Up and Down the Ladder of Abstraction

A Systematic Approach to Interactive Visualization

An arbitrary road could look like almost anything. In order to tame this data space, we choose some aspect of the road which we suspect issignificant — an aspect that reflects some challenge that our algorithm will face. Our algorithm is currently built around a fixed turning rate which determines how sharply the car turns. We might therefore suspect that the sharpness of the bend in the road will play an important role.

 .. Real-world systems may be more complex, but they all share the same general anatomy: an independent variable (such as time), a structure (such as an algorithm), and a dataset (such as an environment).
  • The independent variable is usually time. This is our way of thinking about causality — a system’s state depends on its previous states in time. Even for systems that are normally expressed with multiple independent variables, such as heat diffusion or wave propagation, we typically think of the system as evolving over time.
 .. Unfortunately, development environments generally don’t support this process. Most are actively hostile to it. We live in primitive times.
 .. Perhaps IDE makers will focus on dynamic exploration instead of static analysis, rich visualization instead of line debugging. Perhaps language theorists will stop messing around with arrows and dependent types, and start inventing languages suitable for interactive development and discovery.