Calculating endless love!

Iain JohnstonA light-hearted research project has shown that children named Vivian, Connor and Evie may have been the most lucky in love this Valentine's Day - at least according to popular schoolyard lore. You may be familiar with the "Love Calculator" game, played in playgrounds across the world, which calculates a love score based on the letters in players' names. Dr Iain G Johnston a Birmingham Fellow in the School of Biosciences, used maths and computer simulations to show how and why this game sometimes loops or continues forever ("endless love") and identified the UK children's names most likely to achieve high scores. 

Download the full paper from the Cornell University Library

endless-love-mathsThe "Love Calculator" game is played in playgrounds and online across the world. It computes a playful "love compatibility" by first writing down the counts of l's, o's, v's, e's and s's that appear in two partners' names, then repeatedly adding numbers written next to each other until a percentage score is found -- "Alice loves Bob 54%!" (11010 -> 2111 -> 322 -> 54).

The project found that any point in the game can be described as a point in a mathematical "space", and that each step in the game moves a point in different ways, like different pieces on a chessboard. While individual outcomes are hard to predict, the average behaviour shows patterns that are repeated over games. The space contains a "cliff"; if moves carry a game over the cliff, it will continue forever.

Different patterns of the "loves" letters give different expected scores. Among the most common childrens' names in the UK, Connor has the highest expected score of 67%, with Evie, Holly, Lola, Molly and Olivia also scoring highly. Names with no "loves" letters -- from Adam to Ryan -- have the lowest expected score of 26%. The most successful names have a middling number of "loves" letters, between 2 and 6. Pairs of o's, several l's, and an absence of some other letters seem to be the key to success -- though a full theory of which patterns give which scores "remains elusive".

"Endless love: On the termination of a playground number game" is due to appear in Recreational Mathematics Magazine and is available at http://arxiv.org/abs/1602.03556 .