Definitions of Scientific Terminology in Popular Science Books: An Examination of Definitional Chains

Abstract

This article explores scientific terminology in popular science books. It goes beyond existing approaches to definitions in popularizations to suggest a dual, macro and micro, structure for the majority of definitions. This dual structure manifests as chains of definitions that include prototypical, procedural, and figurative definitions. Analyzing the structure and functions of the chains (macro structure) and their individual components (micro structure), this article does not confirm the phenomenon of substitution observed by Myers yet suggests that even without the replacement of terminology popular science maintains the focus on the specific rather than the general.

Keywords

definition definitional chain popular science terminology

Introduction

Scientific terminology is always associated with professional science and is seen as one of the key obstacles for the public consumption of science. For instance, Boersma, Poortvliet, and Gremmen (2019) and Myrick, Ahern, Shao, and Conlin (2019) point out that terminology can carry negative connotations that influence public’s perception and interpretation of the issues discussed. Priest (2009, p. 760) writes that “the public is largely uninterested in . . . highly technical” aspects of science. As a result, popular science either shuns scientific terms, replacing them with more recognizable equivalents, or it introduces definitions that are designed to guide readers through the texts that choose to keep discipline-specific formulations. Calsamiglia and Van Dijk (2004) see the role of definitions as explanatory and list definitions alongside metaphors and examples. Myers (1990) argues that manipulations of scientific terminology, especially omission of scientific terms in favor of more familiar reformulations, results in shifting the focus away from science and its processes and into specific actants and their actions.

In this article, I propose that while the handling of scientific terminology in popular science texts may result in a shift away from the generalities of the scientific process, definitions are crucial aspects of the popularization process and represent more than simple explanations of esoteric vocabulary. Their value is in their specificity. In fact, modern popular science authors go out of their way to introduce new forms of definitions, some of which show science in action or turn it into art. It is my purpose to demonstrate the variety of definitional strategies used by popular science authors and to encourage more researchers to look at definitions as self-contained units not only as parts of broader communicative categories such as explanation or illustration. To achieve this goal, I focus on linguistic elements that constitute definitions rather taking a more holistic approach and looking at explanatory strategies in general terms. I discuss several studies that do choose to examine definitions in that vein and argue that they are not always as productive because they fail to recognize or, in some cases to qualify, certain constructs as definitions. Thus so far, definitions in popular science have been limited to the sidelines and seen, for the most part, as structurally simplistic. My study demonstrates that this is not the case.

As Calsamiglia and Van Dijk (2004, p. 370) point out, “‘technical’ or ‘specialized’ aspects” of popular science texts are “usually considered the core of the . . . communicative act of popularization.” The explication of such passages would be impossible without defining the associated terminology, and replacements, as Myers (1990) shows, alter the intent and sometimes the message of the professional scientific original. The challenge, then, is to handle definitions in a way that adheres to the norms of popular scientific discourse yet preserves the technicality of the original. I observed that this complex task is often accomplished not through a single definition but through what I shall call a definitional chain—a combination of several definitions that contains commonly recognized approaches to defining (such as X is Y) and novel ways of presenting scientific terminology (e.g., telling the reader what X does).

Definitions of scientific terminology in popular science texts when discussed at all are usually conflated with other communicative strategies such as illustration (e.g., Gűlich, 2003) or mentioned in passing, referred to as “brief” asides (Hyland, 2010, p. 121). It also not unusual to regard definitions in narrow terms that position them as explanations of only “unknown words” (Calsamiglia & Van Dijk 2004, p. 379). Myers (1990, p. 183) acknowledges the importance of definitions but still downplays the complexity of the phenomenon by suggesting that popular science defines the terms “simply.”

However, such views ignore the fact that some scientific terms might be familiar to readers, who at the same time do not have a full grasp of the concepts. Almost everyone has heard of the big bang or dark energy but not everyone understands these terms well enough to navigate through a popular narrative. This is why Brian Greene, for example, supplies definitions of these not-entirely-unknown words, and his approach to defining might be described as simple only on the surface:

1. The big bang model describing a cosmos that began enormously compressed and has been expanding ever since became widely heralded as the scientific story of creation. (Greene, 2011, p. 20)

To someone used to definitions in dictionaries or to Aristotle’s classical approach (A = B), this text segment will not look like a definition at all. Others might argue about its veracity; as Austin (1962) points out, however, “the intents and purposes of the utterance and its context are important; what is judged true in a school book may not be so judged in a work of historical research” (p. 142). Most will not recognize this text segment as a definition because the term (“the big bang model”) and what Aristotle called the definiens (“describing a cosmos that began enormously compressed and has been expanding ever since” and “the scientific story of creation”) are not joined by any connectors, and the definition itself functions as a sentence. Such a method will be unacceptable for a traditional dictionary, but it is quite common for naturally occurring definitions. For instance, Cormack (1998), whose study involved analysis of natural texts, regards the following sentence as a definition: “A mammal suckles its young . . . where mammal has the definiens suckles its young . . . with no intervening connective” (p. 167). While Cormack (1998) recognizes this and similar constructs as definitions, she concedes, “I have no clear examples of such definitions” (p. 167). At the same time, my analysis shows that in popular science this type of definition is the second most common after the traditional definition. See Table 1.

