Up and Down the Ladder of Abstraction

Bret Victor of the Kill Math project has Up and Down the Ladder of Abstraction which uses a very simple driving simulator as an illustration. Everyone doing simulation or in transportation engineering education should read this.

How can we design systems when we don’t know what we’re doing?
The most exciting engineering challenges lie on the boundary of theory and the unknown. Not so unknown that they’re hopeless, but not enough theory to predict the results of our decisions. Systems at this boundary often rely on emergent behavior — high-level effects that arise indirectly from low-level interactions.
When designing at this boundary, the challenge lies not in constructing the system, but in understanding it. In the absence of theory, we must develop an intuition to guide our decisions. The design process is thus one of exploration and discovery.
How do we explore? If you move to a new city, you might learn the territory by walking around. Or you might peruse a map. But far more effective than either is both together — a street-level experience with higher-level guidance.
Likewise, the most powerful way to gain insight into a system is by moving between levels of abstraction. Many designers do this instinctively. But it’s easy to get stuck on the ground, experiencing concrete systems with no higher-level view. It’s also easy to get stuck in the clouds, working entirely with abstract equations or aggregate statistics.
This interactive essay presents the ladder of abstraction, a technique for thinking explicitly about these levels, so a designer can move among them consciously and confidently.
I believe that an essential skill of the modern system designer will be using the interactive medium to move fluidly around the ladder of abstraction.