ignorance and uncertainty

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Posts Tagged ‘Climate Change

Communicating about Uncertainty in Climate Change, Part II

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In my previous post I attempted to provide an overview of the IPCC 2007 report’s approach to communicating about uncertainties regarding climate change and its impacts. This time I want to focus on how the report dealt with probabilistic uncertainty. It is this kind of uncertainty that the report treats most systematically. I mentioned in my previous post that Budescu et al.’s (2009) empirical investigation of how laypeople interpret verbal probability expressions (PEs, e.g., “very likely”) in the IPCC report revealed several problematic aspects, and a paper I have co-authored with Budescu’s team (Smithson, et al., 2011) yielded additional insights.

The approach adopted by the IPCC is one that has been used in other contexts, namely identifying probability intervals with verbal PEs. Their guidelines are as follows:
Virtually certain >99%; extremely likely >95%; very likely >90%; likely >66%; more likely than not > 50%; about as likely as not 33% to 66%; unlikely <33%; very unlikely <10%; extremely unlikely <5%; exceptionally unlikely <1%.

One unusual aspect of these guidelines is their overlapping intervals. For instance, “likely” takes the interval [.66,1] and thus contains the interval [.90,1] for “very likely,” and so on. The only interval that doesn’t overlap with others is “as likely as not.” Other interval-to-PE guidelines I am aware of use non-overlapping intervals. An early example is Sherman Kent’s attempt to standardize the meanings of verbal PEs in the American intelligence community.

Attempts to translate verbal PEs into numbers have a long and checkered history. Since the earliest days of probability theory, the legal profession has steadfastly refused to quantify its burdens of proof (“balance of probabilities” or “reasonable doubt”) despite the fact that they seem to explicitly refer to probabilities or at least degrees of belief. Weather forecasters debated the pros and cons of verbal versus numerical PEs for decades, with mixed results. A National Weather Service report on a 1997 survey of Juneau, Alaska residents found that although the rank-ordering of the mean numerical probabilities residents assigned to verbal PE’s reasonably agreed with those assumed by the organization, the residents’ probabilities tended to be less extreme than the organization’s assignments. For instance, “likely” had a mean of 62.5% whereas the organization’s assignments for this PE were 80-100%.

And thus we see a problem arising that has been long noted about individual differences in the interpretation of PEs but largely ignored when it comes to organizations. Since at least the 1960’s empirical studies have demonstrated that people vary widely in the numerical probabilities they associate with a verbal PE such as “likely.” It was this difficulty that doomed Sherman Kent’s attempt at standardization for intelligence analysts. Well, here we have the NWS associating it with 80-100% whereas the IPCC assigns it 66-100%. A failure of organizations and agencies to agree on number-to-PE translations leaves the public with an impossible brief. I’m reminded of the introduction of the now widely-used cyclone (hurricane) category 1-5 scheme (higher numerals meaning more dangerous storms) at a time when zoning for cyclone danger where I was living also had a 1-5 numbering system that went in the opposite direction (higher numerals indicating safer zones).

Another interesting aspect is the frequency of the PEs in the report itself. There are a total of 63 PEs therein. “Likely” occurs 36 times (more than half), and “very likely” 17 times. The remaining 10 occurrences are “very unlikely” (5 times), “virtually certain” (twice), “more likely than not” (twice), and “extremely unlikely” (once). There is a clear bias towards fairly extreme positively-worded PEs, perhaps because much of the IPCC report’s content is oriented towards presenting what is known and largely agreed on about climate change by climate scientists. As we shall see, the bias towards positively-worded PEs (e.g., “likely” rather than “unlikely”) may have served the IPCC well, whether intentionally or not.

In Budescu et al.’s experiment, subjects were assigned to one of four conditions. Subjects in the control group were not given any guidelines for interpreting the PEs, as would be the case for readers unaware of the report’s guidelines. Subjects in a “translation” condition had access to the guidelines given by the IPCC, at any time during the experiment. Finally, subjects in two “verbal-numerical translation” conditions saw a range of numerical values next to each PE in each sentence. One verbal-numerical group was shown the IPCC intervals and the other was shown narrower intervals (with widths of 10% and 5%).

Subjects were asked to provide lower, upper and “best” estimates of the probabilities they associated with each PE. As might be expected, these figures were most likely to be consistent with the IPCC guidelines in the verbal- numerical translation conditions, less likely in the translation condition, and least likely in the control condition. They were also less likely to be IPCC-consistent the more extreme the PE was (e.g., less consistent foro “very likely” than for “likely”). Consistency rates were generally low, and for the extremal PEs the deviations from the IPCC guidelines were regressive (i.e., subjects’ estimates were not extreme enough, thereby echoing the 1997 National Weather Service report findings).

