Frequent commenter and child logic expert Christopher Danielson recently contributed a very cool video, entitled One is one...or is it?, to the Ted-Ed project in which he explores what it is we really mean when we say "one." The very notion requires an implicit or explicit reference to a unit, and sometimes things aren't quite as simple as they seem. In particular, we might have units that are either built up of (composed units) or divided into (partitioned units) smaller sub-units. Or sub-sub-units. For instance, the loaf of bread in your cupboard is partitioned into individual slices; the pinochle deck you stash in the coffee table is composed of individual playing cards; and Pop Tarts are sold in boxes, which contain packs, which contain individual pastries. One is relative to your choice of unit.
Of course this is all very interesting, but the first thoughts that popped into my head during the dancing apple slices number involved the two conspicuous cases that seem to defy composition and partitioning: (1) units whose sub-units are human, and (2) units whose sub-units are tiny. It's still possible to smoosh them together and rend them asunder, but not so neatly.
Part the First
For just a moment let's consider the North Carolina State Wolfpack. Now that is definitely an all-the-way, one-hundred percent composed unit. It is a singular pack, composed of singular wolves. Unambiguous. Until you read some press releases, which are simply pregnant with phrases like, "the Wolfpack are..." Which is very strange indeed.
Consider two fictitious news stories. In the first, NC State is relocated by the NCAA to South Carolina. In the second, an actual, literal pack of wolves (Canis lupus) is spotted migrating from Raleigh to Charleston. The first headline would read, "Wolfpack Head Across the Border," while the second would read, "Wolfpack Heads Across the Border." These two scenarios are mathematically identical; the only difference is that, in one case, the sub-units are figurative wolves. So why do we require a different verb conjugation? It seems that people somehow resist being subsumed by composed units in a way that, e.g., playing cards do not. Admittedly this is a psycho-linguistic curiosity more than a mathematical one, but still...units can be slippery.
It's maybe more obvious that people resist being partitioned. After all, if you make it through life without anybody partitioning you, let's call that a nontrivial success. But it shows up in the language, too. We are very rarely wont to consider a disembodied finger directly. When we partition people, we replace the corporeal whole with a possessive placeholder, a pointer (ha!) to the original unit. We hold the source object in memory in a much more vivid and deliberate way than with other objects. An apple slice is an apple slice, culinary nuances notwithstanding, but "John's foot" and "your foot" and "the crazy lady in 3B's foot" require modification. Unless you live under fairly abnormal conditions, indefinite articles no longer suffice: "a foot" or "the foot" rarely come up. We make grammatical concessions more readily and more often for human "units" (suppressing, here, many jokes) than nonhuman ones.
Part the Second
Consider the strangeness of the following utterance: "I think the rice is done." Why aren't they done instead? There are tons of those little buggers! There certainly exists a plurality of foodstuffs. But when we deal with tiny sub-units (especially if they're homogeneous), we have a hard time unitizing them naturally. We can go clumpy: "I think the pot/serving/microwave bag of rice is done." We can go grainy: "I think the grains of rice are done." But both of those solutions feel deeply unsatisfactory. There are contortions involved. We either have to create a new group name (think pod of dolphins or murder of crows), or a new unit name (think kernel of corn or drupelet of raspberry). Awkward either way. It's as if, on a fundamental level, we ache for rice to be singular entity, but of no definite unit membership.
And this weirdness, I think, is no longer merely syntactic, but deeply mathematical. When we unitize the world in language, we make an important distinction between that which is countable and that which is measurable. There is an analogy to be made here between discrete and continuous objects, respectively. It is natural to consider the composed unit of a dozen eggs, because eggs are easily countable, and because it's easy to count to a dozen. It is much more difficult to create a conventional composed unit out of water molecules, because water molecules are hard to count, and because it would be hard to count to a number of water molecules that would be useful in most situations. Thus, we measure water and treat it as an un-composed unit. Somewhere in between those two extremes, we have things like rice, much more countable than water, much less countable than eggs. In fact, it's closer to water than eggs in its countability, so we treat rice as measurable/continuous, even though it's technically countable/discrete. Sand. Salt. Data.*
*I will fight to the death, via torturously long diatribes on gerunds and loan words, that "data" should be treated as singular in English, even though it's inflected as a plural in Latin, all based on the composed unit argument above. If you're going to be a total weeny and use it in the plural, at least be consistent. I had better never hear you talk about "an agenda" (singular), because "agenda" is also inflected as plural; each item is technically an "agendum." I'm watching you.
So tiny things resist composition, and they resist partitioning even more vehemently. For one, they're already tiny. It's inconvenient to let these things get any smaller (and our unit choices, after all, have an awful lot to do with convenience), and there's no natural starting point from which to partition things in the first place. If I wanted to decompose "sand" into parts, how big is this parent sand? We've stumbled into a kind of reverse paradox of the heap. A loaf of bread readily admits slices. A _________ of sand admits grains. Tough to fill in the blank.
An Interesting Competition
What happens when these two notions are pitted against each other? Which one wins out in our brains and on our tongues? How fortunate for my blog that the Miami Heat are currently playing in the NBA Eastern Conference Finals, and that the Miami Heat are one of the few professional sports teams with a singular name (as an fun exercise, try to list all the others---major sports only, no AA curling or anything). Did you hear what I just typed? "The Miami Heat are one of..." But wait, that's nuts! I've never in my life heard anybody complain that the humidity are unbearable, so why should the capital-H Heat be any different? Heat is an abstract and amorphous thing. In our everyday usage, it's definitely a measurable substance---like water, a singular. But it's also a unit composed of people. And when I tell you about the current state of the NBA, I tell you that the Heat are in the Eastern Conference finals.
Our bias against making conglomerations out of people is so strong that it can overcome our natural tendency to treat both composed units and measurable substances as singular. We hold ourselves in such high regard that we're willing to regularly construct borderline nonsensical phrases to maintain our artificially inflated position.