Puzzled in Tarragona

In the Hotel Ciutat de Tarragona, the beautiful modern hotel in Tarragona where I am currently staying, I ate breakfast in the 1st-floor restaurant (Americans: that would be the 2nd floor), and then came out to take the elevator back up to my 5th-floor room (Americans: 6 floors up). But I was baffled: there was no button to call the elevator for upward journeys. There was just a button labeled with the Down-Arrow symbol for calling the elevator to go back down to the lobby on level 0. Some sort of security, I assumed, to ensure that random restaurant patrons don't go up in the elevator to wander up and down the halls looking for unlocked doors or stealable items. But then how was I to get back up to my room? I'm ashamed to report just how long it took me to resolve the conundrum here. Perhaps you would like to solve it for yourself before you read on.

Don't cheat. Before I tell you, figure it out. I hope you'll be able to solve the puzzle faster than I did.

It was purely a linguistic problem. The language was a tiny one: a language with two symbols, Up-Arrow and Down-Arrow, and meanings for each. On all other floors there were two buttons, one with each of the two symbols, giving you two choices of what to say. But on the restaurant floor, just one, with Down-Arrow.

My error (I really am far too literal and not nearly intuitive enough in these matters) was to think of the two symbols as conveying propositions, something like "I wish to make an upward journey in this elevator" and "I wish to make a downward journey in this elevator." So it took me a relatively long time to see how I could make an upward journey.

I actually trotted down one flight of stairs and took the elevator from there before I realized my ludicrous error. I would have done better to regard both Up-Arrow and Down-Arrow as signalling nothing more than a peremptory instruction to make the elevator come to me. Things would have been basically fine then. But with my propositional semantics for the buttons, it seemed to me that I couldn't express what I wanted to say.

Under my construal of the button meanings, I actually needed to lie: I needed to tell the machine I wanted to go down, when really I was planning to go up. That seemed so dishonest that I never considered it. But of course, lying to machines isn't really defined. It's like the way you have to go to the Start button on Windows XP systems in order to shut the machine down: it's not a lie, it's just a use of a stupidly labeled button. Once you summon the elevator and get in, you can go up to level 5 just as easily as you could down to street level like the non-hotel-guest restaurant users would.

I don't really understand why they put only a Down-Arrow button on level 1. Or to put it another way, if the buttons just mean "Bring the elevator to me" then I don't really understand why they have two buttons on any of the floors. But what I do understand is that I was thinking too propositionally (too intelligently is the way I'd like to see it). If I had hit the Down-Arrow button on level 1, when I got in the elevator I could have just pressed the button for level 5, and up I would have gone (unless someone had called it to level 0 and it was intent on going down there first; but that happens occasionally even on floors with there are two buttons, depending on what's happening on other floors and whether there are lights indicating the direction of the elevator's current journey — people keep emailing me to tell me this is true, but I know that, I already said it).

The elevator, of course, wasn't classifying me as a person who had got on at level 1 and must therefore not be allowed to go up. It would (probably) take me wherever I wanted to go. If I had just thought of Down-Arrow not as meaning "I wish to go down" but as meaning "Get me the damn elevator", everything would have been simple.

There is probably a lesson here about design of systems with buttons or about nerdview. But I haven't quite figured out in detail what the lesson is.

(Update: People have been writing to tell me I ought to test the system empirically by trying to go up from level 1 after a press of the Down-Arrow button. Well, I've now done that, twice, and the results are inconsistent. The first time, on January 24, to my amazement, the elevator just wouldn't go up. It paused, as if thinking about my request to go to the 5th floor, and then the doors reopened. Another closing of the doors, another push of the level 5 button, and the doors opened once more. I couldn't get from the restaurant level up to the guest rooms. I began to feel I was not so stupid, and the button did indeed mean "Take me down." However, the staff at the reception desk on level 0 refused to believe the results of my experiment. Usually, they insisted, the elevator does indeed go up. They seemed to think it was a sporadic failure: I was just unlucky. So on January 25, after breakfast, I tested it again. And this time the elevator went up, meaning that the button simply called the elevator without imposing any conditions on direction of travel. So now I feel once again that I was stupidly over-literal in originally thinking that pressing the button would be the wrong thing to do.)

[Comments open only for those going down to the lobby.]