I don't think there's actually a rule, in English at any rate, or at least a simple either-or rule, to govern the choice between the singular and the plural. The choice depends on the mental picture that it evokes. That in turn depends on whether the subject of the sentence, though plural, is viewed aggregatively or distributively. The "virgins of Jerusalem hang down their heads" sounds fine, but so does "In prosperous days They swarm, but in adverse withdraw their head." The difference is that the virgins are acting collectively, in unison; the swarmers are not–nor are the ostriches when they bury their heads. Each ostrich does that separately, individually. So the reader thinks of an individual ostrich, and he (or she) has one head. But the virgins are thought of as moving their heads in unison–a bunch of heads moving at once.
This is an interesting analysis, but as a description of general usage, I don't believe that it's accurate.
Among the plural examples that I cited in my earlier post, several clearly refer to heads affected one at a time rather than in unison. Consider Thomas Jefferson's complaint about England's bad influence on some of his colleagues:
It would give you a fever were I to name to you the apostates who have gone over to these heresies, men who were Samsons in the field & Solomons in the council, but who have had their heads shorn by the harlot England.
No harlot, even a metaphorical one, could shear more than one Federalist at a time.
The same analysis applies when Shakespeare's Duke of Orleans scorns the courage of English mastiffs:
Foolish curs, that run winking into the mouth of a Russian bear and have their heads crushed like rotten apples.
We are not asked to imagine the simultaneous crushing of a regiment of mastiffs' skulls, but rather a generic event, like the ostriches' mythical head-hiding, involving individuals acting separately as the occasion arises.
So the principle that plural = group viewed as acting in unison is not always true. What about the generalization in the other direction, singular = individuals viewed as acting separately?
This doesn't seem to be generally true either, though it's hard to tell, because a counterexample would involve the singular noun used to describe a group viewed as acting collectively, and it's hard to distinguish between this and a group acting as individuals, though similarly.
Thus in the King James translation, Lamentations 2:10 has plural "their heads" twice (emphasis added, spelling modernized):
The elders of the daughter of Zion sit upon the ground, and keep silence: they have cast up dust upon their heads; they have girded themselves with sackcloth: the virgins of Jerusalem hang down their heads to the ground.
But Young's Literal Translation has singular "their head" in both places:
Sit on the earth — keep silent do the elders of the daughter of Zion, They have caused dust to go up on their head, They have girded on sackcloth, Put down to the earth their head have the virgins of Jerusalem.
And the Darby translation has one of each:
The elders of the daughter of Zion sit upon the ground, they keep silence; they have cast dust upon their heads, they have girded themselves with sackcloth: the virgins of Jerusalem hang down their head to the ground.
Again, the evoked mental picture might involve the virgins all acting in the same way because of their individual reactions to the same woeful events, or acting as a group — there's no easy diagnostic for the difference. And in any case, there may be some influence of the language(s) from which the translations came; the comments on my earlier post emphasize that English is apparently unusual in this particular area of usage.
Perhaps a clearer example can be found in James Thompson's Winter:
232 … The cherish'd fields
233 Put on their winter-robe of purest white.
234 'Tis brightness all; save where the new snow melts
235 Along the mazy current. Low the woods
236 Bow their hoar head; and ere the languid sun
237 Faint from the west emits his evening ray,
238 Earth's universal face, deep hid, and chill,
239 Is one wild dazzling waste, that buries wide
240 The works of man.
William Hazlitt called Thompson "the best of our descriptive poets", who "always gives a moral sense to nature". Moral or not, it seems clear that the woods are here bowing their metaphorical heads in unison. Unless perhaps the woods, though grammatically plural, are a single metaphorical individual, with a single metaphorical head? So perhaps we'd better turn to some more prosaic sources.
Here's a bit of transcript from ABC's 1992 election coverage:
Rep. JOHN KASICH, (R), Ohio: Let's take a look down at Little Rock now and see that great celebration there. Little Rock is on Eastern time. Am I right?
METEOR: Yes. Everybody's shaking their head no. Help me.
Rep. JOHN KASICH, (R), Ohio: Central time.
METEOR: Is it Central time? Central time.
The context makes it plain that many physical heads were being physically shaken in real-time unison, though the singular "head" was used.
[OK, I should have known better than to bring "everybody ... their ..." into it. Please substitute this passage from Carl Nolte and Patricia Yollin, "The Great Quake: 1906-2006", SF Chronicle, 4/19/2006:
"These old people are really fantastic," said Leo Sapienza, 87, who laid a wreath on Lotta's Fountain in memory of those who died. Sapienza is a former president of the South of Market Boys, a fraternal group of old-time San Franciscans that used to have major political clout in the city.
Sapienza, the survivors and the crowd all bowed their head to remember when police and fire sirens rang just after 5:12 in the morning, the sound echoing off the tall downtown buildings, like the wails of lost souls. It marked the moment 100 years before that the ground ruptured, sending shock waves across Northern California.
Here the head-bowing is not only synchronized, but ceremonially so.]
And likewise this sentence from NPR Weekend:
You know, a lot of people scratched their head in the State of the Union message when President Bush said he wanted to give the real estate industry another boost by bringing back this passive real estate tax write-off.
Again, the head-scratching was necessarily simultaneous, as is the placing of hands on heads in this description of how to play Simon Says:
So a typical sequence goes "Simon says put your hand in the air like this. Now Simon says put them down by your side. Now put them on your head." All those putting their hands on their head are out.
I could multiply examples, but I think the basic point is established.
We're interested in the choice between singular and plural in constructions like "<VERB> their <NOUN(S)>". We observe that different people have different intuitions about particular cases, and that patterns of usage are just as variable. Judge Posner's analysis is that the plural is chosen when the events or states are viewed collectively, whereas the singular is chosen when things are viewed individually. Curiously, my own guess, if I had been forced to make one in advance of looking at the facts, would have been the opposite: it seems to me that the singular suggests a uniform treatment of the group, while the plural suggests a more distributed perspective.
Unfortunately, the interpretive situation is asymmetrical: it's often obvious that we should think of different individuals at different times in different places; but when a single time and place are involved, it usually remains unclear whether the author has a distributed or a collective interpretation in mind. This makes it difficult to evaluate either potential generalization; but it's clear that neither is true as a categorical principle, since events and states distributed in space and time are described by reputable authors with both singular and plural objects. To the extent that I can evaluate the facts, the same thing seems to be true of collective and "synchonized" events or states.
Though both principles are clearly false as a categorical description of usage, there might be a statistical tendency in one direction or the other. I don't have any evidence to offer on this score.
But more generally, it seems to me, this is a useful example of the natural desire to find a logical basis for choice, in cases where our intuitions are complex and variable, and our actions are even more so. An enterprise of this kind usually forces us to invoke or discover a large number of factors that turn out to be relevant; and in this case, it's easy to think of several relevant factors that we aren't taking into account.
But the end, linguistic choices are often as difficult to reduce to simple principles as other social actions are. This is especially true when specific choices bring general principles into conflict, as is arguably the case here.