In the witches’ brew of fearmongering, unkeepable promises and poll-tested metaphors that both parties serve up to the electorate every four years, you can always find this predictable dash of inspiration: the image of Americans uniting and working together for the sake of the country. President Obama said in Charlotte, N.C. that America is “about what can be done by us, together.” In Tampa, Paul Ryan said, “Whatever your political party, let’s come together for the sake of our country.” And Mitt Romney closed his convention speech with three invocations of “That America, that united America.”

But America is not united and it is getting less and less unitable with each passing decade. You can see us coming apart in three simple graphs.

The first graph shows the intensity of the divisions in Congress. The political scientists Nolan McCarty, Keith Poole and Howard Rosenthal have quantified the degree to which the parties have become ideologically homogeneous and separated from each other along a single left-right dimension. High numbers mean that the parties are polarized – House and Senate votes are very predictable, even on issues that have little to do with traditional dividing points like the size and scope of government. Low numbers mean that votes are more mixed and less predictable – there’s more room for bipartisan coalitions and compromise on specific issues.

As you can see, both houses of Congress were quite polarized in the decades after the Civil War and Reconstruction, but then polarization plummeted after World War I, and it stayed low during the Depression, World War II and the post-war decades. Political scientists cite many reasons for the dip in the middle, including shifts in the coalitions that composed each party, the shared experiences of war and economic calamity and very low levels of immigration, which allowed a stronger sense of national identity to form. E pluribus unum takes time.

But things started to change in the 1960s and 1970s, as the Democrats became the party of civil rights and the Republicans forged an alliance with the religious right. By the 1980s, the two parties were well on their way to ideological purification: liberals and more recently moderates no longer felt at home among congressional Republicans, while conservatives felt unwelcome among congressional Democrats. The trend has been steady, continuing right up through the imminent departure from the Senate of Olympia Snowe, one of the last remaining moderate Republicans. On the bright side: it is mathematically impossible for congress to get much more polarized.

The second graph shows that it’s not just politicians who are moving further apart; it’s us – the public – as well. The American National Election Study has been asking Americans since the 1970s to rate different groups on what they call a “feeling thermometer.” You can say how warm or cold you feel toward groups such as immigrants, members of the military, the Republican Party or the Democratic Party, using a scale that runs from zero (really cold, really dislike them) to 100 (really warm, really like them).

When you graph these temperature ratings from Republicans and Democrats toward each of the two parties, you see two lines that are high and steady: Democrats have always felt warmly toward the Democratic Party, and Republicans feel the same fondness for their party. But the two lower lines show a trend that is perfectly consistent with the first graph: increased hostility toward the other party, accelerating in recent years.

During the Carter administration, cross-party ratings were not much below 50 – just slightly cool. But Democrats’ ratings of Republicans go steadily down from there, falling to 33 degrees under George W. Bush and a frigid 17 under Barack Obama. The Republicans show a slightly different trajectory, holding steady during the twelve-year Reagan-Bush period. But beginning with the Clinton years, Republicans sour on Democrats and join them in intensifying mutual dislike (18 degrees) during the Obama administration. To put those low scores in perspective, they are even lower than Democrats’ ratings of Richard Nixon in the years after Watergate.

So far the story has been quite similar for both parties. But the third graph shows us why it’s the Republicans who now seem to be more radicalized, energized and opposed to compromise.

The American National Election Study has long included a question about how much people “trust the government in Washington to do what’s right,” with the possible answers being “just about always,” “most of the time,” or “only some of the time.” In the third graph we plot the responses to this question from 1964 on, when the A.N.E.S. first started to ask the question regularly. The graph shows three major features.

First, the long term trend is down. Way down. During the Johnson years, more than two-thirds of Americans said they trusted the government either just about always or most of the time. After Watergate and the Vietnam War, it dropped down closer to one third.

Second, the graph shows that Republicans don’t trust government less than Democrats do, historically. The real difference is that Republicans are more sensitive to who controls the White House. When their man is in, they trust government more than Democrats do. When their man is out, they trust it less. Democrats hold steadier; they seem to identify “government” less with the presidency than Republicans do.

