# Mathematical Dingbats

When I was growing up, we had a game called Dingbats - it would offer a sort of graphical cryptic clue to a phrase and you’d have to figure out what the phrase was. For example:

West Ham 4-1 Leicester City Chelsea 4-1 Man Utd Liverpool 4-1 Man City Everton 4-1 Newcastle Utd Sunderland 4-4 Stoke City

… might represent the Musketeers’ cry of “All 4-1 and one 4-all!” I loved that game.

Some time later, in discussion with @ajk_44 and @realityminus3, we came up with the idea of Maths Dingbats - instead of graphical clues, mathematical ones. I’ve lost the conversation, but to give an idea of the flavour of it:

- Let $P$ be the population. Then $\diff{P}{t} = 60 \unit{sec}^{-1}$.
- Suppose you play $n$ games and lose $L$ of them. Then $L>0$.

(Please don’t spoil them in the comments.)

I was particularly pleased - briefly - with $\diffn{2}{y}{t} < 0$ for “what goes up must come down.”

### But wait!

That’s no good: a negative second derivative doesn’t imply there will ever be a turning point! (Case in point: let $y= \ln(t)$, so that $\diff{y}{t}=\frac{1}{t}$ and $\diffn{2}{y}{t}=-\frac{1}{t^2}$; the second derivative is negative for all $t>0$, but the first derivative is never zero).

So… I suppose my challenge to you is: can you come up with a better dingbat for that saying? Or for another one?