Three types of bacteria are used in the production of Emmental: Streptococcus thermophilus, Lactobacillus helveticus, and Propionibacterium freudenreichii. Historically, the holes were a sign of imperfection, and until modern times, cheese makers would try to avoid them. Emmental cheese is used in a variety of dishes, particularly in gratins, and fondue, where it is mixed with Gruyère.
“We have to split up… in case somebody better comes along!”
Either from our own real life or from popular culture and the media, we’ve all come across a statement like that. It’s rarely quite so brazen: instead, it’s sometimes concealed behind another reason, whether tactful or simply false. But it still reeks of a lack of commitment and an unwillingness to “give it a try.”
However, it turns out that there’s actually a solid mathematical basis for it. Let’s assume for a moment that you:
- Engage exclusively in monogamous relationships. To each their own, I suppose.
- Are seeking for a relationship that will last indefinitely (e.g. traditional monogamous marriage, “’til death do us part,” and all that jazz).
- Can’t or won’t date your exes.
- Can rate all of your relationships relative to one another (i.e. rank them all, from best to worst)?
- Can reasonably estimate the number of partners that you will have the opportunity to assess over the course of your life. You can work this out by speculating on how long you’ll live (and be dating!) for, and multiplying, though of course there are several factors that will introduce error. When making this assumption, you should assume that you break up from any monogamous relationship that you’re currently in, and that no future monogamous relationship is allowed to last long enough that it may prevent you from exploring the next one, until you find “the one” – the lucky winner you’re hoping to spend the rest of your life with.
Assuming that all of the above is true, what strategy should you employ in order to maximise your chance of getting yourself the best possible lover (for you)?
It turns out that clever (and probably single) mathematicians have already solved this puzzle for you. They call it the Secretary Problem, because they’d rather think about it as being a human resources exercise, rather than a reminder of their own tragic loneliness.
A Mathematical Strategy for Monogamy
Here’s what you do:
- Take the number of people you expect to be able to date over the course of your lifetime, assuming that you never “settle down” and stop dating others. For example’s sake, let’s pick 20.
- Divide that number by e – about 2.71828. You won’t get a round number, so round down. In our example, we get 7.
- Date that many people – maybe you already have. Leave them all. This is important: these first few (7, in our example) aren’t “keepers”: the only reason you date them is to give you a basis for comparison against which you rate all of your future lovers.
- Keep dating: only stop when you find somebody who is better than everybody you’ve dated so far.
And there you have it! Mathematically-speaking, this strategy gives you a 37% chance of ending up with the person who – of all the people you’d have had the chance to date – is the best. 37% doesn’t sound like much, but from a mathematical standpoint, it’s the best you can do with monogamy unless you permit yourself to date exes, or to cheat.
Or to conveniently see your current partner as being better than you would have objectively rated them otherwise. That’s what love will do for you, but that’s harder to model mathematically.
Of course, if everybody used this technique (or even if enough people used it that you might be reasonably expected to date somebody who did, at some point in your life), then the problem drifts into the domain of game theory. And by that point, you’d do better to set up a dating agency, collect everybody’s details, and use a Stable Marriage problem solution to pair everybody up.
This has been a lesson in why mathematicians shouldn’t date.
As you may have noticed, the English-speaking Wikipedia is “blacking out” in protest at SOPA/PIPA. This is a very important thing: SOPA/PIPA are potentially extremely dangerous bits of legislation (if you’re looking for a short explanation of why, here’s a great video).
I’m going to assume that you’re aware of the issues and have already taken action appropriate to your place – if you’re in the US, you’ve written to your representatives; if you’re in the rest of the English-speaking world, you’ve donated to the EFF (this issue affects all of us), etc. But if you’re in need of Wikipedia, here’s the simplest way to view it, today:
And if you just came here for the shortcut without making yourself aware of the issues, shame on you.
How did I get here?
Thankfully, there’s always the back button: famously the second most-used bit of your web browser’s user interface. So… how did I come to be reading about torsion springs?
- I got there from reading about torsion pendulum clocks. My grandmother used to have one of these (an “anniversary clock”, like the one above, and I remember that I used to always enjoy watching the balls spin when I was a child).
- I’d followed a link from the article about the Atmos clock, a type of torsion pendulum clock that uses minute variations in atmospheric temperature and pressure to power the winder and which, in ideal circumstances, will never need winding.
- Before that, I’d been reading about the Beverly Clock, a classic timepiece that’s another example of an atmospheric-pressure-clock. It’s been running for almost 150 years despite having never been wound.
- This was an example of another long-running experiment given on the page about the Oxford Electric Bell, which is perhaps the world’s longest-running scientific experiment. Built in 1840, it uses a pair of electrostatic batteries to continuously ring a bell.
- I got to the Oxford Electric Bell from another long-running experiment – the one acknowledged as the world’s longest-running by the Guinness Book of Records – the University of Queensland Pitch Drop Experiment. Running since 1927, this experiment demonstrates that pitch is not solid but a high-viscosity fluid. A sample of room-temperature pitch in a funnel forms a droplet about once a decade.
- Earlier, I was learning about the difference between the different substances we call tar. Traditionally, tar is derived by baking pine wood and roots into charcoal, and collecting the runoff, but we also use the word “tar” to describe coal tar (a byproduct of coke production) and bitumen (viscous, sticky crude oil).
- I took the initiative to learn about those differences after reading about the name “Jack Tar“, an Empire-era slang term for a sailor in the Merchant Navy or Royal Navy…
- …which in turn was linked from the similar article about “Tommy Atkins“, a term for a British infantryman (particularly in the First World War), which has an interesting history…
- …to which I got from the “Doughboy” article. The Doughboys were members of the American Expeditionary Force during the First World War.
- Finally, I got to that first Wikipedia article while, when reading an article on The Paleofuture Blog, I wondered about the etymology of the term “doughboy”, and began this whole link-clicking adventure.
It’s fascinating to work out “how you got here” after an extended exploration of a site like Wikipedia (or TV Tropes, or Changing Minds, or Uncyclopedia – and there goes your weekend…). Thank you, Back Button.
I just wish I had a Back Button in my head so that I could “wind back” my wandering thought processes. How did I end up thinking about the salt content of airline food, exactly?