“Der Versuch Als Vermittler” Versus Newton's Experimentum Crucis

The Nature of Light and Color: Goethe’s “Der Versuch als Vermittler” versus Newton’s Experimentum Crucis

James A. Marcum Baylor University

In the seventeenth century, Newton published his famous experimentum crucis, in which he claimed that light is heterogeneous and is composed of rays with different refrangibilities. Experiments, especially the crucial experiment, were important for justifying Newton’s theory of light, and eventually his theory of color. A century later, Goethe conducted a series of experiments on the nature of color, especially in contradistinction to Newton, and he defended his research with a methodological principle formulated in “Der Versuch als Vermittler.” Goethe’s principle included two elements: a series of experiments and resultant higher empirical evidence, which functioned as mediator between the objective (a natural phenomenon) and the subjective (a theory or hypothesis). Although the notion of experimentum crucis became popular among scientists for reconstructing experimental research and for justifying theories, especially for rhetorical purposes, Newton’s justiªcation of his theory of light and color is best reconstructed in terms of Goethe’s methodological principle. Finally, Goethe’s principle has important consequences for the contemporary philosophical underdetermination thesis.

1. Introduction In the seventeenth century Isaac Newton conducted experiments to determine the nature of sunlight, especially as it relates to colored I thank Ernst Hamm for drawing my attention to Goethe’s “Der Versuch als Vermittler” essay and Jed Buchwald, William Cowling, Francesco Guala, Robert Iliffe, Clark Muenzer, Den- nis Sepper, Alan Shapiro, Friedrich Steinle, Friedel Weinert, and Gábor Zemplén, for their stimulating discussion and insightful comments on earlier manuscript drafts. Baylor Uni- versity supported my research through sabbatical funding. A shorter version of this paper was presented at the First Conference in Integrated History and Philosophy of Science, Centre for Philosophy of Science, University of Pittsburgh, Pittsburgh, PA, October 11– 14, 2007, and may be found at: http://philsci-archive.pitt.edu/archive/00003602/01/ Marcum-&hps_ms.doc.

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rays.1 These experiments were reported in a letter read, in Newton’s ab- sence, at the Royal Society in London and published in its Philosophical Transactions. According to Newton, sunlight is composed of a “Heteroge- neous mixture of differently refrangible Rays” (1671/2, p. 3079). The theory, he claimed, is established on a single experiment, an experimentum crucis, in which Newton refracted sunlight with a prism into a color spectrum— each colored ray with a speciªc refrangibility, or angle of refraction. With a second prism, he demonstrated that each refracted ray of the color spectrum is dispersed to the same degree as with the ªrst prism. Based on the crucial experiment, Newton distinguished his theory of light, as well as his theory of color, from competing theories—e.g. the notion of light as rotating globules, as championed by René Descartes. And the notion of crucial experiment formed, at that time, an important component of Newton’s experimental philosophy (Sabra [1967] 1981; Sepper 1994). In the eighteenth century, in a critique of Newton’s theory of light and color based on the experimentum crucis, Johann Wolfgang von Goethe claimed that Newton’s theory is an artiªcial construct of the human intel- lect and, as such, is not derived from nature itself. Speciªcally, he argued that Newton’s experiments—especially the experimentum crucis—represent an artiªcial step and not a natural one, in examining nature. The result of Newton’s artiªcial method, argued Goethe, is a distorted view not only of light and color but also of nature itself. “Indeed, according to Goethe,” claims Myles Jackson, “Newton’s entire doctrine was based on an artiªcial case, the crucial experiment” (1994, p. 686). In contradistinction to New- ton, Goethe claimed that he was able to discover nature’s laws without ªrst imposing human preconception onto a natural phenomenon. To that end, Goethe devised and conducted a series of experiments in which he altered systematically the experimental conditions in terms of the prism’s refracting angle, the distance from the subject to the prism, and the object viewed (Ribe and Steinle 2002). The result of these experiments was evidence of a higher sort that mediated between the observer’s theory or hypothesis and the observed, and allowed the phenomenon to be understood in a holistic fashion. The Newton-Goethe historical case study has important implications for the underdetermination thesis (UDT) of contemporary philosophy of science (Hesse 1980; Klee 1997; Ladyman 2002; Laudan and Leplin 1991; and Stanford 2001).2 Brieºy, the UDT claims that evidence, whether from

1. Although “colored ray(s)” is a phrase not used by Newton, it is used herein for con- venience. 2. UDT has also been at the center of the realism-antirealism debate, especially in terms of John Worrall’s notion of structural realism (Kukla 1998; Ladyman 1998; Leplin 1997; Niiniluoto 1999; Psillos 1999; and Worrall 1989).

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the laboratory or the ªeld, is incapable of supporting conclusively a particular theory with respect to its rivals. The reason is that there are always a number of possible competing theories that can account for the evidence equally well. In other words, the various rival theories are empirically equivalent. The case study reconstructed herein corroborates the UDT in that evidence, especially obtained from an experimentum crucis, is incapable of supporting conclusively one theory over its rivals. However, it also chal- lenges the UDT in that the evidence obtained from a well structured experimental series is more likely to support a theory with respect to its competitors, than evidence from a limited or unstructured set of experiments or especially from a single even though crucial experiment. The current case study demonstrates that evidence from an experimental series generally provides the necessary and sufªcient warrant for justifying a particular theory choice, until of course additional evidence is eventually obtained that may lead to either modiªcation or replacement of the theory. In this paper, I examine the difference between Newton’s and Goethe’s approaches to investigating the nature of light and color. First, I discuss brieºy Newton’s famous experimentum crucis, in which he claimed that light is heterogeneous and is composed of rays with different refrangibilities, as well as his experimental philosophy. I then reconstruct Goethe’s experiments on the nature of color and discuss his methodological principle formulated in the well known essay “Der Versuch als Vermittler,” especially in contradistinction to Newton’s methodology. Goethe’s principle is ex- pounded in terms of series of experiments and resultant higher empirical evidence, as mediator between the objective (i.e. a natural phenomenon) and the subjective (i.e. theory or hypothesis). I then reconstruct the experiments Newton reported in the 1671/2 Philosophical Transactions letter to justify his theory of light and color in terms of Goethe’s methodological principle rather than in terms of a crucial experiment, even though New- ton was—or at least his followers were—not necessarily interested in a holistic picture of nature or in the relationship of the subjective to the objective.3 Finally, I conclude the paper with a discussion of the consequences of Goethe’s methodological principle for the contemporary UDT.

