Etymonline has this to say:
-ics
in the names of sciences or disciplines (acoustics, aerobics, economics, etc.) it represents a 16c. revival of the classical custom of using the neuter plural of adjectives with -ikos (see -ic) to mean "matters relevant to" and also as the titles of treatises about them. Subject matters that acquired their names in English before c.1500, however, tend to remain in singular (e.g. arithmetic, logic).
So yes, at some point in history, there were such things as physic (meaning "natural science"), mathematic (meaning "mathematical science"), etc. that were later turned into plural forms but kept being treated as singular.
Edit: having looked in a few more places, it appears that in contemporary English, it still makes some sense to have both the suffix -ic and its plural form -ics. According to the Collins English Dictionary, the former has kind of specialized in forming adjectives, while the latter is happily forming nouns:
-ic
suffix forming adjectives
- of, relating to, or resembling: allergic, Germanic, periodic. See also -ical.
[...]
[from Latin -icus or Greek -ikos; -ic also occurs in nouns that represent a substantive use of adjectives (magic) and in nouns borrowed directly from Latin or Greek (critic, music)]
[...]
-ics
suffix forming nouns (functioning as singular)
- indicating a science, art, or matters relating to a particular subject: aeronautics, politics
- indicating certain activities or practices: acrobatics
[plural of -ic, representing Latin -ica, from Greek -ika, as in mathēmatika mathematics]
The key here is that they are not just two unrelated suffixes. Much rather, one is etymologically a plural form of the other. As the American Heritage Dictionary succinctly puts it, -ics is "-ic + -s".
The meaning of the sentence changes completely if you use each vs. both:
If you say: "Both the datasets ... are stored in two schemas." then you are saying that there is a total of two schemas. (but we don't know how the datasets are divided between the two schemas (50/50? 60/40? 90/10?))
If you say: "Each of the datasets ... is stored in two schemas." then you are saying that there is a total of four schemas: two for one dataset, and two for the other.
If you want to say that there are two schemas, and that one schema contains 100% of one dataset, and the other schema contains 100% of the other dataset, then you should say: "Each of the datasets ... is stored in a schema", or "Each of the datasets ... is stored in its own schema."
Both should only be used when you want to refer to the combination (sum) of two things: The car and driver both weigh 3,510 lbs. (If they each weighed 3,510 lbs, the driver would need to go on a diet)
Best Answer
If you notice that each other, while idiomatic, is not unbreakable, it begins to come clear.
The reciprocal phrase each other can be separated into one determiner binding something in the subject (each, each one), and one determiner binding something in the object (other, the other), viz:
And some of these quantifiers may be floated to pre-verbal position:
From this it's easy to see how each and other hook up:
But that doesn't resolve the number problem that comes from having two determiners potentially conflicting. So both
feel wrong.
Of course, there are other quantifiers that specify more precisely,
especially when they're separated, viz: