Ignorance is not just a blank space on a person’s mental map. It has contours and coherence, and for all I know rules of operation as well.
—Thomas Pynchon
Hanging in my office is an ornately framed map of the world, inked and painted in Florence in 1472, as part of the luxury edition of the Cosmographia. Rather, it is a reproduction; the original is in the Vatican Library. Despite its date, its publication by Jacopo d’Angiolo, and the fact that the map was drawn by Pietro del Massaio with miniatures painted by Ugo de Comminelli, it is known as the Map of the World by Claudius Ptolemy (Klaudios Ptolemaios)—a geographer who lived thirteen centuries earlier. For me, it is not only a lovely, historical artifact; it is a wondrous image of the interplay of knowledge and ignorance.
In the second century CE, Ptolemy produced a remarkably advanced map of the world, using a coordinate system that reflected the spherical form of the Earth. But his text and his map were, for all practical purposes, lost to Europe with the fall of Rome. The rediscovery of his work, and its publication in Latin as Geographia Claudii Ptolemaei in 1406–1407, caused a sensation. New maps of the world could be prepared using his coordinates and incorporating his earlier topographical knowledge along with contemporary understanding. As a result, many maps that followed, including this ambitious map of 1472, were named in his honor.
This one is a map of Oikumene, the inhabited world—more accurately, the world of the pre-Columbian fifteenth century as known to Europeans. In remarkable detail and annotations, it presents geographical information that was hard won over the centuries, and I marvel at the confident delineation it displays in detailing such areas as the headwaters of the Nile River and the interior of Asia. But, at its edges, on three sides, are inked the words Terra Incognita: “Unknown Territory.”
The first and fundamental act of reason, the primal action of the Logos, is the drawing of a line. The setting of a boundary is the drawing of a line, the marking of a distinction between this and that. It is the basis of order, and order is the primary effect of the force of reason. A boundary both distinguishes two domains and simultaneously conjoins them in their adjacency. It is its boundary that identifies a place and defines its shape. The boundary of something also marks the beginning of something else, some other place, the edge of what-is-not-the-defined-place. It may serve as a barrier, protecting the integrity of what it defines; but it may also be a threshold, a limen, channeling and filtering exits and entrances from one place to another. Such boundary crossings, depending on context, may be described as passages, transformations, journeys, filtrations, or violations. The drawing of a boundary creates a border, a liminal area immediately on both sides of the boundary. Where the boundary is in doubt or thought to be moveable, or where the border is a transitional zone, it becomes a frontier. The term suggests the need for exploration or defense and the possibility of alteration or advancement of the boundary. Frontiers are areas where spatial claims are made.1
Maps are visual representations of the relationships of places; they locate places in relation to each other and orient the viewer. Places on a map are “nested”: there are places within places—cities within provinces within countries, for example. Some are only points (such as the North Pole); others are larger and contain many points. Larger-than-a-point places on a map have boundaries; they are domains, places that contain places. The whole territory mapped is the largest place shown. Which places are of which type depends on the scale of the map—whether it is map of Venice, of Europe, or of the world, for example. Cartographers employ criteria of salience to select which features of a territory should be included; these features are represented in symbols, arrayed so as to show spatial relationships. We map many types of terrain today: our maps are geographical, astronomical, political, historical, demographic, architectural, conceptual, curricular, and of many other varieties.
The 1472 Ptolemaic map aspired to map the world. But tracing the boundary of the known or inhabited world, Oikumene, is pointing simultaneously to the unknown world, to that which is beyond. Though it displays geographical knowledge, it also points to ignorance. (Indeed, Ptolemy’s Geographia is believed to be the first to use the term terra incognita.) As an epistemic map, its cartographic message is that, although we do not dwell in ignorance, we dwell with ignorance: our knowledge is bounded by ignorance.
The ideas shift smoothly, subtly, and deceptively in meaning: a map of the world displays our knowledge; our knowledge maps the world; we may map our knowledge; and what is known comprises a domain. It is true that spatial or geographical metaphors for knowledge may be misleading or pernicious—as, for example, in encouraging the territorial attitudes of experts over some domain. They are, nevertheless, suggestive, and what they suggest here is not only the image of ignorance as the boundary of our knowledge, but also the interesting possibility of mapping our knowledge—and our ignorance.