One of the ironic claims by the Budescu group is that the IPCC 2007 report’s verbal probability expressions may convey excessive levels of imprecision and that some probabilities may be interpreted as less extreme than intended by the report authors. As I remarked in my earlier post, intervals do not distinguish between consensual imprecision and sharp disagreement. In the IPCC framework, the statement “The probability of event X is between .1 and .9 could mean “All experts regard this probability as being anywhere between .1 and .9” or “Some experts regard the probability as .1 and others as .9.” Budescu et al. realize this, but they also have this to say:

“However, we suspect that the variability in the interpretation of the forecasts exceeds the level of disagreement among the authors in many cases. Consider, for example, the statement that ‘‘average Northern Hemisphere temperatures during the second half of the 20th century were very likely higher than during any other 50-year period in the last 500 years’’ (IPCC, 2007, p. 8). It is hard to believe that the authors had in mind probabilities lower than 70%, yet this is how 25% of our subjects interpreted the term very likely!” (pg. 8).

One thing I’d noticed about the Budescu article was that their graphs suggested the variability in subjects’ estimates for negatively-worded PEs (e.g., “unlikely”) seemed greater than for positively worded PEs (e.g., “likely”). That is, subjects seemed to have less of a consensus about the meaning of the negatively-worded PEs. On reanalyzing their data, I focused on the six sentences that used the PE “very likely” or “very unlikely”. My statistical analyses of subjects’ lower, “best” and upper probability estimates revealed a less regressive mean and less dispersion for positive than for negative wording in all three estimates. Negative wording therefore resulted in more regressive estimates and less consensus regardless of experimental condition. You can see this in the box-plots below.

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In this graph, the negative PEs’ estimates have been reverse-scored so that we can compare them directly with the positive PEs’ estimates. The “boxes” (the blue rectangles) contain the middle 50% of subjects’ estimates and these boxes are consistently longer for the negative PEs, regardless of experimental condition. The medians (i.e., the score below which 50% of the estimates fall) are the black dots, and these are fairly similar for positive and (reverse-scored) negative PEs. However, due to the negative PE boxes’ greater lengths, the mean estimates for the negative PEs end up being pulled further away from their positive PE counterparts.

There’s another effect that we confirmed statistically but also is clear from the box-plots. The difference between the lower and upper estimates is, on average, greater for the negatively-worded PEs. One implication of this finding is that the impact of negative wording is greatest on the lower estimates—And these are the subjects’ translations of the very thresholds specified in the IPCC guidelines.

If anything, these results suggest the picture is worse even than Budescu et al.’s assessment. They noted that 25% of the subjects interpreted “very likely” as having a “best” probability below 70%. The boxplots show that in three of the four experimental conditions at least 25% of the subjects provided a lower probability of less than 50% for “very likely”. If we turn to “very unlikely” the picture is worse still. In three of the four experimental conditions about 25% of the subjects returned an upper probability for “very unlikely” greater than 80%!

So, it seems that negatively-worded PEs are best avoided where possible. This recommendation sounds simple, but it could open a can of syntactical worms. Consider the statement “It is very unlikely that the MOC will undergo a large abrupt transition during the 21st century.” Would it be accurate to equate it with “It is very likely that the MOC will not undergo a large abrupt transition during the 21st century?” Perhaps not, despite the IPCC guidelines’ insistence otherwise. Moreover, turning the PE positive entails turning the event into a negative. In principle, we could have a mixture of negatively- and positively-worded PE’s and events (“It is (un)likely that A will (not) occur”). It is unclear at this point whether negative PEs or negative events are the more confusing, but inspection of the Budescu et al. data suggested that double-negatives were decidedly more confusing than any other combination.

As I write this, David Budescu is spearheading a multi-national study of laypeople’s interpretations of the IPCC probability expressions (I’ll be coordinating the Australian component). We’ll be able to compare these interpretations across languages and cultures. More anon!

References

Budescu, D.V., Broomell, S. and Por, H.-H. (2009) Improving the communication of uncertainty in the reports of the Intergovernmental panel on climate change. Psychological Science, 20, 299–308.

Intergovernmental Panel on Climate Change (2007). Summary for policymakers: Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Retrieved May 2010 from http://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-wg1-spm.pdf.

