Physics is often spoken of as the archetypical natural science. As discussed in Chapter 2, within the tradition of code theory it is regularly positioned as the prototypical hierarchical knowledge structure (e.g. Christie et al. 2007, Maton and Muller 2007, O’Halloran 2007), with both strong verticality (the ability to develop ever more integrative and general propositions encompassing larger sets of phenomena) and strong grammaticality (the ability to specify relatively unambiguous empirical referents, Muller 2007). Physics is thus characterised as being able to link theory to the empirical world and to generate new knowledge that subsumes current understandings. This characterisation offers a useful insight into the overarching knowledge structure of physics, however, as argued a number of times, it does not allow us to see the organising principles that underpin this structure. In other words, it does not specify the mechanisms that produce this structure, nor how we ‘see’ this in data. As Maton (2014: 109) argues, categorising a discipline such as physics in terms of knowledge structure is good to think with, but it does not provide analytical tools to understand how this comes about.
In order to access the organising principles underpinning the knowledge structure of physics, this chapter will continue the thread developed in the previous chapter and consider the discourse of physics through the LCT variables of semantic gravity and semantic density. Recapping the explanations in Chapters 2 and 5, semantic gravity is concerned with the degree to which meanings are dependent on their context (with stronger semantic gravity, SG+, being more dependent on context and weaker semantic gravity, SG−, being less dependent) while semantic density is concerned with the degree of condensation of meaning in a term or practice (with stronger semantic density, SD+, indicating more condensation of meaning and weaker semantic density, SD−, indicating less condensation of meaning) (Maton 2014, Maton and Doran 2017a). Previous chapters have proposed that a hierarchical knowledge structure’s ability to establish integrative and general propositions encompassing large sets of empirical phenomena depends in large part on being able to generate strong semantic density. Similarly, the ability to produce unambiguous empirical referents arises largely from its broad range of semantic gravity. If we consider physics as a hierarchical knowledge structure, we should thus be able to see in its discourse the potential for strong semantic density, and for movement between a large range of semantic gravity (such as those shown in Conana 2015).
The previous chapter gave an insight into the role mathematics plays in organising the knowledge of physics by tracing the development of mathematical genres and grammar through physics schooling. This chapter will build on this base by characterising the discourse of physics in terms of the images it uses in relation to mathematics and language. By doing so, it continues the progression traced through the previous chapters. Chapter 2 considered how language organises the highly technical knowledge of physics. Chapters 3 and 4 continued this monomodal focus by focusing on the grammatical organisation of mathematics. Chapter 5 brought mathematics and language together and considered them from the perspective of genre. This chapter brings in images and considers their role alongside mathematics and language in construing the knowledge of physics. Whereas the previous chapters have focused on grammar and genre, this chapter will view the role of each resource in the discourse of physics through the SFL register variable of field. By developing a field-based description, this chapter builds upon the rich descriptions of scientific language in SFL (discussed in Chapter 2) and offers a common perspective for comparing mathematics, language and image.1 By combining this with an analysis using LCT’s Semantics, this chapter allows us to understand the specific knowledge-building affordances of each resource and the organisation of knowledge in physics as a whole.
Like any academic discipline, physics has its own distinctive ways of meaning. It puts its language, image and mathematics to work in specific ways to establish its own disciplinary discourse. This discourse manifests itself in texts that are ‘semiotic hybrids’ (Lemke 1998) constituted by a critical constellation of modes (Airey and Linder 2009), where each resource construes disciplinary knowledge in complementary ways. At the same time, different semiotic resources can organise similar disciplinary meanings. Although meanings are often resemiotised (Iedema 2003) across a text, a curriculum or a discipline through an array of different semiotic resources, the disciplinary meanings realised by each resource are still related. This is not only the case for the professional discourse of physicists or researchers, but also the pedagogic and assessment discourse in physics education. Students at various levels are regularly asked to read and write texts that involve mathematics, language and image organising similar technical meanings. For example, Text 6.1 shows a senior high school student assessment and response in which the questions involve both language and image, and the student response (boxed) involves language and mathematics.
Question 27 (4 Marks)
A simple motor consists of 200 coils positioned in a region of uniform magnetic field with a strength of 0.10 T. The plane of the coil is parallel to the magnetic field. The coil is a square with an area 0.01 m2, and carries a current of 1.0 A. The motor drives a pulley of diameter 20 cm.
- (a) In order to prevent rotation should a weight be hung at X or Y?
- (b) What is the magnitude of the net torque acting on the pulley if a mass of 0.3 kg is hung at point X?
- (c) Explain how the use of a radial magnetic field would improve this motor?
A radial magnetic field would mean the plane of the coil is always parallel to the magnetic field lines thus producing maximum torque constantly
Text 6.1 Language, mathematics and image in a senior high school assessment
In order for the student to successfully answer the questions, they must reason from the meanings given in both the language and image. In addition, they must be able to reorganise these meanings into both mathematics and language. This is because each of these semiotic resources present technical meanings associated with the motor described in the initial question, but also present these meanings in a way not precisely translatable across the resources. Such a task requires the student to know what meanings each resource can construe and when each is appropriate. Understanding the similarity and difference of resources in the construal of physics knowledge is crucial to understanding the knowledge of physics itself and so will be a constant theme throughout the chapter. We will see how texts in physics manage to build vast networks of interlocking meanings and how these meanings contribute to physics’ knowledge structure.
The discussion will begin with a brief review of field as viewed from language and an interpretation of mathematics in field-based terms. We will see that language and mathematics organise different dimensions of field and thus complement each other in construing the knowledge of physics. Second, we will consider images, in particular diagrams and graphs, to show the significant meaning potential available in individual images and the possibilities for types of meaning not readily available through language or mathematics. Throughout the chapter, we will interpret the field-based perspective of each resource from the perspective of Semantics in LCT and thus build up a picture step-by-step of the knowledge structure of physics.