We not only speak of “areas of specialization,” “fields of study,” and “domains of inquiry,” we also refer to the “frontiers of knowledge.” Although our knowledge is bounded by ignorance, the border is transitional; the boundary is permeable and may be advanced by research and learning. Ignorance is the domain where learning has not yet penetrated. Not just the exterior, but the interior of a territory may also be unexplored. Ignorance is not only located at the outer rim of our knowledge; it is also found in pockets within the known, impervious and isolated like locked rooms or “eyes” in a game of Go.
We each have personal maps with our own boundaries of terra incognita, of course; we might imagine that these individual maps combine or overlap to form a collective, “human race” map—the universe of the known. My personal terra incognita is vast—incomprehensibly vast, of course—which is to say that even the domain of things I know I do not know is beyond measure. And so, if I may presume, are yours and everyone else’s.
Maps of knowledge change significantly over time, just as the maps of the known world have altered. Antique maps are more often historical artifacts or aesthetic objects than useful representations of their domains today; but when studied in sequence, they show the progress of learning. They also reveal that maps may contain mistakes. My 1472 map is rife with errors. There are significant omissions: much of the Southern hemisphere and of course all of the Western hemisphere are missing. There are displacements and distortions of proportionality and shape. There are fabricated features, even in some areas that are replete with detail: the headwaters of the Nile, the coast of China (“the Silk Land”), and Africa as a broadly extended southern land. These examples are manifestations of false knowledge, that form of ignorance that is obscured by embedded belief. As with other unknown unknowns, the veiled nature of such errors makes them more dangerous in practice than declared areas of ignorance. We expect the unexpected when we enter terra incognita, but not in a tidily mapped domain. Yet sinkholes of ignorance can appear in what were long thought to be cleared, well-plowed fields of knowledge.
Suppose we were to focus on mapping our ignorance instead of our knowledge—at least for a specific domain. It is an interesting proposal, a type of figure–ground reversal, a switch from photographic print to negative. We might well see our situation in a different way. The process of mapping would bring to consciousness the outstanding questions in a topic and prompt us to articulate what we know we do not know. It would require more than locating the boundary, though that is the first step; it would entail the delineation of the contours and structure of our known unknowns. We might indulge this exercise with the hope that the resulting map would deepen understanding, guide practice, and direct research. Though we can map only from the survey of our current knowledge (which may be disrupted), the process of mapping ignorance may incidentally expand what we know.
One field in which this idea has gained some traction is medicine. Medical ignorance is particularly dangerous, whether it involves an attending physician’s not knowing relevant information about a patient, or the lack of knowledge within the medical science community about the proper diagnosis or the effective treatments of a disease. For the practitioner, having a vivid sense of one’s own medical ignorance may produce a prudent outlook and alter therapeutic procedures. For the researcher, carefully specifying what is not known may establish an agenda. Mapping medical ignorance is a more structured task than simply assembling a list or compendium of what is not known in a given field (such as the Encyclopedia of Medical Ignorance);2 while both are useful, the map yields insights that are directed toward a specific problem at hand, and it also marks relationships between what is known and what is not.
At the University of Arizona, Marlys Witte has developed this idea into a signature program. She was inspired by a remark made by her mentor, the celebrated science writer Lewis Thomas: “I wish there was some medical school in this country that taught a class on medical ignorance.”3 Not everyone appreciated the original proposal for a class on medical ignorance: one foundation official even vowed to resign before funding a class focused on ignorance.4 No matter: Arizona’s College of Medicine today offers the “Curriculum of Medical Ignorance” (CMI), a “Medical Student Research Program” (MSRP), and the “Summer Institute on Medical Ignorance” (SIMI) for high school students. The learning goals of CMI are clearly defined: (1) to “gain understanding of the shifting domains of ignorance, uncertainty, and the unknown”; (2) to “improve skills to recognize and deal productively” with those domains; and (3) to “reinforce positive attitudes and values of curiosity, optimism, humility, self-confidence, and skepticism.”5 To achieve these goals, the university deploys the usual array of educational techniques: seminars, clinics, workshops, lectures, logs, conferences, even field trips—all devoted to medical ignorance.
