I think the whole question of meaning in music is difficult enough even if you hear me playing live right now in the same room! What I mean and what you take from it may be two quite different things anyway.
Actually John, Paul Rutherford, and Trevor Watts, and several other rather well known English jazz musicians had got their training by joining the Air Force, which was a pretty standard way for people to get some kind of musical education in those days.
Certain kinds of speed, flow, intensity, density of attacks, density of interaction... Music that concentrates on those qualities is, I think, easier achieved by free improvisation between people sharing a common attitude, a common language.
Improvisation is a compositional method.
A kind of synthesis, but with some elements that perhaps you wouldn't have expected in advance. I always like that when that happens, when something comes that is more than the sum of the parts.