One million deaths. That is now roughly the toll of COVID-19 in the United States. And that official milestone is almost certainly an undercount. The World Health Organization’s data suggest that this country hit a million deaths early in the year.
Whatever the precise dates and numbers, the crisis is enormous. The disease has taken the lives of more than 6 million people worldwide. Yet our minds cannot grasp such large numbers. Instead, as we go further out on a mental number line, our intuitive understanding of quantities, or number sense, gets fuzzier. Numbers simply start to feel big. Consequently, people’s emotions do not grow stronger as crises escalate. “The more who die, the less we care,” psychologists Paul Slovic and Daniel Västfjäll wrote in 2014.
Sign up for e-mail updates on the latest coronavirus news and research
But even as our brains struggle to grasp big numbers, the modern world is awash in such figures. Demographic information, funding for infrastructure and schools, taxes and national deficits are all calculated in the millions, billions and even trillions. So, too, are the human and financial losses from global crises, including the pandemic, war, famines and climate change. We clearly have a need to conceptualize big numbers. Unfortunately, the slow drumbeat of evolution means our brains have yet to catch up with the times.
Our brains think 5 or 6 is big.
Numbers start to feel big surprisingly fast, says educational neuroscientist Lindsey Hasak of Stanford University. “The brain seems to consider anything larger than five a large number.”
Other scientists peg that value at four. Regardless of the precise pivot from small to big, researchers agree that humans, along with fish, birds, nonhuman primates and other species, do remarkably well at identifying really, really small quantities. That’s because there’s no counting involved. Instead, we and other species quickly recognize these minute quantities through a process called “subitizing” — that is, we look and we immediately see how many.
“You see one apple, you see three apples, you would never mistake that. Many species can do this,” says cognitive scientist Rafael Núñez of the University of California, San Diego.
When the numbers exceed subitizing range — about four or five for humans in most cultures — species across the biological spectrum can still compare approximate quantities, says cognitive scientist Tyler Marghetis of the University of California, Merced.
Imagine a hungry fish eyeing two clumps of similarly sized algae. Because both of those options will make “awesome feasts,” Marghetis says, the fish doesn’t need to waste limited cognitive resources to differentiate between them. But now imagine that one clump contains 900 leaves and the other 1,200 leaves. “It would make evolutionary sense for the fish to try to make that approximate comparison,” Marghetis says.
Sign Up For the Latest from Science News
Headlines and summaries of the latest Science News articles, delivered to your inbox
Client key* E-mail Address* Go
Thank you for signing up!
There was a problem signing you up.
Scientists call this fuzzy quantification ability an “approximate number sense.” Having the wherewithal to estimate and compare quantities gives animals a survival edge beyond just finding food, researchers wrote in a 2021 review in the Journal of Experimental Biology. For example, when fish find themselves in unfamiliar environments, they consistently join the larger of two schools of fish.
The approximate number system falls short, however, when the quantities being compared are relatively similar, relatively large or both. Comparing two piles, one with five coins and the other with nine coins, is easy. But scale those piles up to 900,005 coins and 900,009 coins, and the task becomes impossible. The same goes for when the U.S. death toll from COVID-19 goes from 999,995 to 999,999.
We can improve our number sense — to a point.
The bridge between fuzzy approximation and precision math appears to be language, Núñez says.
Because the ability to approximate numbers is universal, every known language has words and phrases to describe inexact quantities, such as a lot, a little and a gazillion. “For example, if a boy is said to have a ‘few’ oranges and a girl ‘many’ oranges, a safe inference — without the need of exact calculations — is that the girl has more oranges than the boy,” Núñez writes in the June 1, 2017 Trends in Cognitive Science.
And most cultures have symbols or words for values in the subitizing range, but not necessarily beyond that point, Núñez says. For instance, across 193 languages in hunting and gathering communities, just 8 percent of Australian languages and 39 percent of African languages have symbols or words beyond five, researchers reported in the 2012 Linguistic Typology.
See all our coverage of the coronavirus outbreak
The origin of counting beyond subitizing range, and the complex math that follows, such as algebra and calculus, remains unclear. Núñez and others suspect that cultural practices and preoccupations, such as keeping track of agricultural products and raw materials for trade, gave rise to more complex numerical abilities. As math abilities developed, people became adept at conceptualizing numbers up to 1,000 due to lived experience, says cognitive scientist David Landy. Those experiences could include getting older, traveling long distances or counting large quantities of money.
Regular experiences, however, rarely hit the really big number range, says Landy, a senior data scientist at Netflix in San Francisco. Most people, he says, “get no experience like that for a million.”
Numbers that exceed our experience perplex us.
When big numbers exceed our lived experiences, or move into the abstract, our minds struggle to cope. For instance, with number sense and language so deeply intertwined, those seemingly benign commas in big numbers and linguistic transitions from thousands to millions or millions to billions, can trip us up in surprising ways.
