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Ben Goertzel
Department of Psychology
University of Western Australia
Nedlands WA 6009
Australia
In order to make strong AI a reality, formal logic must be abandoned in favor of complex systems science. Creative intelligence is possible in a computer program, but only if the program is devised in such a way as to allow the spontaneous organization of "self- and reality-theories." In order to obtain such a program it may be necessary to program whole populations of interacting, "artificially intersubjective" AI programs.
The march of progress toward true artificial intelligence has, in the opinion of many, come to a standstill. There has always been a tremendous gap between the creative adaptibility of natural intelligence and the impotent rigidity of existing AI programs. In the beginning, however, there was an underlying faith that this impotence and rigidity could be overcome. Today enthusiasm seems to be flagging. Very few AI researchers carry out research aimed explicitly at the goal of producing thinking computer programs. Instead the field of AI has been taken over by the specialized study of technical sub-problems. The original goal of the field of AI -- producing computer programs displaying general intelligence -- has been pushed off into the indefinite future.
We have sophisticated mathematical treatments which deal with one or two aspects of intelligence in isolation. We have "brittle" computer programs which operate effectively within their narrowly constrained domains. We have connectionist networks and genetic classifier systems which approach their narrow domains with slightly more flexibility, but require exquisite tuning, and still lack any ability to comprehend new types of situation. What we still do not have, however is a halfway decent understanding of what needs to be done in order to construct an intelligent computer program.
The goal of this paper is to suggest a simple answer for this "million dollar question." The principal ingredient needed to make strong AI a reality is, I claim, the self. A self is nothing mystical, it is a certain type of structure, evolving according to a certain type of dynamic, and depending on other structures and dynamics in specific ways. Self, I will argue, is necessary for creative adaptibility -- for the spontaneous generation of new routines to deal with new situations. Current AI programs do not have selves, and, I will argue, they do not even have the component structures out of which selves are built. This is why they are so rigid and so impotent.
The fashioning of computer programs with selves -- "artificial selfhood" -- is not a theoretical impossibility, merely a difficult technical problem. For one thing, it clearly requires more memory and processing power than we currently have at our disposal. When sufficiently large MIMD parallel machines are developed, we will be able to make a serious attempt at writing an intelligent program. Until that time, it is foolish to expect success at strong AI. Even with appropriate hardware, however, serious difficulties may well arise, related to the problem of bringing a new self to maturity without a real "parent." It may perhaps be necessary to resort to the evolution of populations of intelligences -- what has been called AI through A-IS or "artificial intersubjectivity." But these difficulties cannot be confronted or fully understood until we have appropriate hardware. Arguments about the possibility of strong AI, based on the results of experimentation on 1995 computers, have more than a small taint of absurdity.
The plan of the remainder of the paper is as follows. Section 2 clarifies certain issues regarding the possibility of strong AI and the assumptions underlying different approaches to AI. Section 3 introduces the psychological notions of self- and reality-theories. Section 4 presents an argument for the crucial role of self- and reality-theories in creative intelligence. Section 5 outlines a mathematical model which uses ideas from complex systems science to explain the self-organization of self from simpler psychological constructs. Finally, Section 6 discusses A-IS or "artificial intersubjectivity," a possible technique for evolving AI systems with artificial selves.
Before addressing the problems of AI, it is first necessary to establish what the problem of AI is not. It cannot be emphasized too strongly that there is no fundamental obstacle to the construction of intelligent computer programs. The argument is a simple and familiar one. First premise: humans are intelligent systems. Second premise: humans are also systems governed by the equations of physics. Third premise: the equations of physics can be approximated, to within any degree of accuracy, by space and time discrete iterations that can be represented as Turing machine programs. Conclusion: intelligent behavior can be simulated, to within any degree of accuracy, by Turing machine programs.
As I have pointed out in (Goertzel, 1993), this argument can be made more rigorous by reference to the work of Deutsch (1985).