2. Newton’s experimentum crucis In a published letter to the Royal Society of London, dated 19 February 1671/2, Newton reported an experimentum crucis (Fig. 1) in which he took a board (Bd) with a small hole (x) and placed it behind a prism (A), which received sunlight (S) from a small hole in the window shutter of a dark- 3. Neil Ribe (1985) argues that the conºict between Goethe and Newton is more than simply competing theories of color but also includes methodological issues.

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Figure 1. Newton’s experimentum crucis (reproduced from Newton 1672). See text for details.

ened room. Another board (DE) with a small hole (y) was placed 12 feet from the ªrst board, so that a portion of the incident light would pass through the hole of the second board. A second prism (F) was then placed behind the hole of the second board, which further dispersed the light onto a nearby wall (GH). By slowly rotating the ªrst prism about its axis, Newton was able to make different sections of the initial image pass through the hole in the second board and then observe where it fell on the wall. What Newton observed in the experimentum crucis was that the part of the initial image—an oblong image composed of a spectrum of individual colors—which is refracted greatest (i.e. the color blue) by the ªrst prism is also refracted the greatest by the second prism, compared to that part of the initial image refracted the least (i.e. the color red). From these results, Newton concluded that “Light consists of Rays differently refrangible” (1671/2, p. 3079). He went on in the second part of the letter to outline his “doctrine of colours,” based on his theory of light, in which the various spectral colors exhibited different “degrees of Refrangibility” (Newton 1671/2, p. 3081). Traditionally, especially since Ernst Mach, Newton’s experimental philosophy or methodology has been reconstructed in positivistic terms

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(Ben-Chaim 2004, p. 44; Raftopoulos 1999, p. 108). As such, Newton’s method was inductive in nature and depended, in part, on what he called analysis. “Analysis,” as Newton deªned it methodologically, “consists in making Experiments and Observations, and in drawing general Conclu- sions from them by Induction, and admitting of no Objections against the Conclusions, but such as are taken from Experiments, or other certain Truths” ([1730] 1959, p. 404).4 According to Newton, the optical crucial experiment was sufªcient to demonstrate his theory of light and formed, at that time, the cornerstone of his experimental philosophy. What made the crucial experiment com- pelling for Newton was what he called its “weight,” in clearly or directly demonstrating the optical phenomenon and supporting his interpretation of it vis-à-vis the interpretations of previous experimenters.5 In response to the nine experiments performed by Anthony Lucas to test Newton’s theory of light, for example, Newton counseled him accordingly: “it will con- duce to his more speedy and full satisfaction if he a little change the method which he has propounded, and instead of a multitude of things try only the Experimentum Crucis. For it is not number of Experiments, but weight to be regarded; and where one will do, what need many?” (1676, pp. 702–703). Importantly for Newton, the weight of the experiment was tied to its demonstrative power, i.e. if the experiment is sufªciently weighty then “there needs no further examination of the thing” (1676, p. 703). However, Newton fully realized that no experiment, not even a crucial experiment, can absolutely demonstrate or support a theoretical conclusion. Rather, exceptions are bound to occur. But, those exceptions are to be experimental in nature and not hypothetical. In other words, changes in generalizations could only be allowed or sanctioned through experimental means and not through speculative or hypothetical ones.6 In New-

4. The other component of Newton’s method was called synthesis: “the Synthesis consists in assuming the Causes discover’d and establish’d as Principles, and by them explaining the Phenomena proceeding from them, and proving the Explanations” (Newton [1730] 1959, p. 405). According to Jerry Gravader, Newton’s method of analysis and synthesis, as Newton himself attested, is “a version of the resolution of and composition method” (1975, p. 295). 5. According to Raftopoulos, an important feature of Newton’s crucial experiment is that it allowed Newton “to draw positively a conclusion. It is ‘positive’ exactly because it shows that Newton’s theory withstands the tests its rival alternatives have failed” (1999, p. 116). 6. Alan Shapiro (1993, pp. 12–14) makes a very useful distinction between imaginary and experimental hypotheses, with the latter being an acceptable form of hypothesizing for Newton.

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ton’s words: “Hypotheses are not to be regarded in experimental Philoso- phy,” at least in terms of modifying generalities ([1730] 1959, p. 404). Although he conceded that this method may not be entirely satisfactory for securing absolute knowledge, “it is the best way of arguing which the Nature of Things admits of, and may be looked upon as so much stronger, by how the Induction is more general” (Newton [1730] 1959, 404). Im- portantly, Newton’s method and particularly the use of experimentum crucis “became part of the language of science with, over the centuries, the call for other crucial experiments to enable scientists to choose between alternative, competing theories” (Gjertsen 1986, p. 193).

