The following is the handout that accompanied a paper presented at the December 2001 Messina conference on Horizons in Complex Systems. Currently it presents the basic concepts only. It proposes that one key idea constitutes the key to understanding the brain, namely the fact that abstractions are possible. The particular abstractions relevant to particular aspects of nature define the designs that are capable of handling these aspects of nature. The task of explaining the brain thus reduces to an investigation of the abstractions, the relevant interrelationships, and the corresponding design components.
A more detailed account of some aspects of the ideas presented in this talk can be found in the overheads for an earlier talk entitled The Relevance of Mathematics to Brain Functioning.
This paper is concerned with understanding how
the highly complex structure that is the human brain is able to
accomplish advanced skills such as using language. Of the
existing approaches to understanding nervous system functioning, one
important one is that of experimental studies of brain and behaviour,
and another that based upon computational models of neural networks
(e.g. Elman et.
al). Neither offers insights
into the subtleties of skills such as language, the former because
neural circuitry can account for such behaviour in qualitative terms
only, and the latter because the behaviour that it has been practical
to simulate involves only rather basic aspects of linguistic
behaviour and not at all clear how significantly more complex aspects
of language are to be modelled. A third approach is that
of Minsky's society of
mind, which involves discussion of ways
in which neural networks could emulate the kinds of behaviour
exhibited by conventional computer programs. Such programs
are able to model complexities of behaviour to a certain extent, but
the approach suffers from two drawbacks, firstly in that conventional
computer programs do not provide a good model for brain processes
generally, and more seriously in that the developmental processes
which lead to the acquisition of skills are discussed in the model
only to a very limited degree.
The following approach, inspired mainly by the ideas of workers such
as Baas (hyperstructures and the observer mechanism),
Ehresmann and
Vanbremeersch (relational aspects) and
Karmiloff-Smith (experimentally motivated concepts such as
domain-relevant activity and representational redescription), has a
very different character. It focusses on the relevance of
abstractions and relationships to matters of design. A
simple illustration is provided by Ohm's law, V = IR, where V, I and
R denote the voltage across a resistor, the current through it and
the resistance respectively. Here the entities symbolised
by V, I and R are abstract entities in a scheme embodying one
relationship, namely that specified by Ohm's law. A
physical resistor that satisfies Ohm's law provides a realisation of the
abstract scheme. Designs make extensive use of
realisations of abstract schemes such as resistors and
microprocessors since they can utilise the properties that such
systems possess by virtue of being such
realisations. Properties associated with realisations of
particular abstract schemes conversely feature in explanations of
designs; in practice, labels or descriptive accounts are used to
indicate that particular schemes apply.
In cases such as that of a resistor, the fact that a given
abstractional scheme applies is known through experiment or physical
theory, but in the microprocessor case it is known through logical
inference, the properties of the components in accord with the
schemes that are assumed to apply to them implying the properties of
the whole. Thus in a reductionist analysis, 'conformance
to an abstractional scheme' is something that propagates upwards and
allows us to infer in appropriate cases how highly complex systems
should behave. Ensuring that such inferences are valid is
the essence of design, which consists of a list of abstractional
schemes, combined with a specification of the mechanisms that ensure
conformance to them.
The same ideas apply equally well, but in a less rigorous sense and
as an idealisation, to biosystems. Like mechanisms, they
contain components of various kinds, each type conforming to some
scheme of abstractions that corresponds to our understanding of the
types of entities concerned. The design aspect consists of
the various mechanisms that help the systems concerned conform to
their particular abstractional schemes. Biosystems differ
from machines in that the entities concerned often lack a formal
specification, their properties being inferred from investigations of
instances of the entities concerned that are encountered in
nature. The inferences involved in going from one level of
description to another are similarly typically non-rigorous, being
based instead on a range of ideas justified in various
ways. What makes this a scientific process rather than
mere guesswork is that the various assumptions made are open to
experimental testing and, where appropriate, refinement and
replacement by a better account.
It is reasonable as a working hypothesis to postulate that
explanations of the same general character would apply equally well
to nervous system functioning. The implication is that the
nervous system, in its environment, is capable of being characterised
as a hierarchy of systems conforming to a
range of abstractional schemes, the design being
such as to cause the systems concerned to tend to conform to the
various schemes. This characterisation can be usefully
compared with conventional computing systems, which also depend on
systems that conform to specified abstract schemes, such as one
whereby sending a code for a character to the relevant system leads
to the character concerned being displayed on the
screen. The difference between the brain and the computer
is that in the case of the computer the systems concerned are defined
directly by the (compiled) program, whereas in the case of the brain
most of the systems conforming to given abstractions are created
through the process of development, the design thus determining the
details of the system indirectly, rather than directly as in the case
of a computer program.
