Szymon Kaliski

Ladder Of Abstraction

Notes from reading Up and Down the Ladder of Abstraction ↗ by Bret Victor.

• real-time makes sense for things that need to be watched in real-time (like an animation)

  • sometimes it makes sense to not be limited by this - when editing movie for example, you don't want to keep watching the entire film in real-time, but scrub freely through it
  • to explore a system like that, you need to be able to control its time

• the same way we scrub through time we should be able to scrub through variables

  • then, we can abstract over time - draw a path of what something will look like, and change the variables to see the path change, without having to scrub through it

  • then, we can then abstract over time and a parameter - drawing all possible behaviours of the algorithm

    the purpose of abstraction is to bring out high-level patterns

    We stepped up a level of abstraction to see a high-level pattern, and then stepped down to discover the explanation for that pattern. I believe that this dance is where the deepest insights are born - not at any one level of abstraction, but in the transitions between them. This is why it is crucial that our representations provide both a step up and a step back down.

• when abstracting, it's ok to omit some details to gain better understanding of the system

• interaction is important part of abstraction - being able to interact with the visualization (and see other visualizations change) helps us build mental model of the solution space (Solving Things Visually)

  • human brains are good at matching visual patterns, but slow (and bad) at logical inferences
  • it makes sense to turn these inferences into visual representations, so we can reason about them with our visual side of brain
  • it makes sense to be able to play with them to gain even better understanding of them - static visualization is not enough, interaction with living system combined with visualization is important

• how this relates to programming:

  • "concrete" representation:

    function f() {
      const t = 100;
      const r = 2;
      const [x, y] = calculate(t, r);
      return [x, y];
    }
    

  • abstracting over time:

    function f(t) {
      const r = 2;
      const [x, y] = calculate(t, r);
      return [x, y];
    }
    

  • abstracting over time and rate:

    function f(t, r) {
      const [x, y] = calculate(t, r);
      return [x, y];
    }
    

  • "stepping down" the ladder when we found interesting r is currying:

    const f_of_2 = t => f(t, 2);
    

Backlinks

1. 2024-05-31Programming as a Specific Case of a Bigger Problem¹
2. 2022-07-19Bret Victor's Thesis¹
3. 2022-02-01Simulator¹
4. 2020-12-13Note Titles Becoming Abstractions¹