[–] Lipsy #bornnotworn 15 points Edited

Wait huh? I've never seen this claim before, that a spectrum has to be quantified with units. And it's just flatly not true.

A spectrum is just a one-dimensional range between two poles—originally named after visible light, which is the Roy G. Biv spectrum within the much wider range of electromagnetic radiation.
(This spectrum, exceptionally, DOES have units—wavelengths of light in nanometers—but the spectrum itself was defined long, long before the units were known. And moreover, it's only that way because the spectrum of visible light is a tiny piece taken from a much larger, theoretically unbounded, range of all wavelengths of electromagnetic radiation.)

Height is NOT a spectrum, because it doesn't have two poles that represent actually defined opposite extremes.
There's no upper end of height at all in theory, and the "lower end" is zero, which isn't a valid pole for a spectrum either (because there's no such thing as being zero nothings tall).

Also, there are tons and tons and tons of things commonly described as spectra that do not have 'units' and are not quantifiable. The political spectrum from left to right is probably the most famous, but, practically every individual human psychological trait is also on a non-quantifiable spectrum—including each of the standardized set of personality factors (the set with "Agreeableness" and so on in it), plus others like tendency to violence at one pole vs. peaceable character at the other.

Conversely, most numerical quantifiers with units specifically ARE NOT spectra, because most things with units range from a zero value to theoretical infinity.

but the spectrum itself was defined long, long before the units were known

But you could see that there were at least six different colors. The rainbow is a spectrum and you can't pinpoint exactly when orange starts and red ends, but red is definitely not blue, orange is not green. The obvious colors were the units, I guess.

[–] Lipsy #bornnotworn 4 points Edited

Those are "categorical values", not units. They're not rlly appropriate here, because visible light is a spectrum—there are infinitely many colors blending together.
Categorical values are discrete and can be counted with whole numbers, like the grade school formulation of the rainbow—which is basically just arbitrary, and, notably, not the same from one language to another (e.g. many Asian languages use the same word for blue and green. Other colors, like violet and orange, are named for fruits or flowers and don't correspond well between languages; Chinese people call hot pink "rose red", but have a different word for baby pink).

Units are numerical; the very name itself tells you in Latin that the unit represents exactly 1 of whatever thing. (The "one" in any romance language—un, une, uno, una, etc—is pretty visible in there too.)