In the Fukanzazengi, Dogen says that the secret of zazen is non-thinking [hishiryo]. This is neither thinking [shiryo] nor not thinking [fushiryo].
By way of comparison, we can examine non doing. In the Chinese tradition there is wu wei, the watercourse way. Just as the water will respond appropriately to its environment, in non-doing we act appropriate to our actual situation, and that acting comes from a position of non-dualism, not ego. It is spontaneous fitting action.
Applying that to non thinking, we can envisage a state whereby thought is liberated from thought, language is liberated from language and the world, liberated from both, becomes vivid and alive. And this liberated thought and liberated world are no longer separate.