2 The Virtue of Productive Uncertainty, or, What to Do When You Don’t Know Something

Matthew Stanley

Science textbooks are full of facts—things we know. But scientists spend most of their time thinking about things we do not know. It is not always clear how one should deal with the unknown. Should it be avoided, confronted, minimized, ignored? When an experiment fails, or an equation refuses to yield its solution, what should be done? There are many strategies. Some are productive, some are not. Guidelines for these situations are absolutely essential for the practice of science, though they are rarely stated explicitly. Instead, they are governed by usually unspoken virtues and values. Scientists who make their uncertainty productive are celebrated as insightful, dogged, or sometimes just stubborn. The unknown can be frightening and arresting, and one mark of a “good scientist” is the ability to continue forward despite those obstacles. Where do these virtues come from? Out of the many possible approaches to uncertainty, why did certain scientists or groups of scientists choose one particular approach? Can we understand the kinds of justifications used for specific kinds of scientific practices?

I here trace one kind of justification for scientific virtues: a religious type. Religion has historically provided rich resources for scientists grappling with categories like uncertainty. This paper presents three case studies where religious ideas were used as justification for the epistemic virtue I call “productive uncertainty”—embracing the unknown as a proper source for scientific investigation, even in the absence of firm technical foundations. Essentially, this is the claim that one should continue working on a scientific problem despite gaps and incompleteness. My case studies examine the work of James Clerk Maxwell (1831–79), Arthur Stanley Eddington (1882–1944), and Carl Sagan (1934–96). These physical scientists, from three different generations, thought carefully about issues of productive uncertainty and relied on quite different connections to religious thought.

Maxwell: Explicit Theological Justification

Maxwell’s story is perhaps the most straightforward of the three. His thinking about science, religion, and uncertainty was highly scriptural and connected directly to familiar themes of creation and design. Maxwell is best known today through the equations named after him. These were the first interrelated mathematical descriptions of the behavior of electricity, magnetism, and light (though he never wrote down the quartet that modern physics students memorize).[1] His extraordinary achievement was showing that electricity, magnetism, and light were all unified: what looked to be different phenomena and forces were actually just manifestations of a deeper unity.

Maxwell was also an evangelical Christian. He was raised in both the Anglican and Presbyterian traditions, and as a young man in Cambridge came to evangelicalism through a powerful conversion experience. In the Victorian age, evangelicalism was not a separate sect, but rather an ecumenical outlook that cut across denominations. That outlook was typically associated with a deep respect for scripture and an emphasis on a personal relationship with Jesus Christ, rather than institutional authority. Like most evangelicals, Maxwell thought of humanity as deeply sinful and in need of redemption from a wholly-other divine power. His God was the creator and lawgiver of Genesis who carefully crafted a universe for human beings.[2]

This framework was important for how Maxwell dealt with questions of uncertainty in his work on electromagnetism. By the time he finished college, there were already indications that magnetism was related to electricity, but it was not clear exactly how or why.[3] Neither the laboratory nor theoretical evidence suggested any fruitful routes of study. Maxwell, however, persevered. He developed a mechanical model of ether in which it could support transverse waves of electromagnetic effects, which he realized would travel at the speed of light.[4] This suggested a profound conclusion: “that the luminiferous and the electromagnetic medium are one“—the unification of light and electromagnetism.[5] Maxwell embraced the unification of natural laws suggested by his mechanical model, even though some of his colleagues (such as Lord Kelvin) objected. He was convinced that there was a true connection between optics and electromagnetism, a fundamental unified principle hidden in the chaos of observable phenomena. What reason did he have for taking unity seriously as a guideline?

It was not that he had a naïve belief in the unity of nature. Maxwell seriously considered the possibility that the unification of natural laws was only a feature of the mind and not the physical world.  As a young man he wondered: “[A]re we to conclude that these various departments of nature in which analogous laws exist, have a real interdependence; or that their relation is only apparent and owing to the necessary conditions of human thought?”[6]

Maxwell knew it was entirely possible that the concept of an orderly, unified universe was simply a human psychological construction projected onto the world. To illustrate this danger, he presented two possible metaphors for the laws of nature:

Perhaps the ‘book,’ as it has been called, of nature is regularly paged; if so, no doubt the introductory parts will explain those that follow, and the methods taught in the first chapters will be taken for granted and used as illustrations in the more advanced parts of the course; but if it is not a ‘book’ at all, but a magazine, nothing is more foolish to suppose that one part can throw light on another.[7]

If nature was like a book, then there was a single unified argument. There was a common thread holding together the text that could be used to interpret and understand the whole even if you were only able to read one chapter. If so, then in physics, electricity could help you understand magnetism because they were both part of a single “document.” In that case unity was a reasonable goal.

