• 0 Posts
  • 3 Comments
Joined 1 year ago
cake
Cake day: July 8th, 2023

help-circle
  • It’s because people’s wants have shifted as technology progresses. If everyone was satisfied to live like a medieval peasant and all we needed to produce was clean food/water we probably could have automated most of the agricultural work and done away with the need for the majority of labor.

    But people today now want on-demand deliveries, entertainment, healthcare, telecommunications, international travel, etc. These shifting desires continuously push the boundaries of what we are capable of producing which ends up redirecting labor rather than eliminating it.


  • People who are arguing that one way of expressing these concepts is easier to learn/understand than the other are missing the whole point. Mathematical notation was not designed to teach students how to do math or explain how to design algorithms. It was invented to communicate precise, abstract ideas concisely between mathematicians who already understand what the symbols mean.

    Mathematicians require a notation that has the flexibility to manipulate mathematical objects/symbols in a way that naturally emphasizes their properties and relationships. Often they don’t even care whether the objects they’re studying are even computable or have a numerical representation. They just need them to have certain properties so that they can be manipulated appropriately.

    Discrete sums are a rare example of when the mathematical notation overlaps with the description of an algorithm for computing its value (and the overlap is not even complete; infinite sums are easily represented in math notation but are practically uncomputable when implemented naively). Every other advanced mathematical concept puts a premium on ease of symbol manipulation over computability: integrals, derivatives, matrix multiplication, abstract algebra, etc.

    TL;DR math notation is complex because its intended audience is people who already understand it, want maximum flexibility of symbol manipulation, and historically didn’t really care about practical computation.