If we are reminded of anything this election season, it is that America is a house divided against itself. The anger and mistrust between Democrats and Republicans, liberals and conservatives, often seems as bitter as it is reflexive. Most worrisome of all, we have grown so accustomed to this divide that we no longer flinch at the brazen political attacks on either side — even when the logic underlying these attacks is hard to fathom.

Take the case of two political ads recently shown on television. One, from Mitt Romney, asserts that the employment situation in the United States “doesn’t have to be this way if Obama would stand up to China.” The other, from President Obama’s camp, implies that a Romney presidency would be bad for the coal industry, in part because Mr. Romney has a Swiss bank account.

The truth is, even experts have difficulty spelling out how changing our trade policy with China will make more than a modest dent in unemployment numbers — or how, with or without a foreign bank account, Mr. Romney’s proposed policies are likely to hurt the domestic coal industry. But that doesn’t matter.

Such attack ads work, in large part, because we don’t understand them. Statements take advantage of a fact about human psychology called the “illusion of explanatory depth,” an idea developed by the Yale psychologist Frank Keil and his students. We typically feel that we understand how complex systems work even when our true understanding is superficial. And it is not until we are asked to explain how such a system works — whether it’s what’s involved in a trade deal with China or how a toilet flushes — that we realize how little we actually know.

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