But if nature were like a magazine, where the separate articles had nothing to do with one another or were written by different authors, there was no such assurance. A magazine has no single argument. There would be no guarantee that any one article could help the reader understand any other. There would be no justification to persist in looking for unity. If this were the case, there would be no reason to think that electricity could help us understand magnetism. It was not obvious why scientists should choose one metaphor over the other. Whether nature was like a book or a magazine was of the highest importance. But how was one to decide? For Maxwell, the key was that he knew the book of nature’s author—God—and he knew how that author wrote.

Maxwell thought of natural laws as being “parts of one universal system.”[8] The interrelationship of natural laws was a way that God communicated His existence, and it was the unity of laws that revealed this communication. An arbitrary distribution of individual laws (like the articles of a magazine) would not suggest anything about a divine plan, but unification (like the chapters of a book) would be highly improbable and therefore was a kind of divine communication. Maxwell thought God had a plan for the world, and part of that plan was designing natural laws to fit together like the pieces of a puzzle.

Maxwell often described the importance of unity in his God’s plans. He thought this could be helpful for men of science:

I think that each individual man should do all he can to impress his own mind with the extent, the order, and the unity of the universe, and should carry these ideas with him as he reads such passages as the 1st Chap. of the Ep. to Colossians…, just as enlarged conceptions of the extent and unity of the world of life may be of service to us in reading Psalm viii.; Heb. ii. 6, etc.[9]

For Maxwell, a divinely unified universe was something that could be found in the Bible, not just the laboratory. Persisting in the scientific goal of a unity of nature was therefore encouraged by theology. The scriptural passages Maxwell referred to in this letter emphasized God’s role as creator of the natural world and awe that God had designed his creation for man. Thus Maxwell linked the unity and order of nature not just with divine creation itself, but also with the role of humanity in that creation. He also argued that we can see “wisdom and power” in the uniformity of natural laws: “uniformity, accuracy, symmetry, consistency, and continuity of plan are as important attributes as the contrivance of the special utility of each individual thing.”[10] A properly evangelical reading of scripture could, he thought, justify his searching for unity in the unknown.

This was because Maxwell thought God had designed the laws of nature with the special feature that they were meant to be discovered: “[Once we understand some science] we are prepared to see in Nature not a mere assemblage of wonders to excite our curiosity but a systematic museum designed to introduce us step by step into the fundamental principles which are displayed in the works of Creation.”[11]

In particular, the unity of laws was intended for discovery. The connections of natural laws were systematic, in that they were designed to attract the attention of humans and lead them to deeper principles. Laws were laid out like a trail to guide the attentive person from diverse phenomena to unification via strategic connections. Maxwell’s God wanted him to push through the puzzles. His theology gave him a powerful set of tools for understanding the natural world and for guiding his investigations in physics:

Is it not wonderful that man’s reason should be made a judge over God’s works, and should measure, and weigh, and calculate, and say at last ‘I understand I have discovered—It is right and true’…. We see before us distinct physical truths to be discovered, and we are confident that these mysteries are an inheritance of knowledge, not revealed at once, lest we should become proud in knowledge, and despise patient inquiry, but so arranged that, as each new truth is unraveled it becomes a clear, well-established addition to science, quite free from the mystery which must still remain, to show that every atom of creation is unfathomable in its perfection.[12]

Discovering the design of these laws was not meant to be an easy victory, however. Their revelation was balanced against the deeper truths which humans could never know. God’s intent was to encourage us to always be investigating further, not to be satisfied with what we already had:

While we look down with awe into these unsearchable depths and treasure up with care what with our little line and plummet we can reach, we ought to admire the wisdom of Him who has arranged these mysteries that we find first that which we can understand at first and the rest in order so that it is possible for us to have an ever increasing stock of known truth concerning things whose nature is absolutely incomprehensible.[13]

Note the evangelical warnings against human pride and the evocative image of man’s limited powers represented by “our little line and plummet.” The deepest truths of nature were simply beyond our understanding, except where God allowed us to explore. As with the evangelical position on sin and redemption, our ability to know anything about the universe was the result of God’s grace in making those things knowable. Comprehension of nature came from God’s free choice to set up the laws of nature such that they could be understood, not only a result of human efforts.

Maxwell’s explanations for the importance of unity show that it was not solely a scientific goal. It also had profound religious significance. It was a religious virtue to know that God had intentionally created a mysterious but comprehensible universe. A virtuous person pushed into that uncertainty assured that there were answers and that they were findable. This gave Maxwell confidence that uncertainty could be productive: even if the world looks messy, you should persist in looking for unity. His approach to this problem was typical of conservative religious thought of the time, postulating a close relationship between the physical world and its creator and resting on the idea that the Book of Nature could provide insight into God’s thoughts.

