from phenomenology to field theory: faraday's visual reasoning

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From Phenomenology toField Theory: Faraday’sVisual Reasoning

David C. GoodingUniversity of Bath, U. K.

Faraday is often described as an experimentalist, but his work is a dialecti-cal interplay of concrete objects, visual images, abstract, theoretically-in-formed visual models and metaphysical precepts. From phenomena describedin terms of patterns formed by lines of force he created a general explanationof space-ªlling systems of force which obey both empirical laws and principlesof conservation and economy. I argue that Faraday’s articulation of situatedexperience via visual models into a theory capable of verbal expression owedmuch to his strategy of moving—via conjectural visual models—between thephenomenology of particulars (often displayed as patterns) and the generalfeatures of dynamical phenomena which he depicted as structures.

Everyday human reasoning combines visual, auditory and other sensoryexperience with non-sensory information and of course, with verbal andsymbolic modes of expression. Scientiªc reasoning is no different. Scien-tists use a variety of images that visualize phenomena, visual representa-tions of theories about phenomena and models that display structure andconnectivity. Such objects always combine visual and non-visual elementsbecause scientiªc work requires representations that are hybrid (that com-bine verbal or symbolic expressions with visual and other sensory modali-ties) and plastic, enabling the meaning of an image, word or symbol to benegotiated and ªxed (Gooding 2004a, 2004b). A diagrammatic renderingof a photograph of a fossil, X-ray, fMRI scan or bubble chamber trackmoves the eye and the mind from a barely interpreted visual source to ameaningful construct. This ‘move’ is motivated by the desire to under-

This work has been supported by grants from the Royal Society, London and by aLeverhulme Research Fellowship. I thank Frank James and Ryan Tweney for many stimu-lating discussions, and staff of the Royal Institution and the Institution of Electrical Engi-neers for help with archive material and apparatus.

Perspectives on Science 2006, vol. 14, no. 1©2006 by The Massachusetts Institute of Technology

Jonathan Simpson

muse

stand and communicate understanding. It is informed by expert (oftentacit) knowledge about indicative features that need to be preserved orhighlighted in the diagram abstracted from the source. Labelled dataplots,block diagrams and process models use labels, legends, index numbers andother annotations to integrate different kinds of knowledge. In the ªnalstages of model-based theorising complex structural models are reduced todiagrammatic abstractions that include just those features essential to atheoretical explanation. For example, Watson and Crick’s ªrst publisheddiagram of DNA is a schematic abstraction of their more complex struc-tural DNA model (Watson and Crick 1953). Recent work in psychologyand science studies shows that these features of representations remain asimportant to industrial-scale, technology-based science as they were to themore personal, bench-top science of Faraday’s time (Galison 1997,Goodwin 1995, Gorman 1997, Henderson 1999, Hutchins 1995).

Most philosophical discussion selects just one element of this activ-ity—statements about facts, entities, laws and formulae—as if these ver-balized, public forms of expression are the only generators and carriers ofmeaning. The advantage of verbal formulations is that they can conformto semantic or logical rules, but a preoccupation with syntactical featuresof representation means that we still lack an understanding of how visualthinking works in conjunction with language-based reasoning (Giere1999, p. 119). A further limitation of standard views is due to the as-sumption that science is a search for regularities, preferably expressed aslaws that relate measurable quantities. This quantitative-empirical modelof science prioritizes concepts, theories, experiments and explanations “inwhich causes are only allowed to act singly, and effects can only be ob-served in one dimension at a time” (Ziman 1968, p. 47). Experiments thatdemonstrate a regularity or isolate a dependent variable do have an impor-tant epistemic role. But new knowledge is rarely produced by methods aslinear or one-dimensional as this model assumes. As the physicist JohnZiman points out:

A photograph, a tape-recording, an electronic device, can react tomany causes simultaneously, and yet record the consequences as acomplex pattern, accurately and reproducibly. It thus permits us toentertain theories and explanations whose workings and conse-quences cannot be represented by symbols placed in order on thepage (1968, p. 48.).

This is why scientists design surrogate sensors that can present informa-tion in a form—usually visual—that lends itself to human interpretation.

This aspect of science draws on two features of human cognition ne-glected by traditional theories of science. The ªrst is our ability to recog-

Perspectives on Science 41

nize regularities as visual or auditory patterns—not just as Humean con-junctions of events. Most representations of facts are static, momentaryglimpses into a complex and dynamic world of change. To focus on de-scriptions and ignore their role in the search for process is to miss much ofwhat science is about. The second is our ability to integrate different kindsof sensory information into a single representation—not just consider onevariable at a time. These abilities underlie the use of patterns and the con-struction of phenomenal and explanatory models (Gregory 1981, Ball1999). The search for objects and laws is motivated by the search for ageneral, intellectual understanding of processes that produce our sensoryexperience. Visualization—making and manipulating images—is centralto this intellectual objective in most areas of science.

Images convey directly features of experience that humans are biologi-cally disposed to recognize as patterns (Clark 1997, Giere 2003). Regulararrangement or symmetry may appear to direct inspection, but be inher-ent in the images. Scientists rarely just ‘look at’ patterns. They infer theexistence of more complex regularities and causal mechanisms. Scientistsmanipulate what they are looking at to induce changes that generate newinformation about hidden structures and processes. In this way scienceextends knowledge by playing to human cognitive strengths and lim-itations, as well as by using cultural resources, social conventions andtechno-scientiªc systems. For example, W. L. Bragg manipulated the ge-ometry of his X-ray diffraction setup to deform patterns, generating newinsights about how to solve the problem of crystal structure (Bragg 1913,Gooding 2004a). To integrate cognitive processes into the emerging viewof techno-science as networks of culturally situated practices we need tolocate visualization in the context of other sensory practices withoutwhich it is blind.