Deutsch has defined a generalization of the deterministic Turing machine called "quantum computer," and he has proved that, according to the known principles of quantum physics, the quantum computer is capable of simulating any finite physical system to within any degree of accuracy. He has also proved that while a quantum computer can do everything an ordinary computer can, it cannot compute any functions besides those which an ordinary computer can run. However, quantum computers can compute some functions faster than Turing machines, in the average case sense and they have certain unique properties, such as the ability to generate truly random numbers.
Because of Deutsch's theorems, the assertion that brains can be modeled as quantum computers is not a vague hypothesis but a physical fact. One must still deal with the possibility that intelligent systems are fundamentally quantum systems, and cannot be accurately modeled by deterministic Turing machines. But there is no evidence that this is the case; the structures of the brain that are considered cognitively relevant (neurons, synapses, neurotransmitters, etc.) all operate on scales so large as to render quantum effects insignificant. This point is not universally agreed upon: Hameroff (1988) has argued for the cognitive relevance of the molecular structures in the cytoplasm, and (Goertzel, 1995c) has argued for a relation between consciousness and true randomness. Finally, Penrose (1986) has argued that, not only are brains not classical systems, but they are not quantum systems either: they are systems that must be modeled using the equations of a yet-undiscovered theory of quantum gravity. But all these arguments in favor of the non-classical brain reside in the realm of speculation. It is a physical fact that the brain is a quantum computer, and hence deals only with computable functions. And, given the physical evidence, it is at this stage a very reasonable assumption that the brain is actually a deterministic computer.
This conclusion, however, is of limited practical utility. It leaves a very important question open: how to find these programs that carry out intelligent behaviors! We do not know the detailed structure of the human brain and body; and even if we did know it, the direct simulation of these systems on man-made machines might well be a very inefficient way to implement intelligence. The key question is, what are the properties that make humans intelligent?
The most pessimistic view is that only systems very, very similar to the human brain and body could ever be intelligent. At present this hypothesis cannot be proven or disproven. As has been pointed out, however, it is somewhat similar to the proposition that only systems very, very similar to birds can fly. The difference is that, while we have recently learned how to build flying machines, we have not yet learned to build thinking machines.
On the other hand, it is possible that the key to intelligence lies in a certain collection of clever special-case problem-solving tools; or, perhaps in the possession of any sufficiently clever collection of special-case problem-solving tools. If this is the case then what AI researchers should be doing is to study small scale systems which are extremely effective at solving certain special problems. This, in fact, is what most AI researchers have been doing for the past few decades.
Finally, a third alternative is that the key to intelligence lies in certain global structures, certain overall patterns of organization. If this is the correct possibility, then the conclusion is that clever algorithms for solving toy problems are, while perhaps useful and even necessary, not the essence of intelligence. What matters most is the way that these clever algorithms are organized. This last point of view is the one adopted here. In particular, I wish to call attention to one particular "global structure," one particular overall pattern of organization: the self.
What is the self? Psychology provides this question with not one but many answers. One of the most AI-relevant answers, however, is that provided by Epstein's (1984) synthetic personality theory. Epstein argues that the self is a theory. This is a useful perspective for AI because theorization is something with which AI researchers have often been concerned.
Epstein's personality theory paints a refreshingly simple picture of the mind:
[T]he human mind is so constituted that it tends to organize experience into conceptual systems. Human brains make connections between events, and, having made connections, they connect the connections, and so on, until they have developed an organized system of higher- and lower-order constructs that is both differentiated and integrated. ...
In addition to making connections between events, human brains have centers of pleasure and pain. The entire history of research on learning indicates that human and other higher-order animals are motivated to behave in a manner that brings pleasure and avoids pain. The human being thus has an interesting task cut out simply because of his or her biological structure: it is to construct a conceptual system in such a manner as to account for reality in a way that will produce the most favorable pleasure/pain ratio over the foreseeable future. This is obviously no simple matter, for the pursuit of pleasure and the acceptance of reality not infrequently appear to be at cross-purposes to each other.