3. Goethe’s Optical Experiments and Scientiªc Methodology Goethe’s interest in the nature of color began with his Italian journey, from 1786–1788 (Sepper 1988). While there, he was struck by the inabil- ity of artists to account for the use of colors in a systematic manner. After returning to Weimar, he consulted the scientiªc compendia on the nature of color in which he came across Newton’s prism experiments.7 He then decided to conduct his own experiments. While viewing a white wall through a prism, he observed that the wall remained white unless there was some type of contrast that introduced a boundary between white and darkness. Only along this boundary did color appear. On this evidence Goethe rejected Newton’s theory of light and color, concluding that “it had overlooked an essential circumstance, the boundary between light and dark” (Sepper 1988, p. 27). He then conducted an extended series of experiments to investigate the nature of color, which was subsequently published initially in Beyträge zur Optik and more completely in Zur Farbenlehre.8

7. Goethe was taught Newton’s theory as a student in Leipzig but had obviously for- gotten it (Wells 1968, p. 87). 8. The two Beyträge (there is also an alternative spelling of Beiträge that appears in the literature) were published separately in 1791 and 1792, which were criticized by physi- cists: “As soon as my Beiträge zur Optik had appeared,” bemoaned Goethe, “the whole fra- ternity felt obliged to fall upon me and to show that what I still regarded as problematic had long since been explained” (Wells 1968, p. 99). Goethe then suspended further publi- cation of his optical experiments from 1793 until 1808, at which time the ªrst part of Zur Farbenlehre appeared (Duck 1993). Zur Farbenlehre is composed of four parts, with the ªrst or didactic part containing Goethe’s experiments. It has been translated into English (Goe- the 1970, 1988). The second part includes a review and critique of Newton’s Opticks, which has also been translated into English, while the third part a history of color science and the fourth part illustrations with commentary and an essay by Thomas Seebeck (Duck 1993; Sepper 1988, pp. 22–23).

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3.1. Goethe’s optical experiments In Beyträge zur Optik, Goethe ([1791] 1964) reported optical experiments to determine the conditions under which colors appear or emerge.9 He was systematic in his experimentation, beginning with preliminary experiments in which he viewed through a prism objects, such as a white piece of paper, a blank wall, or a blue sky. Observation of a white piece of paper, for example, did not yield, as Goethe expected, a color spectrum in terms of Newton’s theory of light and color, unless a contrasting feature, such as irregularities, was present on the paper. Under these conditions, he observed through a prism various colors of Newton’s optical spectrum at the boundary of the irregularities. As mentioned above, these experiments initially led Goethe to reject Newton’s theory of color and to search for and to propose eventually an alternative theory, through subsequent experimentation. In an ensuing experiment, Goethe viewed through a prism a white piece of paper with black squiggly lines. He observed colors that clung to the lines. Next, he viewed a rectangular piece of white paper on a black background. What he observed through a prism was a spectrum of colors, with red at the top followed by yellow, green, blue, and then violet at the bottom. He next inverted the arrangement with a black rectangle on a white background and observed through a prism another spectrum of colors, with blue at the top followed by violet, magenta, red, and then yellow at the bottom. Goethe then conducted experiments with a white card painted half black and viewed it through a prism. With the black part above the white, he observed a red and yellow band in between the black and white boundary. With the card inverted, he observed a blue and violet band. Next, he conducted several more experiments, in which he varied the image, such as a checkerboard arrangement of black and white squares, and observed the various colors. From the results of this series of experiments, Goethe derived several rules or principles. One of the chief rules was that color is not generated in a prism upon viewing uniform or “pure” surfaces; rather, a contrasting boundary is critical for color appearance. The boundary is necessary, according to Goethe, because that is where light and darkness meet, with some colors radiating toward the light and others toward the dark. He concluded that the contrast necessary for color generation is the result of polarity, in that the colors red and yellow (warm colors) are at one pole and the colors blue and violet (cool colors) at the other pole. Color appearance

9. For an English translation of the 1791 Beyträge zur Optik, see Schindler (1970, pp. 121–61). For an overview of Goethe’s experiments in the Beyträge, see Sepper (1988, pp. 46–57).

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at the boundary, then, is the result of the colors red and violet radiating towards the black ªeld while the colors yellow and blue towards the white ªeld. Goethe accounted for his ªndings in terms of boundary modiªca- tionism (Zemplén 2001, p. 57). Moreover, these rules and principles were not simply summaries of Goethe’s experiments but functioned heuristi- cally to guide future research, which bore fruit in Zur Farbenlehre (Sepper 1988, p. 53). In Zur Farbenlehre—particularly in the didactic part—Goethe ([1808] 1981) divided colors into a variety of categories, including physiological and pathological colors, physical colors, and chemical colors. The physical colors are further divided into catoptric, paroptic, dioptric, and epoptic colors, depending on how the colors are generated.10 Of special interest are the dioptric colors, which emerge from light passing through a translu- cent body, such as a prism or turbid medium. Goethe further divided the dioptric colors into ªrst and second classes, with the ªrst class emerging from light traversing a turbid medium (gaseous, liquid, or solid) and the second, which represents a special class of the ªrst class, emerging from form or boundary contrast upon viewing through a prism.11 To substantiate ªrst-class dioptric colors, Goethe performed a variety of experiments. For example, starlight viewed through a slightly turbid medium appears yellow while as the turbidity of the medium increases the light ultimately appears red. However, when darkness is viewed through “turbid medium ªlled with light” it appears blue and “grows lighter and paler as the medium becomes more turbid, but darker and deeper as it becomes more transparent” (Goethe 1988, p. 191). Although Goethe ac- knowledged that these experiments are subjective in nature, he identiªed several objective phenomena, such as viewing the sun at different positions in the sky (e.g. yellow at noon and red at sunrise or sunset), which supported the notion that the emergence of colors depends upon the turbidity through which light is viewed. Finally, he recounted a “striking experiment” with sheets of parchment in which addition of these sheets before a hole in a window shutter goes from a whitish to a red appearance. In conclusion, Goethe ultimately accounted for his ªndings in terms of me-

10. Goethe (1988, p. 190) noted that the catoptric colors are similar to physiological colors, while the epoptic colors transition into the chemical colors. 11. According to Zemplén (2001, p. 68), Goethe eventually shifted from boundary modiªcationism to medium modiªcationism, for ªrst-class dioptric colors. However, Goe- the (1988, pp. 195–222) still subscribed to boundary modiªcation for dioptric colors of the second class and included besides boundary also displacement as in the case of double images to explain the emergence of color. The subjective and objective experiments conducted to substantiate dioptric colors of the second class represent an expanded study of the experiments in the Beyträge.

