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I just came across a course name: Geometric and Theoretical Optics. The mismatched endings bug me. Why do we have both -ical and -ic endings?

Is there any difference in meaning between, say, theoretic and theoretical? I know that acoustic and acoustical mean slightly different things, but is this difference inherent in the words, or is it just usage — we happen to use the former for sound, and the latter for ceilings?

Origin

The suffix -ic comes from Greek -ikos, while -ical is a combination of -ic and the French suffix -al. Originally, -al was suffixed to scientific nouns ending in -ics, e.g. mathematics - mathematical. Eventually, the -ical portion of those words was reanalyzed as being a single unit. This is what Marchand (1969) had to say about -ic vs. -ical at this time in their history:

There was, at the beginning, indiscriminate coexistence of two synonymous adjectives. But language does not like to have two words for one and the same notion, and competition was bound to come.

What Marchand is talking about is that these two redundant suffixes eventually settled into certain niches where they exist today (more on this later).

-ic and -ical doublets

There exist many -ic/-ical "doublets" in English, where both forms of the word exist and are used regularly.

For example:

• 
  historic and historical
  


• 
  electric and electrical
  

The words in common doublets have generally developed distinct meanings (or domains of use). For example, historical refers exclusively to things that happened in the past, while historic can refer to an event occurring at that very moment that will have a profound impact on history.

However, the differences in meanings between -ic and -ical words (in cases where both forms are used) cannot be generalized to a specific unique meaning that -ic or -ical itself contributes to the word.

That is to say, there is no general and consistent meaning that -ical uniquely contributes to historical, electrical, etc. Instead, each word as a whole just settles into its specific meaning.

Distribution Today

According to a systematic productivity measure by Lindsay and Aronoff (2010), the more productive of the two suffixes is clearly -ic, which is favored by approximately an 8 to 1 ratio using this measure. So, you are much more likely to have an -ic form of a word, or to have that form be the more commonly used form.

Now, if -ic is clearly used more than -ical, then why do we have both of these suffixes in the language?

Well, -ical has managed to differentiate itself from -ic, but not by contributing a specific meaning to the words it attaches to. Instead, -ical has found a specific morphological domain in which it attaches very productively: stems that end with the morpheme -(o)log-. Examples:

• 
  biological preferred over biologic
  


• 
  technological preferred over technologic
  


• 
  typological preferred over typologic
  

There are nearly 500 stems in Webster's 2nd dictionary that end in -olog. Using the same measure of productivity, Lindsay & Aronoff found that within the domain of these stems, the -ical suffix was itself preferred by an 8 to 1 ratio over -ic. That is to say, when there is an -(o)log morpheme at the end of the word, then people heavily favor -ical.

The notion of one suffix being productive when attaching to a certain suffix is known as "potentiation", coined by Williams (1981). (Another example of potentiation is what we see with words ending in -able. In general, -ness is considered a more productive suffix than -ity, but in words ending in -able, -ity is strongly preferred.)

Bear in mind that these are tendencies; while there is a strong preference for one form over another in certain cases, that does not mean that it is a perfect split.

Summary

-ic and -ical do not differentiate themselves semantically; however, both forms of a word can exist if each one settles into a different meaning, or otherwise has a different domain of usage (for example, one formal and the other informal). The actual differences in meaning between two forms in a doublet are essentially arbitrary.

While -ic is much more common overall (and could be argued to be the "default"), -ical is strongly preferred in stems ending in -(o)log-. Again, this is a tendency that began somewhat arbitrarily during the development of the language, but because words ending in -olog form such a large and relatively uniform group, a subpattern was able to emerge and stabilize, even as -ical remains in the minority.

In some cases, an adjective has both -ic and -ical forms, with no difference in meaning. In some cases, there are two different words for two different meanings. In some cases, only one word exists. And of course, this is often historical and can change with time.

In your case, there are actually differences in meaning (at least as I would use them):

• Geometric roughly means "related to geometry" — geometric optics, geometric algebra, etc. It's a technical word; if I use geometric in a phrase, the field of geometry probably actually enters into it in a non-trivial way. I'd use geometrical in uses like geometrical pattern, geometrical design, etc. — pleasing patterns made out of simple shapes like circles, triangles and squares. (This may be just an idiosyncrasy of mine, there are certainly books talking of geometrical optics, and people do use geometric where I'd say geometrical.)




• The word theoretical is much more common than theoretic: for instance, theoretical physics is contrasted with practical (or applied) physics; something may be theoretical if it exists only in theory and not in reality, and so on. The word theoretic is rarely used, except in usages where you want to make an adjective out of some specific named theory, like set-theoretic definition (a definition that comes from, or uses, set theory), number-theoretic function (a function as usually defined in number theory), game-theoretic equilibrium (the equilibrium predicted by game theory), information-theoretic proof (a proof that uses information theory), etc.

So much for the specific words. Let's turn to the general issue of the two suffixes -ic and -ical. The following is the entry in Fowler (A Dictionary of Modern English Usage) for -ic(al), written in the good old days when one could speculate and have opinions about what would be nice for the language without being shouted down by descriptive linguists for committing grave sins like stifling its natural evolution. (In short, Fowler says that where two meanings can be differentiated, it's good to do so, and otherwise it's good to keep just one word.)

-ic(al). A great many adjectives appear with alternative forms in -ic and -ical. Often the choice between them on any particular occasion is immaterial, so far as the writer's immediate object is concerned. To those who can afford time to think also of the interests of the English language it may be suggested that there are two desirable tendencies to be assisted.

