This fourth post, long-awaited by two people, concludes a two-part post based on my having to watch Disney’s Cinderella roughly 17837 times. After a while, you start noticing the little things, or go mad, or both.
Like a Freudian psycho-analyst asking about mom, screens bring up issues for classical geneticists. Screens are what we do. Conceptually, screens are simple. In fact, they are like your screen door. The goal is start with everything and separate it into two groups – one that passes the screen and one excluded by the screen – based on a particular characteristic. Your screen door tries to do this based on size, letting in the breeze, but keeping out the flies, if everything is working well.
With screens, be they in the genetics laboratory or your back door, the devil is in the details. We need to worry about how well the screen works. If our screen door has holes in it or we are opening the door a lot, bugs are going to get in. If the screen is dirty, it might not let as much of the breeze through as we would like. We need to worry about whether we are actually screening for the characteristic we care about. Screen doors separate bugs from breeze based on size. They do not detect “bug” and zap it with a laser, because one house could not contain that much awesome.
I’m concerned that the King, Grand Duke, and Prince did not think through the details of their attempt to screen their female subjects for Cinderella – i.e., The Great Slipper Screen.
Their plan seems straight forward:
- We have a shoe.
- Find girl who fits shoe.
- Marry girl.
- Yada yada.
- Horsey rides on Grandpa King.
In reality, inasmuch as reality pertains to Disney’s Cinderella, their screen involves multiple steps that each have some risk of allowing people past that should have been screened out (false positive) or screening out people who should have been allowed to pass (false negative), as detailed in the detailed figure below:
Starting with all the women in the kingdom, they attempt to identify the subset of eligible maidens. We know that all the women in the kingdom cannot be eligible maidens as someone must have given birth to the eligible maidens. Therefore, they must screen for eligibility (social class and unmarried) and maidenhood. The film appears to rely entirely on the women declaring themselves to be eligible maidens for this test. It is quite possible that individuals who either not eligible or a maiden or both might lie to get through. Alternatively, an individual could be falsely accused of not being a maiden and be eliminated in error. The false positives could be screened out later when more rigorous testing could be efficiently applied to a much smaller number of individuals, but it is very hard to recover the false negatives.
This subset of eligible maidens may then get to try on the slipper. It is reasonable to think that not everyone in this set would actually get to try on the slipper. Some of them might not be home. I imagine that the eligible maidens have busy days, just like the rest of us. Some of them might be locked in towers by their Wicked Stepmothers. The Grand Duke does not seem to have a definitive list of who all the eligible maidens were. So, it is hard to see how they would know that they have tested the entire subset. This step posed a real threat of eliminating the only true positive (Cinderella) in error.
Similarly, the actual slipper fitting has chances of error. Given the motivation, the eligible maidens might be motivated to painfully cram their foot into the slipper to create the illusion that it fits (as Cinderella’s step-sisters try, with hilarious results). A night of dancing in glass slippers (not known for their cushioning or breathability) might have left Cinderella with sore and swollen feet that might not fit into such precisely shaped footwear the next day.
In addition, it seems quite improbable that Cinderella was the only eligible maiden in the entire kingdom whose foot would fit into the glass slipper. A great weakness in The Great Slipper Screen as presented on-screen is that they appear to call off the search after their first success, which means they do not actually screen the entire subset of eligible maidens. If the first person to fit the slipper had not been Cinderella, they may have missed her entirely or the Prince could have married the wrong girl. This design flaw was mitigated in practice by Cinderella possessing the other glass slipper.
Having found a girl whose foot fits the glass slipper, we need to confirm her identity with the Prince. This depends on how well the Prince remembers her. I know, what am I saying? He loves her. Of course he remembers her. Maybe. Personally, I’m concerned about how much the Prince may have had to drink at this party. Amongst my friends, professions of undying love and adoration after a few hours of dancing only occur in the presence of amounts of alcohol that are severely debilitating to short-term memory. If the Prince had been drinking at his party (and back then everyone drank, because normal water was infested with DOOM! and cholera), his memory might be imprecise allowing someone who is not Cinderella through. He might also use the booze as an excuse to reject Cinderella and get out of his father pressuring him to get married.
At each step in The Great Slipper Screen, there is a plausible and non-zero chance of both false positive and false negative errors. Due to the urgency with which the screen was implemented, it was clear that these issues were not carefully considered. While they were quite likely to find an eligible maiden by this method, it seems that finding the eligible maiden was more about being lucky than good. Fortunately, the King, Grand Duke, and Prince were able to independently fund this screen, because it would never have made it through a grant review board, especially with today’s success rates.
- Issues of an entirely different in nature, we swear, STOP ASKING ABOUT IT ALREADY!
- Especially if we live in Missouri in the summer when it is 95F with 95% humidity and is not raining, everything is just sweating. And you have rugby practice.
- Granted that bug zapping lasers creates a whole raft of false positive/false negative issues of their own.
- Look, I know I called it The Great Slipper Test in earlier posts. I changed my mind. I’m mercurial. Deal.
- The totalitarian kingdom could have had a shockingly high mortality rate amongst mothers due to labor even for Medieval Europe, but the fact that people are not shocked that the Wicked Stepmother survived giving birth twice suggests that surviving labor was not rare. Cinderella’s biological mother, however, may have been lost during childbirth.
- I prefer not to think about the potential testing for maidenhood, especially in a Disney film, but it appears that they were operating on the honor system at this stage.
- But, let’s say you are interested. A betting man might Google image search for “Disney Cinderella ‘Rule 34′” with the safe search option turned off. Just saying. Perv.
- If the Wicked Stepmother was really trying to be vindictive and block Cinderella’s chances of marrying the Prince, this probably would have been a better tactic than breaking the glass slipper. Of course, it would have been smarter to try to make nice with Cinderella, but that is another blog post.
- Quite rightly, the folks at Disney made the risk of this false negative error the dramatic culmination of the film.
- Though one might note that it was impossible for them to verify that she had the matching slipper as the test slipper was destroyed. All we know is that Cinderella possessed a glass slipper.
- It is better to be lucky than good, for small values of N.