Sunday, 15 January 2012

Match-making Age Ranges

Many years ago I was told that, "Half your age plus seven years is the girlfriend limit."

This immediately seemed both sexist and mathematically incompetent, but just as "Feed a cold, starve a fever" isn't medical advice, (it is reassurance for young mothers who are panicking that their feverish child isn't eating,) it is just a guide-line, ( or in that case -  a throw-away anecdote at some debutante party in London.)

What about those looking to date someone older? This guide can easily be reversed as, "Your age minus seven, doubled."

Mathematically, (where x is your age),

        lower_limit = (x/2)+7
     upper_limit = 2(x-7)

Some time later I was looking for mathematically significant differences between two numbers. This is an area of statistics where arguments are had over tea.

I found, on one rather well written site: (I did not bookmark it, sorry.)

      ( ( x - y ) / 2 ) ^2  

which might not look like much but I rather liked it. (Here y is "their age" for lower limit, and ^2 means "to the power of two" i.e. squared.)

It took a while, but eventually I made the connection between these two and the obvious next move was to graph them. I had already found, with a quick script, the intersection at 34 and 54 by hand, (once I noticed that the output of the two functions was not parallel, I had to search,) but somehow I had missed the one at 49, (see! this is why graphs are cool.)

(I was going to add a vertical line marking the age of consent, but that is a topic for another post.)

I have added some sudo-random labels on the graph, using gimp, so that I could refer to particular areas more easily, (see I'm thinking of you.)

The first thing that is worth noting is that the cougar limit, [yes, I typoed in the graph] and the sugar limit are not both straight lines. This is not due to some form of ageism or sexism, but is due to the use of an odd number in "half your age plus". If it was half your age plus six then they would both be straight.

We can see stepping in the two stats lines, (marked mathematically lower and upper). So the question there becomes, why are they stepping at 18, 24, 32, 40, 50, 60. [ I know that I have three errors in the graph: msl{18,32,50} should all be +1 ].
Are these square numbers? Is there something about their factors? How are they related?

The thing I like here is that when you take the output of the two simple equations that is nearest to x, (your age) you end up with a rectification of this old match-makers guide.
If you are a parent then you can explain to your daughter why, when she is sixteen, a twenty year-old boyfriend should only happen in porno-land, (and other fictitious realms.)

So who ends up in the perpetuity zone? If you imagine having a crush on an older film star, (say forty years-old) when you were younger, (e.g. twenty). By the time you are fifty they would be seventy. If you happened to be compatible when you meant thirty years later, they would be in the perpetuity zone, and in this case I could see people making exceptions, (humans being social creatures.)

Despite my choice of labels, I would recommend that everyone stay within the cradle-snatching:Tapping the Grave areas.

Technical details
Data generated using a bash script and bc.
Graph generated using cairo, Chart::Clicker and a perl script.

( The functionality of the bash script could be extended to calculate how long you would have to wait until someone entered the perpetuity zone. )

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