For the purposes of field computation, a field is defined to be a spatially continuous distribution of quantity. Field computation is then a computational process that operates on an entire field in parallel. Often we treat the field as varying continuously in time, although this is not necessary.
It is sometimes objected that distributions of quantity in
the brain are not in fact continuous, since neurons and even
synapses are discrete. However, this objection is
irrelevant.
For the purposes of field computation, it is necessary only
that the number of units be sufficiently large that it may be
treated as a continuum, specifically, that continuous
mathematics can be applied.
There is, of course, no specific number at which the ensemble
becomes ``big enough'' to be treated as a continuum; this is
an issue that must be resolved by the modeler in the context
of the use to which the model will be put.
However, since there are 146 000 neurons per 
throughout most of the cortex (Changeux 1985, p. 51), it is
reasonable to say that activity in a region of cortex more
than a square millimeter in size can be safely treated as a
field.
Mathematically, a field is treated as a continuous, usually
real-valued, function 
over some continuum 
, its
domain or extent.
For example, if 
is a circular disk representing the
retina, then for any point 
, 
might be
the light intensity at p.
The field's domain has some topology (relations of
connectivity and nearness); for example, the topology of the
retina is a two-dimensional continuum.