1973
Representation of Concepts and Augmentation of Intellect
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Originally appeared in 1973 as part of Toward
a Concept Inventory
Representation of concept networks using graph theory
Use of interactive graphic display techniques
Implications of computer augmentation of intellect
Relationship to artificial intelligence projects
Representation of concept networks using graph theory
This project is concerned with the collection of entities and the indication
of relationships, if any, between those entities. Expressed in these general
terms, the techniques of graph theory may be used in this project. Graph theory
is concerned with the "arcs" (links or relationships) between "nodes"
(entities) and the various structural properties of the network so constituted.
It can be of great assistance in dealing with a broad range of combinatorial
problems which occur in various economic, sociological or technological fields.
It is, perhaps, that aspect of the theory of sets which can produce the most
fruitful results not only for the pure mathematician, the engineer, and the
organizer, but also for the biologist, the psychologist, the sociologist and
many others. Graphs can be used to represent structures such as: a network of
roads, an electrical circuit, communication in a group, a complex chemical molecule,
circulation of documents in an organization, kinship structures, etc.(13, 14)
Its use in connection with relations between more abstract social entities
such as organizations and nations is much less frequent (15-20). Its use for
handling psycho-social abstractions appears to be even rarer (21).
The image of a 'network or web of ideas' to represent a complex set of interrelationships
in a sphere of knowledge, and particularly culture, is a fairly familiar one.
This use of 'network', however, is purely metaphorical and is very different
from the notion of a network of concepts as a specific set of linkages among
a defined set of concepts, with the additional property that the characteristics
of these linkages as a whole may be used to interpret the semantic significance
of the concepts involved.
Some features of concept networks
Points 1 to 3 below are concerned with the shape of the network, 4 to 8 with
interactions within the network.
1. Centrality. A measure (in topological not quantitative terms) of the
extent to which a given theoretical entity (e.g. a concept) is directly or indirectly
"related" via links to other entities i.e., the extent to which it
is "distant" from another entity. One can speak of a "key"
concept or of a concept being "central" to the concerns of a particular
discipline. It may also be considered a measure of the degree of "isolation"
of the entity. A systematic analysis of the centrality of theoretical entities
could indicate where new concepts are necessary to bridge conceptual gaps and
link isolated domains.
2. Coherence. A measure of the degree of "interconnectedness,' or
'density" of a group of concepts. This may be considered as the degree
to which a system of concepts is "complete". Differences in density
would reflect the tendency for more highly coherent concept systems to appear
more self-reinforcing in comparison to less organized parts of the network.
In some respects this is an indication of the degree of "development"
of a group of concepts.
3. Range. Some concepts are directly related to many other concepts,
others to very few. The range of a concept is a measure of the number of other
entities to which it is directly related. Range could be considered an indication
of the "vulnerability" of a concept, to the extent that a high range
concept would be less vulnerable to attack than a low range concept, since it
has more bonds anchoring it to its semantic environment. High range points are
therefore either key points in resistance to conceptual change or else key points
in terms of which orderly change can be introduced.
4. Content. The "content" of a relationship between entities
is the nature or reason for existence of that relationship. In general, different
relationship contents are required for each model. Simple graphs have only one
link between any two entities: multigraphs have two or more links, each of different
content.
5. Directedness. A relationship between two entities may have some "direction"
i.e., A to B. or B to A. There may be several types of directedness. The most
important for this project is probably: A "is a subset of" B. i.e.,
directedness points to the more fundamental concept of a pair. In a multigraph,
one link may point from A to B and the other from B to A -- where each is more
significant in terms of different content.
6. Curability. A measure of the period over which a certain relationship
between entities is activated and used. At one extreme, there are the links
activated only on a "one-shot" basis (e.g. a "trial balloon"
ideal, at the other there are links, and sets of links, which are considered
stable over centuries (e.g. the concepts associated with "property").
7. Intensity. A measure of the strength of the link or bond between two
entities. Two concepts may be said to be "strongly bound together".
In some models, the intensity is a measure of the amount of the "flow"
or "transaction" between the entities. The link from A to B may be
strong, and that from B to A, weak.
8. Frequency. A link between two entities may only be established intermittently.
This measure is less significant to this project (except perhaps in cyclic approaches
to the history of ideas or to the activation of concepts over a 24 hour period.)
