The simplest principle for creating a category is enumeration; any resource in a finite or countable set can be deemed a category member by that fact alone. This principle is also known as extensional definition, and the members of the set are called the extension. Many institutional categories are defined by enumeration as a set of possible or legal values, like the 50 United States or the ISO currency codes (ISO 4217).

Enumerative categories enable membership to be unambiguously determined because a value like state name or currency code is either a member of the category or it is not. But there comes a size when enumerative definition is impractical or inefficient, and the category either must be sub-divided or be given a definition based on principles other than enumeration.

For example, for millennia we earthlings have had a cultural category of “planet” as a “wandering” celestial object, and because we only knew of planets in our own solar system, the planet category was defined by enumeration: Mercury, Venus, Earth, Mars, Jupiter, and Saturn. When the outer planets of Uranus, Neptune, and Pluto were identified as planets in the 18^th-20^th centuries, they were added to this list of planets without any changes in the cultural category. But in the last couple of decades many heretofore unknown planets outside our solar system have been detected, making the set of planets unbounded, and definition by enumeration no longer works.

The International Astronomical Union (IAU) thought it solved this category crisis by proposing a definition of planet as “a celestial body that is (a) in orbit around a star, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighborhood around its orbit.” Unfortunately, Pluto does not satisfy the third requirement, so it no longer is a member of the planet category, and instead is now called an “inferior planet.”

Changing the definition of a significant cultural category generated a great deal of controversy and angst among ordinary non-scientific people. A typical headline was “Pluto’s demotion has schools spinning,” describing the outcry from elementary school students and teachers about the injustice done to Pluto and the disruption on the curriculum. 346[LIS]

It is intuitive and useful to think in terms of properties when we identify instances and when we are describing instances (as we saw in §3.3, “Resource Identity” and in Chapter 4, “Resource Description and Metadata”). Therefore, it should also be intuitive and useful to consider properties when we analyze more than one instance to compare and contrast them so we can determine which sets of instances can be treated as a category or equivalence class. Categories whose members are determined by one or more properties or rules follow the principle of intensional definition, and the defining properties are called the intension.

You might be thinking here that enumeration or extensional definition of a category is also a property test; is not “being a state” a property of California? But statehood is not a property precisely because “state” is defined by extension, which means the only way to test California for statehood is to see if it is in the list of states.347[Phil]

Any single property of a resource can be used to create categories, and the easiest ones to use are often the intrinsic static properties. As we discussed in Chapter 4, “Resource Description and Metadata”, intrinsic static properties are those inherent in a resource that never change. The material of composition of natural or manufactured objects is an intrinsic and static property that can be used to arrange physical resources. For example, an organizing system for a personal collection of music that is based on the intrinsic static property of physical format might use categories for CDs, DVDs, vinyl albums, 8-track cartridges, reel-to-reel tape and tape cassettes.348[Cog]

Using a single property is most natural to do when the properties can take on only a small set of discrete values like music formats, and especially when the property is closely related to how the resources are used, as they are with the music collection where each format requires different equipment to listen to the music. Each value then becomes a subcategory of the music category.

The author, date, and location of creation of an intellectual resource cannot be directly perceived but they are also intrinsic static properties. The subject matter or purpose of a resource, its “what it is about” or “what it was originally for,” are also intrinsic static properties that are not directly perceivable, especially for information resources.

The name or identifier of a resource is often arbitrary but once assigned normally does not change, making it an extrinsic static property. Any collection of resources with alphabetic or numeric identifiers as an associated property can use sorting order as an organizing principle to arrange spices, books, personnel records, etc., in a completely reliable way. Some might argue whether this organizing principle creates a category system, or whether it simply exploits the ordering inherent in the identifier notation. For example, with alphabetic identifiers, we can think of alphabetic ordering as creating a recursive category system with 26 (A-Z) top-level categories, each containing the same number of second-level categories, and so on until every instance is assigned to its proper place.349[Cog]

Some resource properties are both extrinsic and dynamic because they are based on usage or behaviors that can be highly context-dependent. The current owner or location of a resource, its frequency of access, the joint frequency of access with other resources, or its current rating or preference with respect to alternative resources are typical extrinsic and dynamic properties that can be the basis for arranging resources and defining categories.

