April 18, 2026
When orders cause disorder
Category Theory Illustrated – Orders
From rainbows to rage: readers call out bad math, bad code, and “arrows‑only” takes
TLDR: An explainer on how things are ordered in math sparked pushback after misstating antisymmetry and showing a broken JavaScript sort example. Commenters split between “it’s just set theory,” “it’s all arrows,” and “why should anyone care,” underscoring how tricky it is to teach abstract ideas accurately and clearly.
A friendly explainer on mathematical “orders” tried to sort the world—from rainbow colors to number lists—into neat lines. But when the author linked it to category theory and dropped a JavaScript sort example, the comments went DEFCON spicy. One camp cheered the big‑picture vibe, with one user declaring it’s all just arrows—as in, the relationships matter more than the things. Another camp slammed the details: readers pounced on a muddled explanation of antisymmetry (the bit about “no ties allowed” drew a firm, all‑caps NO), and then came the fatal twist—the code. A comparator that returns true/false instead of negative/zero/positive? Devs smelled blood.
Skeptics piled on with a “what’s the category theory part, exactly?” vibe, saying the first 90% was just set theory in a wig. Others went existential: if this stuff feels like pouring water over perfectly smooth glass, why should non‑mathematicians care? Meanwhile, the thread traded dad‑joke energy about oranges, yellows, and the world’s most awkward family soccer match (the article’s grandma analogy did not help).
Bottom line: the piece aimed to make orders simple, but the community made it dramatic—fact‑checks, code‑checks, and big‑brain philosophy colliding in one very colorful (and very ordered) pile‑up. Read the explainer here.
Key Points
- •An order is a set with a binary relation that follows specific laws.
- •Linear order is introduced as a deterministic ordering where every pair is comparable.
- •Orders can be represented as subsets of the Cartesian product of the underlying set with itself.
- •In programming, comparator functions can define ordering relations, but not all such functions yield valid orders.
- •A linear order is stated to obey reflexivity, transitivity, antisymmetry, and totality; reflexivity and transitivity are explained, while antisymmetry is introduced and totality is named.