Faraday’s work is particularly relevant to this problem. Creative think-ing involves a dialectical play of mental representations and materialartefacts. The latter are not simply externalised representations of the for-mer, they are as essential a part of the world in which Faraday thought andworked as a partially crafted lump of stone is to a sculptor. This endorsesan early insight of Herbert Simon, that much of the interesting complex-ity of the “inner environment” of human thought and behaviour is locatednot within the mind, but in the environment that we transform in orderto understand (Simon 1969, pp. 157–59). The feature of Faraday’s manydiscoveries most important to philosophy and psychology is the fact thathe recorded them in such detail and over a long period of time. Alongsidehis many discussions in letters, these record his many transformations ofimages and objects. They are a valuable source of information about hownew knowledge was envisioned and verbalized by an embodied, tech-

42 From Phenomenology to Field Theory

nically sophisticated, socially networked investigator. They provideglimpses of the close interplay of the senses (sight, hearing and proprio-ception), the hands, imagination, systematic and critical reasoning andalso at times the institutions and politics of science.

The need for ªne-grained accounts of the interplay of mental images,material artefacts and procedural knowledge is further highlighted by arecent critique of the semantic conception of theories. This recognizes theimportance of non-verbal, procedural and material aspects of scientiªcpractice argued in many sociological and historical studies (Galison andStump 1996, Pickering, ed. 1992). The working content of scientiªcknowledge consists not of universal truths but rather in the sets of model-ling practices and methods of approximation that scientists use to relategeneral and abstract theoretical claims to real observational situations(Baird 2004, de Chadarevian and Hopwood 2004, Morgan and Morrison1999). These are always particular and concrete. The more abstract andgeneral the statement of a theory, the less it actually applies to the worldas engaged by practicable methods of observation and measurement. Theconverse is also true: a low level representation of the phenomenology of adomain can achieve representational adequacy or a good ªt to data, but itlacks generality. There is always a trade-off between abstraction andgenerality, on the one hand, and the concrete achievement of empirical ad-equacy, on the other (Gooding 2003). So how is local knowledge general-ized? Sociologists and historians of science argue that it is made transfer-able via human expertise and technological implementation (Latour 1987)and is made communicable via abstractions such as the models which me-diate between theories and the phenomenal world and material embodi-ments of discoveries (Gooding, Pinch and Schaffer 1989, Pickering 1992).Scientiªc knowledge resides as much in material techniques and technolo-gies as it does in intellectual understanding (Baird 2004, Ihde 1991).

Analysis of work such as Faraday’s also helps clarify the notion of sci-ence as distributed cognition (Giere and Moffat 2003). Since the mid20thC most science has been conducted by teams and networks of practi-tioners. Established knowledge is viewed as a distributed property of net-works of humans, institutions, machines, representation systems, etc.However, one of science’s most distinctive features is that establishedviews embodied in its practices and institutions can nevertheless be chal-lenged and replaced. While established knowledge is readily explained asa distributed property of networks, the production of new knowledge can-not be assimilated entirely to what is ‘known by’ a distributed system.This model requires a way of explaining those innovations that challengethe assumptions and empirical methods of a scientiªc tradition (Kuhn1962, p. 142) by changing the representational conventions, procedures


and technical standards that sustain these methods (Galison 1997, Ras-mussen 1997).

These arguments underline several connected reasons for Faraday’s im-portance. First, Faraday’s records provide a rich, closely observed record ofthe knowledge-producing activity that managed the tension between ab-straction (in his aspiration for a general, synthetic theory of forces) and thepracticalities of obtaining robust empirical results in experimental terrainthat often lacked precursors or guides. Thus he prefaced the ªrst edition ofhis ªrst book with Trevoux’s slogan “C’est n’est pas assez de savoir le principes,il faut savoir MANIPULER” (Faraday 1827).1 Second, Faraday produced apowerful, general new approach to understanding electricity, magnetismand other ‘powers of matter’ using visual methods that Maxwell later de-scribed as mathematics “of a very high order” (Maxwell 1890, vol. 2,p. 360). These visual aspects of Faraday’s work offer insights into an im-portant feature of scientiªc thinking. His visual reasoning strategies aretypical of those used by many scientists before and since (Gooding 2004a,2005), making his records a valuable source of information about thewider cognitive function of visual imagination and of external representa-tions such as sketches, diagrams, physical models, simulations and experi-ments. Third, the survival of many of his instruments has made it possibleto trace, depict and even quantify aspects of the intertwined processes oftheoretical articulation and technological implementation (Gooding1990a, 1990b). It is often possible to trace the development of his appara-tus from exploratory, error-probing prototypes into reliable, visually com-pelling demonstrations (Gooding 1985, 1990a). Reconstruction of experi-ments can also recover un-recorded practicalities of using certain materialsand instruments and knowledge that is implicit in procedures (Tweney(2004), Tweney (this volume), Tweney and Gooding (1991).