Eddington: Implicit Theological Justification

For my next case, the religious context is significantly different. Now we will examine how liberal theology can contribute to questions of productive uncertainty. For this we look at the Cambridge astrophysicist A.S. Eddington, now best known as the man who provided the first observational evidence for Einstein’s theory of relativity. That was extremely important, but his scientific legacy is more significant in astronomy. He was one of the first theorists to understand the inner workings of stars and laid the foundation for stellar astrophysics.[14] But he is of interest here due to his religious belief. He was a lifelong member of the Religious Society of Friends, better known as the Quakers. The Quakers are a Protestant sect that emphasizes the presence of God within everyone and, relatedly, an embrace of mysticism, pacifism, and social activism. As was typical of liberal religion, they contended that personal religious experience was primary, with scripture and institutions secondary.

As with Maxwell, we examine how a particular religious idea intersected with questions of uncertainty: what the Quakers call “seeking.” This refers to the Quaker virtue of constantly exploring, searching, and looking for new things in both the spiritual and temporal worlds. This is an anti-dogmatic stance: one should not try to find complete certainty because this leads to stagnation and a refusal to accept new ideas. Quakers associate this idea with a mystical outlook. Mysticism requires an ability to accept new knowledge at any time, unlike fundamentalism, which rejects in principle that true knowledge is revisable. A seeker is a pragmatist, using whatever knowledge and tools are useful, instead of worrying about whether they are absolutely true.

Eddington tried to follow the ideal of seeking, and this played an important role in his work in astrophysics. It allowed him to make progress on a difficult area of theoretical astronomy. In 1916 he began investigating a problem that had proven intractable for astronomers: what, exactly, are stars? And, how do they shine? Previous attempts to solve these problems involved creating theoretical models of stars based on physical principles that were well-understood, such as Newtonian gravity and thermodynamics.[15] These attempts failed, and the resulting models behaved nothing like stars. It was clear by the twentieth century that gravitation was not enough to explain why stars were hot. It seemed that some critical element was missing from physics. This was a deductive critique: without total certainty in one’s foundations, one has nothing.

Eddington took a different approach to the question of stellar energy. He maintained that the most obvious feature about stars is that they shine, and therefore models must account somehow for this output of energy. Astronomers knew nothing about the detailed behavior of the energy source, so Eddington made a pragmatic, simplifying assumption. Assume that the energy is generated throughout the star in the simplest way possible:

It is clear that we cannot arrive at much certainty with regard to the conditions in a star’s interior…the weak link in the present investigation is that I have assumed without much justification that [energy production] is constant throughout a star. I have given some evidence that if it is variable the general character of the results would not be greatly altered; and, as a step toward the elucidation of the problem of stellar temperatures, I plead to be allowed provisionally one rather artificial assumption.[16]

He justified his uncertain foundations by appealing to the possibility of progress on a difficult problem. And he was able to make progress: with slight adjustments of his provisional assumption, Eddington was able to reproduce many of the observable characteristics of stars without knowing any of the details of where the energy comes from.

This curve turned out to be an excellent fit to the data and was essentially the first success in theorizing about the interiors of stars. Not everyone was impressed, though. His colleague James Jeans argued that the fit between calculation and observation was meaningless because it was not based on firm deductions. Whether forward progress or firm foundations was more important was not obvious, and their disagreements became the basis of their famously vigorous debates at the Royal Astronomical Society.[17] Eddington continued on despite his colleagues’ criticism. He manipulated his new mathematical models and compared them to observations, and the differences allowed him to infer some of the basic behaviors of the source of stellar energy.

In 1917 there were still multiple possibilities for the physical mechanism, with the most likely candidates being either the annihilation of oppositely-charged particles or “transmutation” (what we today call fusion). Eddington argued that the competing theories should be judged on how well they allowed further scientific investigation:

The theory of annihilation of matter is more fertile in astronomical consequences than the other forms of the subatomic theory, and for this reason alone it seems worthwhile to follow it up in detail. We shall not be greatly concerned with how the annihilation is accomplished; but it may perhaps be well to have a scheme in mind.[18]

Even after his success, he was not content to let it stand as a finished product. He presented it as something that needed to be challenged, pushed, and most of all used. Manipulating a theory at the edge of its applicability helped to not just solve the problems at hand, but also indicate where further investigation would be useful: “In this calculation we have pressed the theory to an extreme degree. Our object is not so much to assert the truth of the conclusions, as to use every opportunity of discovering by comparison with observation the directions in which our approximate treatment may be improved.”[19] Intriguingly, he said that a theory should not be like a building (a permanent structure to be admired) but rather like an engine (something to move one forward).[20]

Eddington justified his methodology by pointing out that he had made great steps forward in understanding stars. Seeking new, if tentative, knowledge, rather than restricting himself to what was certain, had allowed him to bypass some of the problems of stellar astrophysics. He also said that this pragmatic, exploratory approach to science explained how progress can be made at all when results are constantly being overturned. This discarding of knowledge is not the tragedy it seems; rather, the tragedy occurs when people think they know everything necessary about a subject. Instead, they need to accept that any result is temporary, and true only so far as it allows further exploration. This makes the danger of disproof into a benefit, forcing a scientist to continually improve. This is how uncertainty becomes productive—if the puzzle piece does not fit, look for another place to use it.