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dium modiªcationism, i.e. the notion that color results from the mixing “between light and a medium that contains darkness-shadow” (Zemplén 2001, p. 4).12

3.2. Goethe’s scientiªc methodology In a well known essay “Der Versuch als Vermittler von Objekt und Subjekt,” Goethe defended his optical experiments and his scientiªc methodology. He argued that experiments act as mediators between the objective and the subjective.13 According to Goethe, experiments allow natural philosophers to “re-create natural or artiªcial phenomena” in an attempt to bridge the gap between their ideas about a natural object and the object itself (1988, p. 13).14 As mediators, experiments are the means natural philosophers often use to navigate between how they think nature functions as articulated in their theories and hypotheses (i.e. the subjective) and how nature actually functions (i.e. the objective). In other words, experiments in general allow such philosophers to link or connect their epistemic claims—claims that assert something about nature’s ontology—with nature itself. Goethe also argued that no single experiment mediates completely or sufªciently between objective nature and one’s subjective experience of it: “As worthwhile as each individual experiment may be, it receives its real value only when united or combined with other experiments” (1988, p. 13). By assuming that “things in nature, especially the commoner forces and elements, work incessantly upon one another; we can say,” Goe- the concluded, “that each phenomenon is connected to countless others” (1988, pp. 15–16). This interconnection of natural phenomena was causal for Goethe and formed the foundation for his holistic approach to the study of nature.15 The problem, as Goethe saw it, was how to determine or establish the link between these phenomena. Based on this holistic approach, Goethe proposed the notion of a series of experiments as mediator. According to Goethe, an experimental series is “a series of contiguous experiments derived from one another” (1988, p. 16). In other words, the experimental outcome of one experiment or set of experiments implies the undertaking of another experiment or set. 12. Although Goethe sought to unify the two types of modiªcationisms, he was not completely successful (Zemplén 2001, p. 73). 13. For further discussion on the notion of mediators in science, see Morgan and Morri- son (2000). 14. Goethe differentiated between Naturphilosophen such as Friedrich Schlegel and his own position as Naturforscher (Richards 2002). 15. For expositions on Goethe’s philosophy of science, see Hegge (1972), Steiner (2000), Stephenson (1995), and Tauber (1993).

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Figure 2. Goethe’s experimental series. Left horizontal arrows represent experimental outcomes obtained from each experimental set, while right horizontal arrows represent experimental suggestions for designing and conducting the next experimental set.

Through sequential experimental suggestions, a series of experiments is composed of linked or connected experiments and thereby acts as a mediator to link or connect a scientiªc theory and hypothesis about natural phenomena with the experience of those phenomena. Goethe’s preliminary prism experiment, as reported in the Beyträge zur Optik and later in Zur Farbenlehre, yielded boundary colors that suggested the generation of color is the result of the modiªcation of light at a boundary between light and darkness (Fig. 2). He next performed a set of boundary prism experiments that substantiated this suggestion. However, his experiments also suggested that the turbidity of the medium through which the light passed or is viewed is also responsible for color generation.16 Subsequent experimentation reported in Zur Farbenlehre, in terms of subjective and objective dioptric experiments, supported this experimental suggestion and led to Goethe’s notion of medium modiªcationism (Fig. 2). The derivation of these experiments through their experimental suggestions formed a united experiment for linking nature (i.e. objective)

16. Goethe does not provide or acknowledge in Zur Farbenlehre, an experimental suggestion to transition directly to experiments on ªrst-class dioptric colors. However, the connection between these experiments at this point in the experimental series may not be so much an experimental suggestion but rather, according to Sepper (1988, p. 90), a reºection of Goethe’s method of varying systematically experiments and not necessarily providing an overarching theory. However, it must also be noted that the experiments conducted on double images or auxiliary forms (Nebenbild) may provide the necessary experimental suggestion for undertaking experiments on ªrst-class dioptric colors (Goethe 1988, pp. 201–5; Zemplén 2001, pp. 70–4; Sepper 1988, pp. 196–200).

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and theory or hypothesis (i.e. subjective). “Studied thoroughly and understood as a whole,” claimed Goethe, “these experiments could even be thought of as representing a single experiment, a single piece of empirical evidence” (1988, p. 16). According to Goethe, a series of experiments—as mediator between the subjective and objective—provides “empirical evidence of a higher sort” (1988, p. 16). This higher evidence bridges the gap between the epistemic claims of a theory or hypothesis and nature itself, through the sequence of experimental suggestions from one experiment or set of experiments to the next. Just as in mathematics axioms are connected by their logical implications, claimed Goethe, so, in an analogous but not identical fashion, in experimental science experimental suggestions connect one experimental set to another: “These pieces of evidence may be expressed in concise axioms and set side by side, and as more of them emerge they may be ordered and related. Like mathematical axioms they will remain unshakable either singly or as a whole” (1988, p. 17). Thus, the greater the number of outcomes from a variety of different experimental series that are contiguously connected and ordered through their experimental suggestions and that support the relevant theory or hypothesis, the better substantiated it is. Of course, the gap between nature and a theory or hypothesis cannot be completely bridged no matter how many contiguously connected experiments or even sets of experiments are performed, as Goethe recognized, because no experimental evidence captures completely the complexity of causal interactions present in nature or exhibited by natural phenomena. For Goethe, rather, natural philosophers—in order to progress in their understanding of natural phenomena—should vary the number and types of experiments they design and conduct. Only then can these philosophers, who engage objective nature in an authentic manner, link with con- ªdence, although provisionally, nature to a theory or hypothesis.