The first of these is DIFFERENTIATION. There are many pairs in -ic and -ical, each form well established and in constant use, but with a difference of meaning either complete or incipient. The final stage of differentiation is seen in politic and political, which are not even content, as usual, to share an adverb in -ically, but make politicly by the side of politically. Between economic and economical the distinction is nearly as clear, though the seal has not been set upon it by a double provision of adverbs; most writers are now aware that the two words mean different things, and have no difficulty in choosing the one required. This can hardly be said of comic(al), the short form of which is often made to do the other's work. And so the differentiations tail off into mere incipiency. Every well-established differentiation adds to the precision and power of the language; every observance of an incipient one helps it on the way to establishment, and every disregard of it checks it severely. It is therefore clear that writers have a responsibility in the matter.

The second laudable tendency is that of clearing away the unnecessary. When two forms coexist, and there are not two senses for them to be assigned to, it is clear gain that one should be got rid of. The scrapping process goes on slowly by natural selection; sometimes the determining cause is apparent, as when hysteric, cynic, and fanatic, give way to hysterical, cynical, and fanatical, because the former have acquired a new function as nouns; sometimes the reasons are obscure, as when electric and dynamic supersede the longer forms while hypothetic and botanic are themselves superseded. But that one or other should prevail is a gain; and it is a further gain if the process can be quickened. With this end in view, this dictionary states about many -ic(al) words, in their places, which appears to be the winning side, so that writers may be encouraged to espouse it.
Separate entries will be found (omitting -ic, -ical) for botan-, casuist-, com-, cub-, cyn-, diabol-, dynam-, econom-, electr-, fanat-, geograph-, geometr-, hypothet-, hyster-, ident-, lyr-, mag-, period-, philosoph-, sto-, trag-.

And there are entries for all those words, if you enjoy reading Fowler. In the third edition (1998) of the book, edited by Burchfield and notorious for radically changing Fowler's entries, there is an entirely new entry, that seeks to find patterns. The author's impression is that -ic is more common, and where both exist -ic is American and -ical is British:

ic(al) (adjvl suffix). This article attempts to assess in practical terms how complex the distribution is of adjectival forms ending in -ic and those ending in -ical. Since the mathematical unattractiveness of analysing the relevant evidence in large computerized corpora is self-evident—the number of adjs. ending in -ic and -ical is very large—I have searched my personal database instead and correlated the evidence with that presented in the COD (1990).

First, it should be borne in mind that we daily encounter many nouns (including proper names) and adjs. that happen to end in -ic but are not relevant to this article, e.g. chic, Eric, logic, music, republic, topic, traffic. Secondly, it would appear that a little more than half of the adjectives that fall within the sphere of this article always and only end in -ic. Thus COD lists alcoholic but not alcoholical, basic but not basical, dramatic but not dramatical, patriotic but not patriotical, plastic but not plastical, and so on. Thirdly, it would seem that about a quarter of all the relevant formations always and only end in -ical. Thus chemical but not chemic, farcical but not farcic, practical but not practic, radical but not radic, and so on. Fourthly, just on a fifth of all such words may end either with -ic or with -ical, sometimes with a difference of meaning and sometimes with no discernible difference. The more important of such words are dealt with at their alphabetical place, e.g. classic/classical, economic/economical, historic/historical.

Fifthly, for those pairs where there appears to be no difference of sense, I have formed a broad impression that the -ic forms are favoured in AmE and -ical ones in BrE; but the distribution is erratic, and is much influenced by the practice of particular publishing houses. Thus in American academic works the shorter forms geographic, geologic, immunologic, lexicographic, and pedagogic are more likely to occur than the longer forms geographical, etc., whereas in British publications the reverse is the case. On the other hand for many ordinary pairs, e.g. comic/comical, ironic/ironical, problematic/problematical, symmetric/symmetrical, the distribution is not governed by geography but by idiomatic or rhythmical considerations in a given context. Sixthly, it is a curiosity that all the above pairs of words have -ically as their adverbial equivalents, not -icly. The main exceptions are that public (which has no corresponding adj. form in -ical) has only publicly as the corresponding adverb; and there is no form politicly.

(Yeah, he directly contradicts Fowler's mention of politicly — it's now rare, I guess, as is the adjective politic — and people do use "publically", though I don't like that word and it isn't listed in some dictionaries.)

I realise that I haven't answered why both endings exist in the first place, but the moral of the story is that sometimes there is a difference in meanings, so the two endings are useful. Other times, the choice is entirely up to you.

‘The Cambridge Guide to English Usage’ acknowledges that there is often no reason for preferring one to the other, but points out that in some cases ‘the -ic spelling corresponds more closely to the core meaning of the stem, while the meaning of the -ical spelling is rather generalised.’

It has dedicated articles on a number of particular word pairs.

Of economic and economical:

Thus economic has generally displaced economical in references
to matters of economics and the structure of the economy at large;
and economical now relates to economy measures (or economies)
by which to avoid extravagance and wastage.

Of historic and historical:

Historic is more self-consciously associated with the making of history, so that a historic event is one which people feel is
particularly significant in the life and culture of the nation.
Historical is more neutral, acknowledging that something belongs to the past, or else that it really happened and is not fictitious.

Of comic and comical:

The first of these adjectives is more closely linked with comedy, as
in comic opera and a comic character. Comical is more loosely
used of anything that generates laughter, as in a comical
expression.

In some cases, the usage changes over time (as noted already)...