Table 1.

Frequency Information for Definitional Chains and Chain Components.

		Chain components
Author	Chains	Prototypical definitions	Procedural definitions	Figurative definitions
du Sautoy	5	52	15	7
Greene	10	87	39	5
Kaku	7	70	45	2

Of the existing analytical frameworks for definitions in popular science, the communicative approach, which is an analytical framework drawing on the interaction between an author and a reader, is the most fruitful. In fact, Gűlich (2003) observed phenomena similar to definitional chains, yet her study does not recognize the multipronged approach to scientific terminology as a formal act of defining. Gűlich (2003) focuses on broad communicative strategies where “reformulations”—the term she uses for text segments that introduce scientific/technical terms—exist in conjunction with other techniques such as illustration and explanation. Overall, her approach is primarily functional (and thus broader) with minimal attention to form; mine is more heavily guided by formal rules of definition construction (and thus more limiting), and I attempt to position my findings alongside the commonly recognized structural frameworks for definitions.

While I do not deny the communicative powers of definitions (in fact, I explore definitional chains as potential reader engagement mechanisms), I choose to emphasize the form in order to position definitional chains as segments that contribute to knowledge construction. It has been shown than when it comes to knowledge construction, especially construction of scientific knowledge among nonspecialists, structure plays an important role (Monteiro & Keating, 2009; Yaros, 2006). Definitions have a particularly recognizable structure, and it is this structural organization that signals new information. The emphasis on structure and a particular order of definition components has been important from the very beginning. Aristotle, for instance, suggests only one acceptable progression for a properly functional definition: from universal features of a defined object to specific elements that make it unique. Monteiro and Keating (2009) report that definitions are the second most important element to construction of knowledge after the presence of an expert voice.

Ouvrier-Buffet (2009) suggests that “the defining process represents a specific constant of the language and of the human thought” (p. 2346). In this respect, the study of the language and structure of definitions provides an insight into the construction of scientific knowledge for nonspecialists. Cormack (1998) takes a broader approach to the cognitive dimension of defining when she states that “the fact that attaching meanings to words is a human activity is frequently reflected in the form of a definition” (p. 166).

Communicative strategies, while also involved in knowledge construction, have additional foci. As Myers (1990) shows, reformulations or replacements of scientific terminology lead to some degree of distortion of the original message because factors other than construction of knowledge come into play. For example, when it comes to communicating science to the public, there are the issues of public trust, perception, and background knowledge in addition to the nature of scientific knowledge itself. Drawing on the works of Myers (2003) and Yang (2003), I suggest elsewhere that the type of knowledge about science that the public possesses is different from that of the scientific community (see Pilkington, 2016, 2018). Public’s perception and understanding of science is often connected to emotionality (Caracciolo, 2013; Moirand, 2003; Pilkington, 2016, 2018, 2019; Sackler, 2014; Turney, 2004a), and emotional appeal becomes an important factor for authors to consider.

Furthermore, popular science authors often address multiple audiences in a single text, and not every popular science book is intended for nonprofessionals exclusively. For instance, Bucchi (1998) and Turney (2007) present evidence that popularizations target professional audiences, and as Hyland (2010) notes, popular science “is a discourse related to the academy” (p. 118).

All the aforementioned studies, however, do not consider definitions and the affect these issues have on incorporation of scientific terminology. Myers’s (1990) approach to definitions is telling. His book takes a more rigid view of definitions than it does of the other aspects of popularizations. Myers’s later works especially show the flexibility of popular scientific writing and its multifaceted approaches to the scientific subject matter with an idea that a popularization is not a direct translation and should not be treated as such (e.g., Myers, 2003). When it comes to definitions, though, issues of “distortion” surface. To me, this suggests that definitions in popular science represent a challenge for all involved: the authors, the readers, and the scholars. These constructs have to combine the ease of a good explanation with the integrity of a scientific fact. No one short sentence or a parenthetical can achieve this goal.

