Mathematical models serve more than one purpose. Sometimes, they help to cast theoretical ideas or hypotheses in precise form. If a model’s behaviour can be understood mathematically, either exactly or in sufficient approximation, then it may provide an invaluable bridge to experimental tests against relevant observations. But just as often, models have another, less technical use as tools for helping us to think clearly, to be more creative and to ask new questions. In this latter case, models aren’t necessarily right or wrong – they’re either instructive and fruitful, or they aren’t. For fifty years, neural networks have proven useful in exploring biological mechanisms underlying processes such as diverse as sensorimotor control, memory and pattern recognition. A neural network is a dynamical system made of many relatively simple units – each modeled loosely along the lines of real biological neurons – that interact and influence one another. Given a period of “training”, such models can learn to identify patterns through trial and error – displaying a rudimentary form of memory – while remaining able to learn new patterns that may emerge in the future. Such units can be connected within diverse complex architectures, and their dynamics can adapt to changing environments. In this sense, neural networks capture basic aspects of both intelligence and biological adaptability, and have achieved impressive success in modeling some basic neural functions – for example, the acquisition of short-term memories, for example, and their transformation into longer-term memories, perceptual categorization, and motor control. But neural networks may also be useful in a metaphorical sense, as a conceptual tool for organizing scientists’ thinking in areas that, for the moment, still lie far beyond the possibility of any detailed mathematical understanding. In the present paper, psychologist Daniel Levine of the University of Texas at Arlington argues that the naturally rich dynamics of neural networks may provide a powerful framework for understanding the roots of human behaviour and personality more clearly. In the next decade, new results in cognitive and social neuroscience may enable such metaphorical models to grow more specific and possibly yield experimental predictions. Specifically, Levine suggests that a dynamical systems perspective, centered around neural networks, can be useful for ordering our thinking about how internal psychic and neurodynamic processes lead us to behave in one way rather than another. In the paper, he proposes that our relatively stable personality types (or character types) may correspond ultimately to distinct attractors in some dynamical system that arises by virtue of interactions between various parts of the brain. Levine also attempts to put a little more “meat” on this abstract picture by appealing to the findings of contemporary empirical neuroscience. He discusses a number of specific brain regions, their apparent psychological functions and the interactions between them, and on this basis proposes a speculative and provocative schematic diagram for the brain’s overall decision-making apparatus. The paper offers no specific predictions; rather, it should be considered more as an exercise in creative scientific thinking – constrained by empirical knowledge – that aims to provoke psychiatrists and other brain researchers to think about human behaviour in dynamical terms. Levine begins by describing a perspective – influential among psychologists – which holds that specific behaviours move from the realm of the potential into that of the actual through a multi-level process that is roughly akin to voting. As proposed by Antonio Damasio, the anticipation of a certain possible behaviour – anything from drug taking, to taking a moral stand against a war, or going to bed early – leads immediately to activity in many parts of the body and mind. These responses, which also depend on the situation or context of the individual, may be pleasant or unpleasant, and they all somehow influence the probability that the behaviour will ultimately take place. As with voting, no one individual response determines the outcome; all have to be tallied and integrated together in some way. Damasio suggests that such integration takes place in the “orbitofrontal” cortex, an important region of the brain involved in social adjustment and in controlling the personality of an individual. The orbitofrontal cortex – many psychologists and neuroscientists believe – is where decisions get made and the potential becomes the actual. Taking this rough framework as a starting point, Levine introduces the terms "angels" and "devils" to refer to neurodynamic processes that tend to promote or inhibit some particular behaviour. Specifically, as he writes, an angel refers to a "stored pattern of neural activities that markedly increases the probability that some specific behavior will be performed in some class of contexts." You can think of angels and devils as elementary promoters and inhibitors for any particular behaviour. Each of us has many angels and devils, which we have either inherited on a genetic basis or learned through culture. Most of us have devils against stealing, for example, or eating rotten meat, and angels for keeping promises and drinking water when thirsty. One might roughly think of angels and devils as the "atoms" of decision-making. Importantly, for any specific behaviour in a particular context, we may have many angels and devils that directly conflict with one another. But angels and devils don't lead to decisions directly on their own. Levine argues that these elementary tendencies feed forward into higher-level structures or processes that somehow “integrate” the angels and devils, and thereby lead to a decision. Two people in the same situation, for example, and having identical angels and devils for some behaviour and context, might still differ in their actual behaviour. This could be because they are operating with different “censors,” which Levine defines as "abstract behavioral filters...which encompass and functionally unify large classes of what we call angels and devils." For example, the devil of "avoiding sex with anyone other than your spouse" could be part of the censor of "honoring