Smithson, M., Budescu, D.V., Broomell, S. and Por, H.-H. (2011) Never Say “Not:” Impact of Negative Wording in Probability Phrases on Imprecise Probability Judgments. Accepted for presentation at the Seventh International Symposium on Imprecise Probability: Theories and Applications, Innsbruck, Austria, 25-28 July 2011.

Communicating about Uncertainty in Climate Change, Part I

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The Intergovernmental Panel on Climate Change (IPCC) guidelines for their 2007 report stipulated how its contributors were to convey uncertainties regarding climate change scientific evidence, conclusions, and predictions. Budescu et al.’s (2009) empirical investigation of how laypeople interpret verbal probability expressions (e.g., “very likely”) in the IPCC report revealed several problematic aspects of those interpretations, and a paper I have co-authored with Budescu’s team (Smithson, et al., 2011) raises additional issues.

Recently the IPCC has amended their guidelines, partly in response to the Budescu paper. Granting a broad consensus among climate scientists that climate change is accelerating and that humans have been a causal factor therein, the issue of how best to represent and communicate uncertainties about climate change science nevertheless remains a live concern. I’ll focus on the issues around probability expressions in a subsequent post, but in this one I want to address the issue of communicating “uncertainty” in a broader sense.

Why does it matter? First, the public needs to know that climate change science actually has uncertainties. Otherwise, they could be misled into believing either that scientists have all the answers or suffer from unwarranted dogmatism. Likewise, policy makers, decision makers and planners need to know the magnitudes (where possible) and directions of these uncertainties. Thus, the IPCC is to be commended for bringing uncertainties to the fore its 2007 report, and for attempting to establish standards for communicating them.

Second, the public needs to know what kinds uncertainties are in the mix. This concern sits at the foundation of the first and second recommendations of the Budescu paper. Their first suggestion is to differentiate between the ambiguous or vague description of an event and the likelihood of its occurrence. The example the authors give is “It is very unlikely that the meridonial overturning circulation will undergo a large abrupt transition during the 21st century” (emphasis added). The first italicized phrase expresses probabilistic uncertainty whereas the second embodies a vague description. People may have different interpretations of both phrases. They might disagree on what range of probabilities is referred to by “very likely” or on what is meant by a “large abrupt” change. Somewhat more worryingly, they might agree on how likely the “large abrupt” change is while failing to realize that they have different interpretations of that change in mind.

The crucial point here is that probability and vagueness are distinct kinds of uncertainty (see, e.g., Smithson, 1989). While the IPCC 2007 report is consistently explicit regarding probabilistic expressions, it only intermittently attends to matters of vagueness. For example, in the statement “It is likely that heat waves have become more frequent over most land areas” (IPCC 2007, pg. 30) the term “heat waves” remains undefined and the time-span is unspecified. In contrast, just below that statement is this one: “It is likely that the incidence of extreme high sea level3 has increased at a broad range of sites worldwide since 1975.” Footnote 3 then goes on to clarify “extreme high sea level” by the following: “Excluding tsunamis, which are not due to climate change. Extreme high sea level depends on average sea level and on regional weather systems. It is defined here as the highest 1% of hourly values of observed sea level at a station for a given reference period.”

The Budescu paper’s second recommendation is to specify the sources of uncertainty, such as whether these arise from disagreement among specialists, absence of data, or imprecise data. Distinguishing between uncertainty arising from disagreement and uncertainty arising from an imprecise but consensual assessment is especially important. In my experience, the former often is presented as if it is the latter. An interval for near-term ocean level increases of 0.2 to 0.8 metres might be the consensus among experts, but it could also represent two opposing camps, one estimating 0.2 metres and the other 0.8.

The IPCC report guidelines for reporting uncertainty do raise the issue of agreement: “Where uncertainty is assessed qualitatively, it is characterised by providing a relative sense of the amount and quality of evidence (that is, information from theory, observations or models indicating whether a belief or proposition is true or valid) and the degree of agreement (that is, the level of concurrence in the literature on a particular finding).” (IPCC 2007, pg. 27) The report then states that levels of agreement will be denoted by “high,” “medium,” and so on while the amount of evidence will be expressed as “much,”, “medium,” and so on.