He divides the human conceptual system into three categories: a self-theory, reality-theory, and connections between self-theory and reality-theory. And he notes that these theories may be judged by the same standards as theories in any other domain:
[Since] all individuals require theories in order to structure their experiences and to direct their lives, it follows that the adequacy of their adjustment can be determined by the adequacy of their theories. Like a theory in science, a personal theory of reality can be evaluated by the following attributes: extensivity [breadth or range], parsimony, empirical validity, internal consistency, testability and usefulness.
A person's self-theory consists of her best guesses about what kind of entity she is. In large part it consists of ideas about the relationship between herself and other things, or herself and other people. Some of these ideas may be wrong; but this is not the point. The point is that the theory as a whole must have the same qualities required of scientific theories. It must be able to explain familiar situations. It must be able to generate new explanations for unfamiliar situations. Its explanations must be detailed, sufficiently detailed to provide practical guidance for action. Insofar as possible, it should be concise and self-consistent.
The acquisition of a self-theory, in the development of the human mind, is intimately tied up with the body and the social network. The infant must learn to distinguish her body from the remainder of the world. By systematically using the sense of touch -- a sense which has never been reliably simulated in an AI program -- she grows to understand the relation between herself and other things. Next, by watching other people she learns about people; inferring that she herself is a person, she learns about herself. She learns to guess what others are thinking about her, and then incorporates these opinions into her self-theory. Most crucially, a large part of a person's self-theory is also a meta-self-theory: a theory about how to acquire information for one's self-theory. For instance, an insecure person learns to adjust her self-theory by incorporating only negative information. A person continually thrust into novel situations learns to revise her self-theory rapidly and extensively based on the changing opinions of others -- or else, perhaps, learns not to revise her self-theory based on the fickle evaluations of society.
There is some evidence that a person's self- and reality-theories are directly related to their cognitive style. For instance, Erdmann (1988) has studied the differences between "thick-boundaried" and "thin-boundaried" people. The prototypical thick-boundaried person is an engineer, an accountant, a businessperson, a strict and well-organized housewife. Perceiving a rigid separation between herself and the outside world, the thick-boundaried person is pragmatic and rational in her approach to life. On the other hand, the prototypical thin-boundaried person is an artist, a musician, a writer.... The thin-boundaried person is prone to spirituality and flights of fancy, and tends to be relatively sensitive, perceiving only a tenuous separation between her interior world and the world around her. The intriguing thing is that "thin-boundaried" and "thick-boundaried" are self-theoretic concepts; they have to do with the way a person conceives herself and the relation between herself and the world. But, according to Erdmann's studies, these concepts tie in with the way a person thinks about concrete problems. Thick-boundaried people are better at sustained and orderly logical thinking; thin-boundaried people are better at coming up with original, intuitive, "wild" ideas. This connection is evidence for a deep relation between self-theory and creative intelligence.
My central thesis here is that the capacity for creative intelligence is dependent on the possession of effective self- and reality- theories. My argument for this point is not entirely an obvious one. I will argue that self- and reality- theories provide the dynamic data structures needed for flexible, adaptable, creative thought.
The single quality most lacking in current AI programs is the ability to go into a new situation and "get oriented." This is what is sometimes called the brittleness problem. Our AI programs, however intelligent in their specialized domains, do not know how to construct the representations that would allow them to apply their acumen to new situations. This general knack for "getting oriented" is something which humans acquire at a very early age.