The crux of the matter was that Eddington was arguing for an open-ended scientific process. Proof was not to be valued; it was the ability to know more that was important. Stars and Atoms, a popular book explaining his technical theory, took pains to explain exactly what this meant:

It would be an exaggeration to claim that this limited success is a proof that we have reached the truth about the stellar interior. It is not a proof, but it is an encouragement to work farther along the line of thought we have been pursuing. The tangle is beginning to loosen. The more optimistic may assume it is now straightened out; the more cautious will make ready for the next knot…. We have taken present day theories of physics and pressed them to their remotest conclusions. There is no dogmatic intention in this; it is the best means we have of testing them and revealing their weaknesses if any.[21]

In his inimitable style, Eddington illustrated the value of seeking over dogmatism with a reevaluation of one of the Greek classics. The story of Daedalus and Icarus was usually told to admonish those who push too far, but Eddington provided a novel perspective:

In weighing their achievements, there is something to be said for Icarus. The classical authorities tell us that he was only ‘doing a stunt,’ but I prefer to think of him as the man who brought to light a serious constructional defect in the flying machines of his day. So, too, in Science. Cautious Daedalus will apply his theories where he feels confident they will safely go; but by his excess of caution their hidden weaknesses remain undiscovered. Icarus will strain his theories to the breaking-point till the weak points gape. For the mere adventure? Perhaps partly; that is human nature. But if he is destined not yet to reach the sun and solve finally the riddle of its constitution, we may at least hope to learn from his journey some hints to build a better machine.[22]

Uncertainty in a scientific investigation was not to be feared, it was to be welcomed as a route to further understanding.

Eddington’s tolerance of uncertainty in his theories was very similar to the Quaker virtues of seeking that he embraced in his religious practice. He considered fundamental certainty to be far less important than maintaining a living, transforming faith and a direct experience of God. Eddington felt that mystical Quakerism required an open attitude toward the world. He liked to cite one of the Queries (short questions meant to stimulate prayer and thought at Quaker meetings): “Are you loyal to the truth and do you keep your mind open to new light, from whatever quarter it may arise?” Eddington felt that religious truth should not be admired on a pedestal, but should instead inspire, and ultimately change one’s life. Certainty was not to be sought after in either science or religion:

We seek the truth; but if some voice told us that a few years more would see the end of our journey, that the clouds of uncertainty would be dispersed, and that we should perceive the whole truth about the physical universe, the tidings would be by no means joyful. In science as in religion the truth shines ahead as a beacon showing us the path; we do not ask to attain it; it is better far that we be permitted to seek…. You will understand neither science nor religion unless seeking is placed in the forefront.[23]

So for this Quaker, science shared a virtue with religion: persist in searching for knowledge, even if there will be no end. A complicated puzzle is just one more step on an unending quest. Eddington’s approach to linking scientific and religious values was typical of early twentieth century liberal religion: avoiding talk about God as creator or direct divine interaction with the natural world, and instead emphasizing personal religious experience and how a religious outlook can work well with science. The practice of science was encouraged by the spiritual virtue of seeking for truth and a pragmatic approach to all experience.

Sagan: Structural Theological Justification

Our third historical actor, the astronomer Carl Sagan, was quite different, in that he was not conventionally religious in any sense. He was an icon of the public understanding of science, from The Tonight Show to his own series Cosmos, and the face of planetary exploration. He was also a dedicated secular humanist, meaning he carried both skepticism toward and respect for religious belief. Wary of dogma, he did not hesitate to denounce creationism or fundamentalism. But he appreciated spiritual perspectives, particularly a kind of Spinozistic Romanticism (“We are a way for the cosmos to know itself”), and admired the power of religion to enact change and shape society.

Religion, then, in so far as it shaped Sagan’s scientific virtues, was not a matter of religious belief or practice as it was with Maxwell or Eddington. Rather, Sagan adopted a kind of religious structure, a religious mode of speech and argument—apocalypticism. The structures of apocalyptic prophecy were widely available and effective in his time and place, the late twentieth century United States, and he adapted them for his own purposes. They were resources that he used for thinking about how scientists should engage with uncertainty.

Sagan began grappling with these issues in the early 1980s when he and his colleagues developed their theories of “nuclear winter.” Inspired by the increase of Cold War tensions in the Reagan administration, they studied the large-scale planetary effects of a nuclear war. Their simulations suggested that even a moderate exchange of nuclear weapons would loft enough soot into the atmosphere to block sunlight and cause temperature drops across the globe.[24] This would shatter the terrestrial ecosystem and destroy humanity. Thus Reagan’s vision of a winnable nuclear war was fantasy; the whole of the human species was now at risk.

