  We point out that if spatial information is encoded through linear operators
$X_i$, or `infinite-dimensional matrices' with an involution $X_i^*=X_i$ then
these $X_i$ can only describe either continuous, discrete or certain "fuzzy"
space-time structures. We argue that the fuzzy space structure may be relevant
at the Planck scale. The possibility of this fuzzy space-time structure is
related to subtle features of infinite dimensional matrices which do not have
an analogue in finite dimensions. For example, there is a slightly weaker
version of self-adjointness: symmetry, and there is a slightly weaker version
of unitarity: isometry. Related to this, we also speculate that the presence of
horizons may lead to merely isometric rather than unitary time evolution.