9. Rearrangeability and blocking. A connecting network is an arrangement
of entities arid relationships allowing a certain set of entities to be connected
together in various possible combinations. Too suggestive properties of such
networks, which are extensively analyzed in telephone communications (22) are:
- rearrangeability: a network is rearrangeable, if alternative paths car,
be found to link any pair of entities by rearranging the links between other
entities.
- blocking: a network is in a blocking state if some pair of entities cannot
be connected.
Examples of types of network patterns
Some of the above features of networks of concepts (or other entities) may
be illustrated by the set of diagrams in Figure 5. Each entity is represented
by a letter of the alphabet. Four simple types of entity groups are shown. Each
type is further distinguished if the relationships between entities are directed.
a) In the non-directed examples of group (1), A is the central concept
in (1.3), A and D in (1.4], A and F in (1.23. In (1.1l, there is no central
concept.
b) In group (1), peripheral concepts are D and C in (1.2); B. C, E and
F in (1.3); B. C and F in (1.4). There are no peripheral concepts in (1.1).
c) In group (1), the range of A in (1.3) is 4, in (1.4) it is 3.
d) In group t1), the reachability of A in (1.1) and (1.2) is 3, in (1.3)
it is 1, and in (1.4) it is 2.
e) In all the directed examples of group (2), ~ is the central concept
with at least B and F as direct component concepts. In all except (2.3), there
are even sub-sub-components of A.
f) In all the directed examples of group t3), A is the central concept
but only as a common sub-component. O is also a common sub-component in t2.13.
g) In all the directed examples of group (43, there is a chain of component/
sub-component links. In (4.1), this is continuously forming a loop. In (4.2)
and t4.4), C is the major concept. in (4.33, A is the central concept but
only by having F and t as sub-components and being itself a common sub-component
to B and C.
The above features are all evident, almost to the point of being trivial. But
most cases of interest are likely to be much more complex, with many nested levels
of concepts and cross-linking relationships. These may be examined by matrix analysis
techniques, particularly using computers (to which the proposed record layout
is suited) (23-26). Computer programs exist to detect properties of networks.
A more complex example is illustrated by Figure 6. There is shown the manner
in which two different models or conceptual structures might interlink the
same concepts to form two very different patterns - which may be analyzed.
Use of interactive graphic display techniques
Description
The suggestion has been made (see previous section) that structuring the relationship
between theoretical entities (concepts, propositions, problems, etc.) could
best be accomplished using graph theory methods. There are three disadvantages
to this approach:
- graphic relationships are tiresome and time-consuming to draw (and are
costly if budgeted as "art work").
- once drawn, there is a strong resistance to updating them (because of the
previous point) and therefore they quickly become useless.
- when the graph is complex, multidimensional, and carries much information,
it is difficult to draw satisfactorily in two dimensions. The mass of information
cannot be filtered to highlight particular features - unless yet another diagram
is prepared.
These three difficulties can be overcome by making use of what is known as
"interactive graphics" (27). This is basically a TV screen attached
to a computer. The user sits at a keyboard in front of the screen and has at
his disposal what is known as a light-pen (or some equivalent device) which
allows him to point to elements of the network of concepts displayed on the
screen and instruct the computer to manipulate them in useful ways. In other
words the user can interact with the representation of the conceptual
network using the full power of the computer to take care of the drudgery of
- drawing in neat lines
- making amendments
- displaying only part of the network so that the user is not overloaded
with
- "relevant" information
In effect the graphics device provides the user with a window
or viewport onto the network of concepts. He can instruct the computer, via
the keyboard, to:
1. move the window to give him, effectively, a view onto a different
part of the network - another conceptual domain
2. introduce a magnification so that he can examine (or "zoom
in" on) some detailed sections of the network
3. introduce diminution so that he can gain an overall view of the
structure of the conceptual domain in which he is interested
4. introduce filters so that only certain types of relationships and
entities are displayed - either he can switch between models or he can impose
restrictions on the relationships displayed within a model, i.e. he has a
hierarchy of filters at his disposal.
5. modify parts of the network displayed to him by inserting or deleting
entities and relationships. Security codes can be arranged to that (a) he
can modify the display for his own immediate use without permanently affecting
the basic store of data, (b) he can permanently modify features of the model
for which he is a member of the responsible body, (c) and so on.
