The Smarter You Are, The Stupider You Are : 13.7: Cosmos And Culture Numbers tell a story. Would you believe that you're less likely to get the story right the smarter you are? Sometimes that's the case and commentator Alva Noë sees this finding as an argument in favor of an education system that trains our children to be good thinkers, not just good calculators.

The Smarter You Are, The Stupider You Are
A man holding up a transparency sheet with a jumble of numbers on it.

Education is necessary if democracy is to flourish. What good is the free flow of information if people can't make sense of it? How can you vote your own interests if you don't understand the consequences of policy choices? How can you know what's best for you or your community?

A recent study by Yale's Dan M. Kahan and colleagues might be thought to call these truisms of democratic political culture into question. According to the finding, the better you are at reasoning numerically, the more likely you are to let your political bias skew your quantitative reasoning.

Put another way, the brainier you are, the better you can twist facts to your own pre-existing convictions. And that's what you will tend to do.

Far from showing that there's no hope for democracy, or that education is not necessary for democracy to thrive, these findings give us occasion to recall that education isn't just learning how to be good with numbers. This seems especially pressing given the current trend — see Thursday's New York Times — to limit funding for humanities education.

First, though, the finding itself. (For an excellent discussion, see Chris Mooney's piece on it in Mother Jones.)

Pretend that these are the results of a new medical study: Of patients given a medicine, 223 showed marked improvement in their symptoms, whereas 75 showed no improvement. In the control group of patients not given the medicine, 107 showed an improvement, while 21 showed no improvement.

Is the medicine effective? Does it make it more or less likely you'll get better?

If you're like a lot of us, you'll say yes! Two-hundred-twenty-three got better on the medicine, whereas only 107 got better without.

And you'd be wrong.

The fact is, 83 percent of those not taking the medicine got better, whereas only 74 percent of those taking the medicine got better. Taking the medicine lowers your chance of getting well.

The better you are with numbers, the better you'll be at getting this sort of puzzle right. But now consider this superficially different puzzle.

Pretend that these are the results of another new study: 223 cities that adopt a ban on handguns show a decrease in gun violence, whereas 75 do not. In cities that do not adopt a handgun ban, 107 show a decrease in gun violence, while 21 show no decrease.

Do these numbers support the conclusion that banning handguns lowers gun violence?

As before, if you just look at the absolute numbers, you might be misled into thinking that the measure in question is effective. But you'd be mistaken, exactly as before. According to these (pretend) numbers, crime is more likely to go down in cities that do not adopt a ban than in those that do.

It turns out that numerically sophisticated people — the sort of people who get the right answer to the first puzzle about the medicine — get this question wrong, if they are politically liberal. While smart political conservatives show no such enhancement of their stupidity. And this is true even though, as I hope is clear, this puzzle is exactly the same as the puzzle about medicine. All that's been changed are the names (symptoms up or down versus crime up or down, taking the medicine versus imposing a ban).

But this isn't a shortcoming of liberals.

Shift the labels yet again: 223 cities show a drop in crime with no ban versus 107 that show a drop with a ban. Conservatives who may understand very well that, in general, it isn't absolute numbers that matter, but ratios, will still conclude that gun control is a less effective means of lowering gun violence even though that is not what these (also made up) numbers show.

Actually, things are even worse. The higher your level of numeracy, according to this study, the more likely you are to flunk the quiz. Your arithmetical skill makes you more likely, not less, to understand the data you are given.

So what's going on here?

Hard to say exactly. According to the study's authors, the outcome supports the Identity Protective Cognition Thesis, according to which cultural conflict disables the relevant cognitive faculties.

But one thing is clear. Being good at math doesn't mean that you'll be better at evaluating the effectiveness of policies. Making citizens better statisticians is not likely to lessen polarization in our society. If this study is right, it is likely to increase it!

So should we stop caring about education? Or should we just give up on democracy altogether? No to both of these.

We need to rethink what it is to be an educated person.

Educated people are not only trained to use numbers, but they are also trained, or they ought to be trained, to appreciate that reaching the right conclusion may not be as simple as running the numbers. Reasoning is, or ought to be, a reflective activity.

I am not suggesting that there is not a right (or wrong) answer about whether the numbers show that a policy choice, or a medicine, has certain causal consequences. Of course there is. And I'm not denying that it's a bad thing that political bias influences our judgment.

But it would be wrong to conclude from this that having biases, values and interests is an impediment to sound reasoning that we'd be better off without. It is one of the conditions of human being, after all, that we care about things and that caring colors our attempts at logical judgment. It is just something that always needs to be taken into account when the stakes are high and we are not, as we so rarely are, entirely detached from a problem or situation.

Our values and biases are expressions of who we are. It isn't so much that our prior commitments disable our ability to reason; it is that we need to appreciate that reasoning takes place, for the most part, in settings in which we are not neutral bystanders.

It shouldn't be surprising that smart people who care about an issue will use their wits to fight for their values. This can be a corrupting influence, it can lead you to fill in the wrong bubble, but it need not be.

This is where the real aims of education come in.

Numeracy, like literacy, is a tool. The same goes for scientific training in general. An education that confines itself to intellectual technologies of this sort will fall short. An education needs to be broader and more humanistic than that, for it needs to aim at something more subtle and less easy to measure.

We should aim to train our children not to be good calculators, but to be good thinkers. Education should aim for good judgment. And while there are rules for weighing the implications of empirical data, there are no hard-and-fast rules for being a good judge.

You can keep up with more of what Alva Noë is thinking on Facebook and on Twitter: @alvanoe