When viewed through these means of accessing it Faraday’s work reca-pitulates a central point of C. S. Peirce’s semiotics, in which the world is adynamical object invoked by science through mediating objects which aremanifested as signs (Gooding 1990b, pp. 177–88).2 The detail of Fara-day’s records allows us to investigate mental processes in relation to the


1. The published researches develop this agenda by describing the practical details ofhis experiments so as to disseminate the procedures that generate new knowledge.

2. Cartwright and others have abandoned the semantic distinction between theories (asrepresentations) and the world (as what is represented) in favor of models as mediating rep-resentations. Cartwright argues that theories are true not of real phenomena but only of themodels abstracted from them (Cartwright 1999a, p. 241–242 ; 1999b, p. 34). Since manypragmatic decisions are involved, the epistemic value of a theory cannot be determined inisolation either from its use in the laboratory or in communicating and evaluating results(De Regt 2004).

actions and objects that engender them and which they are about. Hiswork provides many examples of the art of eliciting, manipulating and in-terpreting complex phenomena in the search for simple explanations thatuniªed different sensory domains. This work produced representations,artefacts and procedures whose cognitive (generative) and social (commu-nicative and critical) functions combine to produce knowledge that can benetworked. New empirical evidence emerges from the interaction of vi-sual, tactile, kinaesthetic and auditory modes of perception together withexisting interpretative concepts that integrate different types of knowl-edge and experience. Mental models that develop purely “in the mind’seye” (without physically engaging the world) would lack this power to in-tegrate (Tallis 2004). Visualisation works with other senses and capacitiesand with deliberative experimental manipulation to produce a phenomen-ology of interpretative images, objects and utterances.3 Thus we can iden-tify some of the cognitive strategies that Faraday is using over a long spanof nearly four decades.

Rather than chronicle a particular discovery (for examples see: James1985, Gooding 1990a, Steinle 2002 and Tweney (this issue) I will showhow his use of visual representations identiªes some local- and long-termstrategies. This account will locate one of Faraday’s most famous images—the lines of magnetic force, Figure 1—by showing how they express rela-tionships between manipulated objects, sensory experience and knowledgegained from different phenomenal domains.

Modeling PhenomenologyWhen investigating electrical and magnetic phenomena Faraday couldhave adopted the established method based on forces that act in straightlines between bodies that have electrical, magnetic, gravitational or otherproperties. This approach was taken by Ampère, Biot, Savart and othersschooled in the Newton-Laplace tradition and by some of Faraday’s Eng-lish contemporaries (Caneva 1980; Steinle 2003). Ampère argued that thetrue phenomenon or ‘fait primitif’ is determined jointly by physical as-sumptions and the requirements of mathematical analysis. Nearly all hiselectromagnetic experiments were designed to establish and quantify lawsof interaction, not to analyse phenomena. By contrast Faraday embracedphenomenal complexity as a source of information about processes. So heexplored the phenomenological possibilities afforded by experiment inminute detail. He developed instruments and techniques to tame, dissect


3. I call these experiential hypotheses construals (Gooding 1990b, chapters 1–3),Magnani describes them as manipulative abductions (Magnani 2001, pp 53–59).

and order aspects of phenomena that Ampère and others rejected as toocomplex to handle with the existing mathematical methods.

Faraday’s methods of generating and investigating patterns show thatto him, a pattern can indicate either an arrested process, a structure that isbeing transformed by some process or the structuring effects of a process.He analysed motile phenomena by methods that slowed or ªxed the un-derlying process, so as to expose patterns. He then modelled these as con-sequences of processes that can be held in abeyance. Conversely, where astatic pattern could be seen or made visible by manipulation, he devisedmethods to explore the phenomenology of its motile form. In this wayFaraday devised procedures that could maximize the capacities of ordinarymodes of perception and also transcend their limitations. As Tweney putsit, Faraday placed a “relatively slow acting perceptual system, the ‘eye’, ina position to see what might be (and turned out in fact to be) fast actingevents.” (Tweney 1992, p. 164). Faraday was just as concerned to showhow and why unaided perception can be deceived. This shows that thegoals of his experiments were complex, motivated by larger concerns, am-bitions and values (Cantor, Gooding and James 1996).

Aware that human expectations regularly and easily mislead perceptionFaraday’s visual method was designed not to copy apparent features of theworld, but to analyse and replicate them.4 Consider the way that Faradaydeprived aquatic rotifers of their wheels. When seen through the regular


4. This goal remained constant from the early concern with optical illusions in his1831 paper to the argument of his 1855 essay on mental education, that since expectations

Figure 1. A. Patterns formed by magnetism in iron filings, engraving made foran encyclopaedia article by John Barlow (Barlow 1824, plate 7 figs. 68-69).B. Faraday’s earliest published image of magnetic lines around a cylinder magnet(1832). Note the attempt to render this in three dimensions (from Faraday 1838-55, vol. 1, plate I, fig 25).

vertical bars of an iron fence, carriage wheels display a variety of patternswhich often take the form of elegant curves. Though static, these curvesare clearly produced by rapid motion. Developing methods used by Roget(1825) and by Wheatstone (1823) Faraday created many versions of thesephenomenon to determine the conditions in which they appear to the eye.He then devised a physical simulation that could reproduce the phenom-ena (Figure 2B). This device made it possible to vary continuously the rel-ative frequency of the occlusion of slits in one rotating disc by those in an-other, anticipating the cinematic technology that has made suchphenomena commonplace. He was able to simulate every feature of thevarious phenomena, concluding that the appearance of both static andmoving patterns is a side-effect of a previously unrecognized parameter:the frequency at which constituent, overlapping parts of two ªlamentedsurfaces intersect (Figure 3A), Faraday 1831a). He then applied thismethod of analysis to a long-standing problem. In 1705 Leeuwenhoek,the great pioneer of microscopy, had described the movement of the ap-pendages of microscopic aquatic rotifers as a wheel-like rotation (Leeuw-enhoek 1705, see Figure 2A). For over a century Leeuwenhoek’s anoma-


often mislead perception, scientiªc methods require a disciplined application of judgement(Faraday 1855, pp. 465–469).

