In his 1982 book
Vision, David
Marr envisioned a research program for the field of vision research,
using a distinction between three complementary levels at which
information
processing systems may be described:
- The computational level, at which a
system's goal is described
- The algorithmic level, at which a
system's method is described
- The implementational level, at
which a system's means are described
Applied to the visual system or, more generally, to the cognitive
system, this distinction yields the following
differentiation
between topics of interest:
More specifically, for the cognitive system:
- The goal corresponds to the outcome of cognitive processes,
that is, to mental representations of incoming stimuli. At the
computational level of description, these representation are specified
in terms of systematicities in the system's output as a function of its
input.
- The method corresponds to the cognitive processes from
incoming stimuli to mental representations. At the algorithmic level of
description, these processes are specified in terms of the mechanisms
that transform the system's input into its output.
- The means correspond to the neural structures in which
cognitive processes manifest themselves by way of changes in activation
state. At the implementational level of description, these changes are
specified in terms of the hardware of the system.
Marr's point was that the levels of
description
should all be taken equally seriously, to arrive eventually at a
comprehensive theory consisting of three complementary
descriptions
which, together, explain "how the goal is reached
with a method that
is
allowed by the means".
Marr's distinction between the three levels of description has
stimulated
integrative theoretical research. It is useful not only
to specify the position of scientific findings in the total field
of cognitive (neuro)science, but also to
check whether seemingly opposed
theories
perhaps yet say compatible things at merely different levels of
description.
The latter is particularly relevant in view of the often unnecessary
heated discussions in cognitive (neuro)science between:
- Representational approaches, which typically use the
computational level as their operation base.
- Connectionist approaches, which typically use the
algorithmic level as their operation base.
- Dynamic system approaches, which typically use the
implementational level as their operation base.
Roughly, representational approaches propose that cognition involves
operations to get structured mental representations, connectionist
approaches propose that it thrives on interactions between bits of
information, and dynamic system approaches propose that it is mediated
by changes in neural activity. That is, these approaches indeed focus
on different aspects of cognition, but these are in fact complementary
aspects, and if one looks beyond the differences in the tools they use
to investigate these aspects, then the conceptual commonalities seem to
prevail.
For instance, all three approaches tend to trace their origin back to
the early 20th century Gestaltist ideas about cognition and about
vision in particular. The founding fathers of Gestalt psychology, Max
Wertheimer (1880--1943), Wolfgang Köhler (1887--1967), and
Kurt Koffka (1886--1941), argued that vision involves a complex
interaction between autonomous rules of perceptual organization. They
captured this in their motto
"the whole is something else
than the sum of its parts" (Koffka, 1935, p. 176), and
they proposed the Law of Prägnanz as governing principle. This
law expresses the idea that the brain, like any physical system, tends
to settle in stable states. Applied to vision, Koffka (1935, p. 138)
formulated this as follows:
"Of several geometrically
possible organizations that one will actually occur which possesses the
best, the most stable shape".
This seminal Gestaltist idea is implemented in many representational, connectionist, and dynamic systems
approaches --- even though, related to the different levels of
description, they use different scientific tools to implement
this idea.
The distinction between, and the complementarity of, the three levels
of
description may not always be clear-cut in cognitive (neuro)science,
but
the next three examples from other domains may clarify the relevance of
this distinction further:
- First, the names of the three levels (i.e., computational, algorithmic,
and implementational) clearly
were triggered by the rise of computers. Computer progammers are well
aware
of the problem to compute things (level 1) with an
algorithm (level 2) that runs on hardware (level 3).
- Second, the distinction between goal, method,
and means, is much older than computers and has a
much broader applicability; for instance, in the kitchen:
Peter
A. van der Helm 