The abstractions we are concerned with typically relate to particular
neural circuits or systems and their behaviour in a given
environment, and are thus similar to abstractions relating to
computer software. The existence of such systems,
logically interrelated in various ways leading to explanations of
complex behaviour, is our key assumption. Their existence
is taken to be the product of an effective design, consequent upon
the processes of evolution, embodying a range of generative systems
that themselves bring such derivative systems into existence in the
course of development or learning. Examples are generative
systems for acquiring the ability to maintain balance, for taking
steps, or for defining routes.
This assumption is similar to Karmiloff-Smith's concept of
modularisation, differences lying in the additional fact that here the
detailed design of the hardware concerned is taken here to be
governed by abstractional schemes, and also the idea that
modularisation can be effective at a number of levels. The
logic of the link between design and abstractional schemes is that
effective designs are grounded upon theory, while theories are
formulated within abstractional schemes. The multilevel
capabilities associated with abstractional schemes, on the other
hand, involve in essence the fact that one mathematical system can
contain entities on which another system can be based, just as when
for example we extract out of the set of all transformations the
subset consisting of all linear transformations, a collection that is
associated with mathematical schemes of its own. The
application to cognitive processes is that a developmental process
may have its eventual outcome 'target processes' subject to their own
simplifying abstractions. For example, one aspect of
learning to walk consists in learning how to walk directly to a
visible destination. This outcome has a particularly
simple abstract specification that can form the basis of higher
capacities such as going to a more distant location indirectly via a
series of intermediate destinations. The abstractional
scheme concerned with the latter is concerned issues as the direct
accessibility of one point on a sequentially defined route from the
previous one.
One can go into the question of design for a specified result more
deeply, while still talking in general terms, by noting (a) that the
links and neural processes in a neural circuit define relationships
while (b) that all relationships associated with a circuit are
determined by the basic relationships of (a). Changing one
of the basic relationships has a specified effect on all other
relationships, in principle allowing the existence of mechanisms for
creating a system conforming to some target condition in a systematic
way. The successful designs are ones that achieve
this.
The above is not intended as a statement as to what a successful
design is, rather it is a clarification of how successful designs
work, an essential to the understanding of how the concepts developed
here may be utilised to make sense of the complexities of the brain,
the key to the latter being to use the information available to
determine what are the abstractions on which are based the various
components of the design.
Finally, we return to the issue with which we began, that of the
processes associated with language, where it is controversial whether
there are specific mechanisms for language (the nativist claim,
connected with the existence of linguistic universals), or whether
language abilities come about as a result of general learning
mechanisms in an environment where language is present (the
constructivist hypothesis), or some intermediate
hypothesis. The present picture leads us to hypothesise
that the design of the brain is linked to a number of abstractions
related to language, use of which facilitates development of the
capacity to use language. There is a connection with the
work of Pinker, who
discusses regularities of language related to its effectiveness, and
proposes that innate mechanisms mediate these
regularities. We also make use of Karmiloff-Smith's
concept of representational
redescription (RR), and begin our
account within that framework, according to which information is
represented in a number of different formats at different times, a
more advanced format coming into play subsequent to a more elementary
one having been mastered in the given context. This idea
can be usefully related to the abstraction of equivalence, whereby
different means may be available for representing the same
information, which differ from each other in regard to particular
characteristics and in the ways in which they may be used.
In Beyond Modularity, Karmiloff-Smith discusses in considerable detail how
the RR scheme can be related to observations of
development. In the following we focus instead in very
general terms how it can be related to the functioning of
language. An important concept is the following: from an
existing representation A, valid in situation S, there may be
developed a different but provisionally equivalent alternative mode
of representation B. The data a and b in representations A
and B are related within some abstractional scheme, which defines the
design of the system that generates b from a. This system
may include a part that verifies the equivalence of A and B according
to the scheme. One may then try to find something in a new
situation S', a', say, which is operationally equivalent to b in the
new situation (and so indirectly equivalent to a). Thus
with appropriate criteria for equivalence it may be possible to adapt
the action in situation S to a new situation. The same
representation b applies to both activities so it may be regarded as
a generalisation.
