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);

the author sees and manipulates indirect symbolic representations, and must imagine how they give rise to dynamic behavior

  • this could be improved by (Future Of Coding):
    • seeing the dynamic behaviour that is being created (Simulator)
    • exploring multiple representations of that behaviour (Ladder of Abstraction)
    • directly manipulating representations and data
  • the titles are one step up on the ladder of abstraction
    • this should compound - allowing one to climb up using progressively abstracted concepts
Szymon Kaliski © 2021
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