before “fat/thin,” before conservation. Minsky (Society of Mind, 10.1-4) gives one hypothesis: 7-year olds group height/width into a concept called appearance with a “noncompromise” principle.

Minsky says that children often appear to grow in stages, and suddenly become more intelligent (SoM, 17.5). I believe that we are often entrenched into thinking that learning is a linear function of time:

But in actuality learning looks more like this (smarts refer to how much you think someone knows looking from the outside)

Why the sudden jumps? Those are the places where things “click”: we make connections. But often curriculum isn’t organized this way, so students feel their pace doesn’t align with the pace of a class: the two curves doesn’t fit. In the flat parts, we might just be trying to organize information.

Take-away points:

1. Knowledge is stored more in connections than in facts.
2. Organize what you learn or teach in a “roadmap,” that addresses the goals of learning the subject or answers the big questions  about that subject. Each piece of knowledge should be placed somewhere. Slowing down to organize saves you time in the long run.
3. Organizing is an iterative process. If you can’t draw the diagram in a nice way, then it is probably too complicated. Consider having these maps on different levels (subject/topic).