Yes, these programs display both the hype of marketing and the desire to make room for irony and fun within medical education,6 but they do present a serious route to learning. There are important cognitive benefits: articulating what we do not know leads to the framing of cogent questions. The framing of a question is like the launching of a grappling hook from what is known into what is not; when it gains purchase in the zone of ignorance, it can be a line for further research and ultimately a stimulus for advances in knowledge.
Moreover, mapping one’s ignorance has affective benefits as well. Wherever mastery of knowledge and skills creates professional status, especially in practices that give professionals power over clients, there arises a natural pride that rests on what one knows, and a regrettable tendency for authority to develop arrogance. We know the effects: failure to listen, premature dismissal of relevant information, overreaching and overbearing professional conduct, mistakes and the denial of them, and so on. An explicit acknowledgment of ignorance may generate a corrective humility, a desire to seek rather than presume understanding, alertness to unforeseen consequences, and openness to alternative approaches. Building such a focus into the training of professionals is a means to developing the reflectiveness of what Donald Schoen has called “the reflective practitioner.”7
Mapping one’s ignorance is a valuable approach for all fields—not just for medicine and not just for practitioners; it is also a stimulating heuristic exercise for all researchers. It is easy to see how it might benefit scientists, historians, biographers, and genealogists, but also detectives, investigative journalists, debaters, lawyers, teachers, and students. The pursuit of scholarship, scientific research, investigations, or strategic planning can all be advanced by mapping what one does not know about the topic. In a broader view, constructing a map of ignorance is but one of many techniques for managing our ignorance (the topic of chapter 10).
Boundaries on maps often follow the natural terrain—where the land meets the sea, along a river, or astride a mountain pass. But boundaries may be political constructs as well—the products of treaties, agreements, decrees, or enforced claims. Maps of knowledge are no exception. Some boundaries of knowledge seem “natural”: our personal knowledge reflects where and when and to whom we were born; our genetically enabled sensory systems and cognitive capacities provide natural boundaries in the terrain of our knowledge. The boundaries may mark personal frontiers of inquiry and learning. Scientific knowledge seeks to “carve nature at its joints,” coordinating concepts and domains of knowledge with natural phenomena. These boundaries are not arbitrary, constructed, or imposed by any agency. They are best understood by contrast with epistemic boundaries that are intentionally drawn. When epistemic boundaries are “artificial,” when they are deliberately drawn or constructed, they are intended as barriers to knowledge; they establish areas of ignorance.
On a map of ignorance, one may locate known unknowns, both matters of “natural” ignorance and zones of constructed ignorance. Unknown unknowns can be acknowledged only at the outer border—“Here there be monsters”—or left outside the frame; there is no way to locate them in relation to what is known. The domain and scale determine what elements of recognized ignorance may be identified and placed on the map.
The whole of what we know we don’t know—individually and collectively—is so vast and so amorphous as to defy listing or counting. We may, however, catalog some object types. We may not know (but seek to learn or discover): (a) facts; (b) data, such as numerical values, dates, correlations, and other quantifications; (c) entities, such as substances, objects, creatures, or places; (d) persons, names, roles, or relationships; (e) causes, origins, motives, or reasons; (f) effects, outcomes, or implications; (g) concepts, principles, laws, or theories; (h) errors or discrepancies; and (i) clusters or systems of all these, including subjects, fields, and disciplines.
When we identify any known unknown, our specification reflects our cognitive frame—that is, the concepts, knowledge, theoretical assumptions, and the like, with which we specify what is unknown. In this way, our recognized ignorance is given structure by our knowledge: it is recognized and acknowledged. Just as on my Ptolemaic map, terra incognita has its coordinates.
In the remainder of this chapter, I will be concerned with boundaries of ignorance that are of the natural or unconstructed type, which I will call simple ignorance; the next chapter will examine created or constructed ignorance.
The proposal to map one’s ignorance relies on the possibility of drawing accurate and reasonably precise borders. In chapter 3, however, I raised the question of whether knowing is an on-or-off state or whether it might be a continuum or spectrum of epistemic states, a matter of gradation. As shorthand, let us call these two views the disjunctive and spectral, respectively. It is obviously more difficult to limn the boundary if knowledge and ignorance are spectral and not disjunctive (as is implied in mainstream epistemology); rather than a precise boundary, we might well have a transitional zone. And that may indeed be the correct view, as the following considerations suggest.
