My dad, who is a mathematician (or rather a statistician), occasionally reads this blog so partly for his amusement I thought I’d share the following vaguely mathematical thought I’ve had lately.
I heard on the radio about a scheme devised to cheer school children up in January to help them through the post Christmas lull. Every child would anonymously write a note to another child complimenting them on all the positive things about them. Phew (sucks air through teeth), I thought, as I heard this. This will be a tricky thing to manage. In mathematical terms, assuming each child only makes one card, that means you have a 1 to 1 function, but what you really need here is an ‘onto’ function. It might cheer people up to make positive cards, but it will matter more to receive one. Or rather, it would make children unhappy if they didn’t get one. If you let children pick who they will give the cards to, some children might get two or more cards and some none at all. An each child gives a card function is a 1 to 1 function. An each child gets a card function is an onto function. A bijection is a function that is both, which is what the poor teachers will have to ensure applies: that each child gives a card and each child gets one.