6.1 The Field of Physics Viewed From Language and Mathematics
As discussed in Chapter 2 language arranges the knowledge of science into deep taxonomies and long sequences of activity (Halliday and Martin 1993). Scientific taxonomies are either compositional, arranging technical terms into part-whole relations (such as the relation between an atom and its constituent nucleus and electrons), or classificational, arranging technical terms into type-subtype relations (such as the relation between atoms and its subtypes, hydrogen atom and helium atom). Complementing these taxonomies are activity sequences that show progressions of events associated with a field. In science, these are typically sequences of implication where the unfolding of events is based on absolute contingency. That is, the progression of happenings is such that there is no possibility for counter-expectation. In language, these implication sequences are often realised by relations of causality, where each event necessarily causes or implicates the next. An example is the implication sequence: the relativistic Doppler effect causes a shift in the frequency of light. In contrast, certain situations allow sequences to be less deterministic. These sequences, known as expectancy sequences, simply display expected or typical unfolding and thus open the possibility for unexpected events to occur. These expectancy sequences are often realised in language through temporal rather than causal relations, such as in: the experiment involves placing gold foil over the slit after pumping all the air out.
From the perspective of language, therefore, the field of physics is organised through a large set of relatively deep taxonomies of composition and classification, and a series of activity sequences involving entities that comprise these taxonomies. Every technical term gains a large swathe of meaning from its position in these intersecting dimensions, and thus displays relatively strong semantic density (Maton and Doran 2017 a, b). Language is, however, only one component of the technical discourse of physics. As the previous chapters have shown, mathematics construes its meanings in considerably different ways to language through a distinct grammar and by realising distinct genres. Accordingly, in physics the technical meanings arising from mathematics are organised along markedly different dimensions than those arising from language. In order to contrast mathematics with language in these terms (and with images further into the chapter), we must now briefly reinterpret mathematics in terms of field.
The overarching grammatical organisation of mathematics raises the question of what type of field-relation it construes. The relations are not composition: in p = mv, m is not a part of p or v. Nor are they classification: in p = mv, m is also not a type of p or v. Nor do they organise any sort of expectancy sequence with probabilistic relations. Rather, the grammatical organisation appears to present a large network of interdependency. When the value of one symbol changes, at least one of the others must necessarily also change. In this way, the relations are closer to those of implication sequences in language that indicate that if one event occurs another must necessarily also occur. However, unlike the implication relations realised in language, those of mathematics do not suggest any type of unidirectional sequence. Each element in the vast network of interdependency is contingent on every other. Moreover, the grammar of mathematics can specify large sets of these relations in one synchronic snapshot. This offers a subtle distinction to implication sequencing in language, and suggests the need for a small reinterpretation of implication for mathematics. Whereas language indicates implication sequences with a definite direction, in mathematics we can view the vast interconnected networks of meanings as implication complexes without any directionality. Seen in these terms, mathematics in physics works to construe large complexes of implication whereby each symbol is contingent on every other.
This interpretation allows us to trace the realisational relationship between the field of physics and the grammar of mathematics. First, each field specifies its own particular implication complexes that are specific to the particular area of physics it covers. Second, these implication complexes are realised by particular covariate relations in the grammar of mathematics (discussed in Chapter 3), which remain stable across the field. Third, in conjunction with the choice of Theme and Articulation, these covariate relations coordinate the univariate organisation of symbols within both statements and expressions. This results in there being only a small set of mathematical statements that are acceptable within any particular field. In effect, these statements and the symbols that comprise them constitute the mathematical technicality of physics.
If we look from this perspective at mathematical genres, we can interpret the function of derivations as building and making explicit field-specific implication complexes. However, it is not so obviously clear what quantifications do in terms of field. Where derivations build new relations between symbols, leading to new implication complexes, quantifications move from generalised statements to specific numerical measurements. In LCT terms, they work to strengthen the semantic gravity of physics by offering a pathway from abstracted theory to specific empirical instances. However, this movement is not accounted for in the current conception of field. The relation between generalised theory and specific instance is not one of taxonomy, nor is it sequencing or complexing. Rather, it appears to be a distinct field-specific dimension. Therefore as an exploratory step, I will propose a new scale that describes the movement between generalised relations and specific instances, termed generality. Under this scale, pronumerical symbols, such as Ei, m and F are at a higher generality than their numerical values, such as 5 and −1.5.
Such a scale allows physics to talk both in general terms about the broader physical world and in specific terms about a particular instance in the world. Although very preliminary in its formulation, it also offers an interpretation of the field-based meanings made by quantifications. Whereas derivations work to build implication complexes, quantifications work to shift physics from higher generality to lower generality (from a generalised description to a measurement of a specific instance). Notably, this occurs in only one direction. Quantifications only allow a movement from the general to the specific, not the other way around. In the data under study, there is no mathematical genre that offers a shift from numbers to generalised equations. Although at a higher level of mathematics such a shift is possible through statistical and mathematical modelling, the algebra and calculus in physics schooling only affords a single direction. However, if we focus on images in physics, we see that graphs do offer movements in the opposite direction. They complement quantifications by arranging empirical data into patterns that can be incorporated into generalised theory.2
Closing the discussion of mathematics, we see that it displays two distinctive features for the field of physics. Mathematics realises large complexes of implication relations developed through derivations, and shifts generality from highly general theory to specific empirical instances through quantifications. From the perspective of LCT, implication complexing affords condensation (strengthening semantic density) and decreasing generality affords gravitation (strengthening semantic gravity) in physics. As the previous chapter discussed, these two movements offer strong potential for developing the knowledge structure of physics. They allow physics to construe integrative propositions and engage with a large number of phenomena, while also creating a pathway for physics to connect its theory with its empirical object of study.
