The reopening of the Waterloo and City line means that now is a good time to discuss the chirality of maps on tube trains.
Let me set the scene.
You're sitting on a moving train in the "usual" style. That is: you're facing other commuters and the walls of the tunnel are in front of you and behind you (the front of the train is thus to your left or right).
You look up and see the route map for that line. It is probably linear, perhaps with a loop or a few branches at one or other end.
An interesting question then arises: does the direction of the train correspond with the direction implied by the map? That is: if you're travelling rightwards, does the map correctly identify that the next station is to the right?
Perhaps it does. Perhaps it doesn't.
Now you stand up, look menacingly at somebody on the opposite bank of seats and take their seat as they correctly sense you are performing an important experiment and choose to sit elsewhere. You now perform the same procedure as before. You look up and ask yourself whether the train is travelling the direction suggested by the map.
And this is where it gets interesting.
On some trains on some lines, the maps are accurate. This means that London Underground have gone to the trouble of producing two versions of the maps - a different one for each side of the train). On other trains, they use the same version of the map on both sides of the train - which means that one will be accurate and one will be "the wrong way round".
The question is: why is this the case and on which trains do they get it "right"?
In some cases, it's just not possible to get it right: The Piccadilly and Central lines, for example, have a loop which mean that, without getting out of your seat, the train would sometimes be travelling in the direction suggested by the map and sometimes not. In such cases, printing two versions is unnecessary - indeed, it runs the risk of having both maps being wrong.
However, on the Jubilee Line (with no loops and no branches), it would be possible to get it right (I can't remember if they actually do).
If a tube train has two maps - one for the left hand side and one for the right hand side of each carriage then we say it is chiral. Otherwise, we do not.
The question I am inviting you to help me answer is: can we compile a list of which lines have chiral maps on their trains and which do not?
Enquiring minds need answers.
[UPDATE 2006-09-19 19:21]
It appears I may have, entirely unintentionally, given the impression that I was
sad clever enough to observe these phenomena. The blame should be spread more widely. As Henry politely poins out,
"As you will recall, on 30 October 2005 - following from her examination of a cellphone advertisement - Polly raised this important issue with the results for the Jubilee and Piccadilly lines. Other notable events in this subject's history: line investigations (you, me, Polly); coining of the term "chirality" for this phenomenon (me), mathematical discourse (Mark, Polly), investigation and discussion of depot positioning and sequence-changing stock movements (Ben, me), proposed solution for the London case (me)."Never let it be said that I don't spread the blame for such triviality as widely as possible.