Sagan put his public stature to good use publicizing the dangers of nuclear winter, emphasizing predictions of global apocalypse in the event of such a war. He used shocking, emotional imagery to describe a nuclear winter, deploying all the skills that he had developed to excite the public about science and turning them to a more menacing task. His soaring imagery, wonder about the unknown, and insightful connections to ordinary life now became tools for evoking horror. He emphasized the possibility of extinction, the literal end of humanity. He liked to estimate that the total deaths from nuclear war would be be 500 trillion—all the humans who would ever have lived in the future.

Both politicians and scientists were unsettled by Sagan’s doomsaying. It was not so much the prediction itself; it was the way he spoke. He sounded like an Old Testament prophet, not a calm, rational astronomer. Critics complained that Sagan was unfairly emphasizing the worst possible interpretation of the results. Sagan had been warned about this by Hans Bethe, who saw early versions of his nuclear winter paper. Bethe cautioned that the paper should be built around the most likely result, not the most dramatic case.[25] But Sagan’s writings seemed to omit any caveats and focus on the worst-case scenario. They began to appear less like honest efforts to educate the public and more like propaganda.[26] Many scientists voiced concerns that this exaggeration was an inherently un-scientific thing.[27] One wrote that scientists “prefer to understate their results than to be blamed for overrating them” and that “apocalyptic views are not serving us well in the long run. At worst, they give science a bad name.”[28]

But Sagan defended discussing science in apocalyptic terms. He acknowledged that our knowledge of nuclear winter was necessarily theoretical and unverifiable. He then contended that the immediate effects of even one nuclear weapon were so devastating that it was our obligation to assume that there would be even further “unpredictable and catastrophic consequences.”[29] Whatever we thought we knew, the reality must be even worse. He justified this by noting that throughout the atomic age humans had continually discovered that nuclear war would be more awful than previously thought.[30] His favorite example was the Bravo H-bomb test, where the explosive yield and fallout spread were vastly greater than predicted.[31] This became a standard move: warning that “we may have severely underestimated how long the cold and the dark would last.”[32] As bad as the known effects were, there “may be others about which we are still ignorant.”[33]

Sagan was more than willing to admit that his predictions were uncertain. His characteristic twist was to assert that that uncertainty should be interpreted as implying an ever-worse reality:

We do not claim that a given sort of nuclear war will inevitably produce a given severity of nuclear winter; the irreducible uncertainties are too large for that. What we do claim is that the most likely consequences of many kinds of nuclear war constitute climatic and environmental catastrophes much worse than the worst our species has ever encountered—and that prudent national policy should treat nuclear winter as a probable outcome of nuclear war.[34]

Apocalypticism, then, was the “prudent” move. Sagan extended this argument to make the case that he, not his critics, was being appropriately conservative. He contended that there were two kinds of conservative thinking: playing down the possibility that something might happen, or assuming that it will happen and taking all the necessary precautions.[35] The first was more typically associated with scientific dialogue, but was no longer appropriate in the world of potential nuclear winter. This was a “tradition of conservatism which generally works well in science but which is of more dubious applicability when the lives of billions of people are at stake.”[36] Conservatism, then, should shift from assuming that results would be better, to assuming that they would be worse.[37] He did not deny that the probability of the extinction of humanity was small. But one was obligated to take that small chance seriously when the stakes were so high.

Sagan repeatedly criticized the reluctance of policymakers to accept this. Unless the chances of the more severe instances of nuclear winter were

not just small, but vanishingly small, risk analysis demands that we give it special attention in making decisions on policy and doctrine; i.e., the value we attach to our civilization and species is so high that even small probabilities that we are placing them in jeopardy must be taken very seriously.[38]

This emphasis on low-probability events had clear implications for policy. Even a 99% effective missile defense could lead to planetary disaster.[39] He hoped that, by this reasoning, the extraordinary consequences of nuclear winter might “help in bringing our species to its senses.”[40]

These moves were productive in the sense this essay has been discussing: other scientists took up the issue, and nuclear winter became the subject of many detailed analyses, even if Sagan did not agree with all of their conclusions. Further, the atmospheric models used in the nuclear winter calculations became a crucial part of modern climate science. Sagan’s science ignited a chain of research just as Maxwell’s and Eddington’s did. But it is important to acknowledge that Sagan’s discussions of nuclear winter had notable characteristics that were unusual for scientific conversation: warnings of imminent, universal disaster; emphasis on worst-case scenarios; policy critiques; remonstrations against political leaders; promises of the possibility of avoiding disaster; calling for a fundamental restructuring of global politics; and requesting specific policy changes. Some felt this discourse inappropriate for a scientist, and it likely played into his humiliating rejection by the National Academy of Sciences. However, if it is unusual in science, there is a kind of discourse that matches these characteristics: prophecy. If we reconsider Sagan as someone speaking in a prophetic register, his otherwise strange rhetorical choices begin to make sense.