When Landy and his team ask participants, often undergraduates or adults recruited online, to place numbers along a number line, they find that people are very accurate at placing numbers between 1 and 1,000. They also perform well from 1 million to 900 million. But when they change the number line endpoints to, say, 1,000 and 1 billion, people struggle at the 1 million point, Landy and colleagues reported in the March 2017 Cognitive Science.
“Half the people are putting 1 million closer to 500 million than 1,000,” Landy says. “They just don’t know how big a million is.”
All aligned
People had to place ‘1 million’ and ‘500 million’ along a number line that spanned from 1,000 to 1 billion. Roughly half the respondents correctly placed both values (top). But the other half placed both numbers too far to the right (bottom). People struggle to envision numbers beyond a million, researchers say.
People’s placement of values on a number line
E. Otwell, adapted from D. Landy et al/Cognitive Science 2017E. Otwell, adapted from D. Landy et al/Cognitive Science 2017
Landy believes that as people transition from their lived experiences in the thousands to the more abstract world of 1 million, they reset their mental number lines. In other words, 1 million feels akin to one, 2 million to two and so on.
Changing our notations might prevent that reset, Landy says. “You might be better off writing ‘a thousand thousand’ than ‘1 million’ because that’s easier to compare to 900,000.” The British used to do this with what people in the U.S. now call a trillion, which they called a million million.
Without comprehension, extreme numbers foster apathy.
Our inability to grasp big numbers means that stories featuring a single victim, often a child, are more likely to grab our attention than a massive crisis — a phenomenon known as the identifiable victim effect.
For instance, on September 2, 2015, Aylan Kurdi, a 2-year-old refugee of the Syrian Civil War, was on a boat with his family crossing the Mediterranean Sea. Conservative estimates at the time put the war’s death toll at around 250,000 people. Kurdi’s family was trying to escape, but when their overcrowded boat capsized, the boy drowned, along with his brother and mother. The next day a picture of the infant lying dead on a Turkish beach hit the front pages of newspapers around the world.
No death up until that point had elicited public outcry. That photograph of a single innocent victim, however, proved a catalyst for action. Charitable contributions to the Swedish Red Cross, which had created a fund for Syrian refugees in August 2015, skyrocketed. In the week leading up to the photo’s appearance, daily donations averaged 30,000 Swedish krona, or roughly $3,000 today; in the week after the photo appeared, daily donations averaged 2 million Swedish krona, or roughly $198,500. Paul Slovic, of the University of Oregon, Eugene, Daniel Västfjäll, of Linköping University, Sweden, and colleagues reported those results in 2017 in Proceedings of the National Academy of Sciences.
Two-year-old Aylan Kurdi (left) and his brother, both Syrian war refugees, died in September 2015 when their escape boat capsized. A photo of Aylan dead on a Turkish beach alerted people to the crisis, including these mourners in Melbourne, Australia. Identifying single victims in large-scale crises can override apathy, research shows.Chris Hopkins/Getty Images
Earlier research shows that charitable giving, essentially a proxy for compassion, decreases even when the number of victims goes from one to two. The flip side, however, is that psychologists and others can use humans’ tendency to latch onto iconic victims to reframe large tragedies, says Deborah Small, a psychologist at the University of Pennsylvania.
Some research suggests that this power of one need not focus on a single individual. For instance, when people were asked to make hypothetical donations to save 200,000 birds or a flock of 200,000 birds, people gave more money to the flock than the individual birds, researchers reported in the 2011 E-European Advances in Consumer Research.
Framing the current tragedy in terms of a single unit likewise makes sense, Västfjäll says. Many people react differently, he says, to hearing ‘1 million U.S. citizens dead of COVID’ vs. ‘1 million people, roughly the equivalent of the entire city of San José, Calif., have died from COVID.’
Milestones do still matter, even if we can’t feel them.
Kurdi’s photo sparked an outpouring of empathy. But six weeks after it was published, donations had dropped to prephoto levels — what Västfjäll calls “the half-life of empathy.”
That fade to apathy over time exemplifies a phenomenon known as hedonic adaptation, or humans’ ability to eventually adjust to any situation, no matter how dire. We see this adaptation with the pandemic, Small says. A virus that seemed terrifying in March 2020 now exists in the background. In the United States, masks have come off and people are again going out to dinner and attending large social events (SN: 5/17/22).
One of the things that can penetrate this apathy, however, is humans’ tendency to latch onto milestones — like 1 million dead from COVID-19, Landy says. “We have lots of experience with small quantities carrying emotional impact. They are meaningful in our lives. But in order to think about big numbers, we have to go to a more milestone frame of mind.” That’s because our minds have not caught up to this moment in time where big numbers are everywhere.
And even if we cannot feel that 1 million milestone, or mourn the more than 6 million dead worldwide, the fact that we even have the language for numbers beyond just 4 or 5 is a feat of human imagination, Marghetis says. “Maybe we are not having an emotional response to [that number], but at least we can call it out. That’s an amazing power that language gives us.”