As it turns out, the phrase “high agreement and much evidence” occurs seven times in the report and “high agreement and medium evidence” occurs twice. No other agreement phrases are used. These occurrences are almost entirely in the sections devoted to climate change mitigation and adaptation, as opposed to assessments of previous and future climate change. Typical examples are:
“There is high agreement and much evidence that with current climate change mitigation policies and related sustainable development practices, global GHG emissions will continue to grow over the next few decades.” (IPCC 2007, pg. 44) and
“There is high agreement and much evidence that all stabilisation levels assessed can be achieved by deployment of a portfolio of technologies that are either currently available or expected to be commercialised in coming decades, assuming appropriate and effective incentives are in place for development, acquisition, deployment and diffusion of technologies and addressing related barriers.” (IPCC2007, pg. 68)

The IPICC guidelines for other kinds of expert assessments do not explicitly refer to disagreement: “Where uncertainty is assessed more quantitatively using expert judgement of the correctness of underlying data, models or analyses, then the following scale of confidence levels is used to express the assessed chance of a finding being correct: very high confidence at least 9 out of 10; high confidence about 8 out of 10; medium confidence about 5 out of 10; low confidence about 2 out of 10; and very low confidence less than 1 out of 10.” (IPCC 2007, pg. 27) A typical statement of this kind is “By 2080, an increase of 5 to 8% of arid and semi-arid land in Africa is projected under a range of climate scenarios (high confidence).” (IPCC 2007, pg. 50)

That said, some parts of the IPCC report do convey disagreeing projections or estimates, where the disagreements are among models and/or scenarios, especially in the section on near-term predictions of climate change and its impacts. For instance, on pg. 47 of the 2007 report the graph below charts mid-century global warming relative to 1980-99. The six stabilization categories are those described in the Fourth Assessment Report (AR4).

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Although this graph effectively represents both imprecision and disagreement (or conflict), it slightly underplays both by truncating the scale at the right-hand side. The next figure shows how the graph would appear if the full range of categories V and VI were included. Both the apparent imprecision of V and VI and the extent of disagreement between VI and categories I-III are substantially greater once we have the full picture.

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There are understandable motives for concealing or disguising some kinds of uncertainty, especially those that could be used by opponents to bolster their own positions. Chief among these is uncertainty arising from conflict. In a series of experiments Smithson (1999) demonstrated that people regard precise but disagreeing risk messages as more troubling than informatively equivalent imprecise but agreeing messages. Moreover, they regard the message sources as less credible and less trustworthy in the first case than in the second. In short, conflict is a worse kind of uncertainty than ambiguity or vagueness. Smithson (1999) labeled this phenomenon “conflict aversion.” Cabantous (2007) confirmed and extended those results by demonstrating that insurers would charge a higher premium for insurance against mishaps whose risk information was conflictive than if the risk information was merely ambiguous.

Conflict aversion creates a genuine communications dilemma for disagreeing experts. On the one hand, public revelation of their disagreement can result in a loss of credibility or trust in experts on all sides of the dispute. Laypeople have an intuitive heuristic that if the evidence for any hypothesis is uncertain, then equally able experts should have considered the same evidence and agreed that the truth-status of that hypothesis is uncertain. When Peter Collignon, professor of microbiology at The Australian National University, cast doubt on the net benefit of the Australian Fluvax program in 2010, he attracted opprobrium from colleagues and health authorities on grounds that he was undermining public trust in vaccines and the medical expertise behind them. On the other hand, concealing disagreements runs the risk of future public disclosure and an even greater erosion of trust (lying experts are regarded as worse than disagreeing ones). The problem of how to communicate uncertainties arising from disagreement and vagueness simultaneously and distinguishably has yet to be solved.

References

Budescu, D.V., Broomell, S. and Por, H.-H. (2009) Improving the communication of uncertainty in the reports of the Intergovernmental panel on climate change. Psychological Science, 20, 299–308.

Cabantous, L. (2007). Ambiguity aversion in the field of insurance: Insurers’ attitudes to imprecise and conflicting probability estimates. Theory and Decision, 62, 219–240.

Intergovernmental Panel on Climate Change (2007). Summary for policymakers: Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Retrieved May 2010 from http://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-wg1-spm.pdf.

Smithson, M. (1989). Ignorance and Uncertainty: Emerging Paradigms. Cognitive Science Series. New York: Springer Verlag.

Smithson, M. (1999). Conflict Aversion: Preference for Ambiguity vs. Conflict in Sources and Evidence. Organizational Behavior and Human Decision Processes, 79: 179-198.

Smithson, M., Budescu, D.V., Broomell, S. and Por, H.-H. (2011) Never Say “Not:” Impact of Negative Wording in Probability Phrases on Imprecise Probability Judgments. Accepted for presentation at the Seventh International Symposium on Imprecise Probability: Theories and Applications, Innsbruck, Austria, 25-28 July 2011.