4. Newton’s Experimental Series Goethe was highly critical of Newton’s theory of light and color, as noted above, especially Newton’s reliance on seemingly one or only a handful of experiments to support or prove his theory.17 In the “Der Versuch als Ver- mittler” essay, with Newton in his sights, Goethe asserted that “we cannot prove anything by one experiment or even several experiments together” (1988, p. 14).18 According to Dennis Sepper, “Goethe rejected the idea of 17. Sepper (1988, p. 69) claims that only three experiments were needed to justify Newton’s theory. 18. Elsewhere, Goethe charged that Newton “made the mistake of using a single phe-

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isolated crucial experiments because they left the phenomenon in its primitive singularity without consulting similar phenomena for comparison and elucidation” (1988, p. 85).19 Unfortunately, some of Goethe’s criticisms are unfounded because of a distorted view of Newton’s work, which Goethe ªrst encountered through the German scientiªc compendia.20 In this section, Newton’s experiments reported in the 1671/2 Philosoph- ical Transactions letter are reconstructed as a series of experiments—although a limited or focused series—with the generation of higher empirical evidence. As Rupert Hall astutely observes: “The ‘New Theory of Light and Colours’ was not framed in a stroke nor as the response to a single experiment, however ‘crucial’. Its evolution had taken time” (1993, p. 42).21 Indeed, the development and justiªcation of Newton’s new theory depended on a series of experiments, in which each experiment or experimental set generally led to or made way for the next, and on the overall evidence obtained from them. In this respect, the crucial experiment is one among many in Newton’s attempt to justify his theory.22

4.1. The common prism experiment In the ªrst of the Cambridge optical lectures Newton described a prism experiment, in which the oblong spectrum was observed, as a “commonly encountered experiment” (1984, p. 285).23 It was also the ªrst experiment described in the 1671/2 letter to the Royal Society.24 In the experiment,

nomenon [crucial experiment], and an over reªned one at that, as the foundation for a hypothesis supposed to explain the most varied and far-reaching events in nature [light and color]” (1988, p. 48). 19. Critical for the aim of Goethe’s investigations was the search for the Urphenomenon, for which light served in its simplicity to generate color vis-à-vis darkness (Sepper 1988, p. 197). Interestingly, Duck (1993) proposes that Goethe rejected Newton’s theory of light and color based on theological considerations. 20. “Virtually all [contemporary] compendia,” according to Sepper, “gave unnecessarily incomplete and inexact accounts of the experiments that Newton had performed, their cir- cumstances, and the course of his argument” (1988, p. 31). However, Goethe did read later Newton’s optical works for himself and offered point-by-point criticisms of Newton’s experiments and conclusions (Duck 1993). 21. Richard Westfall (1962) also made a similar observation that Newton conducted a series of carefully planned experiments to support his theory of light and color. 22. “The experiment which was to become the experimentum crucis,” according to Alan Shapiro, “is described in the Optical Lectures, but it is just another experiment among many and not a crucial experiment” (1980, p. 219). 23. The experiment was not only common in the sense of being well known but also as a template that Newton manipulated to design and conduct other optical experiments to test various explanations of the nature of light and color. 24. The experiment is not the ªrst experiment chronologically, as evident from New-

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Figure 3. Newton’s common experiment (reproduced from Newton 1984). See text for details.

Newton made a small hole (F) in the window shutter and allowed sunlight (O) to pass through a prism (A␣B␤C␬) at the minimum deviation position, i.e. the position at which the angle of the light beam before and after passing through the prism is the same (Fig. 3).25 What Newton observed on an opposite wall from the shutter was not the expected circular image, as predicted from the law of refraction, but rather an oblong image (PTYZ) in which its length (PT) was ªve times greater than its breadth (YZ) (Laymon 1978a). Newton considered the “disproportion so extrava- gant, that it excited me to a more then [sic] ordinary curiosity of examining, from whence it might proceed” (1671/2, p. 3076).

ton’s notebooks (Hall 1993; Sepper 1988; Shapiro 1980). According to Westfall, “Newton did not observe an elongated spectrum by accident. He had carefully designed an experiment, convinced, in the light of his earlier observations, that such a result would occur” (1962, p. 352). The concern in the present paper is not with the historical chronology but with the mental and cognitive process by which one experiment is linked to another to form a series. That process is—for the most part—similar whether the experiments are reconstructed chronologically, as in notebooks, or rhetorically, as in the published literature. 25. Newton does not explicitly state that the prism was placed at this position, although later in the letter he does imply it (Sepper 1988).

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4.2. The elimination experiments26 Newton’s initial experiment generated a conundrum that he investigated in subsequent experiments, which formed an important component of the experimental series reported in the letter. In that set of experiments, New- ton was concerned with eliminating a number of technical and hypothetical or theoretical possibilities that could account for the oblong spectrum (Raftopoulos 1999). He designed the ªrst experiment to explore the possibility that the observation of an oblong image instead of a circle is the result of the prism’s thickness. It was known, as even Goethe pointed out later, that the prismatic image could be altered if the light passed through the prism’s vertex as opposed to its base (Sepper 1988, p. 114).27 To test this possibility Newton allowed the light to pass through different parts of the prism, with varying thickness. He still observed the original oblong image.28 In the next set of experiments, Newton examined whether the oblong colored spectrum or “fashion of colours” is the result of “termination with shadow or darkness” (1671/2, p. 3076). In terms of the traditional mod- iªcationist theory color was thought to be the outcome of mixing light and darkness, with the darkness supplied by the boundary of the hole in the window shutter (Raftopoulos 1999; Sabra [1967] 1981). To test this possibility, Newton conducted two experiments. The ªrst was to vary the hole’s diameter, in the window shutter. The second was to place the prism in front of the window shutter hole. According to Newton, varying these conditions was immaterial to his original observation of an oblong image.29 Newton also designed an experiment to test whether unevenness or some other irregularity of the prism itself could explain the oblong colored spectrum.30 Utilizing a second prism, he positioned it in an inverted

