October 10, 2004

The gopher's eye view

The ground on which they built the Santa Cruz campus of the University of California is honeycombed by the activities of ground squirrels, pocket gophers, and various other burrowing mammals — running across a UCSC meadow is a good way to break an ankle. And below the tunnel-ridden soil is a sort of limestone sponge, riddled with caves, tunnels, sink holes, and water channels.

You're probably wondering how this is going to be linked to a linguistic topic, aren't you? Trust me. A link to a linguistic issue is coming, in two deft strokes. You just have to decide to read on.

Recently I argued that the signs on UCSC shuttles in early October 2004 talking about "westbound" loop shuttles having bike racks on the fronts of the buses are utterly meaningless. Thereafter, two suggestions were emailed to me that claimed to map a particular shuttle loop direction naturally onto an eastbound or westbound direction, but I pointed out that they contradicted each other. My claim was that "clockwise" and "counterclockwise" were the terms to use, and Transportation And Parking Services (TAPS) at UCSC has decided that I am right.

Don Olivier, who actually runs Linux on his digital wristwatch, has written me to suggest that in fact I am wrong. Consider again a shuttle route going up Hagar Drive, turning west at Coolidge Drive after Quarry Plaza, heading out of the West Entrance, and down Empire Grade to the Main Entrance (see the interactive aerial photograph here). It looks counterclockwise, I observed. But that is because I am tacitly taking the view from above ground. Suppose I take the viewpoint of a gopher located under the ground near the McHenry Library in the center of the campus, looking up. Now the same shuttle appears to be travelling clockwise. The clockwise / counterclockwise opposition is relative to observer viewpoint.

Paradoxically, there appears to be no general way to name the direction of travel of a loop shuttle. Leftward/rightward and westward/eastward are self-evidently useless because a loop must involve just as much travel to the left (or west) as to the right (or east), and just as much to the top (or north) as to the bottom (or south), if it is ever to get back to where it once was and thus continue in a loop. But the clockwise/counterclockwise opposition also fails if we cannot agree on where the observer is to be stationed — in three dimensions — relative to the set of points on the loop. (You might, foolishly, have spent a second or two thinking that one could distinguish the two routes by explaining that the one with the bike racks on the fronts of the buses visits Quarry Plaza on Hagar Drive before it gets to the Cowell Health Center on Coolidge Drive. But of course both routes do that. Think about it.)

Now I know that some people will say that the problem is solved by the contingent fact that students (especially those bringing bikes up the hill to the central campus) spend virtually all their time above ground, and that gophers virtually never travel by shuttle bus. But that is just the sort of anti-intellectual observation that we practitioners of lofty theorizing despise. There is a deep issue here. We sit in our campus shuttles travelling a three-dimensional path on the uneven surface of a spheroidal rotating planet orbiting a minor star that drifts in three dimensions in a galaxy drifting along with many other galaxies in a galaxy cluster in a rapidly expanding universe of possibly many dimensions... And the nonsensical reference to westbound loop shuttles in the notice TAPS put up should remind us that they face a serious problem: there is no general way to refer to the direction of travel in a directed loop that does not rely on a known orientation relative to the geography of the loop that can be agreed on by all observers.

God may be able to see the whole universe all at once without any perspectival bias; but if so, He will be unable to tell us unambiguously how to determine whether there will be bike racks on the fronts of our shuttle buses without referring to where we are now and which way we are looking. That is a deep and cosmic fact. And you read it here on Language Log.

Note added later (October 10, 4:15pm Eastern time):

Or at least I thought it was when I hit the Save button. But one can always be mistaken. And I appear to have been wrong once again. What I said was perhaps a deep and cosmic fact if you take shuttle loops to be one-dimensional paths with no referenceable named points; but those assumptions do not hold here, and they are crucial. Here are the two suggestions I received this morning from several readers:

Peter Maydell (and Sweth Chandramouli independently just a few hours later) pointed out that mentioning three stops along the route will unambiguously identify it. So the route with the bike racks could be called (rather longwindedly) the Quarry Plaza - Cowell Health Center - West Entrance route, the other being the West Entrance - Cowell Health Center - Quarry Plaza route. He notes that the London Underground train system does this with the Circle Line: "This is a Circle line train for Liverpool Street via King's Cross," they say, tacitly lining up the station where you are, the King's Cross station, and the Liverpool Street station in such a way as to unambiguously identify the direction of travel as clockwise (counterclockwise if you are on another underground train deeper in the earth and looking up). I missed this one by not extending the reasoning about stop sequence far enough: two points on a closed curve do not identify a direction on it, but three or more do.

Bertilo Wennergren (and again, Sweth Chandramouli independently just a few hours later, and Vardibidian a couple of hours after that, and Anders McCarthy from Seoul after that) pointed out that one of the shuttle routes will have buses travelling a larger loop than the other, because (this being the USA) buses travel on the right hand side of the road. This makes what I was calling the counterclockwise route (clockwise for gophers) trace out a larger loop, strictly outside the other one all the way round. So the route with the bike racks on the buses could be called the Outer Loop shuttle, the other being the Inner Loop. When an Outer Loop shuttle passes an Inner Loop shuttle, the Outer Loop bus is always on a path that is further out from any arbitrary point (say, the McHenry Library) inside the loop than the Inner Loop shuttle is.

Those two ideas are the best I have met with yet, and Bertilo's seems neater: the Outer Loop and the Inner Loop. Hugo Quené reports that they already do this in Paris, calling the two directions on the Périphérique the inner (interieur) and outer (exterieur) directions. I missed this possibility because I was thinking of the loop route as a one-dimensional line enclosing a two-dimensional area on the surface of a three-dimensional planet, an oversimplifying assumption that makes what I said true (unless you can name particularly points on the loop; see the previous paragraph). But a road is in fact a two-dimensional strip: it has width, and buses on it have positions on it relative to the two edges. TAPS might consider adopting that one. Though right now they are busily implementing the clockwise/counterclockwise idea and making new signs. It's always a mistake to move too fast on such things. You have to let the pajamarati of the blogosphere complete their analysis first.

Posted by Geoffrey K. Pullum at October 10, 2004 01:24 AM