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To the flat-man, clairvoyance in space would consist in that power of perception which we exercise in reference to his plane. From the third dimension the boundaries of plane figures offer no impediment to the view of their interiors, and they themselves in no way impede our vision of surrounding objects.
Because we lack the sense of four-dimensional space, we must here have recourse to analogy, and assume three-dimensional space to be the unsensed higher region encompassing a world of two dimensions, To a hypothetical flat-man of a two-space, any portion of his plane surrounded by an unbroken line would constitute an enclosure.
No mechanistic explanation will serve to account for this order of clairvoyance since it is inextricably involved in the mystery of consciousness itself. Yet our already overworked analogy can perhaps cast a little light even here. To the flat-man, the third dimension of objects passing through his plane translates itself to his experience into time.
By continual dwelling upon the predicament of the flat-man, naked, as it were, to observation from an eye which looks down upon his plane, we come to realize our own exposure. In that large world all that we think, or do, or imagine, lies open, palpable; there is no such thing as secrecy.
Suppose such indeed to be the case: that the flat-man on the moving picture screen leads his little life of thought and emotion, related to the mental and emotional life of the living original as the body is related to its photographic counterpart. In similar manner the potencies of the higher self, the dweller in higher spaces, may flow into and express themselves in and through us.