As discussed earlier, a look at any physics text shows that mathematics works not just with language but also with image. So far, we have reflected on field as it is developed by both language and mathematics, the next step is to consider the role of images. Aside from language, images are the only resource to rival mathematics for its pervasiveness in physics. Images are used earlier than mathematics in primary schooling, are prevalent throughout high school and university and form a critical resource in research. They are used to explain processes, report descriptive features and present raw data. They display a multifaceted functionality for organising the technical knowledge of physics and they complement the meanings made in language and mathematics. Thus an account of the discourse and knowledge of physics that avoids images would be significantly lacking.
Much of the power of images comes through the amount of meaning that can be displayed in a single snapshot. As we will see, physics images can present large taxonomies, long sequences of activity, extensive arrays of data and a broad range of generality all in a single image. Like both mathematics and language, images contribute to the hierarchical knowledge structure of physics as they can display a large degree of meaning and can develop generalised models from empirical data. This means they can scaffold the strong semantic density apparent in physics and at the same time invert the shift in semantic gravity afforded by mathematical quantifications. This will be developed in two sections. First we will consider diagrams (broadly interpreted), to highlight the possibility of multiple field-based structures in a single image. This will illustrate images’ strong potential for semantic density and offer an insight into their utility for presenting overviews of these meanings. Second, we will focus on graphs (again interpreted broadly) to show how information can be organised into multiple arrays in ways not readily instantiated in language or mathematics.3 These arrays of information allow for the generalisation and abstraction of patterns, and indicate shifts in semantic gravity in the reverse direction to those seen in mathematics. In conjunction with mathematics and language, we will see that images play a vital role in developing meaning and linking the theory of physics to the empirical world.
6.2 Diagrams in Physics
Diagrams are regularly used in physics to illustrate, exemplify, explain, explore and present a large range of technical meanings. In many textbooks, it is unusual for a page to go by without there being at least one diagram complementing the linguistic and mathematical text. Like language, diagrams present a range of field-specific meanings including activity sequencing and taxonomy. In fact, many of these dimensions appear more easily articulated through image. When considering field, Kress and van Leeuwen’s highly influential grammar of images (2006) is particularly useful. Many of the types of images they describe within their ideational meta-function resonate strongly with the model of field conceived for language. For example, narrative images that involve motion tend to realise activities in field through Vectors, while many conceptual images that show static relations of composition and classification through Carrier•Possessive-Attribute or Superordinate•Subordinate structures tend to articulate taxonomies. Indeed much of Kress and van Leeuwen’s grammar of images appears to have been developed with field-based meanings in mind. For this reason, Kress and van Leeuwen’s model will be the point of departure for the description in this chapter. Its various components will be introduced as they become relevant.
Before moving on, it is important to note that Kress and van Leeuwen are unclear as to whether an image can contain multiple structures of the same status. That is, whether multiple field-specific meanings such as an unfolding activity and a compositional taxonomy can occur simultaneously in a single image. They do indicate that a single structure defining the image as a whole can recur in parts of that structure, but it is not clear whether an image can display multiple structures at the highest level simultaneously. For the purposes of this chapter, I will argue for treating physics diagrams as potentially containing many structures of the same status. This means that various elements in images can play different structural roles, and therefore realise multiple field-based meanings. Indeed the regular use of multiple structures in a single image is one of the most powerful features of images for construing the technical meanings of physics. Before introducing these complex images, we will first explore relatively simple images that realise a single dimension of field.
As mentioned earlier, physics regularly utilises narrative images concerned with motion. From the perspective of field, these images construe activity. Narrative images include events and their participants and minimally involve a Vector. This Vector displays some sort of motion or direction and is often accompanied by a number of participants. An example of this is an experimental set up drawn on a senior high school classroom whiteboard, redrawn as Figure 6.1.4
This image illustrates a series of high-energy electrons (represented by dashes) emanating from an electron gun (the top rectangle) toward a piece of nickel (the bottom rectangle labelled Ni). The arrows among the line of electrons indicate a Vector that makes explicit the direction of motion. The dashed electrons are Actors and the nickel block they are moving toward is the Goal. In Kress and van Leeuwen’s terms, this image is a transactional image that involves a moving Actor with a definite end point as the Goal. To more fully describe the nuance in this image, it is useful to make an addition to Kress and van Leeuwen’s grammar. In Kress and van Leeuwen’s
model, there is not a clear distinction between the element from which the Vector emanates, but which does not itself move (in this case, the electron gun at the top), and the participant that is actually moving (the electrons); they are both considered the Actor. However, for the purposes of this discussion, the Actor will be reserved for the participant that is moving, while the participant from which the Vector emanates but which does not itself move, will be called the Source. So, under this analysis, the electron gun (Source) shoots the electrons (Actors) toward the nickel block (Goal) with the direction of motion indicated by the arrows (Vector).
This image represents a relatively simple image with only a single structure, and realises a single activity at the level of field. More commonly, images tend to display multiple Vectors in a sequence and therefore realise an activity sequence. For example, in another class, the same teacher drew a diagram of an experiment that led to the discovery of the neutron, redrawn in Figure 6.2.
This image can be interpreted as a series of Vectors emanating from Sources (on the left) toward Goals (to the right). The first Vector on the left is labelled Alpha particles and emanates from a Source labelled Polonium source toward a Goal (Beryllium). This Beryllium also functions as a Source from which another arrow Vector emanates to its right (labelled? as at this stage of the verbal explanation what is moving is not known) toward a Goal labelled Paraffin. Again, the Paraffin also functions as a Source for another set of arrow Vectors to its right (this time, with the Actors drawn in little circles with + in them), which lead to the Goal Geiger Counter. Finally, emanating from the Geiger Counter Source is another arrow to the right (Vector) which represents an electric current. Interpreted along these lines, the image shows an activity sequence where one event, an alpha particle moving from a polonium source to a beryllium block, is followed by three others events in succession.
