My oldest son is now 4 years old, which means that we have begun having more detailed conversations about science and math. He’s getting good at addition, totaling single-digit sums on his fingers and, at times, remembering how far past 10 he has gotten. Very quickly, though, you realize the natural limits of how natural it is to consider big numbers. We’ve discussed the hundreds, and I’ve probably said the word “thousand” a few times, but millions? There’s simply no natural way for a 4-year-old to conceptualize a number that big. And then he asked me how many people live on Earth.

       It’s worth considering that for much of human existence there was simply no real need to consider a figure in the millions. Why would you? National populations, maybe, but that probably didn’t come up in conversation much. Incomes generally fell well short of any such mark. There weren’t millions of animals in herds or millions of feet to be measured. Humanity, it seems safe to assume, did not need to spend a lot of time considering a figure anywhere near that large.

       Now we do. Now we routinely talk about tens or hundreds of thousands and millions or billions. But it is safe to say that such figures still don’t resonate intuitively. We can imagine what 1,000 looks like. We know what a million is, even if we can’t readily translate it into something tangible. And a billion? It sounds like it is to a million what 10 is to 20, but, of course, it isn’t.

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       My theory is that our failure to properly contextualize numbers is making our politics worse. Our inability to understand scale and context makes us see some things as more problematic or unusual than they actually are. My theory, further, is that encouraging a better sense of big numbers would make things, however slightly, better.

       And to that point, I offer some examples.

       Vaccination requirements

       The coronavirus pandemic has prompted employers, public and private, to institute either mandates for vaccination or systems aimed at promoting vaccinations among employees. Despite the popularity of such measures in polling, they have spawned a robust opposition. In recent days, as those mandates begin to kick in, a number of news stories have emerged about employees resigning or being fired for failing to get a dose of a vaccine.

       We’ll pick four examples that have gotten a lot of attention: a report that “dozens” of troopers with the Massachusetts State Police planned to resign, another that hundreds of employees in health-care systems in New York and North Carolina were likely to be fired, and an announcement from United Airlines that hundreds of its employees faced termination. We can visualize those threatened/imminent departures like so.

       Some big boxes! And those are only four of the employers.

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       But as The Washington Post’s Aaron Blake pointed out on Wednesday, those boxes also represent only a small portion of those organizations’ total employee pools. The state police, for example, actually saw only one of its 2,000-plus troopers quit so far — but even “dozens” is just a slice of the total. That’s why the box above is colored in light orange: That’s what dozens would look like, should it emerge. Novant Health, the health-care system in North Carolina, actually had 200 hesitant employees — of about 35,000 total — who ended up getting vaccinated, leaving 175 who were fired after not getting the shots. At Albany Medical Center, a similar total declined the vaccine. And United, which may lose almost 600 employees, has more than 100 times that many.

       In other words, the number of people negatively affected by these rules is, in each case, a small percentage of the total. In each case, it’s less than 1 in 50. (The dark-colored section on Novant’s square below indicates the 200 who decided to be vaccinated.)

       It’s also useful to remember that the United States is a very big place. In August, there were about 8.4 million people out of work. If we take the termination and resignation boxes from the graphs above and compare them with the existing pool of unemployed Americans, it is not a large chunk.

       Being unemployed is always a strain, and it’s clear that those who are losing their jobs will have real negative effects from their decisions. But they are still only a very small part of the universe of people affected by the vaccine requirements at their own employers, much less in the country.

       Federal spending

       Eight million people is a lot of people, as the graph above hopefully makes clear. But, again, it pales in comparison to a billion, much less a trillion.

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       How big is a trillion? Well, if we were to show one trillion at the same scale as the 8.3 million above, the image would have to be more than 417,000 times as long. And right now Congress is debating whether to pass legislation that would cost 3？ times that amount.

       Again, context is useful. Yes, $3.5 trillion is an incomprehensibly large amount of money. But the government already spends an even more incomprehensibly large amount of money every year. Last year, for example, it spent $6.6 trillion. How much is that? Well, if you spent a dollar a second, you would finally spend $6.6 trillion by about 6 p.m. (as of writing) on April 30. Of the year 112,932. (It will be Wednesday, presuming the heat death of the universe has not yet occurred.)

       It’s also useful to note that the $3.5 trillion is over the course of a decade. So the amount being proposed annually is, on average, $350 billion. That’s a sum that’s about 5 percent of what the government spent last year. Still a lot, absolutely. But the functional equivalent of your weekly grocery bill going from $300 to $315.

       Then there’s the flip side of this, politically speaking. The tax cuts passed in 2017 were projected to add an estimated $1.9 trillion to the federal debt over 10 years, or an average of $190 billion per year. That’s about 6 percent of the federal deficit last year (though the deficit was particularly high in fiscal year 2020, due to the pandemic).

       Incomprehensibly big numbers — except when you compare them to other incomprehensibly big numbers, which seems warranted.

       The spread of the virus

       Another place this sort of contextualization is useful is in the coronavirus pandemic. We are constantly seeking to understand how the pandemic is evolving, in part by considering where it is and isn’t spreading, information that seems as though it can help us figure out any role played by politics. But for a variety of reasons, that’s hard — including that tracking data is incomplete, operates at a lag and is hard to correlate directly to prevention efforts.

       We can, however, do better. Consider two states that are seemingly moving in different directions, Florida and Maine. In the past week, Maine’s new case total has surged 20 percent, while Florida’s has dropped by a third. Because hospitalizations and deaths lag new cases (you get sick, then you might get sicker, and then you might die), those metrics are changing differently in each state at the same time.

       So what does this tell us? Does it tell us that Maine, a blue state where 74 percent of the population has received a dose of a vaccine, is failing, while Florida, a red state with a 67 percent vaccination rate, is succeeding? Does it tell us that the attention paid to Florida during the fourth surge was overstated?

       Well, let’s evaluate. One thing to consider is that Maine’s new case total is still well below Florida’s. Florida is seeing 11 new cases for every one in Maine, despite the direction in which the two states are heading.

       But, then, Florida has almost 16 times as many people. So, adjusted for population, Maine’s new case total is, in fact, worse than Florida’s.

       That Maine’s population is so much smaller and its past case total so low helps contribute to its increase in new cases. An increase from 100 cases to 150 cases is a 50 percent increase, while a jump from 10,000 to 10,500 cases — 10 times as big a surge in terms of actual people — is only a 5 percent increase. Any increase is worse than any decrease, but context matters, including that Florida’s drop is also a function of it having been absolutely slammed by cases and deaths in the fourth surge.

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       The numbers we highlight and how we highlight them are often choices being made to illustrate a point. Sometimes, though, it’s simply a failure to recognize context, to consider that 600 United Airlines employees is a lot of people but a small number of United Airlines employees. Or to think of 3.5 trillion inches as being 111 round trips to the moon instead of as only about half the trips to the moon that the country travels in a year anyway.

       Speaking of, that’s how I explained the population of the planet to my son. I showed him how long an inch was and asked how long a line of inches would stretch if there was one for every person in the world. He underestimated it quite a bit, since people generally are bad at big numbers, particularly 4-year-olds. So I put it in terms of the circumference of the Earth.

       Try to guess how far around the world it would get you. Then find out. Maybe you’re not so good at big numbers either.