6. supply text labels to features of the network which are unfamiliar
to him. If necessary he can split his viewport into two (or more) parts and
have the parts of the network displayed in one (or more) part(s). He can then
use the light pen to point to each entity or relationship on which he wants
a longer text description (e.g. the justifying argument for an entity or the
mathematical function, if applicable, governing a relationship, and have it
displayed in an adjoining viewport.)
7. track along the relationships between one entity and the next by
moving the viewport to focus on each new entity. In this way the user moves
through a representation of "semantic space" with each move, changing
the constellation of entities displayed and bringing new entities and relationships
into view.
8. move up or down levels or "ladders of abstraction". The
user can demand that the computer track the display (see point 7) between
levels of abstraction, moving from sub-system to system, at each move bringing
into view the semantic context of the system displayed.
9. distinguish between entities and relationships on the basis of user-selected
characteristics. The user can have the "relevant" (to him)
entities displayed with more prominent symbols, and the relevant relationships
with heavier lines.
10. select an alternative form of presentation. Some users may prefer
block diagram flow charts, others may prefer a matrix display, others may
prefer Venn diagrams (or "Venn spheres" in 3 dimensions) to illustrate
the relationship between entities. These are all interconvertible (e.g. the
Venn circles are computed taking each network node as a centre and giving
a radius to include all the sub-branches of the network from that node).
11. copy a particular display currently on the screen. A user may
want to keep a personal record of parts of the network which are of interest
to him. (He can either arrange for a dump onto a tape which can drive a graph
plotter, a microfilm plotter, or copy onto a videocassette, or, in the future,
obtain a direct photocopy.)
12. arrange for a simultaneous search through a coded microfilm to provide
appropriate slide images or lengthy text which can in its turn be photocopied.
13. simulate a three-dimensional presentation of the network by introducing
an extra coordinate axis.
14. rotate a three-dimensional structure (about the X or Y axis) in
order to heighten the 3-D effect and obtain a better overall view "around"
the structure.
15. simulate a four-dimensional presentation of the network by using
various techniques for distinguishing entities and relationships (e.g. "flashing"
relationships at frequencies corresponding to their importance in terms of
the fourth dimension.)
16. change the speed at which the magnification from the viewport
is modified as a particular structure is rotated.
17. simulate the consequences of various changes introduced by the
user in terms of his conditions. This is particularly useful for cybernetic
displays.
18. perform various topological analyses on particular parts of the
network and display the results in a secondary viewport (e.g., the user might
point a light-pen at an entity and request its centrality or request an indication
of the interconnectedness of a particular domain delimited with the light
pen.).
In every current use of interactive graphics there is some notion of geometry
and space, but the geometry is always the three-dimensional conventional space.
There is no reason why "non-physical spaces" should not be displayed
instead and this is the domain of topology. The argument has been developed
by Dean Brown and Joan Lewis (28).
"Both geometry and topology deal with the notion of space, but geometry's
preoccupation with shapes and measure is replaced in topology by more abstract,
less restrictive ideas of the qualities of things...Being more abstract and
less insistent on fine points such as size, topology gives a richer formalism
to adapt as a tool for the contemplation of ideas....
Concepts can be viewed as manifolds in the multidimensional variate space
spanned by the parameters describing the situation. If a correspondence is
established that represents our incomplete knowledge by altitude functions,
we can seek the terrae incognitae, plateaus, enclaves of knowledge, cusps,
peaks, and saddles by a conceptual photogrammetry. Exploring the face of a
new concept would be comparable to exploring the topography of the back of
the moon. Commonly heard remarks such as "Now I'm beginning to get the
picture" are perhaps an indication that these processes already play
an unsuspected role in conceptualization....
By sketching tentative three-dimensional perspectives on the screen and "rotating
thesis on the tips of his fingers", one internalizes ideas non-verbally
and acquires a sensation of sailing through structures of concepts much as
a cosmonaut sailing through constellations of stars.
Such new ways of creating representations break ingrained thought patterns
and force re-examination of preconceived notions. A mapping is a correspondence
is an analogy. Teaching by analogy, always a fertile device, can be carried
out beautifully by topological means....Topological techniques are useful
at even the most advanced levels of scientific conceptualization...."
