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:
"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 them 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...."
2. Facilitating understanding
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, 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 specifiedset 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."
3. Towards conceptual models of requisite complexity
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:
"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 yet 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 mind. 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 the 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 big gains in the substantive scientific areas are going to come when somebody invents new abstractions which can only be represented in computer graphical form."
The availability of devices to restructure information in this way would seem to offer some hope that insights could emerge which respond more adequately to the recorded complexity of societal structure, whilst at the same time being more easily comprehensible to the uninitiated - because of the ease with which such devices can be used as educational tools to develop understanding and comprehension of the same structural data from which the research insights are being derived. Such displays of course lend themselves to videotape recording for wider distribution.
4. Implications of computer augmentation of intellect
There are important intellectual implications emerging from work on advanced computer systems. Still of particular interest is the early work of Douglas Engelbart's team at the Center for Augmentation of Human Intellect (Stanford Research Institute) as the nodal point of the US ARPA Data Network (linking the computers of major universities in the USA). Engelbart worked on the means of creating an "intellectual workshop" to facilitate interaction between conceptual structures. He considers that:
"Concepts seem to be structurable, in that a new concept can be composed of an organization of established concepts and that aconcept 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 be 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 structuring has immensely greater potential for accurately mapping a complex concept structure than does a structure an individual would find it practical 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 favoured 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 were incorporated into the design of an operational computer system that it was hoped to develop so that it would 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 and ease of comprehension. This vehicle gives you a flexible method for separating, as it were, the woods from the trees."
5. Application to the world problem complex
Application of this kind of technology to an understanding of the world problem complex has not been attempted. As explained above, such devices offer a means of developing improved conceptual (and associated organizational) structures to contain the complexity with which humanity has to deal at this point in time. Of vital importance is the ability of these devices to portray the information in a more meaningful (or "iconic") form than emerges from conventional quantitative studies. This is particularly important in communicating with the informed public but specially so with the policy-making community.
As Harold Lasswell notes: "Why do we put so much emphasis on
audio-visual means of portraying goal, trend, condition, projection, and
alternative? Partly because so many valuable participants in decision-making
have dramatizing imaginations...They are not enamoured of numbers or of
analytic abstractions. They are at their best in deliberations that encourage
contextuality by a varied repertory of means, and where an immediate sense
of time, space, and figure is retained."
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