I argue, however, that definitional chains maintain the integrity and intent of the original terminology they introduce while also remaining accessible. This is accomplished by splitting a definition into several subsections each of which is responsible for a specific aspect of the defined entity/idea. So, while a definitional chain may contain metaphors or illustrations, it will also include a more traditional definition. This tactic combines the formal rigor of definition construction with reader-friendly explanations. In effect, a definitional chain represents a middle ground between total omission of scientific terminology and a purely communicative approach to technical language.

My goal for this study is to account for all possible types of definitions that may be present in popular science books and to demonstrate that definitions can take unusual forms—appear as constructs different from those found in dictionaries or commonly regarded as definitions by scholars of philosophy or logic. In doing so, I am confirming that textual segments that previous researchers (e.g., Cormack, 1998; Gűlich, 2003) have tentatively identified as approaching the status of the definition can indeed be considered definitions.

I begin my analysis with a brief overview of the basic definition structure and introduce the idea that there is a debate about the form and function of definitions. I then proceed to the description of my data collection techniques and analytical methods before offering a discussion of specific examples of definitional chains and their components. By positioning definitional chains within the realm of defining strategies, my study contributes to the examination of naturally occurring definitions and shows further support for a variety of approaches and the ingenuity of their creators.

Structure and Classification of Definitions

In Physics, Aristotle (1984a) suggests that the best way to examine “principles, causes, or elements” of a thing would be to “advance from universals to particulars” (p. 315). His view of a proper definition is quite similar. He sees definitions as representing both universal (genus) and particular (differentia/difference) features of the object they define. He argues, therefore, that definitions must include genus but also comments that difference is easier to identify: “It is easier to define the particular than the universal—that is why one should always cross from the particulars to the universals” (Aristotle, 1984b, pp. 161-162). A classic, or prototypical, definition that results from Aristotle’s observations has the A = B structure, where A represents the subject being defined (definiendum), and B is what’s called definiens (describers composed of class and difference). See Table 2 for examples.

Table 2.

Prototypical Definition.

Variations by the position of definiens and the form of the hinge	Representative example
Definiendum hinge Definiens	But they had yet to invent the place-value system, which is a way of writing numbers [genus] so that the position of each digit corresponds to the power of 10 that the digit is counting [difference] (du Sautoy, 2011, p. 20).
Definiendum typographical hinge Definiens	Kaluza-Klein theory, proposition [genus] that our universe has spatial dimensions beyond the three of everyday experience [difference] (Greene, 2011, p. 85).
Definiens hinge Definiendum	To obtain these uniform magnetic fields, physicists start with two large coils of wire [genus], roughly two feet in diameter, stacked on top of each other [difference]. This is called a Helmholtz coil (Kaku, 2011, p. 61).
Definiens typographical hinge Definiendum	The most basic [difference] object of mathematics [genus]: numbers (du Sautoy, 2011, p. 2).

Note. Bolded text indicates definiendum, italics indicate the hinge, underlined portions indicate definiens.

To this day, is it possible to argue about what belongs and what does not belong to the category of definiens. Numerous scholars of language contributed their own approaches (e.g., Copi, 1972; Harris & Hutton, 2007; Moon, 2009; Plato, 1956; Robinson, 1962; Schiappa, 2003). There are also discussions about the hinge—the connector between the definiendum and the definiens. Some argue that an explicit hinge (i.e., a hinge expressed by the verbs “to be,” “to call,” “to identify,” etc.) is essential to proper processing of the information contained in a definition (e.g., Barnbrook, 2002; Moon, 2009). Barnbrook (2002) stresses the “crucial importance” of the hinge “since it specifies the nature of the relationship between the definiendum and the definiens, which is not always one of simple equality” (p. 61). Darian (2003), on the other hand, demonstrates that definitions of scientific terminology found in both professional and popular science often use typographical markers as hinges thus eliminating any possibility on nuanced meaning that a hinge expressed by a verb can deliver. Such typographical marks include equal sign, colon, “pairs of commas,” parenthesis, “pairs of dashes,” quotation marks, and italics (Darian, 2003, pp. 53-54). Cormack (1998, p. 167) makes a similar observation, stating that some text segments that function as definitions in a particular text exhibit no “connective” between the definiendum and its definiens.

One downside to the existing literature on definitions is that significant portion of it (especially explorations that come out of philosophy and logic) does not draw examples from or even consider naturally occurring texts. Cormack’s (1998) study breaks the mold in considering natural or “text definitions”—as she labels them—as the primary subjects of her investigation. Cormack (1998) comes to the following conclusion, “Text definitions are not uniform in even the outline of how they should be interpreted” (p. 322). This statement hints to the origins of the ongoing debates about the form and function of definitions and also suggests that conflating natural definitions with dictionary or logical constructs might be counterproductive. My study takes into account only naturally occurring definitions and contributes to the multiple interpretations of definition. It is also designed to confirm the status of definition for certain constructs that previous researchers have tentatively identified as resembling definitions.

