"When each car with a toilet was coupled, from now until eternity, at its toileted end with a car without a toilet, from then onwards the shunting yard, instead of dealing with N directed cars of two types, could deal with N/2 identical units that, to all intents and purposes, could be regarded as symmetrical."
On the physical "train" side of the analogy, we've got a believable scheme to save money by only having a toilet in every other car. Given the constraints, it is indeed clever to make these two-car atomic units and reimagine them as symmetrical. All the fixes in the story taken together could pale in comparison to the cost of putting a toilets all the cars.
But when we cross the digital divide we get a completely different set of constraints. Even if dealing with 100 million train cars it may be cheaper to just fork the entire train yard and add a toilet object to each car.
Why are there three characters to represent a pair?
Do you mean something like this:
car with toilet: [+-]
car without toilet: [--]
my pair: [+-][--]
your pair: [-+][--]
?
> This is then the "extra few feet" that he talks of.
Using my notation (sorry to flip it):
[-+][--][-+][--]
That's four cars. If someone is sitting at the right end of car #2, they have an arrow pointing them to car #1 for the toilet. If that toilet is broken, then they must walk back through car #2 all the way to the end of car #3.
But I may be misunderstanding your initial notation.
Sorry about the error earlier: "...-+-+-" was a typo that I couldn't edit anymore.
I just want to elaborate on this to show which assumptions you are making. There are two ways to make a paired unit: --+ and -+-.
In your scenario I think you assume the first. The end of the train is thus ...+----+, since you mention the second last car's orientation being reversed. The +'s represent toilets. Then, what you are saying is to consider a passenger located at the ^ symbol: ...+--^--+. In this configuration, your observation makes sense.
I do think that a more practical solution is to work only with (-+,-) pairs. The symmetry that Dijkstra talks of is then that (-+,-) and (-,+-) are equivalent for the purposes of the problem. Then an end of a train would be: ...-+-+-. This is then the "extra few feet" that he talks of.