Notably, in order to interpret this image as an activity sequence, the Goal of each Vector also functions as a Source from which another Vector emanated. That is, the Beryllium functions as both the Goal that the initial alpha particles move toward and the Source from which the? Vector emanates. These elements thus perform two functions. As we will see, such multifunctionality of elements is one of the crucial affordances that give images their power for organising the knowledge of physics.
Activity sequences such as this can become quite complex, with long strings of Vectors emanating from a single Actor. This is demonstrated by Figure 6.3 that illustrates a nuclear chain reaction that is the basis of both nuclear power and nuclear weapons (from a senior high school textbook).
Figure 6.3
Long activity sequence (Marsden 2003: 15)
This image begins with the Actor labeled n (representing a neutron), moving toward its Goal, a uranium atom (labeled U), with the direction of motion indicated by an arrow Vector. In addition to being the Goal of the initial Vector, the uranium atom also functions as the Source from which five other Vectors emanate in different directions. Each of these Vectors in turn represent the motions of other particles, functioning as Actors. One of these particles (also a neutron, but not labeled), moves toward the second uranium atom as its Goal, from which in turn five more Vectors emanate. This process is repeated once more, resulting in 19 Vectors and 19 participants being displayed, with three of the participants performing two functions (Source and Goal). In a single snapshot, this image realises a very large sequence of activity. We will see, however, that this is by no means the upper limit in the degree of meaning that can be displayed in an image.
Before moving on to other structures, it is important to note that multiple activities may be represented in an image without any explicit sequencing between them. This is illustrated in Figure 6.4 from a first year university exam. This image shows a horizontal wire with an electric current running through it (represented by the arrow and labeled I) and a coil (represented by the rectangle) moving upwards.
This image shows two activities of motion; however, they are not clearly sequenced in relation to one another. Although in the field of physics, the motion of the rectangular coil does produce another current in the wire, this is not explicitly shown in the image. Without any language or other resources to specify, it is not clear whether the current shown in the wire is independent of the motion of the coil or whether it arises because of it; both readings are possible. This highlights an important feature of images. Images do not appear to have as nuanced a capacity as mathematics or language to construe sequences or complexes of implication. Although they can realise multiple activities that are related implicationally, they do not grammaticalise the precise nature of these relations. In addition, images do not appear to make a clear distinction between implication and expectancy sequencing. They can show that one Vector follows another; but without labelling, there is seemingly no easy way to distinguish whether sequences of Vectors are related temporally or causally. Nonetheless, despite these restrictions, images can display several activity sequences in a single eyeful.
In addition to realising activity, images display a strong capacity for realising delicate taxonomies of composition. Figure 6.5 presents a relatively simple compositional outline of an atomic model known as the Bohr atom, drawn in a senior high school classroom. Grammatically, this is an analytical image, constituted by a Carrier (the entire atom) and six Possessive Attributes (the inner circle with a + in it, representing the positively charged nucleus, and each circular line surround it, representing different energy levels of electrons) (Kress and van Leeuwen 2006: 87). In terms of field, it realises a two-level compositional taxonomy, with the highest level (the whole) being the atom itself, and its constituents being the energy levels and the nucleus.
Each of the images we have seen so far realises a single dimension of field, either activity or taxonomy. However, the real power of images comes through their ability to present multiple structures that realise multiple types of field-based meanings. This greatly expands the meaning potential of images and often results in elements performing multiple functions. Through this multifunctionality, different field structures can be related, allowing the interlocking meanings of physics to be displayed in a single snapshot. To illustrate this, we will focus on Figure 6.6, an image from a university textbook. This image outlines two experimental apparatuses designed to view patterns of light emitted from different sources (known as the emission line spectrum). We will step through the meanings organised by this image one by one.
First, this image illustrates two examples of the same experimental set up—one on the left and one on the right—that differ only in their source light (the light bulb with heated filament on the left and the lamp with heated gas on the right). Due to their set up and similarity in overall purpose, these two apparatuses are of the same type; they both illustrate sub-types of an experimental set up known as a single slit experiment. At first glance, then, the grammatical structure of the image displays a covert classificational taxonomy involving two Subordinates but without explicitly showing the Superordinate (Kress and van Leeuwen 2006: 87). In terms of field, this image realises a classification taxonomy whereby each apparatus is a subtype of the single slit experimental apparatus.
Second, this image can also be read as an analytical image, displaying part-whole relations between each apparatus and their components. Each apparatus contains five pieces of equipment: a light source, lens, slit, diffraction grating and screen. From the perspective of field, these part-whole relations realise a composition taxonomy of each apparatus. To understand how this relates to the classification taxonomy analysed initially, it is useful to again note the similarity in composition between the two apparatuses. Four of the components in each apparatus (the lens, slit, diffraction grating and screen) are exactly the same; the difference between the two set-ups comes only from their choice of light source. The apparatus on the left utilises a light bulb with a heated filament, while the apparatus on the right uses a lamp with heated gas. Although the difference in a single component distinguishes the two apparatuses as different subtypes, their otherwise similarity strengthens the analysis of them being more broadly of the same type. Thus this image relates two interlocking taxonomies in one go. Their composition taxonomies justify the classification taxonomy and the classification taxonomy anticipates the composition taxonomy. It also shows that the apparatuses themselves function in both of these taxonomies as co-parts in a classification taxonomy and as wholes in two composition taxonomies.