Data Collection and Method

To collect my data, I examined three popular science books: Brian Greene’s The Hidden Reality, Michio Kaku’s Physics of the Future, and Marcus du Sautoy’s The Number Mysteries. I worked with a small corpus of 153,921 words. This corpus represents introductions and the first three chapters from Kaku and du Sautoy and an introduction and the first five chapters from Greene. The limited size of the corpus is due to the process of manual analysis and identification of definitions. Using Atlas TI software, I isolated text segments that introduce one or more scientific terms. The standard for a definition was taken from the classical approach to definitions developed by Aristotle and Socrates, where the definiendum (A) is equated with the definiens (B), which consist of genus and difference. On examination of the definitions in the corpus, it became clear than they represent more than traditional approaches to defining. In addition to prototypical definitions with the A = B structure, I also observed definitions where the hinge does not simply indicate a relationship of equality but rather carries the meaning that describes a process and definitions with metaphors and analogies as definiens. The first group of definitions I labeled procedural definitions, and the second group I called figurative definitions.

Results

Having focused on the structural guidelines for definitions rather than on explanatory functions solely, I observed that definitions in popular science exhibit micro and macro structures. A definitional chain represents a macro structure of a definition with individual components exhibiting micro structures that correspond to some variation of definiendum, hinge, and definiens. See Table 1 for the frequency information on definitional chains and individual string components.

Definitional Chains

A definitional chain itself does not approximate a traditional definitional structure as each component definition is structurally sound but functionally inadequate on its own. All components of a chain must be examined before a full definition emerges.

Consider an example of a definitional chain for the four-sided tetrahedron:

2. (a) The four-sided tetrahedron, or triangular-based pyramid (prototypical definition by genus [pyramid] and difference [triangular-based])

(b) encloses the least volume for a given surface area (procedural definition)

(c) it is the shape that requires the fewest number of faces to make (prototypical definition by genus [shape] and difference [that requires the fewest number of faces])

(d) Consider how a potato-chip bag is made. A cylindrical tube is sealed at the bottom, filled with chips, and then sealed in the same direction along the top. But look what happens if instead of sealing the top in the same direction as the seal at the bottom, you twist the bag 90 degrees and then seal it. Suddenly, you’re holding a tetrahedral bag in your hand. The tetrahedron has six edges: two where the seals have been made, and four that link the two seals—an edge runs from the end of each seal to each end of the opposite seal (figurative definition using analogy). (du Sautoy, 2011, p. 67)

The macro structure of the definitional chain, as observed in the definitions in my corpus, is always a combination of a prototypical definition, a procedural definition, and a figurative definition, not necessarily in this order (I discuss individual components in detail below). The purpose of a definitional chain is to approach the definition from multiple angles, each targeting a particular audience. This may result in doubling some of the definition types as in the above example with two prototypical definitions. Definition (a) might be adequate for a reader who can easily visualize a “triangular-based pyramid.” On the other hand, definition (d) targets the reader who might have trouble imagining such an object. Definitions (b) and (c) work for a more detail-oriented reader.

A definitional chain introduces the scientific term up front and then supplements its prototypical definition with more creative and nonspecialist friendly approaches. Note that there are two prototypical definitions in this particular chain, yet they are deliberately not combined but separated by a less traditional prototypical definition.

As research shows (e.g., Bucchi, 1998; Hyland, 2010; Monteiro & Keating, 2009; Myers, 1997, 2003), popular science deals with a varied audience ranging from scientists who are not experts in the subject covered to readers unfamiliar with science altogether. The strategy of a definitional chain supports the idea of a diverse audience. It clearly demonstrates that the authors of popular science are targeting readers with different educational backgrounds and attempt to address the needs of a wide range of readers. When one considers nonprototypical definitions (b and d) outside of the chain, their status as definitions may seem problematic. However, when a definitional sting is regarded as a whole, the function and value of each component become apparent. As Cormack (1998, p. 322) notes, “What is most striking about text definitions is the variety of linguistic and pragmatic structures and procedures which are exploited in their construction.”

The complex macro structure of a definitional chain eliminates the need for replacement of terminology. A definitional chain provides sufficient scaffolding that should not be confused with reformulation. There is only one “reformulation marker”—to use Gűlich’s (2003) terminology—“Consider,” which introduces the figurative definition. This reformulation marker, however, is not of the kind Gűlich (2003) observed. In addition to signaling one more part of the definitional chain, it also functions as a reader engagement mechanism—a directive to activate the reader’s imagination. As Gűlich’s (2003) examples suggest, reformulation involves replacement of scientific terminology. For instance, her analysis of the description of metabolism by a medical professional to a patient does not mention the term “metabolism.” Instead it discusses “muscles,” “recycling,” and “burning”—terms entirely familiar to any nonspecialist. A definitional chain, on the other hand, combines the introduction of scientific terminology with adequate explanation.

