  We describe a method for counting maps of curves of given genus (and variable
moduli) to $\Bbb P^2$, essentially by splitting the $\Bbb P^2$ in two; then
specialising to the case of genus 0 we show that the method of quantum
cohomology may be viewed as the 'mirror' of the former method where one splits
the $\Bbb P^1$ rather than the $\Bbb P^2$, and we indicate a proof of the
associativity of quantum multiplication based on this idea.