The third structure in this image arises from the fact that, due to their different compositions, each experiment produces different results. This is encoded in the image through a narrative structure. This structure depicts the path of light moving from the light source (light bulb or lamp) through each piece of equipment until it hits the screen. A grammatical analysis indicates that in each apparatus a Vector representing light emanates from the light Source and moves toward the lens, functioning as a Goal. As the shape of the light changes after the lens, it is appropriate to also analyse the lenses as Sources from which the next Vector of light emanates. This pattern continues for each piece of equipment until the final Vector reaches the screen—the final Goal. This structure thus involves four Vectors for each apparatus: the light from the lamp/light bulb to the lens, then from the lens to the slit, then from the slit to the diffraction grating and, finally, from the diffraction grating to the screen. The different compositions of each apparatus shown by the different Sources—the light bulb with heated filament or the lamp with heated gas—results in different patterns on each screen, labelled as: (a) Continuous spectrum: light of all wavelengths is present and (b) Line spectrum: only certain discrete wavelengths are present. The differences in these patterns are important as they effectively present the results of the experiment. In lieu of an appropriate function in Kress and van Leeuwen’s grammar that relates this pattern to the narrative analysis, we will consider these patterns to function as Resultative Attributes (analogous to Resultative Attributes of English, such as straight in he bent that rod straight; Halliday and Matthiessen 2014: 327, Martin et al. 2010: 116).
The overall image thus realises two activity sequences—one for each apparatus—in addition to the classification and composition taxonomies shown previously. These activity sequences involve light moving from each apparatus’ light source to the lens, then from the light source to the slit, then from the slit to the diffraction grating and, finally, from the diffraction grating to the screen, resulting in their particular light patterns (their spectra). The differences in each activity sequence (i.e. the different patterns on the screen) arise from the different apparatus’ set-ups (i.e. the particular subtype of the apparatus and its corresponding composition). Thus the particular activity sequences that occur are intertwined with the particular classification and composition taxonomies. Moreover, they are all displayed in one image.
When analysed for each function impacting the field, the amount of meaning given in a single image is highlighted. By realising multiple activity sequences, compositional taxonomies and a classification taxonomy all from the same field, the image explicitly relates each of these field-specific meanings. If we take a further step to include the dozen labels in the image, the number of meanings displayed increases further. Each label indicates a synonymous relation between the linguistic label and the imagic element being labelled. The effect of this is twofold. First, elements that share the same label are seen to be the same. For example, the two pieces of equipment labelled slit are specified as being the same type of element. This further confirms the compositional analysis given previously and thus reinforces the unity between the apparatuses in terms of their place in the classification taxonomy. Second, the labels allow language and image to share meanings. The field-specific meanings associated with the linguistic technicality are linked with those associated with the elements in the image. For example, the distinction between the continuous spectrum and line spectrum as two subtypes in a classification taxonomy of spectra are related to the patterns displayed on each apparatuses’ screen. As we have discussed, these patterns are determined by the particular activity sequence in each apparatus. This activity sequence is in turn determined by the compositional taxonomy of each apparatus, which is similarly determined by the different types of apparatus in the classificational taxonomy. Therefore, from this single image, we can form an unbroken chain of relations between the separate classification taxonomy of spectra and that of types of apparatus, as well as the different activity sequences and composition taxonomies. A single image makes manifest the interlocking lattice of field-specific meaning.
This image is by no means unusual. In fact it is a relatively unremarkable image that would be easily understood by someone sufficiently trained in physics. In the following section, we will consider an image that shows most of these meanings plus those realised by graphs. Such is the pervasiveness of images like this—especially at the higher levels of physics—that a presentation of this amount of meaning is a common occurrence.
This potential to realise field-based meaning has significant implications for the semantic density of physics discourse. By explicitly relating multiple field structures of activity and taxonomy, images can indicate tremendously strong semantic density in a single ‘eyeful’. This enables the field of physics to be extended (if these relations had not previously been made explicit), and offers an efficient method of displaying this meaning. Through images, relatively large components of the field can be illustrated in a small stretch of imagic discourse. By sharing meaning with mathematics and language, each resource can utilise their own affordances to build the expanding network of meaning that constitutes the hierarchical knowledge structure of physics.
Activity and taxonomy are not the only dimensions of field images may realise, however. In the following section, we will see that graphs bring forward further meaning potential not readily apparent in language, mathematics nor any of the images we have seen so far.
6.3 Graphs in Physics
Graphs are regularly employed in physics to record measurements, illustrate patterns and highlight salient interrelations between technical meanings in physics. They allow a broad range of empirical observations to be related along multiple dimensions and establish a means for these relations to be incorporated into theory. Graphs first become prominent in junior high school before becoming regular features in senior high school and undergraduate university, and ubiquitous in research publications. Like diagrams, they display a rich and multifaceted functionality for organising the technical knowledge of physics. However, the meanings they organise are of a different order to the taxonomy and activity we saw in the previous section. By virtue of their organisation, graphs expand the meaning potential of physics by realising new and distinct dimensions of field. This section will be concerned with highlighting these dimensions and characterising their specific roles in constructing the knowledge of physics. First, it will show that graphs order technical meanings along axes in order to utilise images’ capacity for topological representation (Lemke 1998). This establishes arrays of meaning with the potential for continuous gradation of empirical observations in terms of degree, quantity or amount. Second, it will highlight that through these arrays graphs enable patterns to be abstracted and generalised from empirical measurements. This reverses the direction of generality shown by mathematical quantifications and thus enables the empirical object of study to speak back to the theory of physics. Finally, it will show that, as with the diagrams discussed in the previous section, graphs can be added to other images to enrich the relations between field-specific activities, taxonomies, arrays and generality. From this, we will see that the meaning potential of graphs complements that of mathematics, language and diagrams to extend the range of resources needed to construe physics’ hierarchical knowledge structure.