People do not learn to get oriented all at once. They start out, as small children, by learning to orient themselves in relatively simple situations. By the time they build up to complicated social situations and abstract intellectual problems they have a good amount of experience behind them. Coming into a new situation, they are able to reason associatively: "What similar situations have I seen before?" And they are able to reason hierarchically: "What simpler situations is this one built out of?" By thus using the information gained from orienting themselves to previous situations, they are able to make reasonable guesses regarding the appropriate conceptual representations for the new situation. In other words, they build up a dynamic data structure consisting of new situations and the appropriate conceptual representations. This data structure is continually revised as new information that comes in, and it is used as a basis for acquiring new information. This data structure contains information about specific situation and also, more abstractly, about how to get oriented to new situations.
My claim is that it is not possible to learn how to get oriented to complex situations, without first having learned how to get oriented to simpler situations. This regress only bottoms out with the very simplest situations, the ones confronted by every human being by virtue of having a body and interacting with other humans. There is a natural order of learning here, which is, due to various psychological and social factors, automatically followed by the normal human child. This natural order of learning is reflected, in the mind, by an hierarchical data structure in which more and more complex situations are comprehended in terms of simpler ones. But we who write AI programs have made little or no attempt to respect this natural order.
We provide our programs with concepts which "make no sense" to them, which they are intended to consider as given, a priori entities. On the other hand, to a human being, there are no given, a priori entities; everything bottoms out with the phenomenological and perceptual, with those very factors that play a central role in the initial formation of self- and reality-theories. To us, complex concepts and situations are made of simpler, related concepts and situations to which we already know how to orient ourselves; and this reduction continues down to the lowest level of sensations and feelings. To our AI programs, the hierarchy bottoms out prematurely, and thus there can be no functioning dynamic data structure for getting oriented, no creative adaptability, no true intelligence.
This view of self and intelligence may seem overly vague and "hand-waving," in comparison to the rigorous theories proposed by logic-oriented AI researchers. However, there is nothing inherently non-rigorous about the build-up of simpler theories and experiences into complex self- and reality-theories. It is perfectly possible to model this process mathematically; the mathematics involved is simply of a different sort from what one is used to seeing in AI. Instead of formal logic, one must make use of ideas from dynamical systems theory (Devaney, 1988) and, more generally, the emerging science of complexity (Green and Bossomaier, 1994). In this section I will briefly outline one way of mathematically modeling the self-organization of the self, based on the psynet model of (Goertzel, 1993; 1993a; 1994; 1995; 1995a). The treatment here will necessarily be somewhat condensed; more extensive discussion may be found in the references.
The psynet model is based on the application of dynamical systems theory ideas to self-organizing agent systems (Agha, 1988). An intelligent system is modeled as a collection of memory- and algorithm-carrying agents, which are able to act on other agents to produce yet other agents. Following (Goertzel, 1994) these agents are called magicians. Cognitive structures are modeled as attractors of the magician-interaction dynamic. An hierarchy of nested attractor structures is postulated, culminating in the "dual network" of associative memory and hierarchical perception/control, and the "self- and reality-theory," a particular manifestation of the dual network.
I will adopt throughout this section a parenthesis-free convention for function application, as is found in the programming language Haskell (Hudak et al, 1992). According to this notation, e.g., f x means what would usually be written f(x). Multiple arguments are also dealt with elegantly: f x y means what would normally be written f(x,y), while f (x y) means what would normally be written f(x(y)). Finally, if f is a function which takes two arguments, then f x denotes the "curried" function of the second argument that would normally be written f(x,). This convention significantly simplifies the abstract equations given in this section, especially equation 2.
Let S denote a set, to be called the space of magicians. Then S*, the space of all finite sets composed of elements of S, with repeated elements allowed, is the space of magician systems. Using the convention of the previous paragraph, one may write
Systemt+1 = A Systemt (1)
where Systemt is an element of S* denoting the magician population at time t, and A is the "action operator," a function mapping magician populations into magician populations.
Let us assume, for simplicity's sake, that all magician interactions are ternary, i.e., involving one magician acting on another to create a third. In this instance the machinery of magician operations may be described by a binary algebraic operation *, so that where a, b and c are elements of S, a*b=c is read "a acts on b to create c." The case of binary, quaternary, etc. interactions may be treated in a similar way or, somewhat artificially, may be constructed as a corollary of the ternary case.