Figure 2. Optical illusions. A. Leeuwenhoek’s aquatic animalculae. Each appar-ently bears two rotors (Leeuwenhoek 1705, figs. 1, 5). B. Faraday’s simulation,designed to produce and transform patterns. C. Sample patterns reproduced bythe simulator (Faraday 1831a, plate III).

lous image of rotating ‘wheels’ had been tolerated for lack of a biologicallyplausible explanation. Faraday’s pattern-simulator explained the phenom-enon, removing the need for the anatomically implausible rotatingpropellor.5 His argument consists of a thought experiment informed bythe earlier simulation ªndings. In it he imagines a physical analoguemodel of the arrangement, ªxing and elasticity of the ciliae of the rotifer,shown in Figure 3B. Together with the known illusion reproduced by thesimulator this explains the phenomenon “without requiring any powersbeyond those which are within the understood laws of Nature, and knownto exist in the animal structure” (1831a, p. 309). There are no wheels, andhis own drawing (Figure 3C) shows ªxed ciliae rather than a rotatingstructure implied by Leeuwenhoek’s. The image of motile patterns pro-duced by the simulator provided the crucial link between phenomenonand explanation.

The method of analysing phenomena by simulation is a variation ontechniques he had used earlier with Humphry Davy. Like Leeuwenhoek’srotifers, electrical and magnetic effects are mixed in a way that the eyesimply cannot see. Davy and Faraday’s method of “accumulation” com-bined temporally discrete images into a single geometrical structure andconversely, it could assemble spatially distributed effects into a single im-age. They devised experimental methods that integrate discrete experi-mental events—or more precisely—that integrate the images that depict


5. Biologists now believe that about half of known bacteria have at least one rotatingºagellum, a means of locomotion driven by a protein-based induction motor.

Figure 3. Application of the simulation to the rotifer phenomenon. A. Simula-tion based analysis (top) of a stable pattern (bottom) produced by the relative mo-tion of rotors. B. Faraday’s proposed structure for the rotifer ciliae. C. Faraday’sre-drawing of a rotifer, showing rings of fixed ciliae (Faraday 1831a, plate III).

discrete events. For example, they passed a current through a vacuum toproduce a luminous glow discharge. In May 1821 they observed the dis-tributed and ªlamented character of this electric arc, showing that it pos-sessed magnetic properties (see Figure 4A). Faraday’s notes show that heattempted to describe the relationship between the orientation and direc-tion of the current and its magnetic effects (Figure 4B). In order to ‘ªx’ amagnetic image of the current, Davy and Faraday discharged a currentthrough a cardboard disc on which they arranged steel needles (Gooding1990b, pp. 46–58). This displayed the magnetising effects of the currentas a pattern (Figure 4C), analogous to the arrangement of iron ªlings neara bar magnet (as in Figure 1), but on a much larger scale (Faraday 1821a).The disc displays an ephemeral structure as a ªxed pattern. By Septemberof 1821 Faraday had shown how this structure yields a process. He ex-plored the motive properties of the magnetic ªeld of a constant current,showing in a series of increasingly abstract images (Figure 5A) that theseproperties can be arranged to produce motion in a circle around the wire(see Figure 5B). He then designed a device to produce continuous me-chanical effect from electricity and magnetism (Figure 6A, Faraday1821b). The new process was shown by an apparatus that exploited a


Figure 4. Analysing complex phenomena. A. An excerpt from Faraday’s notes ofhis May 1821 electric arc experiment with Davy. This is a typical illustration ofthe integration of sketches from different viewpoints, symbols and verbal descrip-tion in Faraday’s laboratory notes. The bell jar is drawn at left. The luminous cur-rent is shown in section above the two horseshoe magnets. Arrows indicate the ac-tion exerted when the polarity of the current is reversed (Courtesy of the RoyalInstitution of Great Britain, Faraday MS). B. Magnetised needles used in 1821to explore the magnetism of a constant current (from Gooding 1990b, p. 49).C. Part of the phenomenology of electromagnetism: demonstration device basedon needles arranged to ‘capture’ the pattern of magnetism of electricity dis-charged through the wire (from Faraday 1821-22, fig. 11).


Figure 5. A. Faraday’s sketches recording how he moved from discrete observa-tions with needles and currents (top two rows) to images that integrates his obser-vations of the needles’ tendencies to motion near a wire (next two rows) to the cir-cle heuristic (bottom image). Each row of images accumulates informationcontained in those above it. B. The circle heuristic applied to possible designs;from Faraday’s Diary (Martin 1932-36), vol. 1, pp. 49-50.