26. According to Gravander (1975, Chapter 3), these experiments represent attempts to eliminate methodological and theoretical possibilities for explaining the oblong spectrum. 27. Goethe identiªed the work of Marco Antonio de Dominis, in this regard. Newton also identiªed Dominis in the Opticks as the person who rightly explained the origin of the rainbow, although the accuracy of Newton’s interpretation of Dominis’ work has been questioned (Ockenden 1936). 28. According to Sepper (1988, p. 114), Newton’s experiment does not completely refute an effect of a prism’s thickness—as least from a relative perspective—since prisms with various refracting angles yield different spectrum lengths. 29. According to Gravander (1975, pp. 104ff), these two experiments represent a refutation of the mechanistic dilution theory. Again, Sepper (1988, pp. 114–5) discusses the limitations of these experiments as conclusive refutations. 30. According to Sepper (1994), contemporary prisms in Newton’s time were defective

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manner with respect to the ªrst prism so that it refracted the light from the ªrst prism in a “contrary way” (Newton 1671/2, p. 3076). Newton’s reasoning was that if the dispersion of the light or the dilation of the colors was due to an irregularity of the prism then a second prism would compound the effect. If not, then the second prism should neutralize the effect of the ªrst prism. What Newton observed was an “orbicular” shape or a circle comparable to the shape of the light before passing through a prism. This refutation, according to Athanassios Raftopoulos, “carried special weight for Newton, for it is by means of some kind of irregularities [in the medium through which the light traverses] that Descartes and Hooke sought to explain the phenomena of colors” (1999, p. 102).31 Newton next examined whether the oblong image was the result of rays from opposite sides of the sun (Sabra [1967] 1981). By introducing the notion of ray he advanced the analysis of light quantitatively (Sepper 1988, 1994). To that end, he made a number of measurements and calcu- lations based on them. The measurements included various diameters, lengths, and angles, from which Newton made several computations and noted that the breadth (2 5/8”) of the oblong image corresponds to the ray’s linear propagation over the distance from the hole in the window shutter to the wall and to the subtended angle of sun’s diameter (31’) based on “the Refractions of two Rays ºowing from opposite parts of the 1 Sun’s discus” (1671/2, p. 3077). However, the length of the image (13 4”) and its corresponding subtended angle (2o49’) are roughly ªve times greater than expected, for which the sine law could not account. Since Newton “could not image [the sine law] to be so erroneous,” he designed and conducted another experiment to determine whether something more than the sine law holds for explaining the oblong nature of the image (1671/2, p. 3077). He took the prism in the common experimental set-up, in the position of minimum deviation, and rotated it 4 to 5 degrees. He observed that the oblong image is not varied signiªcantly. New- ton concluded that the difference in rays from opposite sides of the sun cannot account for the image but that another cause must be operative. Newton then investigated the possibility that “the sine law is right

with a number of irregularities, including bubbles and streaks, which could cause light scattering. 31. Raftopoulos (1999, pp. 102–104) goes on to discuss the inadequacy of Newton’s experiment, especially for refuting Hooke’s notion of color. Sepper (1988, pp. 118–121) also criticizes Newton’s experiment, claiming that Newton had to position the second prism so close to the ªrst prism that the oblong colored image could not develop. Conse- quently, Newton did not ªrst produce the oblong image and then revert it to an orbicular one with the second prism.

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about what happens in the prism but that something more happens after the light emerges” (Sepper 1994, p. 34). Newton had observed earlier how a tennis ball, after being struck by a racket, takes a curved path, after ac- quiring spin.32 Newton made the analogy between tennis balls and cor- puscles of light and reasoned that “if the Rays of light should possibly be globular bodies, and by their oblique passage out of one medium into another acquire a circulating motion, they ought to feel the greater resis- tance from the ambient Aether, on that side, where the motions conspire, and thence be continually bowed by the other” (1671/2, p. 3078). How- ever, by conducting experiments in which a board was placed at diverse distances from the prism he found that the rays moved in a straight rather than a curved line.

4.3. The experimentum crucis After exhausting what Newton considered to be the technical and theoretical possibilities for explaining the oblong colored image, he then introduced an experiment that he claimed supports an alternative interpretation of the data: “The gradual removal of these experiments, at length led me to the Experimentum Crucis” (1671/2, p. 3078). Newton’s crucial experiment is considered traditionally to be the culmination of his experimental evidence justifying his theory of light, as composed of rays with different refrangibilities.33 Newton, in the 1671/2 Philosophical Transactions paper, asserted it provided the necessary experimental evidence or weight to support or justify the theory (Laymon 1978b, p. 57). However, I propose that its weight is a result not of the crucial experiment per se; rather, that weight is provided only through the previous experiments that elimi- nated rival hypotheses or technical problems for explaining the nature of light. Newton’s experiment is crucial only because of that context. With- out it, the experimentum crucis provides only anomalous or unpredicted evidence.34 Moreover, according to his critics, on its own the crucial experiment was inadequate for justifying his theory of light (Sabra [1967] 1981).35 32. Newton’s inspiration for this experiment was Descartes’ theory of color, in which he too made the analogy between the curved paths of a tennis ball and spheres of light (Sabra [1967] 1981; Sepper 1994). 33. According to Westfall, the “experimentum crucis became the very anchor of the New- tonian position” (1962, pp. 356–357). According to contemporary historical scholarship, however, Newton’s experimentum crucis does not represent the culmination of his experimental evidence but one more experiment in a set of experiments (Shapiro 1996). 34. For a contemporary case study illustrating a similar conclusion, see Marcum (2007). 35. Laymon contends that only Newton’s idealized crucial experiment is successful,

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4.4. The prism-lens experiment Although Newton considered the experimentum crucis necessary for estab- lishing his theory of light, he did not consider it sufªcient for justifying his theory of color.36 Rather, in the 1671/2 letter to the Royal Society Newton reported two additional experiments—taken from another set of experiments—in defense of his theory. In the ªrst reported experiment he took a prism and placed it next to a small hole in the window shutter of a darkened room, he then placed a focusing lens four to ªve feet from the prism. Newton next took a white sheet of paper and placed it ten to twelve feet from the lens. What he observed on the paper was a colored oblong spectrum proximal to the lens and an inverted spectrum distal to it, along with a white spot at an intermediate position to the two spectra. In the second experiment, the prism was placed endwise. With this experiment he was unable to refract further “uncompounded” colors. From these experiments, Newton concluded that each colored ray exhibited a unique or speciªc refrangibility.