The action operator may be decomposed as
A = F R (2)
where R is the "raw potentiality" operator and F is a "filtering" operator. R is formally given by
R Systemt = R {a1,a2,...,an(t)}
= { ai * aj | i,j = 1,...,n(t)} (3)
Its purpose is to construct the "raw potentiality" of the magician system Systemt, the set of all possible magician combinations which ensue from it. The role of the filtering operator, on the other hand, is to select from the raw potentiality those combinations which are to be allowed to continue to the next time step. This selection may be all-or-none, or it may be probabilistic. To define the filtering operator formally, let P* denote the a space of all probability distributions on the space magician systems S*. Then, F is a function which maps S* x S* into P*.
Magician systems, thus defined, are ageometric, or, to use the chemical term, "well-mixed." But one may also consider "graphical magician systems," magician systems that are specialized to some given graph G. Each magician is assigned a location on the graph as one of its defining properties, and magicians are only allowed to interact if they reside at the same or adjacent nodes. This does not require any reformulation of the fundamental equations given above, but can be incorporated in the filtering operator, by setting F so that the magician combination ai * aj has zero probability unless ai and aj occupy appropriate relative locations. The dual network, a structure postulated below as a prerequisite of self- and reality-theories, is a magician system which resides on a special kind of graph.
This kind of system may at first sound like an absolute, formless chaos. But this glib perspective ignores something essential -- the phenomenon, well known for decades among European systems theorists (Varela, 1978; Kampis, 1991), of mutual intercreation or autopoiesis. Systems of magicians can interproduce. For instance, a can produce a, while b produces a. Or a and b can combine to produce c, while b and c combine to produce a, and a and c combine to produce b. The number of possible systems of this sort is truly incomprehensible. But the point is that, if a system of magicians is mutually interproducing in this way, then it is likely to survive the continual flux of magician interaction dynamics. Even though each magician will quickly perish, it will just as quickly be re-created by its co-conspirators. Autopoiesis creates self-perpetuating order amidst flux.
Some autopoietic systems of magicians might be unstable; they might fall apart as soon as some external magicians start to interfere with them. But others will be robust; they will survive in spite of external perturbations. In (Goertzel, 1995a; 1995b) these robust magician systems are called autopoietic attractors. This leads up to the natural hypothesis that thoughts, feelings and beliefs are autopoietic attractors. They are stable systems of interproducing pattern/processes.
Formally speaking, a (p,q)-autopoietic attractor of a magician system is a region M of the space S* with the properties that
-- Where a is in M, A a lies in M with probability p.
-- Where N is also in S*, and the distance d N M does not exceed x, there is probability q that d (A N) (A M) does not exceed d N M.
These properties may be stated more rigorously in a number of ways. For instance, the references to probability may be made precise in a straightforward way using the Lebesgue measure. And the metric d N M may be defined in terms of the topology of the vector space V S*, where the mapping V associates with each element a of S* a vector v of integers, where vi indicates the number of copies of magician ai in a. Setting V M = {V a, a in M}, and setting V N similarly, one may define d N M = d' (V N) (V M), where d' is, say, the Hausdorff metric (Barnsley, 1988). Setting p=q=1 yields a deterministic definition, but in general, it seems quite possible that natural systems may possess autopoietic attractors only under the more general stochastic definition.
But autopoietic attraction is not the end of the story. The next step is the intriguing possibility that, in psychological systems, there may be a global order to these autopoietic attractors. In (Goertzel, 1994) it is argued that these structures must spontaneously self-organize into larger autopoietic superstructures -- and, in particular, into a special attracting structure called the dual network.