The disjunctive approach suggests that the boundary may be drawn firmly and with a fine line. Anything beyond that line, any cognitive state that fails to meet the standard of certified knowledge is generic not-knowledge. But there are distinct varieties of not-knowledge; it is not generic. Among the various forms are: conjecture, hunch, estimate, prediction, unwarranted belief, false knowledge, the forgotten, the unknowable, and simple ignorance. All these and related forms are varieties of ignorance in a larger sense, since they are forms of not-knowing. But notice that lumping them together discounts germane differences in cognitive content and in their prospective paths to completion as genuine knowledge.
Moreover, there are common experiences of “borderline” knowing that challenge the disjunctive view. Consider how one might set the boundary in this array of cases—is it knowing or not-knowing? Do I know:
Some of these conundrums might be resolved by more precisely specifying the object of knowledge, formulating more precisely the facts I do or do not know. But that would not resolve all the cases. A relevant issue is the expectation of memory and recall in ascribing knowledge: does asserting “Bob knows that p” entail that Bob has immediate recall of p when asked, or that Bob must (simply) be able to remember eventually, to calculate, or to recognize p? Another issue is the role of verbalization: whether one who knows p must be able to articulate, define, or explain p. Conventionally, knowledge of a fact entails belief in that fact; yet, in some of the examples, it is not at all clear how belief is involved: in the examples above, what is it I believe about the wine or polygons or the numerical product?
Yet another issue concerns the role of awareness or consciousness: must Bob’s knowing be focally conscious; must Bob consciously believe p in order to know that p? The traditional disjunctive schema for knowledge is not equipped to accommodate levels of consciousness, though decades of research have shown that consciousness represents only a small portion of our cognition. We continually process perceptions and ideas without attentive awareness of them. Such subliminal cognition can be epistemically effective, affecting decisions, evaluations, and behavior. But it seems, in the disjunctive approach, that only when we bring such cognitions to attentive consciousness—as beliefs expressible in propositional form—can they be known. Beyond that, possessing adequate justification for a belief seems to require being fully aware of the justifying conditions. Only then is the knowledge securely “possessed.”8 Thus, the disjunctive model presumes implicit standards of recall and verbalization, direct awareness of one’s factual belief and its justification, and the formulation of beliefs in propositional form.
Finally, there is the issue of forgotten knowledge. Though it is rarely examined by philosophers, there is an epistemic difference between that which we have not yet learned and that which we once knew but have now forgotten. We are ignorant of both, of course, because we know neither. Yet they are different: something I once knew—perhaps the contents of a book—may have influenced my thinking, altered my conceptual network, and yet I cannot recall it. Knowledge leaves traces, even when it fades.
These considerations suggest that the setting of a boundary will depend on conceptual decisions, and that a disjunctive approach will make those decisions provocatively arbitrary. The spectral approach focuses more on borderlands than boundaries. But where the boundary can be drawn precisely, such as within certain domains of science, relatively specific agendas for research can be formulated; success results in discovery that may expand or realign the boundary. We may fill gaps in our knowledge; occasionally, however, discoveries reveal whole new domains of ignorance that alter and expand our map significantly.
When Antonie van Leeuwenhoek peered into his handmade microscope in 1676 and saw single-celled organisms, he discovered a whole domain of microbiology populated by amazing creatures of which everyone else was ignorant—including the Royal Society, whose members doubted, even ridiculed, reports of his discovery. Or, to take a humbler example, one who becomes curious about stamp collecting may be startled to discover the huge, specialized, philatelic literature that provides a scholarly context for the hobby—a domain well known to aficionados, but astonishing to novices. Moreover, learning can be subversive as well as expansive, both in terms of human discovery and personal knowledge. The borderland in which inquiry and research occur has an unstable dynamic.
