  We present the evidence for two conjectures related to the twistor string.
The first conjecture states that two super-Calabi Yaus -- the supertwistor
space and the superambitwistor space -- form a mirror pair. The second
conjecture is that the B-model on the twistor space can be seen as describing a
4-dimensional gravitational theory, whose partition function should involve a
sum over ''space-time foams'' related to D1 branes in the topological string.
