Spontaneity by-passes the processes of the conceptual (aspect of) mind.
Our ubiquitous error lies in mistaking concepts for reality, for instance our idea of a body - which is only an idea - for an actual body. There is absolutely no reason to suppose that the reality it may have bears any resemblance to our concept.
That which we perceive is a projection and not a thing-in-itself. That, surely, is what the Buddha meant when he told us, in the Diamond Sutra, that we should not cherish the notion of things having intrinsic qualities or not having intrinsic qualities - for 'qualities', or their absence, are notions, concepts, projected on to 'things'.
Spontaneity is no more under 'our' control than is our blood-pressure, but by understanding the unreality of concepts in general and of the body-concept in particular the way for spontaneity should be laid open.
But spontaneity is clearly the aim of the Zen Masters and is the explanation of almost everything recorded of them in word or in act.
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Reintegration with Nature, which we are, is the recovery of spontaneity.