At the end of September, less than a week from now, the world will be caught in a downpour of numbers.

A warm front is developing in advance of the release of the first volume of the fifth assessment report (AR5) by the Intergovernmental Panel on Climate Change (IPCC). At the same time, across the U.S., at least, a cold front of climate denial is developing. When these two fronts collide, one can expect turbulent words and a deluge of numbers about climate change.

How will Americans fare in these rhetorical storms, and what can the media do to help them with their climate understanding? Literature on numeracy, the ability to manage the mathematics of everyday life, offers few grounds for optimism, but it does suggest some ways to respond.


In a series of books published in the late 1980s and early 90s, John Allen Paulos collected many examples of mathematical illiteracy in our public dealings and in the media that report on them.

Since then several studies have documented how the short-cut reasoning people rely on in their daily lives often leads to erroneous conclusions, even about fairly simple mathematical matters.

In a recent study of numeracy directly related to climate change, Sol Hart, now an assistant professor of communication studies at the University of Michigan, found that individuals who scored low on numeracy are more likely to be influenced by numerical arguments. In his study, numerical descriptions of the polar bear’s plight prompted low-numeracy individuals to donate more on its behalf. But in an e-mail exchange with The Yale Forum, Hart acknowledged the possibility that numerical arguments might just as easily persuade such individuals to be less concerned. Political variations in numerate versus innumerate reasoning, he said, should thus be the focus of future studies.

By contrast, in his most recently published studies, Dan M. Kahan, professor of law and psychology at Yale Law School, found that individuals scoring high on the cognitive reflection test, which requires subtle numerical reasoning, were usually able to reason away scientific findings that challenged core convictions they share with their social network. Providing more data or information, even if accurate, will probably not change such minds.

Other researchers, however, suggest that communicators can improve those odds and improve public understanding consideration of complex issues like climate change by facilitating numerical reasoning — in three ways:

— by illustrating the scale of the problem;
— by placing that scale in the context of other, more familiar matters or problems; and
— by noting how personal or group biases play into numerical reasoning.

Playing Well with Numbers

In his 2001 book Damned Lies and Statistics (DLS), Joel Best, professor of sociology and criminal justice at University of Delaware, recalls encountering a striking claim while reviewing a proposal for a doctoral dissertation: “Every year since 1950, the number of American children gunned down has doubled.” Best immediately knew that this could not be true, but not because he knows the particulars of American crime rates — although he does.

The problem is with the doubling. Even if we started with just one child gunned down in 1950, by 1995, the year in which Best encountered the claim, the number gunned down each year would be over 35 trillion, more than 250 times the estimate for the total number of humans who have ever lived. Hence Best’s first point: One needs to know something about the basic properties and interrelationships of numbers.

By doing a little digging on his own, Best discovered that the statistic cited by the graduate student was a flawed transcription of a statistic published in the annual report issued by the Children’s Defense Fund in 1994: “The number of children killed each year by guns has doubled since 1950.”

Although no longer entailing an astronomical number, the claim still sounds dramatic — until one is reminded that since 1950 the U.S. population has also nearly doubled. Which brings us to Best’s second point: To properly assess a statistical claim that has been thrust into the spotlight, one must know the numbers on the background.

So how did these highly educated people — the social scientist author, his peer-reviewers, the journal editor, the PhD student, and his faculty advisor — gloss over such a problematic claim? Because, in accord with Best’s third point, humans are slow to think critically about arguments or data that support views they espouse. In other words, numerical reasoning is often biased or motivated reasoning.

And, as Best explained in an e-mail exchange with The Yale Forum, this bias extends to the perception of bias:

Since writing DLS, I have been assured by conservatives that bad statistics come from liberals, and by liberals that bad statistics come from conservatives. I tend to think bad statistics come from people who assume that they’re right, that the other guy’s numbers are cynical lies, and that their own figures are — maybe not perfect — but fundamentally correct.