Graphs exhibit a significant degree of variability. They can show single or multiple dimensions, they can arrange discrete points or continuous lines and they can specify precise measurements or relative degrees. Minimally, a graph is realised by a single axis that allows data points to be ordered along a single dimension. Figure 6.7, drawn on a high school class whiteboard, exemplifies a one-dimensional graph such as this. This graph presents an array of light wavelengths that form part of what is known as the Balmer series (light that is emitted from a transitioning electron in a hydrogen atom). It arranges a set of discrete points along the horizontal axis, with each point’s relative position indicating its wavelength.
This graph arranges four points (shown as thicker lines), between the wavelengths of 400 and 700 nanometres (shown as nm on the graph). Those to the right are construed as having a longer wavelength than those to the left. In physics, these differences in wavelength indicate different colours of light. This was reinforced in the original drawing on the white board by using different colours to represent each line, with the far right being red, and the three lines to the left being more blue (unfortunately these colours could not be reproduced here). In the graph, the relative distance between each line specifies their relative difference in wavelength. For example, the larger gap between the far right line and the next line to the left indicates a significantly larger difference in wavelength than that shown by the smaller gap between each of the lines on the left.
From the perspective of field, the wavelength represented by position on the graph is not captured by classification, composition, activity or generality. That is, the relative size of wavelength does not indicate a part-whole relation, a type-subtype relation, some kind of event nor a relation between more specific and more general meanings. Rather, this spatial arrangement realises a further field-specific relation that we can term an array. Arrays organise technical meanings in a field along a particular dimension. In this case, the emission lines are being ordered along an array of wavelength. More generally, graphs primarily realise arrays through the spatial ordering of points or lines along an axis. Due to their facility for displaying topological meaning (Lemke 1998) images can in principle construe arrays with infinitely small degrees of gradation. This allows an indefinite number of terms to be related and, in the case of multidimensional graphs, offers the possibility of both continuous and discrete variation.
One-dimensional graphs such as Figure 6.7 are relatively infrequent in the discourse of physics. More commonly, graphs are presented with two intersecting dimensions. These graphs are known as Cartesian planes. Figure 6.8 illustrates a two dimensional Cartesian plane used in an undergraduate university lecture (but originally sourced from an art project focusing on global warming, Rohde 2007). The graph presents the range of wavelengths of light emitted by the Sun and arriving at the Earth. It arranges two sets of points, shown by the light and dark grey bars overlayed on top of each other (the original image coloured these as red and yellow). The lighter grey
bars (the taller ones) indicate the spectral irradiance (crudely, the amount of sunlight) emitted by the sun that hits the top of the atmosphere, while the darker grey bars (the shorter ones) indicate the spectral irradiance that travels through the atmosphere and hits sea level.
Figure 6.8 Solar radiation spectrum graph (Rohde 2007)
This graph coordinates two axes, the vertical y-axis, labelled Spectral Irradiance (W/m2 /nm) and the horizontal x-axis labelled Wavelength (nm). By presenting two dimensions, each point is characterised by two variables: its spectral irradiance measured in W/m2/nm (read as Watts per square metre per nanometre) and its wavelength in nm (nanometres, a billionth of a metre). For example, the dark grey bars at around the 500nm wavelength have a spectral irradiance of ∼1.4 W/m2/nm. As can be seen, each point in the graph shown by the dark or light grey bars is miniscule. This means the arrays present very small gradations in relation to each other, which enables a great deal of precision to be encapsulated in the field. In this particular field, this graph establishes an interrelation between the two arrays of spectral irradiance and wavelength. Thus one of the realisations of the field of the solar radiation spectrum is that each value of wavelength will have the specific value of spectral irradiance specified by this graph.
The arrangement of points into arrays directs us to the second feature of graphs that is significant for knowledge in physics: their potential for increasing generality. Both the light and dark grey bars present empirical observations—relatively specific measurements of spectral irradiance for each wavelength—based on tables published by the American Society for Testing and Materials (2012). In terms of field, they represent relatively low generality. However, by arranging these measurements along an array, the graph abstracts a general pattern of change. Both spectral irradiances peak around 500nm wavelength, drop off quickly at smaller wavelengths (on the left), but more slowly at longer wavelengths (on the right). The graph presents this general pattern in the form of a line that is labelled 5250° C Blackbody Spectrum. This line represents the spectral irradiance vs wavelength for a theoretical construct known as a black body (an idealised object that perfectly absorbs and emits all energy). By fitting this line to the empirical measurements, the graph portrays the solar spectrum as approximating that of a black body (specifically, a black body at a temperature of 5,250° C). It relates the empirical and low generality measurements to the theoretical and higher generality black-body spectrum. The graph thus offers the potential to abstract generalised theory from physical observations, i.e. to move from low to high generality.
In addition, by overlaying the set of dark grey points on the light grey points, the graph highlights a second dimension of generalisation. As the graph states, the light grey bars represent the sunlight that hits the top of the atmosphere. On the other hand, the dark grey bars represent the sunlight that makes it through the atmosphere to sea level. The difference in height (spectral irradiance) between the light and dark bars signifies the amount of light that is absorbed by the atmosphere and thus does not reach sea level. Whereas the array of light at the top of the atmosphere (light grey) closely resembles the idealised line of the black body, the light at sea level (dark grey) is much less smooth. The dark grey displays gaps and bumps where the light grey does not. These gaps indicate wavelengths where the absorption is highest, i.e. where the atmosphere stops the most light. Importantly, these gaps are empirical differences born of observation. By layering the dark grey and light grey measurements on top of each other, the graph compares the two by labelling the gaps absorption bands. Each absorption band is then given a specific classification—H2O (water), CO2 (carbon dioxide), O2 (oxygen) and O3 (ozone)—that signifies the molecule doing the absorbing. The graph therefore groups empirical measurements and generalises them into a classification taxonomy. In doing so, it again construes new higher generality field-specific relations from lower generality observations.