The micro structure of a definitional chain is best analyzed as individual component definitions. I introduce a discussion of each below.

Prototypical Definition

This aspect of a chain micro structure represents a classical definition on the A = B model. The only possible structural variations I observed came from the position and the realization of the hinge. See Table 2.

For the purposes of this study, I will consider any definition a prototypical definition based on the type of the relationship between the definiendum and the definiens that the hinge indicates. A hinge that signals equality between the definiendum and its definiens (be it in the form of a verb, a typographical marker, or by implication) appears in prototypical definitions.

Functionally, a prototypical definition is the most straight-forward of all chain micro structure components. It is meant to supply a general definition positioned at the head of the chain. It serves as an introduction of the term and is deliberately vague at times to allow other components to fill the gaps. Despite its classical structure, a prototypical definition that appears as a micro structure component of a chain is not always a viable definition option on its own.

Procedural Definition

A procedural definition is characterized by a hinge that describes how the definiendum functions. It is a definition by action:

3. To obtain these uniform magnetic fields, physicists start with two large coils of wire, roughly two feet in diameter, stacked on top of each other. This is called a Helmholtz coil, [prototypical definition with definiens preceding definiendum] and provides a uniform magnetic field in the space between the two coils. [procedural definition]. (Kaku, 2011, p. 61)

The above combination of a prototypical and procedural definition is interesting because of its structure and its function. It is also a prime example of the interconnectedness of chain components. The definiendum is placed in the middle of the two sets of definiens and serves both of them. Formally, the demonstrative pronoun is the definiendum, but functionally it is the phrase “Helmholtz coil.”

The prototypical definition follows all the classical guidelines and defines by genus (“coils of wire”) and difference (“two large,” “roughly two feet in diameter, stacked on top of each other”). The procedural definition identifies the definiens not by genus and difference but by the process (“provides a uniform magnetic field”), in which the definiendum is a participant, with the phrase “in the space between the two coils” as the spatial circumstance. The verb “provides” does not only describe the process but also represents a hinge for the procedural definition. According to Calsamiglia and Van Dijk (2004, pp. 384-385), the process or function of an object described within a definition corresponds to “a general schema of knowledge categories” that are the fundamental components of knowledge construction. Thus, a function of a procedural definition within a chain is similar to that of a prototypical definition, which is knowledge creation.

It is possible to dispute the nature of that knowledge and argue that Kaku’s (2011) definition of a Helmholtz coil is imprecise or places an emphasis on wrong elements. However, to follow Austin’s (1962) discussion about truthfulness of linguistic statements,

It is essential to realize that “true” and “false” . . . do not stand for anything simple at all; but only for a general dimension of being a right or proper thing to say as opposed to a wrong thing, in these circumstances, to this audience, for these purposes and with these intentions. (p. 144)

Thus, Kaku (2011, p. 61) is producing a definition that he deems appropriate and “true” for the audience of his text.

Figurative Definition

A figurative definition is a definition that relies on figurative language and thus embodies the act of imagination on the part of the author and the reader. It is a definition where a writer gets to demonstrate not only scientific knowledge but also a considerable amount of creativity. The information provided by a figurative definition is not the straight reflection of the knowledge possessed by the scientific community but rather the author’s interpretation of this information through an analogy or a metaphor that function as the definiends. In other words, figurative definitions are stipulative—they introduce a meaning appropriate for a particular communicative context and not necessarily acceptable in others; these are, in some ways, personal definitions that represent the view of reality by a particular individual, in this case the author.

4. Mathematicians say that the infinite tabletop and the video-game screen are shapes that have constant zero curvature. “Zero” means that were you to examine your reflection on a mirrored tabletop or video-game screen, the image wouldn’t suffer any distortion, and as before, “constant” means that regardless of where you examine your reflection, the image looks the same. (Greene, 2011, pp. 21-22)

This example shows Greene’s (2011) personal approach to defining “constant zero curvature.” Even though the author is not openly asking the reader to imagine anything (there is no directive), he calls on the reader’s imagination. Using familiar objects (mirror, tabletop) to explain complex terminology is not the only way Greene (2011) makes this definition more accessible. Structurally, it follows the traditional guidelines of A = B with a hinge (“means”) that is very common in prototypical definitions. However, in addition to expressing definiens as an analogy, this definition splits the definiendum (“constant zero curvature”) into two subdefiniendums—“zero” and “constant”—and thus provides two definitions for the initial definiendum. In each case, the definiendum is clearly identifiable, and so is the hinge that remains the same for both subdefiniendums and serves as a unifying structural construct. Splitting of the definiendum is a strategy used by Greene (2011), but it is not observed in the other two texts.