Scaling Climate Change — Numbers Chosen More to Impress than to Inform

In his synopsis for Sustainable Energy–Without the Hot Air, the open access book he published in 2008, David J.C. Mackay, professor of engineering at Cambridge University, lamented the misuse of numbers in the debate on climate change: “When numbers are used, their meaning is often obfuscated by enormousness. Numbers are chosen to impress, to score points in arguments, rather than to inform.”

To inform, as MacKay seeks to do, one must clarify the relationships between key numbers. The challenge in the case of climate change is not only the enormity of some numbers but their sometimes paradoxical connections with numbers that are very small. Consider this prime example: The 365 billion metric tons of carbon that humans have emitted since the Industrial Revolution now comprises just ~.04 percent of the atmosphere. A very big number, 365 billion metric tons, becomes a very small number: ~04 percent. With such widely divergent numbers, Climate Institute chief climate scientist Michael McCracken explained in an e-mail to The Yale  Forum, “one can make mitigation numbers seem large or small, depending on how one frames it. . . . I like to say that, for the U.S., a penny a day for each citizen adds up over a year to $1B!”

Here, for example, is Paul Driessen, one of the 80 columnists tracked by researchers Shaun Elsasser and Riley Dunlap in their content analysis of climate-skeptical op-ed pieces: “And the daily human contribution of CO2 to our atmosphere is equivalent to a penny out of $1 million.”

The numbers for doing something about climate change yield a contrast nearly as dramatic. All efforts to reduce carbon dioxide emissions are undertaken in the hope of reducing future increases in the global temperature by a few degrees. Thus the cost of action per degree saved will inevitably be enormous.

Here’s Holman W. Jenkins delivering “The Climate Speech Obama Didn’t Give”:

We could cut our emissions in half overnight and the impact would be just three-tenths of a degree a century from now.

And here’s Bjorn Lomborg, citing the work of Richard Tol, mocking EU efforts to reduce CO2 emissions by promoting the use of renewable energy.

An analysis of the costs and benefits of the policy in 2010 by climate economist Richard Tol showed that the annual price tag would be around €210 billion. Running the policy through the RICE climate-economic model reveals that by the end of this century, it will reduce temperature rises by just 0.05°C (0.1ºF).

Who would want to spend €200 billion per year to shave just .05 degrees off the global temperature? Especially if, as conservative skeptics repeatedly remind their readers, global warming has virtually stalled over the past 16 years? Before contextualizing the numbers from Driessen and Lomborg, one should consider the numerical mis-perceptions embedded in the “no-warming” claim.

Penn State climate scientist Richard Alley and folks working with the Skeptical Science site have explained how one might “see” declining trendlines in short-term, cherry-picked data. Key to skeptics’ claims about the last 16 years is the highly anomalous global temperature recorded for 1998. Since then only two years, 2005 and 2010, have been warmer. But if all 10 years from 2001 to 2010 were warmer than nine out of 10 years from the 1990s, can one say that no warming has occurred since 1998? Only if one uses a conspicuous outlier to tilt a trendline.

The first graph was appended to an Oct. 10, 2010 post at Skeptical Science; and the second was taken from the May 2013 report, WMO Statement on the Status of the Global Climate in 2012.

Contextualizing the Numbers

A conservative GOP representative recently argued that it is “arrogant” to think humans “can somehow change the climate of the whole earth.” It is easier to hold this view when one focuses, as Driessen does, on the dramatically small ratio (ppm) of CO2 to the whole atmosphere. But there are common-sense ways to explain why Americans should be concerned with a problem measured in parts-per-millions and in solutions that may well cost billions to avoid fractions of degrees.

A two-degree change in body temperature can make a very big difference in how one feels and performs. And that’s two degrees Fahrenheit. Others have drawn this analogy, referring to climate change as a “global fever.”

On a much more regular basis, humans also expect parts-per-million concentrations to make palpable differences in their lives. Take, for example, the 65 to 74 year old, non-Hispanic white male “Dismissive” statistically constructed by The Yale Project on Climate Change Communication and its partners. Perhaps he’s a bit pudgy around the middle and feeling more than a touch of arthritis. After being swallowed into his 200-pound body, a 200-milligram capsule of Celebrex becomes 2.2 parts active ingredient per 1 million parts pain-relieved human.

