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Ben Goertzel

Psychology Department

University of Western Australia

My goal in this brief speculative essay is (quite modestly, as usual) to hypothesize a unifying principle for psychological pattern recognition and formation. I call this principle "form-enhancing distance distortion," or FEDD. Intuitively speaking, FEDD may be thought of as a special kind of "curvature of mental space." FEDD, I will argue, may be observed in perception, cognition and social psychology. It also fills a theoretical gap in my own system-theoretic model of mind.


Theoretical psychology is fragmented to a remarkable extent. The concepts used to model perception are by and large completely different from those used to model personality, which in turn are different from those used to model cognition, etc. While there are bound to be significant differences between different aspects of mental process, it seems likely that there is more underlying commonality than current theory reveals.

Two examples will serve to illustrate this point (if indeed it needs illustration). First: memory. While cognitive psychologists tend to speak in terms of memory systems, the cognitive neuroscientists tell us that memory, as an independent entity, does not exist. The brain does not store inactive "memory tokens"; it contains active processes, which construct the neural activity patterns we interpret as memories, and often do other things as well.

In a similar way, until very recently, perceptual psychologists tended to speak of perceptual processing systems as independent modules. However, input from cognitive neuroscience has consistently contradicted this, and has taught us that much of vision processing (to name only the sense mode that has received the most attention) is based on interconnections with cognitive, motor and emotional centers of the brain.

In one case after another it is revealed that, what psychologists model as separate systems operating under their own principles, are actually carried out by the brain in an interconnected and unified way. This fact has led several researchers to construct general "systems theories" of mental process, emphasizing the interconnectedness and the self-organizing nature of the mind/brain. My own "psynet model" falls in this category, as does Kampis's component-systems model, and the Abrahams' dynamical-systems psychology.

From the point of view of psychology, however, these system-theoretic models are perhaps excessively general (my own model is no exception here). They speak of the general structure of mental systems, rather than of what is particular to human intelligence. Thus it is of interest to extend these models in a more concrete and definite direction, by looking for general principles of human mental function.

One such principle, I believe, is curvature of mental space, in the specific version that I call FEDD.


FEDD applies wherever one has a mental process P that is responsible for judging the degrees by which other mental processes differ. This process P may be distributed or localized. P's judgement of the difference between x and y will be denoted d_P(x,y). (Note that this function d_P need not necessarily satisfy the property of symmetry, nor the triangle inequality.)

FEDD states that, over time, process P's judgement of distance will change in a specific way. Namely, for each x, the distance d_P(x,y) will decrease by an amount which reaches its maximum at a certain finite distance F. To use a physics metaphor, each element x pulls the other elements y closer to it, but the maximum amount of attraction is experienced at distance F. This process of adjustment does not continue forever, but will dwindle after a finite period of time. When new entities are introduced to P, however, the process will be applied to the new entities.

What effect does the pull of x have on the distances between two entities y and z? It is not hard to see that, if y and z are sufficiently close to x, then their mutual distance is decreased; while, if y and z are at a moderate distance from x, their mutual distance is increased. The fabric of the space judged by P is thus distorted in a somewhat unusual way, similar to the way mass distorts space in General Relativity Theory.

What is the purpose of mental-space-distorting force, this FEDD? As the name suggests, it gives additional form to the processes judged by P. In particular, it enhances clusters. If a large number of processes are all close to each other, the distance adjustment process will bring them even closer. On the other hand, processes surrounding the cluster will tend to be pushed further away, thus making an "empty space" around the cluster. The net effect is to create much more clearly differentiated clusters than were there before. This may be verified mathematically and/or by computer simulations.

FEDD will not create significant structure where there was no structure before. However, it will magnify small structures into larger ones, and will "clean up" fuzzy structures. Furthermore, it acts in a form-preserving manner. For instance, if there is, instead of a circular cluster, a cluster in the shape of a line, then FEDD will enhance this cluster while retaining its line shape.

FEDD causes patterns to emerge from collections of processes. Thus it is both a pattern recognition process and a pattern formation process. To obtain more concrete characterizations of what FEDD does, it is necessary to look at the different areas of psychological function separately.


Here I will mention a few places where FEDD is, or may possibly be, useful in psychology. This is certainly not intended to be an exhaustive list.

3a. Perception

First, visual perception. According to a theory published by A.S. Watson in 1978, a FEDD-like process acting on monocular visual space can explain all the simple geometric illusions (Muller-Lyer, Poggendorff, Enclosure, etc. etc. etc.). Watson has lines acting on other lines and on "fictitious points," inducing a metric distortion equivalent to FEDD.