Figure 6. A. Sketch of a possible electromagnetic rotation device. Faraday’s firstsketch of the design of the prototype rotation motor. The letters ‘c’ and ‘z’ denotecontacts to the copper and zinc plates of the battery. From Faraday’s Diary (Mar-tin 1932-36), p. 50. B. A compact demonstration version Faraday mailed to anumber of European scientists in 1821. To us this is a protean electric motor; toFaraday it was a kinaesthetic demonstration of the phenomenon Faraday wantedto disseminate. From Faraday 1838-55, vol. 2, plate IV, fig. 5.

structural property of the magnetic ªeld of a current—the ªrst electricmotor (Figure 6B, Faraday 1821c).

In 1831 Faraday investigated the phenomenon of acoustical Figures (orChliadni patterns). These form in granular material distributed over aglass or metal plate which is made to vibrate, e.g. by a violin bow (Faraday1831b, Tweney 1992, Ippolito and Tweney 1995). Patterns form at reso-nance nodes and are characteristic of particular frequencies. The size of theparticles and the density of the ambient medium also affect the patterns.Faraday doubted that these distinctive patterns are produced by direct ac-tion of the vibrating surface on the particles (as Felix Savart had argued),suspecting instead that they are caused by the vibration imparted tothe ambient medium in which the particles become suspended (Faraday1831b, p. 318). He made the behaviour of this medium visible by usingmuch ªner powders. To test Savart’s hypothesis of direct mechanical ac-


Figure 7. A. Powdered material transferring from a fixed surface (top) to a sur-face made to vibrate by the application of a bow at ‘X’, from Faraday 1831b, p.320. B. Sketch of the air currents created by vibrations of the plane, which hemade visible using smoke. The currents act on particles to produce patterns.From Faraday’s Diary (Martin 1932-36), vol. 1, p. 331, para. 45. C. Patternswhose form (see top ‘Fig. 6’) is affected when vertical blocks are introduced (indi-cated as the dark line left of centre in the middle figure (‘Fig. 7’) and at top rightin ‘Fig. 8’. From Faraday 1831b, p.321.

tion he placed powdered silica on a ªxed, solid surface (see Figure 7A). Hefound that it migrates onto an adjacent vibrating plate “as if in the midstof all the agitation of the air in the neighbourhood of the two edges, therewas still a current towards the centre of vibration, even from bodies notthemselves vibrating” (ibid., p. 320). Having dismissed the alternative ex-planation his experiments were “[g]uided by the idea of what ought tohappen, supposing the cause now assigned were the true one” (ibid.,p. 319). These experiments were also ‘guided’ by the need to determineempirically the effect of varying each parameter of a sophisticated processmodel that relates frequency and amplitude of vibration, density of theambient medium, and particle size.

As with many of his investigations Faraday arrived at this model by im-aging the process from different viewpoints (see Figure 7B and note simi-lar changes of viewpoint in Figures 4A and 5A). The model relates pat-terns and variations in patterns to the interaction of the acousticalvibrations of the plate, the induced vibration of the medium and its inter-action with the particles. He then tested his air-current model (Figure 7B)by inventing ways of obstructing the formation of air currents. These ex-periments showed that obstructing the currents alters the form of nodallines produced on an elongated plate (see Figure 7C). This use of instru-ments to manipulate invisible, high-frequency processes shaped Faraday’sexperimental approach to electromagnetism when he returned to it in1831. There too he construed patterns elicited by experimental manipula-tions as spatio-temporal snapshots of complex, high-frequency processes.

Structural Models that Integrate Pattern and ProcessThese three examples display the same underlying visual logic. Faradayinferred from patterns the processes that produce them, by modelling orsimulating the structures by which they are arranged. This pattern of in-ference could start from different phenomena. Given patterns, he created astructure used to analyse and simulate the process that produces the pat-terns (Figures 2B, 3A). Given a pattern produced directly by a force (e.g.magnetism, in Figures 1 and 4C), a pattern whose direct cause was in dis-pute (Figure 7), or a pattern elicited by analysis of a process (electromag-netism, Figures 4B, 5A) he produced a new structural model that repro-duced or simulated a process (Figure 3C, Figure 6B). In some cases it isevident that patterns involve process (Figures 2A, 4A, 7A). The result is aprocess-explanation of a known phenomenon (often a pattern), or a newphenomenon-producing device (Figures 2B, 6B). With suitable manipula-tion and analysis via apparatus he could show sometimes that what is seenis misleading as to its cause (Figures 2A and 3C) or has an unambiguous


explanation (Figure 7A). The simulation explanation (Figure 2B), thedemonstration device (Figure 6B) and experiments (such as Figure 7C)show more than the eye could ever see. They produce images that visualizefeatures of phenomena.

This visual logic has a second feature already noted in connection withhis explanation of acoustical patterns (Figure 7B). To work out structuresFaraday sketched phenomena both from the side (e.g. in Figure 4A, to in-dicate ªlamentation and conduction in the electric brush) and as viewedfrom above (to indicate the forces acting between current and magnet).These views feature different aspects of a phenomenon. He had used thismethod of rendering a phenomenon from different points of view to estab-lish the geometry of electromagnetism that led to the ªrst electric motor(Figures 5A, 5B, 6A). This method of observation involves integratingsensory information from vision with the kinaesthetic ‘feel’ of current-magnet interactions. Hearing was also an important source for under-standing the acoustical patterns and the electric brush (see below).

