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".
I agree that your citation sounds strange; at least, it does to my ear. Reading that I almost wonder whether the author hasn’t somehow conflated progeny and prodigy, since the latter’s plural form is unremarkable.
However, digging deeper, one finds that the OED entry for progeny, last updated in 2007, makes no mention one way or the other. It gives as its sense 1a
1a. Offspring, issue, children; descendants. Occas.: a child, a descendant; a family.
a definition that is already in the plural, but which admits a singular sense “occasionally”. Sense 1b is more figurative:
1b. fig. Spiritual, intellectual, or artistic descendants; successors; followers, disciples.
And is still plural, and gives this citation of progeny itself taking plural concordance:
- 1994 H. Bloom Western Canon ii. iii. 80
Dante’s progeny among the writers are his true canonizers.
However, down under sense 1d:
1d. The product of the breeding of animals or plants; the offspring of sexual or asexual reproduction. Now chiefly Agric. and Genetics.
We find that there is indeed an inflected plural version — progenies — given as an example:
- 1977 Crop Sci. 17 909/2
Twenty-one clones whose polycross progenies ranked high for rate of seedling emergence under field conditions or had high forage yield..were selected for this study.
So it appears that when dealing with people, progeny is taken as a plural with some use as a singular, but when used in a genetic sense, it can occasionally be taken as a count noun that inflects regularly.
Best Answer
There are confusing and conflicting terminologies surrounding this subject, not least as offered by dictionaries; I feel a well-formatted answer is needed.
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