Wednesday, December 10, 2008

A mathematical solution to the door holding problem

It seems strange that such a simple custom as holding a door open for someone should cause as much trouble and confusion as it does. It started out as a highly gendered, benevolent sexist activity (men holding doors for women). Later, feminists began to reject the door holding custom along with many other benevolently sexist actions, leading many to refuse to allow a man to hold a door for them at all. More recently, door holding seems to be a relatively gender neutral activity, with women and men holding doors for each other, irrespective of gender. (Except in a dating context...)

So - common courtesy, or sexist holdover? To hold a door, or not to? I know almost nothing about etiquette, but the scientist part of me has come up with a rather different solution...


It seems to me, that the entire purpose of social courtesy is to work for the common good - to improve society a bit at your own expense, with the idea that the favor will be returned. So, correct door holding behavior must satisfy these criteria:

  1. It must contribute to the overall good of society - in this instance, it must decrease the collective walking time.

  2. It must not be biased or unfair toward any group.

Thus, that surprisingly large minority of men who still insist on holding doors for women immediately fail the second criteria - they can be dismissed offhand.

Some quick numbers: The distance in question is defined as the distance from the swing of the door, plus an equal area on the other side. It took me, walking at an average speed, around 2 seconds to traverse that difference on a typical door. It took twice as long (4 seconds) if I had to open the door toward me. It took almost no time longer if I had to open the door away from me - several trials averaged out to about .25 seconds.

Now, there are two different ways of holding a door:

  • Simply holding it after you, so that the other person does not have to open it, and

  • Holding the door while letting the other person pass through in front of you.

The latter option we can dismiss immediately. Even in the ideal case (the other person is exactly two seconds behind you), it takes 2 seconds to open the door, 2 seconds for the follower to pass through, and 2 seconds for you to pass through. 2+2+2=6. In the worst case, the other person might have to wait up to two seconds for you to get the door open and get out of their way, for a total of eight seconds. Of course, holding the door for someone farther away might take even more time. Thus, even those super-polite types who hold doors for everyone, are still not really helping society as a whole!

The former option, at best, only takes the same four seconds that one person would take. How long to hold the door open behind you? Maximum 2 seconds. Your total time comes to 4+2=6 seconds, and the other persons time is 2 seconds, bringing the total time to eight - the same time as two separate operations would take, with only half the effort.

Holding a door opening away from you is almost pointless - you could only hold it for 1/4 of a second!


The maximum benefit to walking time will come from holding a door open behind you for approximately two seconds. Just don't open a door, count "one, two", and let it shut in someone's face - people might not like that! Certainly, don't hold the door and let someone walk through unless they are disabled or carrying something - there is no overall benefit otherwise.

Following these guidelines, you can still be polite and help people without feeling like your actions are derived from sexist tradition.

(If you have actually managed to read this far, congratulations - you are almost as weird as I am! I do have an excuse - CS class was really, really boring, and I couldn't exactly leave, so I wrote this instead! Crossposted on Constant Thoughts)

1 comment:

Anonymous said...

You made my day. I think that's the funniest thing I've read all week.