Faraday’s method integrates sensory information into a few simple butpowerful images. This has four related aspects: integrating many observa-tions into a few images (as in Figure 5A), envisaging or making observa-tions from different viewpoints (Figures 4A, 5A, 7A-B), combining obser-vations made in different sensory modalities and by different methods(Figure 2B, 4) and fourth, to reach a uniªed theory, integrating the infor-


Figure 8. Dynamical model of the interaction of electricity, magnetism and mo-tion, March 1832. A. This image integrates felt (proprioceptive) experiences ofhow magnets and currents interact with visual observation of the behaviour ofiron filing patterns. B. Faraday’s memo explaining how to animate the diagram(from Faraday’s Diary (Martin 1932-36), vol. 1, p. 425).

mation-bearing images into a single visuo-temporal model which can ex-plain most of the phenomena.

Two examples of theorising with visualizations of phenomena reveal thedevelopment of his electromagnetic theory. The ªrst is a 3-D processmodel of March 1832, sketched in Figure 8. On paper the 1832 sketchlooks like a 3-D structural model such as Faraday’s well known image oflines of magnetic force (Figure 1). However when animated by his verbalinstructions (see Figure 8) this image becomes a visual theory that inte-grates and generalises what he had learned from many experiments aboutthe interactions of electricity, magnetism and motion. This image repre-sents experiential knowledge obtained through the modalities of sight,touch and proprioception yet it is more abstract and general than thebetter-known visualization of lines of force (Figure 1). By 1832 the imageof a ‘bundle’ of lines had come to represent both the magnetic lines andthe physical independence of a system of lines from a magnet or the circuitin which current is induced. Faraday demonstrated this independence inan experiment designed via a thought experiment in which he imaginedthe system of magnetic lines to rotate around a cylinder magnet (Martin1932–36, vol. 1, pp. 402–404). He soon realized this thought experimentby making a cylinder magnet rotate within a conducting circuit of whichit formed a part, producing the new phenomenon of unipolar induction(Faraday 1832b). The second example is an image of interlocking rings.This generalizes from his visual models of electromagnetism and from ex-periments speciªcally designed to operationalise models (Figure 11a, seeGooding 1990b). The image (Figure 11b) enables expression of the lawthat “the sum of power contained in any one section of a given portion of[magnetic] lines is exactly equal to the sum of power in any other sectionof the same lines . . . ” (Faraday 1851a, reproduced in Faraday 1838–55,vol. 3, p. 329, para. 3073). He expressed this quantitative law visually inJune 1852.

In all these discoveries setups and procedures support visual inferencesby producing and organizing phenomena into phenomenological models.These models are complexes of material things, active manipulation, ef-fects and visualized interpretations of the outcomes. They generated newphenomena which Faraday inspected for features which in turn offer cluesabout process. As visual hypotheses they showed the dynamical or processequivalent of the static structure implied by images of ªling patterns (Fig-ure 1), electromagnetic interactions (Figure 5A) and retrospectively, themanipulation of objects, forces and images in May 1821 (Figure 4A) andSeptember 1821 (Figure 5A). As I show below, they also support the ana-logical transfer of learned properties of phenomena from one domain toanother.


Visual Analogical ModelsAnalogical conjectures may be expressed by new images which guide ex-ploration of structures hidden from ordinary vision. An example is the ex-planation of several interconnected phenomena observed in the electric arcexperiment of May 1821 (see Figure 4A). Where Davy construed the ªla-mentation as indicating a structure for conduction Faraday went further.This feature suggested a relationship between electricity, magnetism andmotive action, as indicated by the arrows in Faraday’s sketches in Figure4A. By March of 1832, following his discovery of electromagnetic induc-tion, he expressed this as the unifying model shown in Figure 8b. Thisdeªnes the relationship between the four variables he had shown to be in-volved in electromagnetic induction: magnetism (e.g. of an iron bar), elec-tro-magnetism (of a current), magnetically induced current, and motiveeffects. It provides the basis for his explanation of the ‘rotating’ effect ofa magnet on the electric arc (1821) and the ‘dragging’ effect of a non-magnetic conducting disc (discovered by Arago in 1825). Another exam-ple is Faraday’s application in 1835–36 of another aspect of this phenome-non to the analysis of electrical discharge. Here visualization assists theanalogical transfer of ideas between what others still regarded as distinctphenomenal domains. Faraday attempted to reproduce in the electricbrush the same structuring or ‘striation’ ªrst seen in the luminous electricarc observed with Davy in May 1821. The work with strobes in 1830–31to analyse patterns and movement enabled him to approach electrical phe-nomena in the same way. In 1836 Faraday mapped the structure of elec-trostatic potential around large conductors. Recording and plotting manydiscrete observations made with an electroscope (these are the dots in Fig-


Figure 9. The lines in the right-hand image denote surfaces of equal electro-static induction (equipotential surfaces) near a copper boiler. This 2-D pattern ac-cumulates in a single image many discrete observations (denoted by dots, left)made in the space around the boiler, from Faraday’s Diary (Martin 1932-36),vol. 2, pages 412-14.

ure 9) he built up a picture of lines of equal potential. These ºat images(Figure 9) represent a structured set of phenomena produced by explora-tion of a 3-D electriªed space. Like so many scientists before and since,Faraday construed the 2-D patterns as sections through a 3-D structure.