A scientific prophet is not as strange a concept as it might seem. The late twentieth century United States was steeped in prophecy talk. Paul Boyer has shown that “prophecy belief” was widely filtered throughout American culture in this period, even into typically secular contexts.[41] He argues for concentric circles of prophecy belief: a core group who study the Bible intensely, a further group who live by the Bible but do not typically read it, and an outer circle of “superficially secular individuals who exhibit little overt prophecy interest, but whose worldview is nevertheless shaped to some degree by residual or latent concepts of eschatology.”[42] The profusion of apocalyptic literature produced by fundamentalist and evangelical communities during the Cold War effectively flowed into mainstream culture; for example, Hal Lindsey’s The Late Great Planet Earth became the best-selling non-fiction book of the 1970s. By the 1980s, prophecy belief was a kind of collective discourse found throughout the country. It was a mode of conversation that was both accessible to, and recognizable by, almost everyone, regardless of religious belief.

I am not, of course, arguing that Carl Sagan had a hidden fundamentalist agenda. No one should doubt Sagan’s commitment to secular humanism. Rather, by the 1980s prophetic language had become axiomatic in American life” even among “avowedly secular citizens.”[43] The ubiquity of prophecy belief in America has given rise to a particular mode of speech in which a public figure criticizes political leaders through warning of imminent disaster that can only be avoided through profound, genuine acknowledgement of some deeper truths.[44] Sagan’s adoption of this way of talking helps us make sense of his noted tendency to draw from “the top of the error bars.” Prophets were supposed to be audacious, not conciliatory. They were supposed to arouse strong emotions, not calm their audience. Sagan’s peculiar mix of pessimism and optimism was standard for prophets. It was necessary to alarm everyone and show the proper route for redemption. And as was traditional, his prophetic speech both moved the citizenry to demand change and invited ad hominem attacks on the speaker as a false prophet. The arguments of both Sagan and his critics were significantly shaped by Cold War America’s embrace of prophecy talk.

This was the frame for Sagan’s approach to productive uncertainty. When uncertainty intersected with possibly apocalyptic outcomes, he argued, scientists should emphasize the worst possibility. He demanded that they call for policy based on the worst possible non-zero probability outcome—nuclear winter and the extinction of humanity. This higher standard was characteristic of prophetic dialogue and was intended to shame leaders and mobilize listeners to demand immediate change to avert disaster. This prophetic precautionary principle seemed very strange to scientists, but makes perfect sense if we understand that Sagan was drawing on the widely available resource of prophetic culture. No one was particularly shocked when Jonathan Schell or Jerry Falwell drew on this resource. But the distinctive character of the prophetic mode of speech was very different from the conventional expectations of scientific communication. To Sagan, doing good science in an apocalyptic age meant assuming the worst. For him, this was the virtuous way to deal with uncertainty.

Conclusion

We have seen three versions of the epistemic virtue I call productive uncertainty. It deals with how scientists should proceed when their knowledge of a situation is unclear, incomplete, or nebulous. We have seen how this virtue was conceived of and articulated in rather different ways over three generations. For Maxwell, the maxim was “have faith.” For Eddington, “there is always more.” For Sagan, “assume the worst.” But in these exemplars’ own times and places, not everyone agreed with their approaches. While most scientific investigators would agree that uncertainty could be mediated or made useful, exactly how to do so was (and is) not always clear. Indeed, our three historical actors would likely have some lively conversations even as they agreed that uncertainty can be a starting point and not an end. They would all agree that uncertainty should not discourage scientific investigation, and that one should push forward even when there are doubts or shaky foundations.

All three of these approaches marked off certain scientific practices as good, virtuous, or valuable. All three also drew on religious resources to articulate and justify those scientific practices. Again, they did so in importantly different ways. Maxwell’s scientific values were explicitly religious; he literally cited chapter and verse to guide investigations of the natural world. Eddington’s were implicitly religious; one can see the links between his Quaker epistemology and his scientific practice, but it takes some careful investigation and could easily be missed. Sagan’s scientific values were structurally religious; his own religious beliefs and practices were largely irrelevant, and instead he used efficacious forms of communication that had traditionally belonged to a religion to which he did not adhere. It seems that each case has increasing distance between religious propositions and scientific values.

One could read this diachronic story as a secularization narrative, though that is misleading. It would be perilous to claim that 1980s America was less religious than Edwardian England. Rather, I think this is an indicator of the changing acceptability of professional scientists speaking about religious matters. This was expected in the Victorian period, frowned on in the early twentieth century, and completely shocking by the end of the twentieth century. Conversely, this narrative arc indicates how religion can still affect scientific values even without explicit discussions of God in technical journals. Science is more than facts and equations; religion is more than scripture and rituals. Both are sets of values, and those sets can sometimes overlap productively—say, when asking how to address uncertainty. A good life for a scientist is one that productively links the known and unknown, and one that can find solidity among mystery. This, it turns out, is something with which religion has some experience.

