When More is Less: Quantitative Numbing

There is an effect, which I will call “quantitative numbing,” that results in greater quantities of things that concern us producing less rather than more concern. This is an expression of “psychic numbing,” which is well documented. This phenomenon is chillingly described in a quote that is probably misattributed to Joseph Stalin, “A single death is a tragedy; a million deaths is a statistic.” According to Paul Slovic and Daniel Västfjäll, in a chapter titled “The More Who Die, the Less We Care” that appears in the book Numbers and Nerves:

There is considerable evidence that our affective responses and the resulting value we place on saving human lives follow the same sort of psychophysical function that characterizes our diminished sensitivity to changes in a wide range of perceptual and cognitive entities—brightness, loudness, heaviness, and wealth—as their underlying magnitudes increase.

 As psychological research indicates, constant increases in the magnitude of a stimulus typically evoke smaller and smaller changes in response. Applying this principle to the valuing of human life suggests that a form of psychophysical numbing may result from our inability to appreciate losses of life as they become larger.

(Numbers and Nerves: Information, Emotion, and Meaning in a World of Data, Scott Slovic and Paul Slovic, editors, 2015, page 31)

This effect exhibits a logarithmic pattern, with larger numbers resulting in a diminishing response. Slovic and Västfjäll go on to point out, however, that feelings of compassion suffer an even greater loss as quantities increase. In fact, increases in the growth of compassion are not merely reduced as quantities increase, but compassion actually decreases and does so quite dramatically.

For example, studies have shown that charitable contributions in response to appeals are greatest when intended to help a single individual, are reduced somewhat when helping two, and decrease at a greater and greater rate as the numbers grow. Beyond a certain threshold, we stop giving altogether, even to save lives.

Our moral intuitions often seduce us into calmly turning away from massive losses of human lives, when we should be driven by outrage to act. This is no small weakness in our moral compass. (ibid, page 35)

This is a tragic response that we must learn to overcome, but it is difficult for it is built into our brains.

This phenomenon of more producing less is not limited to compassion. It seems to broadly apply to our greatest concerns. Current events involving president-elect Donald Trump have made me particularly sensitive to quantitative numbing. Because he exhibits so many examples of bad behavior, those behaviors are having relatively little impact on us. The sheer number of incidents creates a numbing effect. Any one of Trump’s greedy, racist, sexist, vulgar, discriminatory, anti-intellectual, and dishonest acts, if considered alone, would concern us more than the huge number of examples that now confront us. The larger the number, the lesser the impact, because increases in quantity inoculate us against the effects. This tendency is built into our brains; it is automatic, immediate, and unconscious.

The cause of this psychic numbing effect is not entirely understood, but it is surely related to the fact that our brains developed during eons of living much simpler—although harsh—lives as hunter-gatherers. Our needs were relatively few, as were the types of risks and opportunities that we faced. We didn’t need to manage large numbers of things. Subitization—our preattentive ability to recognize the quantities one, two, and three immediately, without conscious thought—was perhaps built into our brains for this same reason.

To overcome the numbing effect of large quantities, we must engage our slow, rational, and reflective System 2 thinking processes. For example, in relation to Trump’s onslaught of bad behaviors, we should consider each infraction individually, allowing its full weight to affect us. Then, when thinking of his bad behaviors cumulatively, we should consciously remind ourselves that more is more, not less. We must rationally reframe the information. Abel Hertzberg reframed the Holocaust to effect this shift when he said, “There were not six million Jews murdered: there was one murder, six million times.”

We can and must fight quantitative numbing. If we don’t, we will remain its victims.

Take care,


4 Comments on “When More is Less: Quantitative Numbing”

By Enrico Bertini. November 25th, 2016 at 7:07 am

Thanks Steve for sharing this! I have been lately extremely fascinated (terrified?) by Paul Slovic’s research. Please allow me do a bit of self-advertising here by pointing you and your readers to our data stories podcast we recently recorded with him. Here is the link: http://datastori.es/84-statistical-numbing-with-paul-slovic/. He is incredibly thoughtful and articulate.

I have been thinking a lot about this problem lately and I am wondering what the role of visualization could be here. I’d be curious to hear your take on this. Can visualization, by making some quantities more visible and explicit at least partially better engage our System 2? Or maybe we should rely more on imagery and more empathy-provoking solutions?

