The value judgment normal has an extremely normal history. It originates with PIE ǵneh₃-, meaning “to know”, incidentally also the ancestor of the English word know. 3000 years ago, one of its descendants was Ancient Greek γνώμων (gnṓmōn), meaning “examiner” or “carpenter’s square”, the tool you use to measure right angles. It also referred to the thing that sticks up at a right angle in the middle of a sundial due to its similar shape, from where we borrowed English gnomon.

The word was borrowed into Classical Latin maybe 2200 years ago as norma, meaning only “carpenter’s square”. Over the next thousand years, the meaning became generalized to “rule” or “pattern”, from where we borrowed English norm. A derived word, Classical Latin normālis, meant “made according to a carpenter’s square”. This is the sense we borrowed normal from around 1704, then meaning “at right angles” or “perpendicular to”. Normal still refers to right angles in some modern technical usages like normal vector (often shortened to normals, in the graphics sense).

By the 1840s, influenced by norm, normal started typically meaning “according to a rule or pattern” instead. With the help of new fields of ergonomics and standards, by 1890 the word’s meaning had generalized to referring to usual or common values, based on observed patterns. Within a few decades, its usage had changed to almost always mean “typical state or condition”.

Abnormal is attested as early as 1817. The normal distribution was named by Carl Gauss in 1823 based on the “perpendicular” meaning, which is why we interchangeably say Gaussian distribution (or Gaussian blur). In 1835, we calqued normal school from French école normale, meaning “teacher’s college” by way of teaching the teachers to enforce the norms. Most US schools founded as normal schools are now public colleges, including the Normal University founded in 1857 in Illinois, now Illinois State University but located in the eponymous city of Normal, Illinois. Paranormal shows up in 1905. Normie is from 1950. Normcore first appears around 2008. Having a normal one starts becoming popular around 2022.