The dual network, as its name suggests, is a network of magicians that is simultaneously structured in two ways. The first kind of structure is hierarchical. Simple structures build up to form more complex structures, which build up to form yet more complex structures, and so forth; and the more complex structures explicitly or implicitly govern the formation of their component structures. The second kind of structure is heterarchical: different structures connect to those other structures which are related to them by a sufficient number of pattern/processes. Psychologically speaking, as is elaborated in (Goertzel, 1993b; 1994), the hierarchical network may be identified with command-structured perception/control, and the heterarchical network may be identified with associatively structured memory. Mathematically, the formal definition of the dual network is somewhat involved; one approach is given in (Goertzel, 1995b). A simplistic dual network, useful for guiding thought though psychologically unrealistic, is a magician population living on graph each node of which is connected to certain "heterarchical" neighbor nodes and certain "hierarchical" child nodes.
A psynet, then, is a magician system which has evolved into a dual network attractor. The core claim of the "psynet model" is that intelligent systems are psynets. This does not imply that all psynets are highly intelligent systems; for instance, (Goertzel, 1995a) describes a simplistic Haskell implementation of the psynet model which runs on an ordinary PC, and certainly does not deserve the label "intelligent." What makes the difference between intelligent and unintelligent psynets is above all, or so the model claims, size. Small psynets do not have the memory or processing power required to generate self- and reality-theories. Thus they can never possess general intelligence.
Obviously the power and flexibility of the component magicians also plays a role in determining system intelligence. But a substantial number of magicians is also necessary, in order to support the hierarchical and heterarchical build-up of processes for "getting oriented," as described in the previous section. Self- and reality- theories, in the psynet model, arise as autopoietic attractors within the context of the dual network. This means that they cannot become sophisticated until the dual network itself has self-organized to an acceptable degree. The dual network provides routines for building complex structures from simple structures, and for relating structures to similar structures. It provides a body of knowledge, stored in this way, for use in the understanding of practical situations that occur. Without these routines and this knowledge, complex self- and reality- theories cannot come to be. But on the other hand, the dual network itself cannot become fully fleshed out without the assistance of self- and reality-theories. Self- and reality-theories are necessary components of creative intelligence, and hence are indispensible in gaining information about the world. Thus one may envision the dual network and self- and reality-theories evolving together, symbiotically leading each other toward maturity.
A speculation? Certainly. And until we understand the workings of the human brain, or build massively MIMD parallel "brain machines," the psynet model will remain in large part an unproven hypothesis. However, the intricate mathematical constructions of the logic-oriented AI theorists are also speculations. The idea underlying the psynet model is to make mathematical speculations which are psychologically plausible. Complex systems science, as it turns out, is a useful tool in this regard. Accepting the essential role of the self means accepting the importance of self-organization and complexity for the achievement of flexible, creative intelligence.
The recognition of the cognitive importance of the self leads to a number of suggestions regarding the future direction of AI research. One of the most interesting such suggestions is the concept of A-IS, or "artificial intersubjectivity." The basis of A-IS is the proposition that self- and reality-theories can only evolve in an appropriate social context. While almost self-evident from the point of view of personality psychology, this proposition has been almost completely ignored by AI theorists. Today, however, computer science has progressed to the point where we can begin to understand what it might mean to provide artificial intelligences with a meaningful social context.
In AI, one seeks programs that will respond "intelligently" to our world. In artificial life, or Alife, one seeks programs that will evolve interestingly within the context of their simulated worlds (Langton, 1992). The combination of these two research programmes yields the almost completely unexplored discipline of AILife, or "artificially intelligent artificial life" -- the study of synthetically evolved life forms which display intelligence with respect to their simulated worlds. A-IS, artificial intersubjectivity, may be seen as a special case of artificially intelligent artificial life. Conceptually, however, A-IS is a fairly large step beyond the very general idea of AILife. The idea of A-IS is to simulate a system of intelligences collectively creating their own subjective (simulated) reality.
