{"id":610,"date":"2012-06-08T15:56:12","date_gmt":"2012-06-08T20:56:12","guid":{"rendered":"http:\/\/linesoftangency.wordpress.com\/?p=610"},"modified":"2012-06-08T15:56:12","modified_gmt":"2012-06-08T20:56:12","slug":"human-composure","status":"publish","type":"post","link":"http:\/\/blog.chrislusto.com\/?p=610","title":{"rendered":"Human Composure"},"content":{"rendered":"

Frequent commenter and child logic expert Christopher Danielson<\/a> recently contributed a very cool video, entitled One is one...or is it?<\/a><\/em>, to the Ted-Ed project in which he explores\u00a0 what it is we really mean<\/em> when we say \"one.\"\u00a0 The very notion requires an implicit or explicit reference to a unit, and sometimes things aren't quite as simple as they seem.\u00a0 In particular, we might have units that <\/em>are either built up of (composed units) or divided into (partitioned units) smaller sub-units.\u00a0 Or sub-sub-units.\u00a0 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.\u00a0One<\/em> is relative to your choice of unit.<\/p>\n

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<\/em> composition and partitioning: (1) units whose sub-units are human, and (2) units whose sub-units are tiny. \u00a0It's still\u00a0possible<\/em> to smoosh them together and rend them asunder, but not so neatly.<\/p>\n

Part the First<\/strong><\/p>\n

For just a moment let's consider the North Carolina State Wolfpack<\/a>. \u00a0Now that is definitely an all-the-way, one-hundred percent composed unit.\u00a0 It is a singular pack, composed of singular wolves.\u00a0 Unambiguous.\u00a0 Until you read some press releases, which are simply pregnant with phrases like, \"the Wolfpack are<\/strong>...\"\u00a0Which is very strange indeed.<\/p>\n

Consider two fictitious news stories.\u00a0 In the first, NC State is relocated by the NCAA to South Carolina.\u00a0 In the second, an actual, literal pack of wolves (Canis lupus<\/em>) is spotted migrating from Raleigh to Charleston.\u00a0 The first headline would read, \"Wolfpack Head Across the<\/strong> Border<\/strong>,\" while the second would read, \"Wolfpack Heads Across the Border<\/strong>.\"\u00a0 These two scenarios are mathematically identical; the only difference is that, in one case, the sub-units are figurative<\/em> wolves.\u00a0 So why do we require a different verb conjugation?\u00a0 It seems that people somehow resist being subsumed by composed units in a way that, e.g., playing cards do not.\u00a0 Admittedly this is a psycho-linguistic curiosity more than a mathematical one, but still...units can be slippery.<\/p>\n

It's maybe more obvious that people resist being partitioned. \u00a0After all, if you make it through life without anybody partitioning you, let's call that a nontrivial success. \u00a0But it shows up in the language, too. \u00a0We are very rarely wont to consider a disembodied finger directly. \u00a0When we partition people, we replace the corporeal whole with a possessive placeholder, a pointer (ha!) to the original unit. \u00a0We hold the source object in memory in a much more vivid and deliberate way than with other objects. \u00a0An 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. \u00a0Unless you live under fairly abnormal conditions, indefinite articles no longer suffice: \"a foot\" or \"the foot\" rarely come up. \u00a0We make grammatical concessions more readily and more often for human \"units\" (suppressing, here, many jokes) than nonhuman ones.<\/p>\n

Part the Second<\/strong><\/p>\n

Consider the strangeness of the following utterance: \"I think the rice is done.\"\u00a0 Why aren't<\/strong> they done instead?\u00a0 There are tons of those little buggers!\u00a0 There certainly exists a plurality of foodstuffs.\u00a0 But <\/strong>when we deal with tiny sub-units (especially if they're homogeneous), we have a hard time unitizing them naturally.\u00a0 We can go clumpy: \"I think the pot\/serving\/microwave bag of rice is done.\"\u00a0 We can go grainy: \"I think the grains of rice are done.\"\u00a0 But both of those solutions feel deeply unsatisfactory.\u00a0 There are contortions involved.\u00a0 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).\u00a0 Awkward either way.\u00a0 It's as if, on a fundamental level, we ache for rice to be singular entity, but of no definite unit membership.<\/p>\n

And this weirdness, I think, is no longer merely syntactic, but deeply mathematical.\u00a0 When we unitize the world in language, we make an important distinction between that which is countable<\/strong> and that which is measurable<\/strong>.\u00a0 There is an analogy to be made here between discrete and continuous objects, respectively. \u00a0It 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. \u00a0It 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. \u00a0Thus, we measure water and treat it as an un-composed unit. \u00a0Somewhere in between those two extremes, we have things like rice, much more countable than water, much less countable than eggs. \u00a0In 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. \u00a0Sand. \u00a0Salt. \u00a0Data.*<\/p>\n

*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. \u00a0If you're going to be a total weeny and use it in the plural, at least be consistent. \u00a0I had better never hear you talk about \"an agenda\" (singular), because \"agenda\" is also inflected as plural; each item is technically an \"agendum.\" \u00a0I'm watching you.<\/em><\/p>\n

<\/em>So tiny things resist composition, and they resist partitioning even more vehemently. \u00a0For one, they're already tiny. \u00a0It'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. \u00a0If I wanted to decompose \"sand\" into parts, how big is this parent sand? \u00a0We've stumbled into a kind of reverse\u00a0paradox of the heap<\/a>. \u00a0A loaf of bread readily admits slices. \u00a0A _________ of sand admits grains. \u00a0Tough to fill in the blank.<\/p>\n

An Interesting Competition<\/strong><\/p>\n

What happens when these two notions are pitted against each other? \u00a0Which one wins out in our brains and on our tongues? \u00a0How 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). \u00a0Did you hear what I just typed?\u00a0 \"The Miami Heat\u00a0are<\/strong>\u00a0one<\/strong>\u00a0of...\"\u00a0 But wait, that's nuts!\u00a0 I've never in my life heard anybody complain that the humidity\u00a0are<\/strong>\u00a0unbearable, so why should the capital-H Heat be any different? \u00a0Heat is an abstract and amorphous thing. \u00a0In our everyday usage, it's definitely a measurable substance---like water, a singular. \u00a0But it's also a unit composed of people. \u00a0And when I tell you about the current state of the NBA, I tell you that the Heat\u00a0are<\/strong> in the Eastern Conference finals.<\/p>\n

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. \u00a0We hold ourselves in such high regard that we're willing to regularly construct borderline nonsensical phrases to maintain our artificially inflated position.<\/p>\n

Go, Pack!<\/p>\n","protected":false},"excerpt":{"rendered":"

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\u00a0 what it is we really mean when we say \"one.\"\u00a0 The very notion requires an implicit or explicit reference to a unit, and sometimes things aren't quite […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[24,32,58],"class_list":["post-610","post","type-post","status-publish","format-standard","hentry","category-math-musing","tag-language","tag-math","tag-units"],"_links":{"self":[{"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=\/wp\/v2\/posts\/610","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=610"}],"version-history":[{"count":0,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=\/wp\/v2\/posts\/610\/revisions"}],"wp:attachment":[{"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=610"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=610"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.chrislusto.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=610"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}