MATTHEW STANLEY teaches and researches the history and philosophy of science at New York University–Gallatin. He holds degrees in astronomy, religion, physics, and the history of science and is interested in the connections between science and the wider culture. His most recent book is Einstein’s War (Dutton/Viking, 2019). He is also the author of Practical Mystic, examining how scientists reconcile their religious beliefs and professional lives, and Huxley’s Church and Maxwell’s Demon, exploring how science changed from its historical theistic foundations to its modern naturalistic ones. He is working on a history of scientific predictions of the end of the world. In his spare time he is the co-host of the science podcast What the If?

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  • ——, ed. The Scientific Letters and Papers of James Clerk Maxwell. 3 volumes. Cambridge: Cambridge University Press, 1990.
  • Hufbauer, Karl. Exploring the Sun: Solar Science Since Galileo. Baltimore: Johns Hopkins Press, 1991.
  • Jones, R.V. “James Clerk Maxwell at Aberdeen, 1856–1860.” Notes and Records of the Royal Society of London 28.1 (1973): 57–81.
  • Oreskes, Naomi, and Erik M. Conway. Merchants of Doubt. London: Bloomsbury, 2010.
  • Rubinson, Paul. “Containing Science: The U.S. National Security State and Scientists’ Challenge to Nuclear Weapons during the Cold War.” Ph.D. diss, University of Texas at Austin, 2008.
  • Sagan, Carl. “The Atmospheric and Climatic Consequences of Nuclear War.” In The Cold and the Dark: The World After Nuclear War, edited by Paul R. Ehrlich, Carl Sagan, Donald Kennedy, and Walter Orr Roberts, 1–40. New York: W.W. Norton, 1984.
  • ——. “Nuclear Winter.” Parade (October 30, 1983).
  • ——. “Nuclear War and Climactic Catastrophe: Some Policy Implications.” Foreign Affairs 62.2 (Winter 1983/84): 257–92.
  • ——, and R.P. Turco. A Path Where No Man Thought: Nuclear Winter and the End of the Arms Race. New York: Random House, 1990.
  • Siegel, Daniel. Innovation on Maxwell’s Electromagnetic Theory. Cambridge: University of Cambridge Press, 1991.
  • Shulman, George. American Prophecy: Race and Redemption in American Political Culture. Minneapolis: University of Minnesota Press, 2008.
  • Smith, Crosbie. The Science of Energy: A Cultural History of Energy Physics in Victorian Britain. Chicago: University of Chicago Press, 1998.
  • Stanley, Matthew. Huxley’s Church and Maxwell’s Demon. Chicago: University of Chicago Press, 2015.
  • ——. Practical Mystic. Chicago: University of Chicago Press, 2007.
  • ——. “So Simple a Thing as a Star: The Eddington-Jeans Debate over Astrophysical Phenomenology.” The British Journal for the History of Science 40.1 (2007): 53–82.
  • Theerman, Paul. “James Clerk Maxwell and Religion.” American Journal of Physics 54 (1986): 312–17.
  • Wise, M. Norton. “The Maxwell Literature and British Dynamical Theory.” Historical Studies in the Physical Sciences 13 (1982): 175–205.
  • ——. “The Mutual Embrace of Electricity and Magnetism.” Science 4387 (1979): 1310–18.