4.5. Conclusion The notion of crucial experiment is a relative concept and, as such, depends on a historical context as well as other contexts, as demonstrated above. In the Opticks, for example, Newton did not identify the experimentum crucis of the 1671/2 article as such. “Although Newton in the Opticks retained the experiment of 1672,” notes J. A. Lohne, “he no longer called it crucial” (1968, p. 196). Rather, it is identiªed as experiment number 6 (Book I, Part I) and represents one of eight experiments reported by Newton to support or defend his notion of light as composed of different refrangible rays. Indeed, in the Opticks Newton relied on an entire series of experiments to substantiate his theory of light and color, with some experiments carrying more weight than others. However, it was the combined evidence from this experimental series that functioned in a Goethean higher sense. The proof or justiªcation of Newton’s theory of light and color, then, was the consequence of accumulated evidence from an experimental series

while the actual experiment is not: “the experimentum crucis refutes . . . diffusion theories only if Newton’s idealized descriptions are used; if more accurate descriptions are used then the experiment does not refute diffusion theories” (1978b, p. 62). In addition, some histo- rians of science view Newton’s crucial experiment as a rhetorical device, part of a logical re- construction (Hall 1993, p. 35; Raftopoulos 1999, p. 116). Furthermore, according to Mi- chael Ben-Chaim (2004), Newton’s experimentum crucis does not meet the criteria for a crucial experiment outlined originally by Francis Bacon. 36. According to Lohne, Newton later “changed his mind and to Lucas denied that the Experimentum Crucis had anything to do with colours” (1968, p. 185).

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Figure 4. Newton’s experimental series. Left horizontal arrows represent experimental outcomes obtained from each experimental set, while right horizontal arrows represent experimental suggestions for designing and conducting the next experimental set.

and not from a single crucial experiment. That series, as reported in New- ton’s Philosophical Transactions letter, consisted of consecutive experiments or sets of experiments connected in terms of experimental suggestions (Fig. 4). First, the common prism experiment represented the problem that Newton wanted to solve—the oblong rather than orbicular image from refraction of sunlight through a prism, at the position of minimum deviation. This experiment suggested that other experiments could be designed and conducted to test whether contemporary hypotheses on the nature of light or technical problems could account for his experimental result (Fig. 4). However, these experiments did not account for Newton’s observation. Through the outcomes of the above experiments, Newton claimed he was then “led” to the suggestion that sunlight is composed of rays with different or speciªc refrangibilities (Fig. 4). This he then tested with the experimentum crucis, which in turn supported his notion of the nature of light and suggested that the various colored rays differ in terms of their refrangibilities. To test this notion about the nature of color he designed and conducted the prism-lens experiment, among other experiments, which substantiated his theory of color (Fig. 4). In all, the experimental series provided the necessary and sufªcient evidence to support his theory of light and color vis-à-vis competing theories and technical problems—at least for Newton and his followers.

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5. Underdetermination Thesis Goethe’s methodological notion formulated in “Der Versuch als Vermittler,” in terms of experimental series and of higher empirical evidence, has important implications for the contemporary philosophical UDT. Brieºy, proponents of the thesis claim that experimental evidence is inadequate for choosing between competing theories, i.e. empirical evidence does not determine but rather it underdetermines scientiªc theories (Hesse 1980; Klee 1997; Ladyman 2002; Laudan and Leplin 1991; and Stanford 2001). Two versions of the thesis are generally cited in the literature. The ªrst is a strong version: “all the evidence we could ever have is not sufªcient to rule out an alternative hypothesis” (Ladyman 2002, p. 167). In other words, no matter how much evidence is ever obtained it would be insufªcient for choosing one theory over its rivals. Thus, it would always be the case that the empirical evidence supports different theories equally and does not support any one theory unequivocally—at least in principle. A second version of the UDT is weaker than the ªrst: “as all the data we have gathered to date are consistent with more than one theory, we ought to suspend judgment as to which theory is true” (Ladyman 2002, p. 165). In other words, since all the current evidence is incapable of supporting a particular theory then no theory can be chosen with conªdence vis-à-vis its rivals.37 However, the UDT—whether its strong or weak version—assumes that empirical evidence is unproblematic, i.e. the evidence is uniform or homogeneous. The current case study suggests that there is an alternative interpretation of empirical evidence, with respect to the UDT. Empirical evidence can support—to diverse degrees—competing theories because parts or portions of that evidence, or completely different evidence not accepted by all, buttress each of the competing theories dissimilarly. Although some of the evidence is shared by competing theories, the overall evidence is not quite the same evidence for each of the competing theories. Rather, there is generally signiªcant development of empirical evidence as scientists vary the type and increase the number of experiments performed to choose one theory over its rivals. For example, some evidence utilized to support a particular theory may be dismissed in support of an alternative theory, while the alternative theory may draw on different evidence or emphasize the available or shared evidence differently. Not all of the theories are empirically equivalent since not all of the evidence is used to support every

37. As Ladyman (2002) acknowledges later, the weak version of the UDT does not pre- clude the possibility that a choice can be made based on additional or future evidence. The question here is why would that later evidence sufªce, when earlier evidence did not. The notion of experimental series, as developed herein, helps to address that question.