Using analogies and metaphors as definiens is the key feature of a figurative definition. At the same time, it is not only the common everyday objects that function as reference points in figurative definitions. In some instances, basic scientific notions are used alongside everyday objects to create imagery that defines a more complex scientific term. For example, du Sautoy (2011) introduces a definition for the Rienmann hypothesis using the behavior of gas molecules as a starting point. He relies on his reader to know what a molecule is:

5. Another way to interpret Rienmann hypothesis is to compare the prime numbers to molecules of gas in a room. You may not know at any one instance where each molecule is, but the physics says that the molecules will be fairly evenly distributed around the room. There won’t be a concentration of molecules in one corner and a complete vacuum in another. (p. 53)

Later, du Sautoy (2011) provides a figurative definition that helps the reader understand the structure of a molecule; however, he never shows any evidence that he thinks the reader is not at least partially familiar with a concept of a molecule:

6. A molecule can be visualized as a collection of Ping-Pong balls joined together with toothpicks. (p. 68)

Figurative definitions are often exciting and unexpected. They represent one of the creative sides of popular science texts. Table 3 provides additional examples of figurative definitions and identifies possible structural variations.

Table 3.

Figurative Definition.

Variations	Representative example
Definiendum hinge Definiens	A molecule can be visualized as a collection of Ping-Pong balls joined together with toothpicks (du Sautoy, 2011, p. 68).
Definiendum typographical hinge Definiens	. . . the cosmic horizons—the patches in the cosmic quilt (Greene, 2011, p. 28).
Definiens hinge Definiendum	This new way of looking at shapes, in which I’m allowed to push and pull them around as if they were made from rubber or Plasticine, is called topology (du Sautoy, 2011, p. 98).

Note. Bolded text indicates definiendum, italics indicate the hinge, underlined portions indicate definiens.

Discussion

Scientific terminology is usually seen as inaccessible to nonspecialist readers, an undesirable vestige of professional discourse (Boersma et al., 2019; Myrick et al., 2019; Priest, 2009). Research in this area is sparse and leaves gaps in the understanding of the form and function of definitions in popularized accounts. It is commonly assumed that popular science either omits scientific terminology entirely or supplements it with explanations that range anywhere from short phrases to several pages (Gűlich, 2003; Myers, 1990; Turney, 2004a, 2004b). In general, there are very few studies devoted to exclusively a systematic exploration of the presentation of scientific terminology in popularizations. Researchers tend to focus either on definitions of individual concepts (Calsamiglia & Van Dijk, 2004; Gűlich, 2003; Molek-Kozakowska, 2016; Ouvrier-Buffet, 2009) or on the blanket strategy of explanation that includes constructs that formally do not constitute definitions, for example, narratives, dialogues, and so on (Hinnant & Len-Ríos, 2009; Monteiro & Keating, 2009; Turney, 2004a, 2004b). In fact, Hinnant and Len-Ríos (2009, p. 96) consider definitions and substitution of scientific terminology as “story elements.” Such approaches, however useful, do not shed more light on the forms definitions take in popular science. More so, examinations of “unusual” natural definitions by researchers who do not recognize them as parts of definitional chains can lead to misunderstandings.

If a prototypical definition provides primary information about the subject, and a figurative definition addresses the emotional aspect of the defined term, a procedural definition offers a description of function. Procedural definitions are steeped in classical philosophers’ approaches to describing reality. These definitions are, essentially, what Aristotle and Socrates regarded as demonstrations, and while Socrates denied demonstrations properties of definition, Aristotle accepted them. “The principles of demonstrations are definitions” (Aristotle, 1984b, p. 149). As Deslauriers (2007) explains, a demonstration tells us what a thing does and thus affirms its existence, “When we know something of what a thing is, we can know that it is” (p. 90).

Procedural definitions contribute to a trend in popular science texts that Myers (1990) describes as emphasizing of individual objects and their actions instead of describing general processes. Myers (1990) attributes this change in emphasis to “the substitution of popular terms for scientific terms” (p. 182). However, procedural definitions preserve terminology yet place emphasis on individual instances of performance. Myers (1990) sees the transformation from the general to the specific as problematic, as I have mentioned above. He blames the lack of scientific terminology, among other things. As my data show, however, preserving scientific terminology does not automatically lead to the original, more general view of the scientific processes.

