Our fascination with miniature objects and worlds is much more than a diversion. The purpose of all brains, human and otherwise, is to move the body; to guide its motions through a complex and hostile world. To this end, brains construct mental representations, or models, of the worlds in which they find themselves. Even the simplest brains do this. C elegans is a tiny worm with a brain consisting of just 302 neurons. Some are sensory neurons that fire in the presence of food, chemicals, other worms, and so on. Others are motor neurons whose firings activate the muscles. (The remainder are “interneurons” that only connect to other neurons.) The firings of the sensory neurons, along with the subsequent firings they induce, constitute a real-time representation of the worm’s environment, which informs the firings of the motor neurons. C elegans can thus move towards beneficial things and away from harmful things. But in a complex world populated by numerous obstacles and competing organisms, the shortest and safest path from A to B is rarely a straight line. We, like C elegans, seek out what’s good and avoid what’s bad, but our human brains have evolved countless layers of indirection and abstraction on top of these basic motor functions. Our mental models have grown enormously sophisticated, and they are adaptive; we continuously elaborate upon them as new information is acquired, and we seek out novelty expressly to support this process. Our formidable brains not only enrich our actions, but they also enable an entirely new kind of action. We can enlist our advanced motor skills to build models comprised not of neurons, but of environmental materials such as marble, ink, and silicon. In this way, we extend our mental models into the physical world. Unconfined by our skulls, such external models can be manipulated, experimented with, or simply appreciated, not just by ourselves, but by others as well. An external model, like the mental kind, is a simplified representation of some aspect of reality. The thing being modeled — the “target system” — might be an object, a person, a phenomenon, an ecosystem, a sequence of events, or a law of nature; anything that exists can be modeled in some way. This includes things that only exist hypothetically. Architectural plans, for instance, depict buildings that don’t yet exist; fiction describes events that never took place. It is evident that humans possess an innate drive to create and interact with such models, and to share their creations with others. We can see this modeling instinct at work just by watching children play. They require no formal instruction to assemble a castle from blocks, or to enact a drama inside a dollhouse, or to seek an audience for their creations. The Many Types of Models Since a model might represent any aspect of reality, and be made from any number of materials, there are obviously very many kinds of them. Classifying them is a challenge, and the problem is compounded by the fact that some models are composites of many smaller sub-models, each with its own characteristics. To manage this complexity, I’ll consider just four dimensions that I feel are both fundamental and — at least for the purposes of this series of articles — useful. They are: purpose, dynamism, composition, and realism. Dimension 1: Some models serve a utilitarian purpose. For others, the purpose is to provide an experience. are created to aid real-world interactions with the target system. They are thus a special kind of tool. A map, for example, is a tool for navigating the terrain modeled by the map. A flight simulator, because it models the dynamics of flight, is a tool for learning to fly. Utilitarian models are a special case. They are utilitarian (or can be), but their primary purpose is to accurately and thoroughly explain their target systems. Scientists devise and test explanatory models of incompletely understood systems, and it’s up to engineers to develop utilitarian applications of the models, should any exist. Scientific models , by contrast, are created to provide an audience with an experience. They are taken to be valuable in and of themselves, without appeal to their utility. This intrinsic value arises from the fact that, at some level of cognition, we experience models as though they are real. They can thus provoke a wide assortment of emotions according to the kinds of experiences they provide. Experiential models A model can have both utilitarian and experiential aspects, and few are purely one or the other. A fictional story, for example, might deliver useful life lessons, just as a flight simulator might enthrall a person who has no intention of piloting an actual plane. NASA’s Systems Engineering Simulator (here configured to simulate operations aboard the International Space Station) is a utilitarian spaceflight simulator with experiential qualities. (Credit: NASA) Dimension 2: Some models incorporate the laws that govern how their target systems change in time, while others do not. are functional. They are “run,” whereas are observed or experienced. Dynamic models static models The distinction, however, is not as straightforward as it might seem. A work of fiction, for example, is experienced in time, and it describes