These properties can have a large number of values or are continuous measures, but as long as there are explicit rules for using property values to determine category assignment the resulting categories are still easy to understand and use. For example, we naturally categorize people we know on the basis of their current profession, the city where they live, their hobbies, or their age. Properties with a numerical dimension like “frequency of use” are often transformed into a small set of categories like “frequently used,” “occasionally used,” and “rarely used” based on the numerical property values.350[Cog]

While there are an infinite number of logically expressible properties for any resource, most of them would not lead to informative and useful categories. Therefore, it is important to choose properties that are psychologically or pragmatically relevant for the resource domain being categorized. Whether something weighs more or less than 5000 pounds is a poor property to apply to things in general, because it puts cats and chairs in one category, and buses and elephants in another.351[Cog]

To summarize: The most useful single properties to use for creating categories for an organizing system are those that are formally assigned, objectively measurable and orderable, or tied to well-established cultural categories, because the resulting categories will be easier to understand and describe.

If only a single property is used to distinguish among some set of resources and to create the categories in an organizing system, the choice of property is critical because different properties often lead to different categories. Using the age property, Bill Gates and Mark Zuckerberg are unlikely to end up in the same category of people. Using the wealth property, they most certainly would. Furthermore, if only one property is used to create a system of categories, any category with a large numbers of items in it will lack coherence because differences on other properties will be too apparent, and some category members will not fit as well as the others.

Organizing systems often use multiple properties to define categories. There are three different ways in which to do this that differ in the scope of the properties and how essential they are in defining the categories.

Property-based categorization works tautologically well for categories like “prime number” where the category is defined by necessary and sufficient properties. Property-based categorization also works well when properties are conceptually distinct and the value of a property is easy to perceive and examine, as they are with man-made physical resources like shirts.

Historical experience with organizing systems that need to categorize information resources has shown that basing categories on easily perceived properties is often not effective. There might be indications “on the surface” that suggest the “joints” or boundaries between types of information resources, but these are often just presentation or packaging choices, That is to say, neither the size of a book nor the color of its cover are reliable cues for what it contains. Information resources have numerous descriptive properties like their title, author, and publisher that can be used more effectively to define categories, and these are certainly useful for some kinds of interactions, like finding all of the books written by a particular author or published by the same publisher. However, for practical purposes, the most useful property of an information resource is its aboutness, which may not be objectively perceivable and which is certainly hard to characterize.355[LIS] Any collection of information resources in a library or document filing system is likely to be about many subjects and topics, and when an individual resource is categorized according to a limited number of its content properties, it is at the same time not being categorized using the others.

When the web first started, there were many attempts to create categories of web sites, most notably by Yahoo! As the web grew, it became obvious that search engines would be vastly more useful because their near real-time text indexes obviate the need for a priori assignment of web pages to categories. Rather, web search engines represent each web page or document in a way that treats each word or term they contain as a separate property.

Considering every distinct word in a document as a property stretches our notion of property to make it very different from the kinds of properties we have discussed in the previous two sections of this chapter. We do not need that generality yet, so we will defer further discussion of document representation for search engines until Chapter 8 and stick with our more intuitive and limited concept of property.

In general, categorization based on explicit and logical consideration of properties is much less effective, and sometimes not even possible for domains where properties lack one or more of the characteristics of separability, perceptibility, and necessity. Instead, we need to categorize using properties in a statistical rather than a logical way to come up with some measure of resemblance or similarity between the resource to be categorized and the other members of the category.

Consider a familiar category like “bird.” All birds have feathers, wings, beaks, and two legs. But there are thousands of types of birds, and they are distinguished by properties that some birds have that other birds lack: most birds can fly, most are active in the daytime, some swim, some swim underwater; some have webbed feet. These properties are correlated, a consequence of natural selection that conveys advantages to particular configurations of characteristics; birds that live in trees have different wings and feet than those that swim, for example. In the end, there is no single set of properties that are both necessary and sufficient to categorize a bird.

There are three related consequences of this complex distribution of properties for birds and for many other categories in cultural or natural (as opposed to man-made) domains.