“Negative knowledge”: From Wicked Problems and Rude Surprises to Mathematics

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It is one thing to know that we don’t know, but what about knowing that we can never know something? Karin Knorr-Cetina (1999) first used the term negative knowledge to refer to knowledge about the limits of knowledge. This is a type of meta-knowledge, and is a special case of known unknowns. Philosophical interest in knowing what we don’t know dates back at least to Socrates—certainly long before Donald Rumsfeld’s prize-winning remark on the subject. Actually, Rumsefeld’s “unknown unknowns” were articulated in print much earlier by philosopher Ann Kerwin, whose 1993 paper appeared along with mine and others in a special issue of the journal Science Communication as an outcome of our symposium on “Ignorance in Science” at the AAAS meeting in Boston earlier that year. My 1989 coinage, meta-ignorance, is synonymous with unknown unknowns.

There are plenty of things we know that we cannot know (e.g., I cannot know my precise weight and height at the moment I write this), but why should negative knowledge be important? There are at least three reasons. First, negative knowledge tells us to put a brake on what would otherwise be a futile wild goose-chase for certainty. Second, some things we cannot know we might consider important to know, and negative knowledge humbles us by highlighting our limitations. Third, negative knowledge about important matters may be contestable. We might disagree with others about it.

Let’s begin with the notion that negative knowledge instructs us to cease inquiry. On the face of it, this would seem a good thing: Why waste effort and time on a question that you know cannot be answered? Peter Medawar (1967) famously coined the aphorism that science is the “art of the soluble.” A commonsensical inference follows that if a problem is not soluble then it isn’t a scientific problem and so should be banished from scientific inquiry. Nevertheless, aside from logical flaw in this inference, over-subscribing to this kind of negative-knowledge characterization of science exacts a steep price.

First, there is what philosopher Jerome Ravetz (in the same journal and symposium as Ann Kerwin’s paper) called ignorance of ignorance. By this phrase Ravetz meant something slightly different from meta-ignorance or unknown unknowns. He observed that conventional scientific training systematically shields students from problems outside the soluble. As a result, they remain unacquainted with those problems, i.e., ignorant about scientific ignorance itself. The same charge could be laid on many professions (e.g., engineering, law, medicine).

Second, by neglecting unsolvable problems scientists exclude themselves from any input into what people end up doing about those problems. Are there problem domains where negative knowledge defines the criteria for inclusion? Yes: wicked problems and rude surprises. The characteristics of wicked problems were identified in the classic 1973 paper by Rittel and Webber, and most of these referred to various kinds of negative knowledge. Thus, the very definition and scope of wicked problems are unresolvable; such problems have no definitive solutions; there are no ultimate tests of whether a solution works; every wicked problem is unique; and there are no opportunities to learn how to deal with them by trial-and-error. Claimants to the title of “wicked problem” include how to craft policy responses to climate change, how to combat terrorism, how to end poverty, and how to end war.

Rude surprises are not always wicked problems but nonetheless are, as Todd La Porte describes them in his 2005 paper, “unexpected, potentially overwhelming circumstances that are likely to deliver punishing blows to human life, to political or economic viability, and/or to environmental integrity” (pg. 2). Financial advisors and traders around the world no doubt saw the most recent global financial crisis as a rude surprise.

As Matthias Gross (2010) points out at the beginning of his absorbing book, “ignorance and surprise belong together.” So it should not be, well, surprising that in an uncertain world we are in for plenty of surprises. But why are we so unprepared for surprises? Two important reasons are confirmation bias and the Catch-All Underestimation Bias (CAUB). Confirmation bias is the tendency to be more interested in and pay more attention to information that is likely to confirm what we already know or believe. As Robert Nickerson’s 1998 review sadly informs us, this tendency operates unconsciously even when we’re not trying to defend a position or bolster our self-esteem. The CAUB is a tendency to underestimate the likelihood that something we’ve never seen before will occur. The authors of the classic 1978 study first describing the CAUB pointed out that it’s an inescapable “out of sight, out of mind” phenomenon—After all, how can you have something in sight that never has occurred? And the final sting in the tail is that clever people and domain experts (e.g., scientists, professionals) suffer from both biases just as the rest of us do.