In principle, any AILife system one constructed could become an A-IS system, under appropriate conditions. That is, any collection of artificially intelligent agents, acting in a simulated world, could come to collude in the modification of that world, so as to produce a mutually more useful simulated reality. In this way they would evolve interrelated self- and reality-theories, and thus artificial intersubjectivity. But speaking practically, this sort of "automatic intersubjectivity" cannot be counted on. Unless the different AI agents are in some sense "wired for cooperativity," they may well never see the value of collaborative subjective-world-creation. We humans became intelligent in the context of collaborative world-creation, of intersubjectivity (even apes are intensely intersubjective). Unless one is dealing with AI agents that evolved their intelligence in a social context -- a theoretically possible but pragmatically tricky solution -- there is no reason to expect significant intersubjectivity to spontaneously emerge through interaction.
Fortunately, it seems that there may be an alternative. I will describe a design strategy called "explicit socialization" which involves explicitly programming each AI agent, from the start, with:
1) an a priori knowledge of the existence and autonomy of the other programs in its environment, and
2) an a priori inclination to model the behavior of these other programs.
In other words, in this strategy, one enforces A-IS from the outside, rather than, as in natural "implicit socialization," letting it evolve by itself. This approach is, to a certain extent, philosophically disappointing; but this may be the kind of sacrifice one must make in order to bridge the gap between theory and practice. Explicit socialization has not yet been implemented and may be beyond the reach of current computer resources. But the rapid rate of improvement of computer hardware makes it likely that this will not be the case for long.
To make the idea of explicit socialization a little clearer, one must introduce some formal notation. Suppose one has a simulated environment E(t), and a collection of autonomous agents A1(t), A2(t),..., AN(t), each of which takes on a different state at each discrete time t. And, for sake of simplicity, assume that each agent Ai seeks to achieve a certain particular goal, which is represented as the maximization of the real-valued function fi(E), over the space of possible environments E. This latter assumption is psychologically debatable, but here it is mainly a matter of convenience; e.g. the substitution of a shifting collection of interrelated goals would not affect the discussion much.
Each agent, at each time, modifies E by executing a certain action Aci(t). It chooses the action which it suspects will cause fi(E(t+1)) to be as large as possible. But each agent has only a limited power to modify E, and all the agents are acting on E in parallel; thus each agent, whenever it makes a prediction, must always take the others into account. A-IS occurs when the population of agents self-organizes itself into a condition where E(t) is reasonably beneficial for all the agents, or at least most of them. This does not necessarily mean that E reaches some "ideal" constant value, but merely that the vector (A1,...,AN,E) enters an attractor in state space, which is characterized by a large value of the society wide average satisfaction (f1 + ... + fN)/N.
The strategy of explicit socialization has two parts: input and modeling. Let us first consider input. For Ai to construct a model of its society, it must recognize patterns among the Acj and E; but before it can recognize these patterns, it must solve the more basic task of distinguishing the Acj themselves. In principle, the Aci can be determined, at least approximately, from E; a straightforward AILife approach would provide each agent with E alone as input. Explicit socialization, on the other hand, dictates that one should supply the Aci as input directly, in this way saving the agents' limited resources for other tasks. More formally, the input to Ai at time t is given by the vector
E(t), Acv(i,1,t)(t),..., Acv(i,n(t),t)(t) (4)
for some n < N, where the range of the index function v(i,,) defines the "neighbors" of agent Ai, those agents with whom Ai immediately interacts at time t. In the simplest case, the range of i is always {1,...,N}, and v(i,j,t) = j, but if one wishes to simulate agents moving through a spatially extended environment, then this is illogical, and a variable-range v is required.
Next, coinciding with this specialized input process, explicit socialization requires a contrived internal modeling process within each agent Ai. In straightforward AILife, Ai is merely an "intelligent agent," whatever that might mean. In explicit socialization, on the other hand, the internal processes of each agent are given a certain a priori structure. Each Ai, at each time, is assumed to contain n(t) + 1 different modules called "models":
a) a model M(E|Ai) of the environment, and
b) a model M(Aj|Ai) of each of its neighbors.