Third, and most important for our current predicament, Republicans showed an unprecedented plunge in trust when Obama took office. They were at a 40-year-high water mark under George W. Bush, and then cascaded to a 50-year-low point – an astonishing 5% – under Barack Obama. And it’s not just Tea Partiers, it’s nearly all Republicans who distrust government today.

So what can we do? Do these three graphs foretell our future? Are we going to see more cross-party cooling? Ever more distrust and paralysis? Not necessarily. In the long run, we see two possible ways out – two reasons why polarization may be lower in a decade or two.

The first is generational change. Most Americans who lived through the Second World War were profoundly influenced by it. America was attacked and it pulled together to fight back. Americans rallied on to wage a bipartisan cold war against communism. Politics, it was said, stopped at the waters’ edge. Politicians from those generations could work together and achieve compromise despite their differences, as Ronald Reagan and Tip O’Neill famously did.

But as those generations aged out of leadership positions, they were replaced by baby boomers whose formative political experience was more akin to a civil war, a divisive struggle over a handful of issues that we are still fighting about today: race, abortion and women’s rights, respect for authority and protection of the environment. In a decade or two, when the millennial generation starts taking the reins, things might be very different. If their formative experiences are 9/11, a long recession and the discovery that their parents and grandparents spent all the money, leaving them a mountain of debt, they might well find the will to work together to dig themselves out.

The second reason for hope is that there are many changes we can make now, over the next few years, that might roll back the polarization by a decade or two. Several recent books contain lists of great ideas backed up by years of insider experience (see in particular Thomas Mann and Norm Ornstein’s “It’s Even Worse Than It Looks” and Mickey Edwards’s “The Parties vs. The People”; see also the list from Some of these changes would reduce gridlock directly by making it easier for the majority party to implement its program – and then be held accountable by the public for the results. For example: making it harder to launch and sustain a filibuster in the Senate, or making it easier for a president to obtain a quick up-or-down vote on nominations for judicial and administrative appointments.

Other changes would push the parties back from their recent strategies of “energize the base” to the strategy that usually prevailed before 2004, which was “win the center.” The key is to draw in more moderate and centrist voters, for example by expanding the electorate by making it easier to vote (why on Earth do we vote on a work day?). Many commentators address the need to undo the pernicious effects of the Citizens United ruling, which has opened the floodgates for nasty anonymous advertising. Nasty ads, it almost goes without saying, tend to energize partisans and turn off moderates.

Other changes would work more gradually by making it easier for politicians to recover the sort of human relationships that have always lubricated the gears of government. For example, in 1995 Newt Gingrich changed the legislative calendar to encourage House members to keep their families in their home districts, rather than moving to Washington where they often fraternized with the enemy. Nowadays, all business is conducted midweek. Many members fly in on Tuesday morning and fly home Thursday evening, leaving few possibilities for meeting members of the other party off of the battlefield and out of sight of the press. Mann and Ornstein propose changing the calendar in both the House and the Senate so that Congress is in session five days a week for three weeks each month. Such an arrangement would be both more efficient (less time wasted in transit) and more humane (more opportunities for relationships to form).

The few months after Election Day offer us the largest window we’re likely to have in the next four years to make any of these changes. Averting the fiscal cliff – the automatic spending cuts and tax increases scheduled to take effect in 2013 if a deal isn’t reached before then – will clearly be the top priority during those months. But if our leaders manage to avert catastrophe, and even more pressingly, if they don’t, will they then turn their attention to bridging our political canyon? Or were they just blowing smoke in our eyes when they said that America is about “what can be done by us, together.” If ever there was a need for us all to “come together for the sake of our country,” our “united America,” it is now. Whatever our ideological differences, can we at least agree to push our leaders, after the election, to get their house in order?

Jonathan Haidt is a professor of business ethics at the NYU-Stern School of Business and the author of “The Righteous Mind.” Marc J. Hetherington is a professor of political science at Vanderbilt University and the author of “Authoritarianism and Polarization in American Politics.” They both write for Civil