  There is a parallelism between growth in arithmetic combinatorics and growth
in a geometric context. While, over $\mathbb{R}$ or $\mathbb{C}$, geometric
statements on growth often have geometric proofs, what little is known over
finite fields rests on arithmetic proofs. We discuss strategies for geometric
proofs of growth over finite fields, and show that growth can be defined and
proven in an abstract projective plane -- even one with weak axioms.