One can respond to Jenkin’s and Lomborg’s claims about efforts to mitigate climate change in a similar fashion. Neither spells out all the factors that go into their calculations — and these should never be accepted without critical review — but simply by considering U.S. and EU populations as shares of the global population one can provide some context for their results.

U.S. population is just under 5 percent of global population. On a per capita basis, then, one would expect the U.S. to solve roughly 5 percent of the problem. If the goal is to keep global temperature increases at or below 2C rather than 4C (i.e. to prevent two additional degrees of warming), then the U.S. per capita share would be .1 degree (.05 x 2). The .3 degree decrease dismissed by Jenkins would exceed that share, even if it must still be converted to Celsius (.3 ÷ 1.8 = .16).

The calculations for the EU are similar, but the results are farther from the mark. With a collective population about 50 percent larger than that of the U.S., the EU’s share of global population is 7 percent, and so its per capita share of a 2C target would be .14C, a figure considerably larger than the .05C Tol calculated for the net result of that particular EU policy.

As for the cost, considered in isolation it seems far too high. Compare it with other EU expenditures, such as the €200B the EU countries spend on their militaries, and it no longer seems so outlandish. As a percentage of EU GDP, €200B comes to just 1.5 percent.

Even if undertaken together, these measures would solve a small fraction of the world’s CO2 problem. Clearly the biggest reductions in future emissions will have to be achieved by the countries where the other 88 percent of the world’s peoples live. But unless the EU and U.S. decisively reduce their emissions first, developing countries are unlikely to set the necessary goals.

Contextualized in these ways, the very small numbers mocked by Driessen, Jenkins and Lomborg no longer seem absurd, and their very large numbers no longer shock. These still may not be the real numbers, but they now look more realistic.

Numerical Biases

In an op-ed he penned in response to Al Gore’s An Inconvenient Truth in 2006, Jenkins expressed his doubts that CO2 could be the cause of so many problems. But he closed on an upbeat note: “Whatever the truth of climate change turns out to be, today’s vast investments in climate research will likely lead someday to technologies that will allow us to alter local and global weather.”

To doubt that the hundreds of billions of tons of CO2 humans have emitted over the past 250 years has had an impact on the climate, while expressing confidence that a small fraction of that tonnage will someday “allow us to alter local and global weather” clearly indicates that Jenkins is processing these two sets of numbers very differently. Deliberate human actions seem more real to Jenkins than the unintended negative consequences that result when ecosystems combine and recombine the elements and actions that humans impose on them.

By contrast, when they question the benefits of some new innovation or invention, or when they insist on accounting for the environmental and health impacts, however indirect, of any course of action, liberals/environmentalists sometimes seem to regard side effects as more real or more important than the intended results. This even if the onset of these unintended consequences is decades, hundreds, or even thousands of years off. (See recent articles on “committed sea level rise.”)

This expansion of concern presumes an ability to plan for futures far more distant than modern societies have previously contemplated. The longest long-term planning in most communities, the 100-year floodplain map, is based on historical data, on hindcasts not forecasts. Nascent attempts to base coastal urban codes and plans on projections of sea-levels in 2100 mark a major change in human practices. Given the significant shift in mindset required, one should not be surprised that conservatives are quick to question the confidence behind such predictions, and quick to seize on evidence — like the current lulls in global warming and hurricane activity — that that confidence may be misplaced.

IPCC’s AR5 Offers Opportunities for Improved Understanding

Any debate sparked by the release of the first volume of AR5 is unlikely to be resolved quickly — or quietly. Nevertheless, AR5 will provide an extended opportunity to refresh and to clarify what we think we know about climate change. Communicators can facilitate that process by explaining and contextualizing key numbers and by highlighting the biased ways they sometimes are used.

As if to aid in that work, the University of California Press has just released an updated edition of another work by Joel Best — Stat-Spotting: A Field Guide to Identifying Dubious Data. Prudent climate communicators should keep their checklists handy.

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