My own simulations indicate that FEDD can also serve to do some simple pre-processing operations in vision processing. E.g., it fills in gaps in lines and shapes, and generally makes forms clearer and more distinguishable.

3b. Social Psychology

Lewin's theory of force fields in social psychology is well-known. Dirk Helbing, in his book "Quantitative Sociodynamics," has given a mathematical formulation of Lewin's theory in terms of diffusion equations.

Lewin and Helbing's force fields do not necessarily satisfy the form of FEDD. However, it would be quite possible to seek evidence that social fields do, in reality, satisfy this form.

For instance, I contend that individuals tend to:

1) overestimate the similarity of individuals in their own social group to one another

2) underestimate the similarity between individuals in their group and individuals "just outside" their group

If this is true (and it may well have been proven already; I don't know the social psych literature), it provides evidence that individuals' measures of interpersonal distance obey the FEDD principle.

Intuitively speaking, FEDD would seem to provide a very neat explanation for the formation of social groups, meta-groups, and so on.

3c. Cognition

There would seem to fairly strong evidence for something like FEDD in the areas of concept formation and categorization. A "concept" is just a cluster in mental-form space; a collection of mental forms that are all similar to each other. Things which we have grouped together as a concept, we tend to feel are more similar than they "really" are. Differences between entities in the concept grouping, and entities outside, are overestimated. This is FEDD.

As in the case of perception, here FEDD serves to create structure, and also to cause errors. According to Mark Randell, cognitive errors created in this way should perhaps be called a "cognitive illusion," by analogy to perceptual illusions.

Another possible relationship is with our tendency to make systematic errors in reasoning by induction. Human beings tend to jump to conclusions: as a rule, we are overly confident that trends will continue. This may be seen as a consequence of bunching previously seen situations overly close together, and putting new situations in the bunch.


How does FEDD relate to other ideas about the mind/brain? As it turns out, it relates naturally to neural network models (going down a level), and to the my abstract "psynet" model of mind (going up a level).

First for neural networks. Working in the context of visual illusions, Mike Kalish and I have worked out a connectionist system that gives rise to FEDD dynamics. The system uses two phases, one of spreading activation, and the next of nonlinear filtering. The two phases are repeated in sequence, a finite number of times, to yield the result of a form-enchancing distance distortion. Among other possibilities, the system could be implemented as a two-level recurrent neural network (representing, speculatively, two layers of cortex).

Next, for the psynet model. The psynet model, as I have presented it on this listserver before, is as follows,

1. Minds are "magician systems" residing on graphs (magicians are entities that act on each other to produce other magicians; they are a special class of computational "agents")

2. The magicians involved are "pattern/process" magicians (the way they act on each other is primarily to recognize patterns)

3. Thoughts, feelings and other mental entities are "structural conspiracies," i.e. autopoietic attractors of the mind magician system

4. The structural conspiracies of the mind join together in a complex network of attractors, meta-attractors, etc.

5. This network of attractors approximates a fractal structure called the "dual network," which is structured according to at least two principles: associativity and hierarchy.

Where FEDD fits in here is at the final stage: the hypothesized emergence of the "dual network."

The dual network is a network of processes which is simultaneously structured according to associative memory (similar things stored "near" each other) and hierarchical control (elements obtaining information from, and passing instructions to, lower-level elements). The only way to combine hierarchy and associativity is to have a "fractal" or recursively modular structure of clusters within clusters within clusters.... Each cluster, on each level, is a collection of related entities, which is govered implicitly by its own global attractor. It is this global attractor which carries out the hierarchical control of the smaller-scale attractors of the entities making up the cluster. This sort of structure has been instantiated in a neural network by David Alexander.

FEDD is a method for inducing and enhancing clusters; it explains how the dual network might emerge in the first place. Each pattern/process P in the hypothesized mind magician system induces its own distance measure: namely, d_P(x,y) is the amount of structure that P recognizes in x but not y, or in y but not x. Here structure can be defined in a number of ways, e.g. by algorithmic information theory. The emergence of the dual network in the mind magician system is explained by the assumption that these distance measures are updated in the manner prescribed by FEDD.

This idea has interesting implications for human memory. Not only does FEDD explain the nature of concept formation within memory systems but, via the theory of the dual network, it explains the formation of memory systems themselves. What psychologists call separate memory systems are just different clusters in the overall dual network. The clusters all have smaller clusters within them, which is why, having begun to divide memory into separate systems, memory researchers keep coming up with more and more and more different subsystems, subsubsystems, etc. It may be that some of this clustering is there from birth (e.g. episodic versus semantic memory, perhaps). But FEDD could enhance this innate clustering, and help along the more refined clustering that comes along with experience.