Big O Notation
How cost grows as a system gets larger — O(n²) means quadratic growth
Big O notation describes how some cost — time, effort, coordination, money — grows when a problem gets larger, without requiring exact arithmetic. It is a shorthand computer scientists use; the idea is accessible without calculus.
Write n for “how many things you have” — teams, services, people who must align. O(n) means cost grows in proportion to n: double the teams, roughly double the coordination work. O(n²) means cost grows like n × n — because every item may need to pair with every other item.
For teams that must coordinate pairwise: at 10 teams there are 45 pairs; at 20 teams there are 190. The number of coordination channels rises much faster than the number of teams. That is O(n²) — quadratic growth.
When coordination overhead is O(n²), adding teams quickly crowds out the work coordination was meant to enable — a signature pathology of the locking organisation. Clear domain ownership reduces coordination pairs by localising decisions; the reservation pattern scales cross-cutting checks without restoring global serialisation.
Other common forms: O(1) — cost stays flat as n grows; O(log n) — cost rises slowly (halving search space each step). Big O ignores constant factors and lower-order terms: it answers “what happens if we 10× the size?” not “what is the exact bill this quarter?”