The fundamental importance of interactive graphics, in whatever form, is its
ability to facilitate understanding. Progress in understanding is made through
the development of mental models or symbolic notations that permit a simple
representation of a mass of complexities not previously understood. There is
nothing new in the use of models to represent psycho-social abstractions. Jay
Forrester (29), making this same point with respect to social systems, states
"Every person in his private life and in his community life uses models
for decision making. The mental image of the world around one, carried in
each individual's head, is a model. One does not have a family, a business,
a city, a government, or a country in his head. He has only selected concepts
and relationships which he uses to represent the real system. The human
mind selects a few perceptions, which may be right or wrong, and uses them
as a description of the world around us. On the basis of these assumptions
a person estimates the system behaviour that he believes is implied....The
human mind is, excellent in its ability to observe the elementary forces and
actions of which a system is composed. The human mind is effective in identifying
the structure into which separate scraps of information can be fitted. But
when the pieces of the system have been assembled, the mind is nearly useless
for anticipating the dynamic behaviour that the system implies. Here the computer
is ideal. It will trace the interactions of any specified set of relationships
without doubt or error. The mental model is fuzzy. It is incomplete.
It is imprecisely stated. Furthermore, even within one individual, the mental
model changes with time and with the flow of conversation. The human mind
assembles a few relationships to fit the context of a discussion. As the subject
shifts, so does the model. Even as a single topic is being discussed, each
participant in a conversation is using a different mental model through which
to interpret the subject. And it is not surprising that consensus leads to
actions which produce unintended results. Fundamental assumptions differ but
are never brought out into the open."
These structured models have to be applied to any serially ordered data in
card files, computer printout or reference books to make sense of that data.
Is there any reason why these invisible structural models should not be made
visible to clarify differences and build a more comprehensive visible model?
The greater the complexity, however, the more difficult it is to use mental
models. For example, in discussing his examination of an electronic circuit
diagram, Ivan Sutherland writes (30):
"Unfortunately, my abstract model tends to fade out when I get a circuit
that is a little bit too complex. I can't remember what is happening in one
place long enough to see what is going to happen somewhere else. My model
evaporates. If I could somehow represent that abstract model in the computer
to see a circuit in animation, my abstraction wouldn't evaporate. I could
take the vague notion that "fades out at the edges" and solidify
it. I could analyze bigger circuits. In all fields there are such abstractions.
We haven't vet made any use of the computer's capability to "firm
up" these abstractions. The scientist of today is limited by his
pencil and paper and mired. He can draw abstractions, or he can think about
them. If he draws them, they will be static, and if he just visualizes them
they won't have very good mathematical properties and will fade out. With
a computer, we could give him a great deal more. We could give him drawings
that move, drawings in three or four dimensions which he can rotate, and drawings
with great mathematical accuracy. We could let him work with them in a way
that he has never been able to do before. I think that really trig gains
in the substantive scientific areas ore going to come when somebody invents
nets abstractions which can only be represented in computer graphical form."
Implications of computer augmentation of intellect
There are important intellectual implications emerging from work on advanced
computer systems. Of particular interest is the work of Douglas Engelbart's
team at the Center for Augmentation of Human Intellect (Stanford Research Institute)
which is the centre for the U.S. ARPA Data Network (which links the computers
of major universities in the U.S.A.) Engelbart has worked on the means of creating
an intellectual workshop to facilitate interaction between conceptual structures.
The following extracts are from Engelbart, D.C., Augmenting Human Intellect;
a conceptual framework. (32)., He considers that:
"Concepts seem to be structurable, in that a new concept can be composed
of an organization of established concepts and that a concept structure
is something which we might try to develop on paper for ourselves or work
with by conscious thought processes, or as something which we try to communicate
to one another in serious discussion....A given structure of concepts can
be represented by any of an infinite number of different symbol structures,
some of which would be much better than others for enabling the human perceptual
and cognitive apparatus to search out and comprehend the conceptual matter
of significance and/or interest to the human.
But it is not only the form of a symbol structure that is important.
A problem solver is involved in a stream of conceptual activity whose course
serves his mental needs of the moment. The sequence and nature of these needs
are quite variable, and yet for each need he may benefit significantly from
a form of symbol structuring that is uniquely efficient for that need.
Therefore, besides the forms of symbol structures that can de constructed
and portrayed, we are very much concerned with the speed and flexibility with
which one form can be transformed into another, and with which new material
can be located and portrayed.