events that (ostensibly) unfolded in time, but the words on the page, or the individual photographic frames, are unchanging. The same holds true for a history book, or the data collected from an experiment. Such models are , or memories, of a single run-through of a dynamic target system. Although the recorded system is dynamic, the recording itself is static because it does not incorporate the laws of cause and effect that gave rise to its content. recordings A dynamic biomechanical model of Tyrannosaurus rex. (Credit: University of Manchester) Dimension 3: Some models are made from physical materials, such as plastic or paint, while others are made from symbols, such as mathematical notations, computer code, or the words of a language. are made from physical materials and typically depict the geometric characteristics of their target systems. A utilitarian example might be a model airplane in a wind tunnel. Sculptures, paintings, and theme park attractions are experiential examples. Physical models A physical model of the San Francisco Bay Area constructed to test the feasibility of dams and other projects. , by contrast, are made from symbols with predefined meanings. The symbols themselves must be made from some type of material, of course, but symbolic models are distinguished by the fact that the choice of material does not alter the logical attributes of the symbols. In the case of an abacus, for example, plastic beads give the same result as wooden ones. Symbolic models An abacus with individual carbon molecules as beads. (Credit: IBM Research — Zurich) Symbolic models can be further characterized by the kinds of symbols they use. Although we don’t generally speak of “word models,” is in fact a symbolic means of describing, or modeling, reality. Its dependence on nouns and verbs — objects in motion — reflects its original concern with physical things and actions. But once nouns, verbs, and other parts of speech exist, they can be used to represent abstract things as well. language first arose from the need to count and measure things. But as more and more symbols were devised, along with new rules for manipulating them, mathematics developed an extraordinary capacity to represent natural phenomena. Mathematical symbols is unique in that some of its symbols (defined as “instructions”) represent changes to be made to other symbols. An “instruction pointer,” itself a changeable symbol, keeps track of which instruction to perform next. This arrangement means that computers are especially good at modeling systems that evolve in time. Computer code There are, of course, other kinds of symbols besides these. Dimension 4: Models exhibit varying degrees of realism depending on how accurately they represent their target systems, and with how much detail. On the realistic end of the spectrum are computer simulations designed to reflect their target systems as faithfully as possible. Such models can be extremely detailed, sometimes containing millions or even billions of interacting elements, all behaving according to known scientific principles. They are commonly used for prediction (of the weather, for example), or to gain knowledge about a system that would otherwise be too difficult, costly, or dangerous to obtain. A snapshot of a cosmological simulation that consisted of more than 10 billion massive “particles” in a cubic region of space 2 billion light-years to the side. (Credit: Max-Planck-Institute for Astrophysics) Perfect verisimilitude is impossible (without replicating the target system exactly, which is absurd), but it’s not necessary anyway. A model need only incorporate those aspects of the target system that help to fulfill its purpose. The purpose of a subway map, for example, is to help riders decide where to embark and disembark. Details that don’t aid in that decision can be left out. A map of the NYC subway system in the “Vignelli style,” a style of design favoring simplicity. (Credit: CountZ at English Wikipedia [ ], via Wikimedia Commons) CC BY-SA 3.0 Experiential models can go further than just leaving out unnecessary details — the details that are included can be depicted in nonrealistic ways. Artists are free to explore the full spectrum, from realistic to stylized to incoherent. Why would an artist choose to create a model that is not realistic? One reason is to provide novelty. Novelty counteracts the blinding effect of familiarity, thereby engaging the imagination. Once engaged, the imagination can turn to the aspects of the model that reflect reality. do J.R.R. Tolkien’s map of Middle Earth. (Creative Commons) What is a Good Model? Starting from the premise that a good model fulfills its purpose, it follows unremarkably that a good utilitarian model is , a good scientific model is , and a good experiential model is . useful accurate engaging But are there general principles of goodness that apply to all kinds of models? Here I’ll propose three: novelty, relevance, and economy. Principle 1: A model is novel if it provides new information about its target system, or if it represents its target system in a new way. This principle applies most directly to experiential models, whose purpose is to engage an audience. Novelty, practically by definition, is what