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> the least lucky passenger would have to walk six car lengths I just want to elaborate on this to show which assumptions you are making. There are two ways to
by mikorym 8y ago
> the least lucky passenger would have to walk six car lengths
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.
- mikorym 8y agoCorrection on the second last sentence: "...-+--+-".
- mannykannot 8y agoYes, though I think the last three feet refers to the vestibule connecting the two carriages, which a passenger in the non-toilet carriage must traverse.
- mikorym 8y agoThanks, that does make sense. So he means three extra feet of travelling that our equivalence relation with (-,+-) ~ (-+,-) ignores.
- mcguire 8y agoIndeed. Dijkstra specifies two cars joined with the toilet in the middle: "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."
- jancsika 8y agoI think what bothers me about this is that it's an analogy which crosses the digital divide. 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.
- jancsika 8y ago> I just want to elaborate on this to show which assumptions you are making. There are two ways to make a paired unit: --+ and -+-. 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.
- mikorym 8y agoYour bracket notation in effect works the same as mine. The difference is that -+- could be any of [-+][--] or [--][+-] by symmetry and so leaving out brackets. In my notation "+" is a character which does not occupy space. Hence [-+][--][-+][--] is the same as -+--+-. Sorry about the error earlier: "...-+-+-" was a typo that I couldn't edit anymore.