What fascinates me of this problem is how solutions leveraging System 1 and System 2 are intertwined. Most people, and some research, seems to point to a solution that leverages System 1, that is, “use one single image of a starving child”. But empathy and emotions are capricious material and I am not sure I am ready to abdicate on rationality (are you familiar with Paul Bloom’s essay “Against Empathy”? – http://bostonreview.net/forum/paul-bloom-against-empathy). But rational thought is hard to activate and I have not seen many solutions proposed in this direction. Again … maybe visualization can play a role here? Or maybe we need clever and innovative ways to engage System 1 AND System 2? Maybe “Data Documentaries” with a mix of images, story telling, and visualization? Just thinking aloud here …

By Stephen Few. November 25th, 2016 at 10:24 am


We’re only beginning to understand how to effectively communicate information that elicits quantitative numbing by developing techniques that direct people to engage both System 2 and System 2 thinking as appropriate. Scott and Paul Slovic did a good job in “Numbers and Nerves” of raising awareness about the problem and in providing a few techniques that people are trying out to address it, but we’re just scratching the surface at this point. Data visualization clearly has a role in this. How data visualizations should be designed to counter quantitative numbing is a ripe area for research. I can say with confidence that the answer is not to gratuitously dress up data visualizations in the ways that are typically done, especially in infographics, because doing so doesn’t engage the viewer in a meaningful way.

We need to better understand perception and cognition before we can figure out how to visualize data in ways that allow our brains to embrace the enormity of big numbers. System 1 thinking has a role to play in this, but System 2 thinking must be engaged to produce the necessary understanding. I suspect that one approach is to do what some of the folks who were quoted in Numbers and Nerves have suggested, which is to begin with small quantities that our brains can handle and then magnify the effect by helping people imagine those quantities being multiplied. Stated differently, to overcome cognitive limitations, we probably need to find ways to help people combine manageable quantities together into larger and larger chunks. Data visualization will likely be the mode of presentation that will enable this.

By Berry Boessenkool. November 30th, 2016 at 3:03 am

This discussion reminded me of a famous project:

By David. November 30th, 2016 at 9:45 am

This is a really great topic. I’m reminded of an incident a few years ago where someone was denied coverage for a very expensive transplant operation through one of my state’s Medicaid insurers. It led to an outrage and a reversal of the denial, at the cost of nearly a million dollars. Now compare — this is the same state whose Medicaid, at least at the time, did not cover fees for routine foot exams for diabetics to help avoid disabling complications of the disease.

Similarly, I’ve done a lot of volunteer work in animal rescue. It is all too common to see folks rally around a severely sick animal requiring thousands of dollars of care and a lifetime of maintenance for their condition, while in the meantime many otherwise healthy animals are euthanized.

I’m not passing judgment here, just pointing out more examples where outrage/empathy seems to be invoked much more strongly by exceptional stories about individuals rather than the far greater cumulative toll incurred by the masses.

I think this helps explain why Elford’s “Plan and Sections of a Slave Ship” is far more impactful than a set of bar charts or line graphs showing the distribution of humans in sections of a slave ship, or the human toll of slavery over time. Maybe not more effective at conveying the precise figures, but certainly more effective when it comes to invoking a more appropriate emotional reaction (though I’d also argue that Elford’s drawing still fails to invoke anything resembling an appropriate response to the barbarism of slavery, but I don’t think any drawing could do that).

Agreed that more research is needed. I definitely do NOT think everyone should go out and try to copy Elford’s approach…it was effective at persuading folks that slavery should be ended, but that was really a moral debate and Elford’s figure, in my opinion, is really ‘data art’ and not so much infoviz, given that the intended emotion, and not the conveyance of information, is clearly the focus. I think most of us here operate in domains that are not nearly as cut-and-dried, and that require much more analytical precision than the famous slave ship figure.

There is a lot more I’d like to say on this subject, but I’m getting long-winded so I’ll stop. I work in healthcare, so this issue is near and dear to my heart. Quantitative numbing seems to have so much in common with the compassion fatigue our caregivers sometimes experience — like the toll of so much human suffering causes the brain to fire up its defenses, and suddenly you are less sad about a ward full of pediatric cancer patients than you would have been 10 years prior had you heard about a single kid with cancer.