Again, like every other scientist Faraday was not satisªed with thestatic image. The structure is electrostatically charged so it must have thepotential to produce a current and, therefore, magnetism as well. He ana-lysed luminous discharge in air, using ‘process-freezing’ strobe devices toproduce the images in Figure 10 (Faraday 1831a, Wheatstone 1834).These show how variations in parameters such as conductivity, electric in-tensity, density of the medium and the positioning of terminals producedistinct, repeatable variations in the form and distribution of electric lines(Figure 10). Just as important was the fact that these variations correlateto changes in the pitch of an electric brush: pitch rises or falls as conduc-tivity increases or decreases. Changing frequency indicated the vibrationof a medium, suggesting a possible application of the same model Faradayhad developed to explain acoustical patterns such as those in Figure 7. Italso hinted at a way of dealing with the paradox that electricity appearsboth as discontinuous (as static charge on discrete bodies and the electro-chemical combining force of atoms and molecules) and as continuous cur-rent.6 The dynamic patterns imaged in Figure 10 extend to electrostaticsthe same dynamical geometry Faraday had already worked out for acousti-cal patterns (Figure 7), electromagnetic motions (Figures 5 and 6) and forelectromagnetic induction (Figure 8). Much later, encouraged by WilliamThomson’s campaign of displaying imprints of iron ªling patterns at theBritish Association (Gooding 1990b, pp. 251–52), he adopted the samedemonstrative approach with these patterns (see Figure 12).

Images that IntegrateAn important feature of creative processes is the ability to maintain sev-eral lines of inquiry and transfer ideas and methods between them (Gruberand Davis 1988). In many cases the transfer involves analogies achieved inseveral ways and at different levels of abstraction. The most concrete andintuitive would be ‘direct’ recognition of a similarity at the perceptual level.This would rely on fast cognitive processing that is closely coupled toevolved neural structures. At a more abstract, conceptual level are similari-ties whose signiªcance derives from being features implied by a modelthat links different phenomenal domains. Images of lines making struc-


6. Since discovering the effect of freezing on the conductivity of an electrolyte in 1833,Faraday had been perplexed by the need to understand this transition, via the conditionsthat can be varied to make a continuous transition between static and current electricity.


Figure 10. Making electric lines visible. A. Sketch of Faraday’s mental image ofstatic tension prior to luminous electric discharge, from Faraday’s Diary (Martin1932-36), vol. 2, paras. 3435-3436. B. an engraving of the variable form of the“electric brush” as viewed via a stroboscope, from Faraday 1838-55, vol.2, plateX, figures 119-121.

Figure 11. An instrumental definition of a quantitative relationship betweenelectricity and magnetism (left) and its visual statement (right). A. Apparatus of1851 designed to measure the quantity of electricity induced by a conductingloop (labelled ‘L’) that cuts a defined quantity of magnetic lines as the crank isturned (from Faraday 1851a, reproduced in Faraday 1838-55, vol. 3, p. 333). Far-aday wanted to establish that “the sum of power contained in any one section of agiven portion of [magnetic] lines is exactly equal to the sum of power in any othersection of the same lines . . .” (from Faraday 1851a, reproduced in Faraday 1838-55, vol. 3, p. 329, para 3073). B. This quantitative law of electromagnetic induc-tion is expressed visually in June 1852. This image integrates and quantifies mostof the phenomenal properties of electricity and magnetism known to Faraday. Itconstrues forces as fluxes (quantities of action measured across a unit area or sec-tion). A change in the area of one circle (magnetic flux) implies a contrary andequal change in the area of the other (electromotive force); from Faraday 1852, re-produced in Faraday 1838-1855, vol. 3, p. 418, para. 3265 and plate IV.

tures that are involved in processes enabled Faraday to compare features ofthe phenomena he observed and to make analogies at the highest level ofgenerality that his skills of material and mental manipulation could sup-port. Examples include his recognition of the signiªcance of relationshipsbetween the behaviour of electric ªlaments (Figures 4A and 10B), electro-static lines (Figures 9 and 10A) and magnetic lines (Figures 1 and 12).The sketch of March 1832 (see Figure 8) expressed what Faraday hadlearned by active manipulation of magnets and currents. Its ªnal, most ar-ticulate and general statement appeared in June 1852 (Figure 11B, Fara-day 1852). This ‘animated’ image of the interactions of electricity, magne-tism and motion captures the ªndings of prolonged and systematicexperiments to establish a quantitative relationship between the sectionaldensity of magnetic lines, the rate of ‘cutting’ of lines by a conductor, andthe quantity of electricity produced. Faraday established this using the ap-paratus in Figure 11A. Like his sketch of 1832, it is a unifying visualstatement that generalizes over the larger set of phenomena that it bringstogether (Faraday 1851a, 1851b).

This visual-verbal formulation (Figure 11B) formed a starting point forThomson and Maxwell’s mathematical theory of the ªeld (Wise 1979).The image expresses the relationship between electric and magnetic actionas vector quantities by construing them as ºuxes (quantities of actionmeasured across an area; Faraday 1852, pp. 417–19). At a similar level ofabstraction is his recognition of the signiªcance of changes in the appear-ance of high frequency processes such as the rotifer phenomenon (Figure2A) and acoustical patterns (Figure 7) with changes such as frequency andthe density of the ambient medium (e.g. pitch of the sound made by theelectric brush, Figure 10B). The ability to see the signiªcance of similari-ties that are perceived ‘directly’ and with different senses depended on rea-soning with and about visual-verbal models of inferred processes, guidedby experimental trials.