The effect of specificity that a procedural definition creates comes from the absence of genus. A procedural definition defines by difference alone. The genus is usually implied and easy to reconstruct:

7. Einstein Field Equations . . . tell us precisely how space and time will curve as a result of the presence of a given quantity of matter [procedural definition]. (Greene, 2011, p. 14)

8. [my paraphrase] Einstein Field Equations are equations (genus) that tell us precisely how space and time will curve as a result of the presence of a given quantity of matter (difference) [prototypical definition].

By acquiring a genus, the definition becomes more generalized since it is, according to Aristotle and Socrates, the feature of a genus to represent a general class.

Procedural definitions are the second most common type after prototypical definitions (see Table 1), which indicates a preference for the specific and points to one more way popular science authors achieve the shift of focus that Myers (1990) observed. Like figurative definitions, procedural definitions work well as components of definitional chains but will not be as effective on their own.

Figurative definitions usually suffer the most criticism when it comes to applying traditional frameworks to definitions in popular science. Examinations of metaphors and analogies in popular science abound (Caracciolo, 2013; Pilkington, 2018; Smith, 2013; Turney, 2004a, 2004b). They focus, for the most part, on the effectiveness of figurative language to communicate scientific concepts and very rarely on the structure of such text segments. These common approaches regard figurative formulations as inauthentic to professional science—devices that ultimately lead to “translations” or “re-creations” (Turney, 2004a), constructs that have to do more with imagination and affective domain (Caracciolo, 2013) or even with misrepresentation of facts (Pilkington, 2018) than with reality.

Such background coupled with Myers’s (1990) concern about substitution and reformulation of scientific terminology does not suggest figurative language as appropriate for defining. At the same time, if structure is taken into account, it is evident that these text segments are intended to work as definitions. There are many other ways a popular science text can make use of figurative language; it can appear as part of presented discourse, as a set up for a narrative, or become a through line for a book or article. So why use it to construct definitions? Especially when, as Turney (2004a, p. 337) points out, many of these text segments end up being “only marginally intelligible” because they often join metaphors and rely on the reader’s prior knowledge of certain scientific concepts, as the Rienmann hypothesis definition above does. What Turney (2004a, p. 337) is noticing is the increased cognitive load figurative definitions produce. He singles out “one-line descriptions” that is, segments that are most likely to exhibit definition-like structure, as the most problematic. In fact, all his examples of failed figurative comparisons are what I label figurative definitions.

Turney (2004a) looks at these constructs as stand-alone definitions, and as such, they, of course, seem inadequate. Designed to be interpreted within a definitional chain, figurative definitions make poor introductions of scientific terminology and cannot (and should not) compare with prototypical definitions as far as their information carrying properties. Turney’s is a common assumption that only prototypical definitions are present in popular science texts. Therefore, anything that does not function as a prototypical definition is seen as a failure.

Another frequent argument against figurative definitions, which Turney (2004a) voices, is their unintelligibility. This concern also stems from demanding the function of a prototypical definition from a figurative one. Figurative definitions should be judged by different criteria. As creative constructs, figurative definitions are interactive segments. Research in linguistics (e.g., Tagg, 2009) sees creativity as a collaborative process between the creator and his or her audience. Each act of creativity, in this interpretation, builds on prior knowledge. Thus, a figurative definition carries a double cognitive load for the reader. As Cockroft and Cockroft (2005) note, “Definition is inevitably part of every act of cognitive engagement” (p. 85). To that initial act, a figurative definition adds the element of creativity that in itself requires mutual understanding of the references made by metaphors or analogies.

Certainly, when examined out of context short segments with figurative language and definition structure might seem problematic. They are, however, never intended to function on their own—that is, outside definitional chains. As chain components, they are highly effective, yet their purpose is not entirely explanatory. This is why judging them by purely informational standards is not productive.

According to Tagg (2009, p. 163), figurative language functions to signal “involvement,” “convergence between speakers,” and “a sense of belonging.” Often these aspects of author/reader interaction manifest through directives—a unique feature of figurative definitions. To return to Example 2, the chain concludes with a figurative definition that contains directives “consider” and “look” in addition to reader pronouns “you.” The definition encourages the reader to imagine the process of creating a tetrahedron and presents this process as an easy one to duplicate if the reader is interested in a hands-on experience. At the same time, the remaining definitions in the chain are not interactive; they fulfill informational purposes in the more traditional ways.

