October 07, 2004

Loopy defenses of the shuttle bus sign

I have just a small afterword on the strange case of the shuttle bus signs at UC Santa Cruz that describe the counter-clockwise direction loop shuttle as "westbound" when by the nature of loops it must go east just as much as it does west. And I must caution the reader who might be inclined to go on: Warning — high level of nerdiness.

John Cowan writes confidently from a perspective informed by naive geography and an analogy with the everyday cognitive/motor experience of using a steering wheel:

Conceptually, left is treated as counter-clockwise and right as clockwise; consider the way we talk about steering wheels (we turn them left, meaning that points near the *top* move leftward). Likewise, west is normally mapped onto left and right onto east, based on the notion that north = top. So what we need to know to interpret the phrase "westbound shuttle" is what counts as the top of the loop. Fortunately, the loop is in three dimensions, and so the top is ... the top, the point of highest elevation.

So he is telling me that I should see the shuttle route as a steering wheel with the top at the north (up the hill, roughly at Crown College), so that west is left, and regard a shuttle as westbound if it is going the way a left turn would move the wheel. But meanwhile the delightfully, brilliantly nerdy Fernando Pereira of the University of Pennsylvania (how nerdy? Fernando's shirt buttons are microchips and he runs Debian Linux on his microwave oven) writes to say:

Consider a single directed loop on the Earth's surface that does not cross the Equator. Consider a homotopy between it and the Equator in which each intermediate loop is also on the Earth's surface, and no such loop crosses the Equator. If it maps the direction of the loop to the westward direction on the Equator, the original loop is westward, otherwise the original loop is eastward.

What he means (and I did have to ask him: I can handle rocket science but I need a little help with topology) is that if you stretch the line of a directed loop shuttle route in the northern hemisphere as much as necessary and move it down to collapse it onto the equator, you can call the shuttle route westward if it collapses to an east-west equatorial route (one that proceeds through the time zones the same way the sunrise does) and eastward otherwise.

And what I now have to point out to you is this. I have carefully considered what these two defenses of UCSC's Transportation and Parking Services (TAPS) department entail, and I have to tell you that they predict differently. One identifies the direction of the shuttles that have the bike racks as westbound, and the other identifies those shuttles as eastbound. They contradict each other!

So I rest my case. It's not me, it's TAPS. There is no guaranteed, unambiguous, intuitive way to say of a shuttle running a loop that it is in general running westward or eastward. (It's very much like the way there is no ambiguous common-sense basis for the interpretation of the terms incall and outcall as used by massage services.) The shuttle must make eastward progress at some point and westward progress at some other point if it is ever to come back to its starting point. So the guys who wrote the signs are completely nuts. (They're probably relatives of the guys who paint the signs on the road that say >A href="http://itre.cis.upenn.edu/~myl/languagelog/archives/001183.html"> ONLY LANE BIKE.) Language Log has spoken.

And in fact cognizant and duly empowered officials at TAPS have already accepted that this is true (everyone who is anyone reads Language Log), and they are going to change the signs. Language Log has once again been a positive force for the good of humankind.

Posted by Geoffrey K. Pullum at October 7, 2004 01:02 PM