The Modeling Instinct – Hacker Noon

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.

Utilitarian models 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.

Scientific 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.

Experiential 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.

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.

Dynamic models are functional. They are “run,” whereas static models are observed or experienced.

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 recordings, 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.

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.

Physical models 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.

A physical model of the San Francisco Bay Area constructed to test the feasibility of dams and other projects.

Symbolic models, 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.

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,” language 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.

Mathematical symbols 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.

Computer code 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.

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 [CC BY-SA 3.0], via Wikimedia Commons)

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 do reflect reality.

J.R.R. Tolkien’s map of Middle Earth. (Creative Commons)

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