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possible theory equally. Basically, the experimental evidence must be se- verely limited to sustain the UDT. For example, the thesis holds true for a limited set of experimental evidence generated early on in the experimental series but as that evidence grows vis-à-vis development of an experimental series scientists do choose a theory from among competitors based on the overall evidence. Goethe’s methodological notion formulated in “Der Versuch als Vermitt- ler” supports and illustrates the above conclusion. For Goethe, the evidence forms a unity that depends on the structure of the experimental series and the links between experiments within the series. For example, Newton and Goethe constructed and conducted very different experimental series to investigate the nature of light and color (compare Figs. 2 and 4). In their respective series, the experiments were ordered or structured differently and some experiments appeared in one series and not in another or were emphasized differently.38 Thus, each theory is supported by a different series of experiments with different higher empirical evidence.39 Again, this case study supports the notion that the UDT is warranted only for a limited set of experimental evidence. For example, Newton’s common experiment or even the crucial experiment—if considered alone— could be interpreted differently by competing theories. But place that evidence in a larger or more complete or mature experimental series context, such as Newton’s experimental series (Fig. 4), and that evidence supports Newton’s interpretation, as he claimed. Finally, the comparison between Newton’s theory of light and color, which was based on an experimental series (and according to some, not just a single crucial experiment), and Goethe’s theory of light and color, which was also based on a series of experiments, reveals an important distinction between their respective series of experiments. That distinction involves the type of series conducted by either Newton or Goethe with respect to the link between experiments in the series. The link or connection between experiments or set of experiments can emphasize either the empirical or the rational. For the empirical link, experiments are varied systematically in terms of experimental design or structure. That systematic variation depends upon or is guided by experience, with little or, even at

38. For instance, Goethe dismissed Newton’s crucial experiment as artiªcial. 39. Of course, the stronger UDT remains unresolved since, in principle, an empirically equivalent theory can always be proposed. Although the strong version appears unassail- able, especially in principle, it is problematic in terms of empirically equivalent theories cohering with other theories that constitute a discipline’s epistemic core. For example an alternative theory may be proposed, but if it violates another well established theory then it is not as viable as one that does not violate the established theory.

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times, no theoretical or rational considerations. The link is derived from practical considerations rather than rational or logical ones. For the rational link, however, theoretical considerations are important. The links are derived from rational and logical considerations of the experimental outcomes. Goethe’s links between the various experiments or sets of experiments were mostly empirical in nature, while Newton’s links were chieºy rational or theoretical. For example, Goethe conducted his experimental series beginning with irregularities on white paper, followed by squiggly lines on paper, and followed next by patterns in one orientation and then in inverted positions. Newton, on the other hand, was concerned with theoretical and technical issues that could account for his experimental observation, from the common experiment. It was these theoretical issues that drove Newton’s experimental series, serving to link the experiments or sets of experiments in more of a rational or logical—rather than an empirical or a practical—fashion. Although theoretical issues, especially mod- iªcationism, were also important in linking Goethe’s experiments, such issues were generally not at the foreground of his concern in designing experiments and resulted in an experimental series that did not cohere with current optical and other physical and geometrical theories. For example, the connection between the Beyträge experiments and the dioptric experiments in Zur Farbenlehre, as already noted (see footnote 16), do not represent a theoretical concern or issue as much as a methodological exercise of varying experiments, in order to investigate natural phenomena.40

6. Conclusion In a 1671/2 Philosophical Transactions paper Newton relied on a single experimentum crucis to justify, especially for rhetorical purposes, a theory that light is composed of different refrangible rays. He also situated the notion of crucial experiment in a methodological framework of analysis and synthesis. However, the community of natural philosophers interested in the nature of light did not accept the evidence of Newton’s experimentum crucis as sufªcient for supporting his theory of light. Newton was soon em- 40. Shapiro also argues that theoretical considerations and not just experimental considerations were also critical for Newton’s theory of light and color: “Experiment was not the central issue in the acceptance of Newton’s theory. Agreement with other theories and ªelds of knowledge, internal coherence, explanatory power, and rival explanations mat- tered as much as experimental tests or agreement with nature” (1996, p. 61). Moreover, there were metaphysical differences between Newton and Goethe, e.g. causation must be reductionistic in nature, rather than holistic. Consequently, Newton’s reduction of light to rays satisªed this metaphysical position rather than Goethe’s holistic metaphysics.

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broiled in controversy concerning the theory, upon which he conducted additional experiments that were reported in a book on optics. In that book, Newton no longer identiªed the crucial experiment as such but rather as one experiment among many to justify his theory not only of light but also of color. Around a century later, Goethe criticized Newton’s theory of light and color, especially its reliance upon a single experimentum crucis. In contrast to Newton, Goethe proposed that a series of experiments is the best or most appropriate means by which to investigate natural phenomena—like the nature of light and color. The reason, according to Goethe, is that the col- lected or higher empirical evidence from such experiments provides evi- dential support that is sufªcient or adequate to justify the choice of one theory over its competitors, even though that choice may only be tempo- rary. In the present paper, the justiªcation of Newton’s theory of light and color in the Philosophical Transactions paper is reconstructed in terms of Goethe’s methodological principles of experimental series and of higher empirical evidence. Goethe’s above methodological notions have important implications for the contemporary philosophical UDT, which claims that experimental evidence is inadequate to choose a theory over its competitors. What is problematic with the thesis, however, is that empirical evidence is treated ho- mogeneously, i.e. philosophers assume that scientiªc practitioners do not distinguish among the data but rather regard them uniformly or equally. However, the present case study demonstrates that the data from New- ton’s and Goethe’s experimental series diverge signiªcantly from each other. The reason is that both series are structured differently (compare Figs. 2 and 4). Although the UDT may be applicable to the early stages of experimental series, as such series unfold, however, the experimental data—as higher empirical evidence—are sufªciently different from one another to warrant choosing one theory over its competitors. Finally, Goethe is certainly correct in claiming that “the greatest ac- complishments come from those who never tire in exploring and working out every possible aspect and modiªcation of every bit of empirical evidence, every experiment” (1988, p. 15). However, experiments cannot be conducted from a strictly empirical framework; rather, there must be some prevailing theoretical framework—as the current case study illustrates— in order to situate experiments rationally so as to choose among competing theories. Consequently, only when experiments are linked coherently with accepted rational and theoretical considerations can scientists then choose with conªdence or in an authentic manner, although only provisionally, a theory over its competitors.

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