As this figure shows, graphs present opportunities for heightening generality. They allow arrays of specific measurements to be generalised into patterns, which then opens the path for these patterns to be abstracted into other field relations (such as classification). However, this is not to say that graphs only allow a shift from low to high generality. The nature of images is such that this reading path can be reversed; we could have begun at the generalised black-body line and moved to the empirical observations. But it does illustrate that graphs offer opportunities to shift from lower to higher generality. This movement contrasts with that afforded by mathematical quantifications. Mathematics organises movements from generalised theory in the form of implication complexes to specific measurements in the form of numbers (from high generality to low generality). Graphs, on the other hand, offer the possibility of movements from specific measurements to generalised theory (from low generality to high generality). In LCT Semantics terms, physics thus can strengthen and weaken semantic gravity. Quantifications present movements from weaker to stronger semantic gravity, while graphs present movements from stronger to weaker semantic gravity. Put another way, quantifications offer a tool for gravitation, graphs offer a tool for levitation (following the terminology used in Maton 2014). The two resources are thus complementary for physics’ knowledge structure. Together, they provide the means for the theory of physics to reach toward its empirical object of study, and for the empirical to speak back to the theory.
Figure 6.9
Energy level diagram for a hydrogen atom
In terms of semantic density, the arrays in graphs enable an enormous set of measurements with indefinitely small gradations to be related along a single dimension. This supports relatively strong semantic density and bolsters the range of empirical phenomena that can be encompassed in a single image. Moreover, semantic density can be strengthened by the abstraction
of field structures such as taxonomies, as greater constellations of meaning are assembled. The fact that, like diagrams, graphs can be combined with other structures in a single image further expands the strongest potential for semantic density. Series of activities, taxonomies, arrays and levels of generality can be presented in a single image, offering great power for integrating physics’ knowledge structure. To illustrate this, we will consider in detail at Figure 6.9, an ‘energy level diagram’ from a university physics textbook. This image illustrates a set of possible energy transitions available to an electron in a hydrogen atom.
First, this figure presents a one-dimensional graph. It arranges its points, shown by horizontal lines labelled n = 1, n = 2, etc., along the vertical axis and measures them in terms of their energy (e.g. −3.40 eV, −13.60 eV). It thus construes an array of energy levels in the hydrogen atom.
Second, the image presents a narrative structure with the series of arrows indicating a number of Vectors. Each Vector arrow emanates from a point on the graph. These points thus also function as Sources. Additionally, each Vector moves toward other points on the graph that function as Goals. As all points except two (the top and the bottom) have both a Vector emanating from it and a Vector moving toward it, these function as both a Goal and a Source. From the perspective of field, then, the 20 Vectors and their respective Goals and Sources in this image realise a large number of activities. Each activity corresponds to a transition from a particular energy level to another energy level.
Third, as there are 20 Vectors but only seven points from which a Vector can emanate or transition toward, many activities share the same beginning or end point. This forms the basis for a classification taxonomy. Each Vector is grouped according to its end point (its Goal, n = 1, n = 2, etc.) and is labelled as a type of series. Those moving toward n = 1 are labelled the Lyman series, those moving toward n = 2 are labelled the Balmer series, those moving toward n = 3 are labelled the Paschen series and so on. The end result is a classification taxonomy with three levels of delicacy. The most general superordinate arises from the fact that each arrow is structured the same way and is labelled as part of a series. It suggests that at some level all of the transitions (arrows) are of the same type (i.e. they are electron transition lines). At the second level, the image presents five subtypes of transition lines according to their end-point, each of which are labelled. The five subtypes of transition lines are the Lyman transition lines, the Balmer transition lines, the Paschen transition lines, the Brackett transition lines and the Pfund transition lines. Finally the third level within each subtype of transition line includes the specific transitions distinguished by their starting point. The Lyman transition series includes six lines, the Balmer includes five, the Paschen includes four and so on. In all, the image realises a three-level classification taxonomy that includes 26 nodes.
This three-level, 26 node classification taxonomy supplements the 20 activities being realised, the seven points on the graph and the 19 labels. The image thus encodes a large degree of meaning for what may, at first glance, look like a relatively simple diagram. This is relatively typical of many images in physics. They provide a means to synoptically integrate meaning, with little extra information given that is superfluous to the technical meaning of the field. Just as mathematics is geared toward construing ideational meanings, so are physics’ images.
This analysis also highlights the number of relations presented in the image by offering a path from the array to the activities to the classification taxonomy. The points on the array function as the beginning and end points for activities involving electrons transitions (though the electrons aren’t shown).5 Through the similarity in end points, the image organises the arrows into a classification taxonomy. The different types within this taxonomy are then labelled, allowing these field meanings to be discussed in language. By presenting an array, a taxonomy and a series of activities, this image realises much of the field-specific meaning associated with hydrogen atom electron transitions in a single snapshot.
Images clearly hold great power for organising the knowledge of physics. In LCT terms, this offers physics strong semantic density by allowing a significant spectrum of phenomena to be encapsulated and vast swathes of technical meaning to be combined. Further, they offer a large range of semantic gravity. They can present empirical measurements or generalised theory, and illustrate a pathway between both. In this way, they complement the gravitation of mathematical quantifications by affording a tool for levitation (weakening of semantic gravity). Finally, they can be labelled by both mathematics and language, and thus allow the meanings developed in one resource to be expanded in another. In sum, images allow meaning to be related and proliferated while maintaining contact with the empirical world.