Visualization as Situated CognitionFaraday accomplished this process of theorizing as much through his ma-nipulation of images as by the many words that he wrote. We can now seeFaraday’s well known magnetic lines (Figures 1 and 12) not only as de-picting phenomena but also as generative elements of the experientialknowledge that produced them. The examples discussed here show that,far from working in isolation from other modes of perception or fromother persons as sources of experience, visualization integrates differenttypes of knowledge and experience. Much of the cognitive power of im-ages resides in this integrative capability, which is central to inference inmany sciences. It follows that the use of any particular image cannot be


understood independently of the way it is generated from and used withother images. Verbalization is but one part of this context.

We have seen that many of Faraday’s sketches are far more than depic-tions of observations, they are tools for reasoning with and about phenom-ena. Visualized phenomena are attempts to image complex 3-D phenom-ena which cannot be seen directly, are produced by active manipulationand sometimes by a simulation model or other imaging technique. Thus,many of his sketches represent something that is dynamic and emergent.This is because he is trying to visualize a set of changing relationships.The sketches are early manifestations of a process of establishing anepistemic basis in shared experience and for communication about that ex-perience. The more familiar, depictive role of a set of images or their ver-bal counterparts is developed during many days or weeks work. Someimages are more abstract and general than others, standing for an accumu-lation of perceptual, practical and theoretical knowledge.7 The meaningand function of an image varies, depending upon how it is used in relationto others that represent earlier and later work. Some of his images repre-sent particulars such as the details of an experimental apparatus or thestructure of a process while others state generalizations about phenomena,often observed through more than one sensory mode. Use of an image inone context implies a particular cognitive mechanism is at work while thesame image in another context may imply that a different underlying cog-nitive process has been invoked. For example, Faraday’s initial sketches of


7. On sketches as short-hand for accumulated experiential knowledge see Gorman1992, pp. 213–17.

Figure 12. Iron filing patterns made by ferro-magnets (figure 12A), diamagnets(figure 12B, left) and paramagnets (figure 12B, right). These images are producedby laying a sheet coated with gum or shellac over the iron filings. This fixes thepattern and makes it transportable. It is then reproduced by an engraver. FromFaraday 1851b, reproduced in Faraday 1838-55, vol. 3, plate III.

magnet-needle interactions (Figures 4A and 5A) owe more to embodiedperceptual interaction with objects and forces and less to rational delibera-tion about physical meaning than the electromagnetic disk (Figure 4C)which is used both evidentially and to enable others to interpret the phe-nomenon. Function also varies for images that are entirely in the social do-main of published representations. The magnetization patterns (Figure12) and intensity plots (Figure 9) were at ªrst a cognitive resource for inter-pretation and modelling. These were crafted into an epistemic resource thatcould provide pictorial evidence for the visual theory constructed fromthem, and aid intellectual comprehension of it.

We have seen that Faraday’s constructive method involved movingfrom 2-D patterns to 3-D structures which could then be animated eitheras thought-experiments in time or as material, bench-top simulations ofthe invisible processes. Images of lines making up structures involved inprocesses also enabled Faraday to compare and make analogies betweenfeatures of phenomena in different domains. These multiple functions areessential to the process of discovery which requires many moves betweenwhat makes sense and what can be demonstrated, both for innovators andtheir audiences.

Visual ReasoningThe received view of scientiªc inference is that it is accomplished in lan-guage capable of preserving consistency, both in the use of signs and in re-lationships between propositions. Does this mean that Faraday’s visual andmaterial manipulations were not really reasoning, or that what these pro-duced was not knowledge? On the contrary, while successful science doesrequire a stable linguistic formulation, creative research cannot be con-ducted solely with well-formed linguistic representations.8 There are non-visual ways of forging an isomorphism of words, images or symbols towhat they denote, but images are particularly conducive to the essential,dialectical movement between the creative stages of discovery and the de-liberative, rational stages in which rules and evaluative criteria are intro-duced to ªx meanings and turn images from interpretations into evidence.

Visual perception is an established metaphor for intellectual under-standing (Kemp 2000). Faraday’s work allows us to show in some detailwhy this should be. The co-evolution of his powerful physical conceptsand his experimental procedures shows him creating a cognitive landscapein which, by getting things to work experimentally and locally, aspects ofthe world are made accessible to the senses and subsequently to verbal ex-


8. Word-pictures emerge alongside drawn images in the development of Faraday’smagnetic ªeld theory between 1845 and 1852, (Gooding 1981).

pression, generalization and intellectual understanding. Similar examplesof the dialectical play of phenomenology, mental imagery, models and the-ories can be found throughout the sciences (see Ball 1999, Ziman 2000).9

Far from being mere illustrations of reasoning that had been accomplishedverbally, Faraday’s sketches and engravings are integral to his process ofinvestigation. He did not ªrst produce new knowledge and then verbalizeor image it. Words and images emerged in a context which they jointlyhelped to generate. Faraday’s sensual images express his theoretical aspira-tions and intentions just as much as the many words that he wrote.

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from phenomenology to field theory: faraday's visual reasoning

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