coordinates fixed on a momentary line of sight (which makes the volume
retinocentric), and where each distinguishable point in the volume is assigned
‘color’ values of hue, brightness, and saturation. In effect, one ends up with a
map of the finest color–space discriminations of which the human visual system
is capable at a moment. This map can be used to describe ‘what is seen at a
moment’ in color and spatial terms, for any normal human organism. All that is
required is a specification of the ‘input’ values for the retinal array. The theory
provides a much finer-grained description of the colors and (retinocentric)
spatial positions than does anything like “red surface there now.” Generally,
the science of vision can produce much better descriptions of qualia – rather, of
possible total qualia spaces at a moment – than can the color and position terms
of natural languages. It does not, of course, describe colors and experience of
space “from the inside”–whatever that might mean. But given what it can do,
that surely does not matter, and for any serious work on “what one can see,”
it does – or aims to, when complete – do as well as humans are likely to be able
to do.
Chomsky’s linguistics has much the same aim: given an I-language specifi-
cation of a person’s lexicon at a time,
33
plus parameter settings, it is possible (in
principle) to specify the set of linguistically expressible “perspectives” that that
I-language has to offer. That is, it is possible to map “ what can be meant” (in the
linguistic technical sense of “ mean”–i.e., possible SEMs. Naturally, that is a
long way off, but it does indicate what the ultimate aim of a computational
theory in another faculty aims towards. There is an important difference
between SEM-mappings and retinocentric space color-volume mappings:
in a way, the visual mapping does capture possible experiences, while SEM-
mappings remain out of touch of consciousness. Both represent, however an
‘output’ level of a system, and the theory of the system says what they can be.
It is certainly no fault of Descartes that he did not offer anything like a
complete computational theory of vision – any more than that it was his fault
that he did not anticipate Newton. But he did, I think, begin to move in what we
now think of as the right direction. For one thing, he realized that vision
depended on processing that can and must be represented mathematically; he
was on the way to a computational theor y. Second, on the determination of
visual depth, he made a crucial observ ation: the visual system utilizes ocular
convergence measurem ents (it utilizes much more, but this is a central contri-
bution). He came to this view, in part, by noting that the blin d can tell the
distance from them of some object – that is, judge depth – by using a couple of
sticks that they hold in front of them that touch at their tips. They – or, surely,
their minds – calculate the distance from the angle that their hands and con-
verging sticks subtend. Descartes also noticed that the eyes converge more
when a person looks at a nearby object and less when it is further away. Noting
the parallel betw een what the blind do and what the eyes ‘do,’ he drew the
Introduction to the third edition 47