“When looking to explain the conditions of political life and political judgment, the unconstrained mind seems compelled to travel up and out: up toward those things that transcend human existence. … The urge to connect is not an atavism.” Those thoughts rise up in The Stillborn God, a provocative new book by Columbia University’s Mark Lilla.

Though he doesn’t employ this specific analogy, Lilla sees the imaginary line we draw to enforce separation of church and state as similar to our border with Mexico. It’s legitimate and important, at least in principle. But there are so many compelling reasons to cross the border that people do it, legally or not.

The most fascinating segment of the nationwide study, released two weeks ago, relates to voters’ views of the presidential candidates’ religiosity. Pew simply asked: “How religious” is each major contender?

First off, it’s noteworthy that many poll respondents were clueless about the religiosity of the candidates, with the exception of Hillary Clinton, whose piety was characterized by almost eight in 10 voters. But despite their spotty knowledge, what the voters do profess seems pretty accurate and reliable.

Mitt Romney is seen as the most religious presidential contender, doubtless a by-product of the controversy surrounding his Mormon faith. About one in five voters (22 percent) describe Romney as “very religious,” while another 21 percent describe the former Massachusetts governor as “somewhat religious.” Given this strong base, it’s surprising that 53 percent couldn’t tell Pew whether Romney is religious or not. Fred Thompson is in a similar situation. Voters don’t know what he is. Two-thirds (65 percent) of those polled couldn’t rate his religiosity.

At the other end of the church pew sits Rudy Giuliani, the Catholic prodigal. Only 9 percent of Americans think that Giuliani is “very religious,” though 41 percent feel that he’s somewhat so. Giuliani, in fact, once considered joining a religious order, the Montfort Fathers, and becoming a priest. But as he faced the seminary, he presciently pondered a vow of celibacy and changed direction: “My budding interest in the opposite sex was something that wouldn’t be suppressed.” Because Giuliani’s stance on abortion offends many good Catholics, and because some clerics have called him out, the former priest-to-be has surrendered the priestly mantle of piety.

On the Democratic side, it’s been an interesting campaign because the field has not eschewed religion as in years past. In debates and forums, candidates talk of their faith openly. It shows through in the numbers. Most Americans can place the candidates, and it seems pretty accurate. Preachy John Edwards, the Right Reverend Southern Baptist of the bunch, is seen as most religious. But he’s trailed closely by Barack Obama, a man who has made much of his religious evolution. Yet, like Romney and Thompson, a sizeable share of Americans hasn’t yet heard his story.

The surprise of the poll is that just 12 percent of Americans think Hillary Clinton is very religious. Her numbers are eerily like those of fellow front-runner Rudy Giuliani. While few see her as very religious, many (41 percent) see her somewhat that way. This may be the fate of politicians in a nation where many consider religiosity an atavism. We want our leading politicians to be somewhat religious, but not too, too much that way.

That’s the plurality view, but I’d keep my eyes on those with starchier numbers. Their perceived piety may ultimately have a more decisive impact on the race’s outcome.

Hill is director of Hill Research Consultants, a Texas-based firm that has polled for GOP candidates and causes since 1988.