The model M(X|Ai) is intended to predict the behavior of the entity X at the following time step, time t+1.
At this point the concept of explicit socialization becomes a little more involved. The simplest possibility, which I call first order e.s., is that the inner workings of the models M(X|Ai) are not specified at all. They are just predictive subprograms, which may be implemented by any AI algorithm whatever.
The next most elementary case, second order e.s., states that each model M(Aj|Ai) itself contains a number of internal models. For instance, suppose for simplicity that n(t) = n is the same for all i. Then second order e.s. would dictate that each model M(Aj|Ai) contained n+1 internal models: a model M(E|Aj|Ai), predicting Aj's internal model of E, and n models M(Ak|Aj|Ai), predicting Aj's internal models of its neighbors Ak.
The definition of n'th order e.s. for n > 2 follows the same pattern: it dictates that each Ai models its neighbors Aj as if they used (n-1)'th order e.s. Clearly there is a combinatorial explosion here; two or three orders is probably the most one would want to practically implement at this stage. But in theory, no matter how large n becomes, there are still no serious restrictions being placed on the nature of the intelligent agents Ai. Explicit socialization merely guarantees that the results of their intelligence will be organized in a manner amenable to socialization.
As a practical matter, the most natural first step toward implementing A-IS is to ignore higher-order e.s. and deal only with first-order modeling. But in the long run, this strategy is not viable: we humans routinely model one another on at least the third or fourth order, and artificial intelligences will also have to do so. The question then arises: how, in a context of evolving agents, does a "consensus order" of e.s. emerge? At what point does the multiplication of orders become superfluous? At what depth should the modeling process stop?
Let us begin with a simpler question. Suppose one is dealing with agents that have the capacity to construct models of any order. What order model should a given agent choose to deal with? The only really satisfactory response to this question is the obvious one: "Seek to use a depth one greater than that which the agent you're modeling uses. To see if you have gone to the correct depth, try to go one level deeper. If this yields no extra predictive value, then you have gone too deep." For instance, if one is modeling the behavior of a cat, then there is no need to use a fifth-order model or even a third-order model: pretty clearly, a cat can model you, but it cannot conceive of your model of it, much less your model of another cat or another person. The cat is dealing with first-order models, so the most you need to deal with is the second order (i.e. a model of the cat's "first-order" models of you).
In fact, though there is no way to be certain of this, it would seem that the second order of modeling is probably out of reach not only for cats but for all animals besides humans and apes. And this statement may be made even more surely with respect to the next order up: who could seriously maintain that a cat or a pig can base its behavior on an understanding of someone else's model of someone else's model of itself or someone else? If Uta Frith's (1989) psychology of autism is to be believed, then even autistic humans are not capable of sophisticated second-order social modeling, let alone third-order modeling. They can model what other people do, but have trouble thinking about other peoples' images of them, or about the network of social relationship that is defined by each person's images of other people.
This train of thought suggests that, while one can simulate some kinds of social behavior without going beyond first order e.s., in order to get true social complexity a higher order of e.s. will be necessary. As a first estimate one might place the maximum order of human social interaction at or a little below the "magic number seven plus or minus two" which describes human short term memory capacity. We can form a concrete mental image of "Joe's opinion of Jane's opinion of Jack's opinion of Jill's opinion on the water bond issue," a fourth-order construct, so we can carry out fifth-order reasoning about Joe ... but just barely!
More speculations, perhaps too many speculations. But if intelligence requires self, and self requires intersubjectivity, then there may be no alternative but to embrace A-IS. Just because strong AI is possible does not mean that the straightforward approach of current AI research will ever be effective. Even with arbitrarily much processing power, one still needs to respect the delicate and spontaneous self-organization of psychological structures such as the self.
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