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 $L>0$.

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?

Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.

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• Barney

Ooh, I get the dP/dt one, does that mean I’m in the club?

Haven’t got the L>0 yet, but if it were 0<L<n then I can think of a well-known saying, what do you say Mr Beveridge?

• Colin

That’s a different one to the one I have in mind!

• Christian Lawson-Perfect

$(\forall t \in \mathbb{R}, \exists n : f(t) = f(t+n) )\implies f(t-n) = f(t)$

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