Maps are snapshots of the state of our knowledge and ignorance. The boundaries of our knowledge, however we locate them, not only expand over time; they are redrawn as the terrain of our knowledge changes, and not just at the borders. Indeed, the period of “obsolescence” for our knowledge is rapidly shortening. (Or, if you prefer the more stringent interpretation: much of what we believe we know turns out to be false knowledge—it never was real knowledge.) Even the most accurate map of our knowledge and ignorance is soon outdated. As sociologist Sheldon Ungar has stated, “Clearly, ignorance is inextricably tethered to knowledge, and in so far as the latter is uncertain, contested and possibly permeated with ignorance, no sharp divide can be drawn between knowledge and ignorance.”9
All maps, including maps of ignorance, are drawn with a purpose. Frankly, much of our ignorance is of no matter to us; it is therefore inconsequential for our mapping purposes, and we rightly ignore it. A physician who attempted a map of medical ignorance for a specific case would exclude trivial and irrelevant unknowns. If she does not know the number of hairs on the patient’s head, the make of automobile the patient drives, or the patient’s high school grades, it is in all probability irrelevant to her purposes. There is no need to mark such distracting ignorance. When dealing with the unknown, however, it is not always an easy matter to know what might be relevant and what is not. Symptoms are not always conclusive, nor are other forms of evidence. The hunches, guesses, and intuitions that generate hypotheses certainly help determine salience. In the end, however, only coming to know will settle the matter.
The borderlands between knowledge and ignorance, like all borderlands, are dynamic places. The buzz of cognitive activity reflects our attitudes: for the inquisitive, these are frontiers of learning, gateways to new knowledge; for the defensive, these are militarized zones, blockades of willful ignorance against the forbidden or the undesired. Gazing at the Grand Canyon of our ignorance, we might be simply in awe at how much is not yet known. Or we might be anxious at the prospect of learning or depressed at the impossibility of learning it all.
An immense subset of our recognized ignorance comprises things it is possible to learn. Of course, the specific set varies by individual, since we already have different bases of knowledge from which to learn. But for each of us, there are additional practical constraints: some unknowns would be immediately comprehensible; some could be learned given proper instruction; other things (like fluency in an exotic language) might take a lifetime. Some learning requires concentration and long practice, and we differ dramatically in our aptitudes. Learning some things is dependent on elaborate technology or special access: it was, for instance, impossible to know the major features of the dark side of the moon until our space technology permitted its imaging. Yet another practical constraint is that our attempt to know may be hindered or prevented by other agents or social systems that occlude relevant information or forbid our learning. It is helpful, therefore, as we map our unknowns to distinguish those that are knowable in principle from those that are knowable in practice (for a particular person at a particular time).
Nonetheless, although we have different individual epistemic profiles, and although each of us is subject to a gradient of practicality for learning, we all have a huge territory of known unknowns that it is quite possible to know. Regarding these things, taking time to learn is an option. Of course, merely having the option to know X does not imply any particular attitude toward learning or knowing X. It does not even imply that learning X is a “live option,” in the sense that learning X is retained in consciousness as a plausible activity. One may be quite indifferent toward X; having the option to learn X means one also has the option not to learn it.
Given the profusion of public ignorance (chapter 1), it appears that many citizens are exercising their options not to know. Ungar has called public ignorance “an under-identified social problem.” Indeed, he believes the situation has become so extreme that it is “pockets of observed public knowledge—rather than ignorance—[that] are exceptional and require specific explanation.”10 The worry is that this “undertow of ignorance” diminishes public life and discourse, debilitates private life and social interactions, and introduces dangers for one and all in public policy.
Such extensive personal ignorance—whether political, historical, mathematical, scientific, or whatever—is judged to be reprehensible, I believe, because of a combination of factors: (1) any citizen has many occasions for acquiring the knowledge; (2) it is not difficult to learn; (3) the knowledge is functionally important in our daily lives and basic to our culture; and therefore, (4) others will rightly expect and rely on what should be “common knowledge.” What excuse is there for public ignorance? And what causes it?
“Incompetent teaching” is a handy explanation, and when that is challenged, “intellectual laziness” is a cheap alternative. Though there is certainly a worrying amount of each, it seems misguided to blame individuals when the phenomenon is so widespread. A more likely explanation would be found in large-scale cultural forces or aspects of our social system.
A defensive response is that surveys of public ignorance cover information that is of less interest in today’s society, especially to students, who are frequently the target of these surveys and reports. Today’s students, one might claim, may be ignorant of the information asked in a survey, but they now cultivate a sophisticated knowledge of other things. Perhaps, but the concern is about functional knowledge deficits, and its inescapable implication that some knowledge is just more important than other knowledge. So, when we see a viral video taken at a public university,11 in which most interviewees do not know who won the Civil War (some cannot even name the two combatants), and yet know details about reality TV celebrities, the claim that public ignorance is no more than “old knowledge” giving way to new seems weak—more an accusation than a defense.