Now let’s move to the second major issue raised at the outset of this post: Not being able to know things we’d like to know. And let’s raise the stakes, from negative knowledge to negative meta-knowledge. Wouldn’t it be wonderful if we had a method of finding truths that was guaranteed not to steer us wrong? Possession of such a method would tame the wild seas of the unknown for us by providing the equivalent of an epistemic compass. Conversely, wouldn’t it be devastating if we found out that we never can obtain this method?

Early in the 20th century, mathematicians underwent the experience of expecting to find such a method and having their hopes dashed. They became among the first (and best) postmodernists. Their story has been told in numerous ways (even as a graphic novel), but for my money the best account is the late Morris Kline’s brilliant (1980) book, “Mathematics: The Loss of Certainty.” Here’s how Kline characterizes mathematicians’ views of their domain at the turn of the century:

“After many centuries of wandering through intellectual fog, by 1900 mathematicians had seemingly imparted to their subject the ideal structure… They had finally recognized the need for undefined terms; definitions were purged of vague or objectionable terms; the several branches were founded on rigorous axiomatic bases; and valid, rigorous, deductive proofs replaced intuitively or empirically based conclusions… mathematicians had cause to rejoice.” (pg. 197)

The tantalizing prospect before them was to establish the consistency and completeness of mathematical systems. Roughly speaking, consistency amounts to a guarantee of never running into paradoxes (well-formed mathematical propositions that nevertheless are provably both true and false) and completeness amounts to a guarantee of never running into undecidables (well-formed mathematical propositions whose truth or falsity cannot be proven). These guarantees would tame the unknown for mathematicians; a proper axiomatic foundation would ensure that any proposition derived from it would be provably true or false.

The famous 1931 paper by Kurt Gödel denied this paradise forever. He showed that if any mathematical theory adequate to deal with whole numbers is consistent, it will be incomplete. He also showed that consistency of such a theory could not be established by the logical principles in use by several foundational schools of mathematics. So, consistency would have to be determined by other methods and, if attained, its price would be incompleteness. But is there a way to ascertain which mathematical propositions are undecidable and which provable? Alan Turing’s 1936 paper on “computable numbers” (in addition to inventing Turing machines!) showed that the answer to this question is “no.” One of the consequences of these results is that instead of a foundational consensus there can be divergent schools of mathematics, each legitimate and selected as a matter of preference. Here we have definitively severe negative knowledge in an area that to most people even today epitomizes certitude.

“Loss of certainty” themes dominate high-level discourse in various intellectual and professional domains throughout the 20th century. Physics is perhaps the most well-known example, but one can find such themes in many other disciplines and fascinating debates around them. To give one example, historian Ann Curthoys’ and John Docker’s 2006 book “Is History Fiction?” begins by identifying three common responses to the book title’s question: Relativists who answer in the affirmative, foundationalists who insist that history is well-grounded in evidence after all, and a third (they claim, largest) puzzled group who says “well, is it?” To give just one more, I’m a mathematical modeler in a discipline where various offspring of the “is psychology a science?” question are seriously debated. In particular, I and others (e.g., here and here) regard the jury as still out on whether there are (m)any quantifiable psychological attributes. Some such attributes can be rank-ordered, perhaps, but quantified? Good question.

Are there limits to negative knowledge—In other words, is there such a thing as negative negative-knowledge? It turns out that there is, mainly in the Gödelian realm of self-referential statements. For example, we cannot believe that we currently hold a false belief; otherwise we’d be compelled to disbelieve it. There are also limits to the extent to which we can self-attribute erroneous belief formation. Philosophers Andy Egan and Adam Elga laid these out in their delightfully titled 2005 paper, “I Can’t Believe I’m Stupid.” According to them, I can believe that in some domains my way of forming beliefs goes wrong all of the time (e.g., I have a sense of direction that is invariably wrong), but I can’t believe that every time I form any belief it goes wrong without undermining that very meta-belief.

Dealing with wicked problems and rude surprises requires input from multiple stakeholders encompassing their perspectives, values, priorities, and (possibly non-scientific) ways of knowing. Likewise, there is no algorithm or sure-fire method to anticipate or forecast rude surprises or Nicolas Taleb’s “black swans.” These are exemplars of insoluble problems beyond the ken of science. But surely none of this implies that input from experts is useless or beside the point. So, are there ways of educating scientists, other experts, and professionals so that they will be less prone to Ravetz’s ignorance of ignorance? And what about the rest of us—Are there ways we can combat confirmation bias and the CAUB? Are there effective methods for dealing with wicked problems or rude surprises? Ah, grounds for a future post!

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