We might not be done with this *gno- just yet.
Norm
Many centuries ago in ancient Rome, a norma was a carpenter’s square, a tool used to measure out angles, especially right ones. Something normalis, then, was “made according to a carpenter’s square” (Klein). Even in antiquity, though, this norma was metaphorical, naming a “standard,” “pattern,” or “rule,” and hence we have the English norm and normal. The Oxford Dictionary of English Etymology cites normal as “rectangular” and “perpendicular” as of the 17th century, with “conforming to the standard” in the 19th.

Abnormal is “out of the norm,” with ab– meaning “away from.” The history of this form, though, is itself a bit abnormal, for it is ultimately a blend. An earlier form was abnormous, and it competed with anormal. Latin had abnormis, literally “away from the standard,” and in Late Latin we find anomalus for “uneven.”
Source of the English anomaly, anomalus squares up with the Greek anomalos, joining the prefix an– (“not”) and homalos (“even”). This homalos, I should note, is from homos, which is essentially the same as our English same. It’s also the source of the prefix homo-.
Abnormous might make you think of enormous, and it should. Despite its “size,” enormous is a small jump from Latin’s enormis, literally, and again, e- (“out of”) and norma. Enormis could mean “irregular,” “shapeless,” and “very large.” Today, enormous is reserved to describe great size, although some centuries ago it did mean “outrageous.” An enormity–something outrageous, particularly in the moral sense implied by “out of the standard”–preserves this sense.
*Gno- or Nope?
Do we know anything further about this Latin norma?
Many etymologists end with norma, but Klein suggests that it could have been borrowed from the Greek, “probably through the medium of Etruscans.” Partridge offers gnorimos as a “carpenter’s square,” though the word is also glossed as “well-known.” Klein offers gnomon with respect to “carpenter’s square,” adding “literally, one who, or that which, knows; judge, indicator.” If this is the case, at root would be the Greek gignoskein–and thus the Proto-Indo-European *gno-. (Remember diagnosis and can?) It would also be related to the rather academic but nonetheless occasionally useful gnomic, essentially, “aphoristic.” A gnome is a “maxim.” Unrelated to your garden-variety gnome.
If anything, the etymology of norm is a reminder that what is considered “normal” is not natural but indeed man-made. And here, constructed in the most literal sense. But the question remains: What would be considered normal in a non-Euclidean world?

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