  Conventional wisdom holds that any region of 3-space contains infinitely many
points, and the Planck length scale determines the uncertainty in every
measurement of distance between two separate points. Against such a backdrop,
this uncertainty may be interpreted as resulting from either foaminess or
discreteness of 3-space. But, as it is demonstrated in the present paper,
neither of those interpretations is consistent with the holographic principle.
In the paper it is shown that the statement ``The holographic principle holds
true'' and the statement ``Each region in 3-space contains only a finite number
of points'' are logically equivalent.