  1. The most useful biography of Maxwell (despite some Victorian hagiography) remains Lewis Campbell and William Garnett, Life of James Clerk Maxwell (London: Macmillan, 1882).
  2. Maxwell’s religious views are discussed in Matthew Stanley, Huxley’s Church and Maxwell’s Demon (Chicago: University of Chicago Press, 2015) and Paul Theerman, “James Clerk Maxwell and Religion,” American Journal of Physics 54 (1986): 312–17.
  3. On the development of Maxwell’s theory overall see P.M. Harman, The Natural Philosophy of James Clerk Maxwell (Cambridge: University of Cambridge Press, 1998), 98–124; Daniel Siegel, Innovation on Maxwell’s Electromagnetic Theory (Cambridge: University of Cambridge Press, 1991); Crosbie Smith, The Science of Energy: A Cultural History of Energy Physics in Victorian Britain (Chicago: University of Chicago Press, 1998), 218–38; M. Norton Wise, “The Mutual Embrace of Electricity and Magnetism,” Science 4387 (1979): 1310–18; M. Norton Wise, “The Maxwell Literature and British Dynamical Theory,” Historical Studies in the Physical Sciences 13 (1982): 175–205.
  4. See Harman, Natural Philosophy, 64–67, 102–8, and Smith, Science of Energy, 226–27.
  5. James Clerk Maxwell to Michael Faraday, 19 Oct 1861, in P.M. Harman, ed., Scientific Letters and Papers of James Clerk Maxwell, Vol. 1 (Cambridge: Cambridge University Press, 1990), 685–86. (Hereafter, SLP.)
  6. James Clerk Maxwell, “Essay for the Apostles on ‘Analogies in Nature,’ February 1856,” in SLP 1, 376–77.
  7. James Clerk Maxwell, “Analogies,” in SLP 1, 381–82.
  8. James Clerk Maxwell, “Inaugural lecture at King’s College, London,” October 1860, in SLP 1, 670.
  9. James Clerk Maxwell to Charles John Ellicott, Bishop of Gloucester and Bristol, 22 November 1876, in SLP 3, 418.
  10. Ibid., 417.
  11. James Clerk Maxwell, “Inaugural Lecture at Aberdeen,” in R.V. Jones, “James Clerk Maxwell at Aberdeen, 1856–1860,” Notes and Records of the Royal Society of London 28 (June 1973), 71.
  12. Ibid., 77. Punctuation is Maxwell’s.
  13. Ibid., 77.
  14. The only major biography of Eddington is A.V. Douglas, Life of Arthur Stanley Eddington (London: Thomas Nelson, 1956), though it has significant gaps. Matthew Stanley, Practical Mystic (Chicago: University of Chicago Press, 2007) examines the religious and scientific aspects of his life. On Quakers and science more broadly see Geoffrey Cantor, Quaker, Jews, and Science (Oxford: Oxford University Press, 2005).
  15. Karl Hufbauer, Exploring the Sun: Solar Science Since Galileo (Baltimore: Johns Hopkins Press, 1991).
  16. A.S. Eddington, “The Radiative Equilibrium of the Sun and Stars,” Monthly Notices of the Royal Astronomical Society 77 (1917): 17.
  17. Matthew Stanley, “So Simple a Thing as a Star,” British Journal for the History of Science 40 (2007): 53–82.
  18. A.S. Eddington, Internal Constitution of the Stars (Cambridge: Cambridge University Press, 1926), 306.
  19. A.S. Eddington, Stars and Atoms (London: Oxford University Press, 1927), 40–41.
  20. A.S. Eddington, “The Internal Constitution of the Stars,” The Observatory 43.557 (October 1920): 357. This was Eddington’s Presidential Address to Section A of the British Association.
  21. Eddington, Stars and Atoms, 40–41.
  22. Ibid, 41.
  23. A.S. Eddington, Science and the Unseen World (New York: Macmillan Company, 1929), 88.
  24. See Lawrence Badash, A Nuclear Winter’s Tale (Cambridge, MA: MIT Press, 2009).
  25. Paul Rubinson, “Containing Science” (Ph.D. diss, University of Texas at Austin, 2008), 296–97.
  26. Naomi Oreskes and Erik Conway, Merchants of Doubt (London: Bloomsbury, 2010), 52. For example, MIT professor Kerry Emanuel criticized the TTAPS team for not being clearer about the uncertainties in “Nuclear Winter: Towards a Scientific Exercise,” Nature 319.6051 (January 23, 1986): 259.
  27. Ibid., 53.
  28. Florin Diacu, Megadisasters: Predicting the Next Catastrophe (Princeton, NJ: Princeton University Press, 2009), 29, 106.
  29. Ibid., 257–58.
  30. Carl Sagan, “The Atmospheric and Climatic Consequences of Nuclear War,” in The Cold and the Dark: The World After Nuclear War, edited by Paul R. Ehrlich et al. (New York: W.W. Norton, 1984), 24.
  31. Carl Sagan, “The Nuclear Winter,” Parade, October 30, 1983, 4.
  32. Ibid., 5.
  33. Carl Sagan, “Nuclear War and Climactic Catastrophe: Some Policy Implications,” Foreign Affairs 62.2 (Winter 1983–84): 264.
  34. Carl Sagan and R.P. Turco, A Path Where No Man Thought: Nuclear Winter and the End of the Arms Race (New York: Random House, 1990), 41.
  35. Ibid., 87–88.
  36. Sagan, “The Nuclear Winter,” 4.
  37. Ibid., 7.
  38. Sagan and Turco, A Path Where No Man Thought, 197.
  39. Ibid., 83–5.
  40. Ibid., 22.
  41. Paul S. Boyer, When Time Shall Be No More: Prophecy Belief in Modern American Culture (Cambridge, MA: Belknap Press of Harvard University Press, 1992).
  42. Ibid., 3.
  43. George M. Shulman, American Prophecy: Race and Redemption in American Political Culture (Minneapolis: University of Minnesota Press, 2008), ix.
  44. James Darsey, The Prophetic Tradition and Radical Rhetoric in America (New York: New York University Press, 1997); Shulman, American Prophecy.