committed relationships." The same devil can also be, perhaps in a different person, part of the censor of "obeying God's commandments." Angels and devils, the atoms of decision-making tendencies, can be organized into higher-level structures in many different ways. In this sense, the angels and devils are analogous to one layer of neurons that feeds upward to another layer, and a censor is roughly akin to the overall pattern of interconnections that leads the network to have one dynamics rather than another. That’s the dynamical view. But Levine goes on to suggest that, in psychological terms, these censors are loosely akin to someone having a certain character, which would generally dispose them to act one way or another depending on the context. In other words, character somehow corresponds to a particular way that the lower level angels and devils get integrated to make decisions. Levine’s equation (1) isn’t meant to represent any of this explicitly, only to show one example of the dynamical structure generic to neural network models, in which information at one level feeds upward into another. Any network aiming to represent the dynamics of angels and devils realistically would be immeasurably more complex – and, as of yet, of course, impossible to construct on any meaningful basis – but it would include elements such as Eq. (1) as components. Levine then goes on to make all of this more specific by discussing a number of specific brain regions that could play a role in the abstract picture just described. In particular, he describes three major brain pathways – fight or flight, cooperate or dissociate – which represent common dynamical routes, based on our evolutionary history, through which decisions frequently get made. These terms refer to archetypal behavioural responses to specific kinds of situations, each of which has a plausible basis in specific neural pathways shared by all people. The idea is that these biologically relevant pathways probably have something to do with the action of “censors.” Levine also explores the roles of the orbitomedial cortex, hippocampus, nucleaus accumbens, and other brain regions in decision making, as well as psychiatrist Robert Cloninger's work on personality, which proposes that the common possibilities for individual character can usefully be viewed in terms of three components. As listed by Levine, these are “selfdirectedness (relating to acceptance of the individual self); cooperativeness (relating to acceptance of other people); and selftranscendence (relating to acceptance of nature in general).” Levine suggests that these three character traits, considered as essential by Cloninger, correspond closely to the three main pathways – fight or flight, cooperate or dissociate – as know empirically from neuroscience and cognitive psychology. The three pathways aren't meant to be censors taken on their own; rather, in reference to Cloninger's cube of character (see Levine’s figure 7);, eight possible attractors correspond to the relative weights given to the three pathways – fight or flight, cooperate or dissociate. (Obviously, the eight attractors is a simplification, only corresponding to the extremes of the various traits. More realistically, every point within the cube should correspond to a different possible character). Each one of these corners corresponds to a particular way of behaving and, so, to a particular censor. Along the way, Levine also reviews evidence that the orbitomedial prefrontal cortex, the hippocampus, amygdala and nucleus accumbens all have some particular role in the biology that underlies such censors. But for Levine, there is still one further step to take. Angels, devils and censors, and the dynamical attractors to which they might hypothetically be associated, do not quite capture the richness of real human behaviour. While censors may fix a person’s character, Levine suggests that they are not the final level of decision-making, for an individual with fixed censors may sometimes exhibit different behaviours. As he suggests, "... the most creative individuals possess strong character-based controls (censors) but can, in unusual circumstances, override their censors.” As an example, he points to a man who normally refrains from stealing but would steal drugs if needed to save his wife's life. Somehow, higher-level “executive” controls must come into play in a way that enables an individual to overcome censors that would otherwise fix his or her character and behaviour. Taking the metaphorical connection with neural networks further – and making an intriguing connection with physics – Levine goes on to suggest that "discontent" could play a role in this higher-level “executive” control, which monitors the overall needs of a person. Specifically, he suggests that discontent could be dynamically similar to noise, and thereby permit a person to move from one attractor to another – knocking the dynamical system from one character attractor to another. His discussion on “simulated annealing” uses the mathematics again to provide a useful metaphor and picture for thinking about character and its changes. There may be other brain "modules", he suggests, that monitor the needs of the organism and their level of satisfaction, and institute noise like perturbations to help the system seek better states. Finally, in his figure 11, he offers an overall schematic diagram meant to depict a very rough “best guess” of how the overall apparatus of the human brain works together to make decisions. The remainder of the paper then goes on to make some suggestions about how the dynamical and complex systems perspective might help therapists in general. Again, Levine’s point isn’t to make any specific predictions, or to explain any specific data. Rather, it is to explore how a dynamical metaphor – derived from the study of lower level neural processes and embodied formally in the mathematical models of neural networks – might be helpful in understanding human behaviour as determined by the entire brain. This perspective leads Levine to a few specific ideas about how the practice of psychotherapy might be made more effective and supportive. Psychologists, psychiatrists and neuroscientists will ultimately judge how useful this suggestive perspective really is.