engages attention. It signals that new information is available for integration, and that one’s senses and other cognitive resources should be redirected to this task. The preeminence of novelty is the reason that good artists are so careful to avoid clichés. Novelty is crucial to utilitarian models as well, since their utility depends on providing information about — or simulated experience with — a target system that is unfamiliar to the user. A map, for example, is most useful to those who are unfamiliar with the terrain. But different people are familiar with different things, and what is novel to one might be mundane to another. It seems reasonable to conclude that a model is novel in proportion to the number of people who consider it so. That reasoning might be justified for utilitarian and experiential models, but for scientific models, the situation is a bit different. The “audience” for a scientific model is all of humanity, and what is discovered by one person (and published) is known by all collectively. For a new scientific theory to be novel, therefore, it must explain an aspect of reality that has not been explained by (that we know of), or it must offer a previously undiscovered means of representing an already explained system. anyone Principle 2: A model is relevant if it accurately depicts a target system that matters to someone. If it is novelty that attracts attention, it is relevance that determines how much attention is warranted. A page of random letters, for example, is both utterly novel and utterly irrelevant. Even if the letters capture your attention, they won’t hold it for long because they don’t represent anything that matters to you. For non-scientific models, relevance is, like novelty, a function of the audience. To be relevant, a utilitarian model must aid an activity that someone intends to undertake, and an experiential model must depict a system that someone cares about. And in both cases, if a model is not faithful to the aspects of the target system that matter, its relevance will suffer. An inaccurate map is not only useless to its audience, but it might even infuriate them, and poorly motivated fictional characters might have the same effect. With respect to relevance, scientific models are again a special case. The goal of science is to explain all of reality, so all non-imaginary systems matter to science. It is thus accuracy that is paramount. Indeed, much of the work of science involves testing models to see if they are accurate, and models that cannot be tested are regarded as unscientific. Novelty in the form of an alien weapon, and relevance in the form of human targets. (Still from “War of the Worlds,” © DreamWorks LLC and Paramount Pictures) Principle 3: A model is economical if it incorporates the fewest elements necessary to fulfill its purpose. Economical models have the quality that even the slightest alteration will degrade them. They are information-dense, often containing elements that perform double or triple duty. For experiential models, deciding which elements to include and which to exclude is a matter of . It is a subjective process that depends entirely on the judgement of the artist. For utilitarian models, though, the process can be more objective. Here the guiding principle is — the imperative to not waste resources on useless or redundant elements. artistic emphasis efficiency As one might expect, there is overlap between the utilitarian and experiential cases. Artistic judgement is often helpful when designing utilitarian models (to the extent that they incorporate experiential elements), just as experiential models are often subject to resource constraints. With respect to economy, scientific models are the least subjective of all because their purpose is to provide accurate explanations, and accuracy can be tested. If two scientific models are equally accurate, the simpler one is more economical. About This Series Physical models (miniature buildings, dioramas, and so on) delight us because they encapsulate the modeling instinct at a glance, but the instinct encompasses many kinds of models besides just these. This series of articles will focus on three kinds in particular — (as models of complex systems), (as models of human endeavor), and (as models of the mind). simulations games intelligent agents The first part of the series will investigate the nature of such models and how they are typically built, with an emphasis on computer-based implementations. The second part will consider their philosophical and sociological implications, especially as the prospect of hyper-powerful computers — and thus hyper-powerful models — becomes increasingly real. TLDR : Humans instinctively create, share, and interact with models. A model is a simplified representation — material or symbolic, static or dynamic, realistic or stylized — of some aspect of reality. Models are created with a purpose in mind, which may be utilitarian, experiential, or some combination of the two. Good models are novel, relevant, and economical. Thanks for the read! Please have a look at my game on Steam — it’s the first application of an experimental game engine I’m developing for evolving intelligent agents in physics-based environments. Thetaball
