# The human costs of innumeracy

“I don’t do math!” How often have you heard this expression, sometimes more as a brag than an excuse for some consequential mistake?

As of December 19, 2019, seventy-seven people, many of them small children, had died in the small South Pacific island nation of Samoa. The cause of the epidemic was a confluence of several factors, but a significant one, and one that continues to fester around the developed world, is the simple mathematics principle of HIT, or the herd immunity threshold. Measles immunizations in Samoa had dropped well below the safe threshold, and the results have been tragic.

One of the great failures of American education, copied in much of the rest of the world, is our continued inability to educate children and adults in the basic concepts of mathematics required to function in the modern world. This is a version of illiteracy called innumeracy, and examples abound in the news.

The “human costs” of innumeracy are also underplayed. People die of long-conquered diseases. Struggling families make poor financial choices that make their situation much worse. My bank lobby is empty when I visit, but multiple teller windows are busy seven days a week at the “payday lender” a block away. But let’s start back in Samoa, or possibly at your kid’s elementary school.

Anti-vaccination innumeracy

Anti-vaxxers are a curious bunch. As contrasted with some other conspiracy theorists, many are well-educated and economically successful. Driven by celebrity social media, they have a problem with some basic math and the evaluation of risk, not to mention a lack of care for the harm caused to innocent children and social cohesion.

The mathematics of “herd immunity” has transformed human health ever since Edward Jenner (1749 –1823) began to purposely inject pus from cowpox infections into uninfected people to protect them from the much more deadly smallpox. A key number to understand about communicable diseases and their vaccine conquerors is the HIT, or the herd immunity threshold. This is the percentage of the population that needs to be immunized in order to stop an outbreak of a particular disease.

For some diseases the HIT is amazingly low. We normally perceive influenza as quite virulent, but it only takes a HIT of 33-44% to stop a widespread flu outbreak. In other words, if you can convince just four out of ten people to get the annual flu vaccine, the spread of that year’s versions gets attenuated very quickly. This attenuation is critical in protecting the very people who cannot get vaccinated, the very young and the frail elderly, who still die annually because of influenza.

Measles is much more virulent than is influenza, however, and so it takes a HIT of between 92% and 95% to protect a population, and there’s the rub. The percentage of children and adults who should not be given the measles vaccine due to existing fragile health and immune deficiencies is already close to that remaining 5% gap. Note that this is not because the vaccine is dangerous per se, but rather that any exposure to unexpected external substances can substantially change their personal risks of complications. Your child is likely not in that group, but is in danger from declining herd immunity. The math matters!

That means that free riders, who are the parents that refuse to immunize their children, relying on that herd immunity to protect them, are doing exactly the opposite. By playing at the edge of that high HIT for measles, they are risking not only their own children by “ripping the fabric” of the herd immunity. They are also risking the lives of the very young children and the frail elderly who make up most of the “at risk” population. That is the major “human cost” and social cohesion breakdown caused by anti-vaxxers. We only fight these diseases together, not as individuals.

So, how much of this is ignorance of the math, how much is bad information from social media, and how much of it is just plain refusal to participate in the social contract? While the latter two certainly have power in this cultic community, neither would have the power they do if the math skills of the parents were better.

Anti-vaxxers often justify their stances by citing the “dangers” of vaccines, but I contend that this is more a factor of inaccurate information and “risk innumeracy,” the poor human ability to rationally evaluate different kinds of mathematical risks. The probability math says, for instance, that it is far safer to fly commercially across the country than it is to drive. But even knowing that math, you still may have a hard time getting on an airplane. Our “gut” often pushes us into the riskier behavior.

Likewise with vaccines, parents often don’t know how to evaluate the very high probability of catching and spreading a known disease, one like measles with a significant risk of serious complications, against the very small probability of a bad vaccine reaction. The difference is several “orders of magnitude,” or powers of 10 (that’s a lot), but our brains are often bad at that evaluation.

Bank fee innumeracy

Switching to basic economic innumeracy, the most common bank fees are caused primarily by the inability or the lack of discipline to perform the simple math of balancing a checkbook. Overdraft fees and check return fees (also called NSF fees for “non-sufficient funds”) are commonly now in the range of \$35 per infraction. They add up quickly, usually for the people who can least afford them.

And they also add up for the banks. The FDIC estimated in 2017 that consumers were charged \$11.45 billion annually in overdraft fees. For small and medium banks, fees make up about 18% of non-interest income, so this is a significant source of revenue for them. Essentially consumers are paying over \$11 billion annually to not do the math of balancing their checkbooks. And once checks start bouncing, the charges escalate.

While there certainly is a large amount of laziness, wishful thinking and intentional petty bank fraud that generates these fees, my contention is that poor math skills are a big part. Just as people will often say “I don’t like to read” when they really mean “I can’t read very well,” my experience is that the same thing is true for basic math skills. People don’t keep close track of their bank account balances because they don’t know how, or they make basic mistakes. ATMs and debit cards can compound this problem because small transactions easily get forgotten.

A single \$35 NSF fee is more than enough to feed a family of four from the grocery store for a day. In the meantime, the rest of us actually benefit from that innumeracy. Most commercial banks have shifted their revenue models to capitalize on these types of fees, aimed directly at their less-numerate customers, and they give the rest of us free services in return. The innumerate poor are funding the numerate wealthy. I see a bit of a justice problem here.

Credit cards and payday lending

I wrote in a prior post about how credit cards, while beneficial to so many, have contributed to widening the income inequality gap by charging interest rates that were once illegal. These high rates, in turn, cause unpaid balances to grow every month. Most people do not understand the math of the “Rule of 72,” where you can compute how long it takes a debt to double by dividing the annual interest rate into 72. For instance, 72 divided by a 24% annual rate, common with credit cards, means a doubling of your unpaid debt in just three years unless you get ahead of it.

Contrary to popular understanding, the “minimum monthly fee” charged by your credit card supplier has the primary purpose of maximizing interest paid without causing you to stop paying. Assume they know the math better than you do.