We are generally used to thinking of our symbol structures as a pattern of
marks on a sheet of paper. When we want a different symbol-structure view,
we think of shifting our point of attention on the sheet, or moving a new
sheet into position.
With a computer manipulating our symbols and generating their portrayals
to us on a display, we no longer need think of our looking at the symbol structure
which is stored -- as we think of looking at the symbol structures stored
in notebooks, memos, and books. What the computer actually stores need be
none of our concern, assuming that it can portray symbol structures to us
that are consistent with the form in which we think our information is structured.
A given concept structure can be represented with a symbol structure that
is completely compatible with the computer's internal way of handling symbols,
with all sorts of characteristics and relationships given explicit identifications
that the user may never directly see. In fact, this struc turing has immensely
greater potential for accurately mapping a complex concept structure than
does a structure an individual would find it pr tical to construct or use
on paper .
The computer can transform back and forth between the two-dimensional portrayal
on the screen, of some limited view of the total structure, and the aspect
of the n-dimensional internal image that represents this "view". If the human
adds to or modifies such a "view", the computer integrates the change into
the internal-image symbol structure (in terms of the computer's favored symbols
and structuring) and thereby automatically detects a certain proportion of
his possible conceptual inconsistencies.
Thus, inside this instrument (the computer) there is an internal-image, computer-symbol
structure whose convolutions and multi-dimensionality we can learn to shape
to represent to hitherto unattainable accuracy the concept structure we might
be building or working with. This internal structure may have a form that
is nearly incomprehensible to the direct inspection of a human (except in
minute chunks)".
These insights have been incorporated into the design of an operational
computer system which is now being developed so that it will be possible
to use computer devices as a sort of:
"electronic vehicle with which one could drive around with extraordinary
freedom through the information domain. Imagine driving a car through a landscape
which, instead of buildings, roads, and trees, had groves of facts, structures
of ideas, and so on, relevant to your professional interests? But this information
landscape is a remarkably organized one; not only can you drive around a grove
of certain arranged facts, and look at it from many aspects, you have the
capability of totally reorganizing that grove almost instantaneously. You
could put a road right through the center of it, under it, or over it, giving
you, say, a bird's eye view of how its components might be arranged for your
greater usefulness arid ease of comprehension. This vehicle gives you a flexible
method for separating, as it were, the woods from the tiess." (33)
Clearly some possibilities of this system could be used to explore the concept
structures resulting from this project.
Relationship to artificial intelligence projects
In considering the possibility of coding definitions of concepts, propositions
and like entities, it is important to benefit as much as possible from related
work on artificial intelligence, and possibly pattern recognition. Artificial
intelligence projects to simulate human personality or belief systems have had
to develop methods and computer techniques which can handle and interrelate
entities such as concepts and propositions. Clearly the object of such projects
is not attained once an inventory of entities can be examined, even if it is
highly structured in the form of a thesaurus. It is therefore interesting to
look at both the techniques used to handle concepts and the types of computer
based interrogations that are then possible (34-37).
The suggestion that techniques of handling individuals' "beliefs" should have
some parallel to a community of scholars' attitudes towards the concepts, propositions,
etc., which constitute its territory, may appear somewhat provocative. Does
a school of thought constitute a belief system?
T.S. Kuhn (38) uses the terms "belief", "metaphysic", "commitment", and "conversion"
in connection with a scientific community's attitude towards a paradigm and
paradigm change. It might be useful for disciplines to examine their own conceptual
structures in the same way as an aid to the development of the discipline. It
could be particularly important as a means of highlighting tensions within the
conceptual structures which lead up to Kuhn's paradigmatic changes.
This approach suggests a number of stages of sophistication in the possible
development of this project.
- A static inventory of concepts and propositions
- A static network of interrelated concepts and propositions
- "Activation" of propositions as rules governing the relationships between
entities
- Treatment of a school of' thought as a belief system
- Extension to natural language interaction
On this last point, it may be possible to allow a (non-computer-oiiented)
specialist in a particular field to "dialogue" with the concept data base to
permit him to discover and indicate where he differs from its contents and what
new he thinks should be included (39). This approach might be a useful method
of getting around the behavioural problems associated with the power position
of official classifiers in committees.
It may eventually be possible to have many such people interacting in natural
language wi - th the data base via terminals to facilitate communication (e.g.,
at a special seminar).
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