There is a more thoughtful response to public ignorance that focuses on effects of the explosion of knowledge and our access to it. Ignorance is increasing—for all of us. Because of the overwhelming cascade of information and the expansion of knowledge, the ratio of what any one individual knows to the total sum of available knowledge is shrinking rapidly. Knowledge is not only exploding; it is evolving into highly specialized forms. As we go our separate, specialist ways, our personal maps of knowledge have less and less overlap. Professional, academic, and technical occupations require specialized knowledge. These domains of discourse are not easily entered by the nonspecialist public. In fact, great effort is required of experts to stay current in their fields, a pressure that leads to the adoption of even narrower subspecialties that comprise a more manageable domain. Technical terminology proliferates. Interspecialty communication becomes more difficult as language actually becomes an obstacle to discourse; the public, baffled by jargon, becomes disinterested. In addition, our more complex world demands more in terms of functional knowledge. To cope, we increasingly rely on what Ungar calls “pre-digested knowledge packets”—summaries, abstracts, blurbs, cut lines, headlines, and articles that promise “the five things you need to know about X.” In addition, preference-based information delivery serves to diminish common knowledge as well (a topic for the next chapter).
Beyond specialization, there is the impact of technology, which has given us immediate access to enormous banks of information; one consequence is valuing the access to knowledge over the assimilation of knowledge. Why learn the names of your political representatives when you can easily locate them if needed? Why memorize the provisions of the Constitution when you can look up any passage? The logical extension is: why learn anything except the skills of “finding out”? Ungar’s observation is on point: “Information is no longer a scarce resource: attention and interest are.”12
But accessing is not learning. The genuine assimilation of information into knowledge, which requires attention and interest, affects the knower. It creates within the mind of the learner informational networks, conceptual connections, cognitive frameworks, and expanded moral, intellectual, and artistic imagination. These aspects of the life of the mind alter our ways of speaking, acting, and responding to the world—and influence what other knowledge we might choose to “look up.” In the end, access to information is only as valuable as the intelligence that selects and applies it.
The democratic ideal of the well-informed citizen is premised on the concept of “common knowledge.” But today it seems impossible in practice to secure a consensus on what content basic public knowledge must include. Well-intentioned essentialist proposals for a list of “what every American needs to know” have been widely and rightly criticized as conservative, biased, idiosyncratic, and hegemonic. Yet where there is no shared agreement regarding expectations for public knowledge, there will be no agreement as to which aspects of public ignorance are reprehensible.
Even if exponential increases in human ignorance are an inevitable by-product of the advance of knowledge, we need not resign ourselves to a parallel growth in reprehensible public ignorance. But we cannot simply look to enlightened media or more education to solve the problem—at least not advanced, commodified, specialized education. Liberal arts education is designed to address this issue, and I have elsewhere argued for its many merits;13 but it is unfortunate that liberal arts programs are now subject to the same social pressures I have described here: increasingly specialized majors, reduced breadth of study, short-term utilitarian approaches to valuing knowledge and skills, and a lack of consensus regarding expected knowledge. Ungar argues that the issue of public ignorance is, regrettably, not a “marketable issue.”14 Among his reasons: there is no clearly discernible class of victims who can organize and drive for reform. I would add that when the problem is identified, the all-too-common knee-jerk response is to blame schooling and ascribe stupidity.
Much of the ignorance we can map is removable both in principle and in practice. In this chapter, I focused on the open borders of simple ignorance, where the only hindrances are those involved in the tasks of learning. Attitudes and aptitudes, as I noted, determine our interest in learning, and I’ll later consider other factors, such as our desires, needs, rights, and obligations regarding knowledge (chapter 7). Simple ignorance, however, is not constructed, not intended, and not deliberately preserved; it is natural in that it is “found” and usually vincible. We may recognize it as a known unknown, but simply acquiesce: we neither decide to maintain our ignorance nor to remove it, and it pales in our consciousness. Let us turn now to artificial ignorance, to the ways in which we actively choose, even construct, our ignorance.