Thus activity is developed on to a more abstract plane. It
may be extended over time to the activity of planning, where one
develops processes at the B level that are equivalent to those at the
A level. Equivalence can then be used to try out a process
at the B level before enacting it at the A level.
Such processes can now be envisaged at a more subtle level, C say,
where the representations are of a more symbolic character, including
in particular symbols for relationships. In other words,
relationships which were explicit at say the B level are indicated in
accord with an associated token at the C level. The
explicit-symbolic relationship is itself an abstraction that can
determine the design of circuitry to implement it. Such
more abstract representations can be investigated for their utility
and used to expand the possibilities further.
Language is a more subtle level again, characterised by the fact that
it involves coding processes, or equivalently procedures for defining
equivalence, that can be adapted to needs. The system
derives it power from the fact that it embodies a range of options
for linking strings of signs to various powerful representations at
other levels. The development of a language is in essence
the trying out of various possibilities with the exploration of what
they can do. One possibility is simply the assignment of a
name to something, and another the linkage of particular forms at the
language level to forms at other levels according to a specific rule,
these two being the main basis of the expressive power of language
according to Pinker. These processes can be accommodated within
particular abstractional schemes related to universal grammar, which
determines what kind of neural circuitry could implement such
schemes.
In more detail, language is assumed to be based upon the equivalence
of information represented as language and information expressed in
other levels. Equivalence is a matter both of definition
(and the operations of the brain's translation mechanisms for
determining equivalence) and of the pragmatics of language as a
communication. In other words, language use presupposes
that a listener will generate an equivalent and be predisposed to act
as if the information came from a different source, this providing a
test for whether the translation was done correctly. In
other words, correct translation should generate an 'idea' that fits
the demands of the current situation.
The question now is whether such ideas are sufficient to generate
something like language as it occurs naturally. This
requires in particular correct syntactic analysis and the creation of
the appropriate corresponding data structures. The answer
that one would hope for would be the case is along the following
lines. A language system (or more accurately the users'
linguistic processes) defines certain equivalences that form the
basis of its use. Comparatively simple cases allow users
to determine which equivalences are part of the language and build up
their own translation systems (on the basis of mechanisms adapted to
the various kinds of abstractions involved in the
equivalence). Through the use of devices such as working
memory, these systems can handle complex language equally well, but
increased complexity brings more risk of error. But
language users adapt their use of the relevant systems so as to
minimise the risk of error, thereby continually increasing the
possibilities of the language system. These considerations
apply equally to pragmatic use of language (the use of language to
achieve particular goals) and to the complexities of the language
system itself.
A technical aspect of language is the conversion from linear strings
to hierarchical structures which, as is well known, is connected with
the ability to detect a valid group and 'iconise' it as a single
entity, forming a node of a tree. This detection is based
on pattern detection, itself utilising categories, some of which
appear to be innate. Innate categories are in principle
expected on in the present picture, assuming that they feature in
some of the abstractional schemes, thus being expected to have
correlates in the neural hardware.
This completes our discussion, which is of a tentative
character. A principle has been established involving
general connections between abstractions and design. Since
abstractions of many kinds appear to feature in how we perceive and
understand the world, and the organisation of the nervous system
appears to reflect such abstractions, it is tempting to see this as a
fundamental principle behind the workings of the brain, exploitation
of which will radically advance our detailed understanding of how it
works.
Baas, N.A. (1994); Emergence, Hierarchies and Hyperstructures; Artificial Life III (ed. C.G. Langton, Addison-Wesley (pp. 515-537).
Ehresmann, A.C. and Vanbremeersch, J.-P. (1987); Hierarchical Evolutive Systems: a Mathematical Model for Complex Systems; Bulletin of Mathematical Biology; Vol. 49, No. 1 (pp. 13-50).
Elman, J.L., Bates, E.A., Johnson, M.H., Karmiloff-Smith, A.; Paresi, D. and Plunkett, K. (1996); Rethinking innateness: A Connectionist Perspective on Development, MIT Karmiloff-Smith, A. (1992); Beyond Modularity: a Developmental Perspective on Cognitive Science, MIT.
Karmiloff-Smith, A. (1992); Beyond Modularity: a Developmental Perspective on Cognitive Science, MIT.
Minsky, M. (1987); The Society of Mind; Heinemann.
Pinker, S. (1994); The Language Instinct: the New Science of Language; Penguin.
I am grateful to Professors Nils A.
Baas and Andrée Ehresmann for numerous discussions which
assisted in the formulation of the above ideas.
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