(Two geeks are waiting for the elevator on the seventh floor of a seven-story building. The elevator ascends to five and then begins to descend.)
Geek 1: I hate when people do that.
Geek 2: Yeah. Why should they care where the elevator’s going when they’re getting out anyway?
Geek 1: If they have to press a button, they might choose four at least. That would make sense.
Geek 2: Not so fast. If we disregard the intra-building trips — which are probably negligible in a residential building — then half of the elevator trips will originate from the first floor and the other half will start at floors two through seven, randomly distributed.
Geek 1: OK, I see where you’re going with this…
Geek 2: So, if we take a sample of twelve trips according to the expected distribution, six will originate from the first floor, and one each from floors 2 through 7, which comes to [sums 2 through 7 using Gauss’s trick] 27 + 6 is 33, divided by 12, so in fact the optimal floor for the elevator to rest at, to minimize its travel time, is less than 3.
Geek 1: Immaterial, since floors are integral. But wait a second. Who on the second floor is going to use the elevator anyway?
Geek 2: Good point. So if we remove the second floor then we’ll add the floors for ten random trips, 5 + 25, divided by 10, looks like the third floor even.
Geek 1: No way it could be less than the third floor.
Geek 2: You live on seven. That sounds like special pleading.
Geek 1: Anyway the whole calculation is off. People tend to leave in the morning and return at night, therefore the optimal floor for the elevator is time-dependent…
Yes, it’s very, very sad.
How do you know my husband? And what’s he doing in New York in an elevator!?? And who’s that guy with him???
I have never participated in such a discussion about elevators.
I’ve thought about it, though.
I was once in a laboratory in Japan run by Otis Elevator. It was their job to think that way, while bowing.
I’ve always pondered the optimal elevator door closing time. Too fast and the door has to reopen possibly keeping it open longer than a slower door. Too slow and…
And those Citibank Building elevators…don’t get me started.
I’ve had part of that conversation with myself — does that count?
i’ll have to second the dreadfulness of citibank’s offering. bill, i assume you are referring to that paired-up unidirectional (yet non-deterministic) elevator wannabe disaster. it drove me insane when i had a 6-month consulting gig there…
Well I have to disagree that no one uses the elevator to go to the second floor. In fact, I rarely see anyone on the stairs going to any floor at all.
does the good ole Hotel Coronado in San Diego still have the human operated elevator?
No, the person who operated it went insane listening to conversations like the one above.
Argh — I’ve had that conversation with myself, too. At least, I now know that I’m not alone…
Tes Alex, THOSE elevators. I hate the feel of stopping to let the top off when your own door doesn’t open. It is like getting caught on a chairlift.