6.4 Field and the Knowledge Structure of Physics
Mathematics, images and language all display a powerful utility for physics. They each utilise their own ways of meaning, their own types of texts and their own functional organisation to construe physics’ intricate and multi-faceted knowledge. This chapter has considered images and mathematics from the perspective of field in order to develop a means of comparison with each other and with language. Viewing each resource from the same vantage point allows a consistent basis for understanding the disciplinary affordances (Fredlund et al. 2012) images, language and mathematics exhibit for physics. The chapter has shown that while each resource demonstrates its own functionality, many of the same dimensions of field can be realised across language, mathematics and image. For example, language and image can both realise taxonomy, language and mathematics can both construe types of implication, and mathematics and image can both organise differing levels of generality. This shared possibility for meaning has implications for the broader stratal framework proposed in this book as it suggests a common stratum of register realised by language, mathematics and image may be productive for understanding their complementarity. Further to this, by examining each resource in relation to field of physics, we can approach the knowledge structure of physics in a more holistic way. We can see its potential for shifting semantic gravity and developing semantic density, and we can recognise the influence this has on the breadth of empirical phenomena integrated in the discipline. The final chapter will be focused on these two themes of disciplinary affordance and knowledge structure. First, it will overview the disciplinary affordances of language, image and mathematics in relation to the field of physics. Second, it will consolidate the work presented in this book to characterise role of each resource for the knowledge structure of physics as a whole. And, finally, it will look to the broader implications of this book for our understanding of knowledge and semiosis.
Notes
References
American Society for Testing and Materials (2012) G173–03 Standard Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 37o Tilted Surface, West Conshohocken, PASTM International. Retrieved from www.astm.org/Standards/G173.htm on 01/09/2015.
Airey, J. and Linder, C. (2009) A Disciplinary Discourse Perspective on University Science Leaning: Achieving Fluency in a Critical Constellation of Modes. Journal of Research in Science Teaching. 46. 27–49.
Christie, F., Martin, J. R., Maton, K. and Muller, J. (2007) Taking Stock: Future Directions in Research in Knowledge Structure. In F. Christie and J. R. Martin (eds.) Language, Knowledge and Pedagogy: Functional Linguistic and Sociological Perspectives. London: Continuum. 239–258.
Conana, C. H. (2015) Using Semantic Profiling to Characterize Pedagogical Practices and Student Learning: A Case Study in Two Introductory Physics Course. PhD Thesis. Department of Physics, University of the Western Cape.
Fredlund, T., Airey, J. and Linder, C. (2012) Exploring the Role of Physics Representations: An Illustrative Example from Students Sharing Knowledge about Refraction. European Journal of Physics. 33. 657–666.
Halliday, M. A. K. and Martin, J. R. (1993) Writing Science: Literacy and Discursive Power. London: Falmer.
Halliday, M. A. K. and Matthiessen, C. M. I. M. (2014) Halliday’s Introduction to Functional Grammar. London: Routledge.
Iedema, R. (2003) Multimodality, Resemiotization: Extending the Analysis of Discourse as Multi-Semiotic Practice. Visual Communication. 2:1: 29–27.
Kress, G. and van Leeuwen, T. (2006) Reading Images: The Grammar of Visual Design. 2nd ed. London: Routledge.
Lemke, J. L. (1998) Multiplying Meaning: Visual and Verbal Semiotics in Scientific Text. In J. R. Martin and R. Veel (eds.) Reading Science: Critical and Functional Perspectives on Discourse of Science. London: Routledge. 87–113.
Marsden, G. R. (2003) Timesavers Senior Physics: Quanta to Quarks. Peakhurst: Timesavers.
Martin, J. R. (2017) Revisiting Field: Specialised Knowledge in Ancient History and Biology Secondary School Discourse. Onomazein. Special issue on Systemic Functional Linguistics and Legitimation Code Theory. 111–148.
Martin, J. R. and Matruglio, E. (2013) Revisiting Mode: Context In/Dependency in Ancient History Classroom Discourse. In Huang Gouwen, Xhang Delu and Yang Xinzhang (eds.) Studies in Functional Linguistics and Discourse Analysis. Beijing: Higher Education Press. 72–95.
Martin, J. R., Matthiessen, C. M. I. M. and Painter, C. (2010) Deploying Functional Grammar. Beijing: The Commercial Press.
Maton, K. (2014) Knowledge and Knowers: Towards a Realist Sociology of Education. London: Routledge.
Maton, K. and Doran, Y. J. (2017a) Semantic Density: A Translation Device for Analyzing the Complexity of Knowledge Practices through Discourse, Part 1: Wording. Onomázein. Special issue on Systemic Functional Linguistics and Legitimation Code Theory. 46–76.
Maton, K. and Doran, Y. J. (2017b) Condensation: A Translation Device for Analyzing the Complexity of Knowledge Practices through Discourse, Part 2: Clausing and Sequencing. Onomázein. Special issue on Systemic Functional Linguistics and Legitimation Code Theory. 77–110
Maton, K. and Muller, J. (2007) A Sociology for the Transmission of Knowledges. In F. Christie and J. R. Martin (eds.) Language, Knowledge and Pedagogy: Functional Linguistic and Sociological Perspectives. London: Continuum. 14–33.
Muller, J. (2007) On Splitting Hairs: Hierarchy, Knowledge and the School Curriculum. In F. Christie and J. R. Martin (eds.) Language, Knowledge, Pedagogy: Functional Linguistic and Sociological Perspectives. London: Continuum. 65–86.
O’Halloran, K. (2007) Mathematical and Scientific Forms of Knowledge: A Systemic Functional Multimodal Grammatical Approach. In F. Christie and J. R. Martin (eds.) Language, Knowledge and Pedagogy: Functional Linguistic and Sociological Perspectives. London: Continuum. 205–238.
Rohde, R. A. (2007) Solar Radiation Spectrum. Image created as part of Global Warming Art. Retrieved from www.globalwarmingart.com/wiki/File:Solar_Spectrum_png on 31/08/2015.
Young, H. D. and Freedman, R. A. (2012) Sears and Zemansky’s University Physics with Modern Physics. 13th ed. San Francisco: Pearson.