We conclude that instead of using properties one at a time to assign category membership, we can use them in a composite or integrated way to determine similarity. Something is categorized as an A and not a B if it is more similar to A’s best or most typical member rather than it is to B’s.359[Cog]

Similarity is a very flexible notion whose meaning depends on the domain within which we apply it. Some people consider that the concept of similarity is itself meaningless because there must always be some basis, some unstated set of properties, for determining whether two things are similar. If we could identify those properties and how they are used, there would not be any work for a similarity mechanism to do.360[Cog]

To make similarity a useful mechanism for categorization we have to specify how the similarity measure is determined. There are four major psychological approaches that propose different functions for computing similarity: feature- or property-based, geometry-based, alignment-based, and transformational.361[Cog] Each of these psychological definitions or models of similarity has analogues in or can be applied to organizing systems.

An influential model of feature-based similarity calculation is the contrast model proposed by Amos Tversky. This model matches the features or properties of the two things being compared and computes a similarity measure according to three sets of features:

The similarity that results from the set of shared features is reduced by the two sets of distinctive features. The weights or importance assigned to each of these three sets can be adjusted to explain how items are assigned to a set of categories.

We often use a heuristic version of feature-based similarity calculation when we create multi-level or hierarchical category systems to ensure that the categories at each level are at the same level of abstraction or breadth. For example, if we were organizing a collection of musical instruments, it would not seem correct to have subcategories of “woodwind instruments,” “violins,” and “cellos” because the feature-based similarity among the categories is not the same for all pairwise comparisons among the categories; violins and cellos are simply too similar to each other to be separate categories given woodwinds as a category.

Geometric models are a second type of similarity framework, in which items are represented as points in a multi-dimensional feature- or property-space and similarity is calculated by measuring the distance between them. How distance is measured depends on the type of properties that characterize a domain. When properties that are psychologically or perceptually combined, a Euclidean “point-to-point” distance function best accounts for category judgments; but when properties can be conceptually separated, a “city block” distance function works best to explain psychological data, because that ensures that each property value contributes its full amount. Geometric similarity functions are commonly used by search engines; if a query and document are each represented as a vector of search terms, relevance is determined by the distance between the vectors in the “document space.” We will discuss how this works in greater detail in Chapter 9, “Interactions with Resources”.

Alignment-based similarity models have been proposed for domains in which the items to be categorized are characterized by abstract or complex relationships with their features and with each other. With this model an entity need not be understood as inherently possessing features shared in common with another entity. Rather, people project features from one thing to another in a search for congruities between things, much as clue receivers in the second round of the Pyramid game search for congruities between examples provided by the clue giver in order to guess the target category. For example, a clue like “screaming baby” can suggest many categories, as can “parking meter.” But the likely intersection of the interactions one can have with babies and parking meters is that they are both “Things you need to feed.”

Transformational models for calculating similarity assume that the similarity between two things is inversely proportional to the complexity of the transformation required to turn one into the other. For example, one way to perform the name matching task of determining when two different strings denote the same person, object, or other named entity is to calculate the “edit distance” between them, the number of changes required to transform one into the other. Two strings with a short edit distance might be variant spellings or misspellings of the same name.362[Com]

Another principle for creating categories is organizing things in ways that fit a theory or story that makes a particular categorization sensible. A theory-based category can win out even if family resemblance or similarity with respect to visible properties would lead to a different category assignment. For example, a theory of phase change explains why liquid water, ice, and steam are all the same chemical compound even though they do not share their most visible properties.

Theory-based categories based on origin or causation are especially important with highly inventive and computational resources because unlike natural kinds of physical resources, little or none of what they can do or how they behave is visible on the surface (see §2.4.1, “Affordance and Capability”). Consider all of the different appearances and form factors of the resources that we categorize as “computers” —their essence is that they all compute, an invisible or theory-like principle that does not depend on their visible properties.363[Cog]

A final principle for creating categories is to organize resources that go together in order to satisfy a goal. Consider the category “Things to take from a burning house,” an example that cognitive scientist Lawrence Barsalou termed an ad hoc or goal-derived category.364[Cog] What things would you take from your house if your neighborhood were burning? Possibly your cat, your wallet and checkbook, your important papers like birth certificates and passports, and grandma’s old photo album, and anything else you think is important, priceless, or irreplaceable—as long as you can carry it. These items have almost no discernible properties in common, except for somehow being your most precious possessions. The category is derived or induced by a particular goal in some specified context.