Figurative definitions are designed to appeal to the affective domain of the reader and, at times, to demonstrate emotions of the authors. For example, when du Sautoy (2011) at the opening of a definitional chain introduces prime numbers as “the hydrogen and oxygen of the world of mathematics” (p. 6), the metaphor aims not so much at the creation of a memorable image but at reinforcing the author’s attitude that prime numbers are very important. Declaring the primes as essential as water is likely to spike readers’ interest; at the same time, this figurative definition is still preserving a traditional approach to defining scientific terminology—relating “the strange and exotic” to “the commonplace and unexceptional” (Hyland, 2010, p. 121). Hyland (2010, p. 121) also notes that this method of defining represents “the reader’s perspective.”

Other figurative definitions employ the affective factor by generating memorable visual imagery. For example, Greene (2011, p. 22) effectively uses a combination of a Pringles chip and a reader pronoun to produce an easy-to-remember mental picture:

9. Constant negative curvature . . . means that if you view your reflection at any spot on a mirrored Pringles chip, the image will appear shrunken inward.

According to Tlauka and McKenna (1998), mental images can be as effective as pictorial images in enhancing understanding, “the cognitive processes mediating imagined stimuli and responses are functionally equivalent to those mediating physical (perceptual) stimuli and responses” (p. 69).

Metaphors and analogies of figurative definitions act as reader engagement elements, but figurative definitions have yet another purpose. They help popular science authors shape and control their audience. Martin and White (2005) argue that when an author demonstrates his or her attitude toward a subject, this author is trying to persuade the reader to feel the same way. Thus, figurative definitions that express author’s positive evaluations of terminology influence the reader to be excited or to feel the importance of a certain concept. In this, figurative definitions are a vital component of definitional chains.

The presence of definitional chains across all three books indicates the universality of the approach. It also points to the complexity of the definition structure in popular science texts. Definitions could be formulated as more rigid constructs as well as less formal segments to account for the learner’s abilities, and variety of definitions can be combined to form a definitional chain. This fact that definitions adapt to their audience was first observed by Aristotle when he suggested that when “dealing with persons who cannot recognize things through [prototypical definitions], it may be necessary to frame the account through terms that are familiar to them” (Aristotle, 1984c, p. 239). As Chakrabarti (1995, p. 10) elaborates, Aristotle understands the importance of “the state of the person to be instructed” by the definition. Ouvrier-Buffet (2009, p. 2346), observes a similar point, “The forms, the status and the roles of definitions change notably . . . through teaching and learning processes” (p. 2346). As a result, definitions in popular science include figurative language, express the authors’ attitudes, and describe the processes in which a definiendum is involved. Such adjustments, I propose, do not diminish the role of the definition but make the information more accessible especially in the case of definitional chains, where a prototypical definition is supplemented by nontraditional types.

Conclusion

This article analyzed definitions of scientific terminology in three popular science books by Marcus du Sautoy, Brian Greene, and Michio Kaku. The results revealed a specific strategy of handling scientific terminology—a definitional chain. It is a chain of three types of definitions: prototypical, figurative, and procedural. One of the conclusions that this study reaches and that explains the dissatisfaction of previous researchers with certain definitions found in popularizations is that all components of a definitional chain must be considered before evaluating the quality of a definition.

I propose that, on the basis of my findings, it is possible to argue for a double structure for the majority of definitions in popular science: a macro structure, that is a definitional chain comprised a prototypical, figurative, and procedural definitions; and a micro structure that is represented by the individual components of a chain and corresponds to the classic A = B arrangement of the definiendum and definiens. Functionally, however, only the prototypical definition component of the chain closely embraces the classical approach. Figurative definitions may preserve the relationship of equality between the definiendum and the definiens, expressing it through the use of hinges similar to those observed in prototypical definitions (mean, call, is, etc.). At the same time, the definiens in a figurative definition are expressed by metaphors and analogies, so the equivalency is tentative. Procedural definitions are closer to prototypical definitions in terms of function; however, they present an entirely different relationship between a definiendum and its definiens—that of a process. The hinge in such definitions is realized by the verbs that indicate an activity of the definiendum.

In this classification of the micro structure as related to the classical arrangement of definition components, I preserve the formal approach to definitions and recognize that in order to be labeled a definition a text segment must include certain structural requirements. At the same time, by addressing the function of these components in context I expand my parameters and as a result account not only for prototypical definitions but identify new forms and functions and ultimately discover the strategy of a definitional chain.

Footnotes

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Olga A. Pilkington

Author Biography

Olga A. Pilkington, PhD, in applied linguistics, University of Birmingham (UK), is an assistant professor of English at Dixie State University. She is the author of The Language of Popular Science (McFarland), Presented Discourse in Popular Science: Professional Voices in Books for Lay Audiences (Brill), and coeditor of Lab Lit: Exploring Literary and Cultural Representations of Science (Lexington).

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