In the toxic boiling cauldron that is today’s partisan politics, it’s hard to imagine how the current temperature among the thrashing combatants could be cooled down to any meaningful extent. Aggressive name-calling is commonplace, and the parties double down on groundless claims reminiscent of grammar school playground accusations. The theory is apparently that if even the most outrageous statements are spewed forth enough, they’ll eventually gain enough traction to affect the outcome of elections, which will then only perpetuate the wars of words.

Those with cooler heads and those trained in dispute resolution suggest having meaningful conversations between the parties, but when the differences are so extreme and entrenched — and when the goal isn’t solving a problem but bludgeoning opponents into submission — it’s hard even to begin a dialogue, much less achieve any results based on voluntary compromises. You may have heard about the mythical Gordian Knot that even the strongest and wisest of the ancients couldn’t disentangle, and you may have wondered whether such a dilemma could have been fact instead of fiction.

But first, a little political history. The platforms of today’s parties aren’t chiseled on granite tablets, with their faithful followers swearing oaths to the Ten Commandments of their beliefs. As a matter of fact, the philosophies of today’s parties would shock their founders as being totally contrary to the purposes that led to their creation. For example, the Republican Party of Lincoln and Teddy Roosevelt would recoil in horror at the pronouncements of Reagan and the current administration. And the Democrats from Jackson’s and Wilson’s days would find no home at all in the party of FDR or Obama.

So, what does that mean for us? If we insist on being termed Republicans or Democrats these days, does that require us to decide whether we’re old school or new age members of our parties, and does it also suggest that there could be common ground between those historically extreme positions? After all, their ancestors once held those contrary beliefs themselves.

Which brings me back to the Gordian Knot. The Encyclopedia Britannica calls the knot “a metaphor for solving a complex or seemingly unsolvable problem through bold, creative, or unconventional means.” Dozens of people were said to have tried to untie it and then to claim the kingship of Phrygia (modern-day Turkey). However, until Alexander the Great arrived and tried new methods, no one had been successful — the lore is that he either sliced the knot in half with his sword or found the loose ends that enabled the knot to be untied.

Either way, the current knot of American political stagnation caused by irreconcilable partisanship needs new thinking, too. Here’s a proposal.

With the parties so evenly divided, it doesn’t take much to swing the pendulum of decision-making one way or the other. The Supreme Court that included Justice Anthony Kennedy is a fitting example. The conservative and liberal justices were often equally balanced, so when a significant decision had to be made, Kennedy was often the tie-breaker, and he alone ended up controlling the outcome.

And so, with the two parties paralyzed by nearly equal numbers of proponents, a group of perhaps 12 independent and cooperative members in each house of Congress might well make the difference on many contentious issues. That magnificent dozen could still call themselves by their party names if it made them feel better, but they would be functional independents who put the “general welfare” of the majority of Americans — where have we seen that wording? — ahead of benefiting only those who need no help or penalizing those who need meaningful opportunities just to survive.

In the old days of different party dynamics, those people actually did exist and were called “statesmen”; perhaps “people of goodwill” would be a more apt term today. I’m referring to those like our own Walter Peterson, Warren Rudman and John Lynch, as well as to others like John McCain, Howard Baker and Margaret Chase Smith. Walter Peterson used to say, “You can accomplish anything if you don’t care who gets the credit.” The problem today is that everyone either wants all the credit or is worried about the blame.

I know those people of good faith still exist. Their voices are just being drowned out by the loudmouthed firebrands who now set their party agendas — and they’re being intimidated to toe the party line or get tossed out of their positions in favor of even more extreme replacements who would make the potential for balancing competing considerations still more difficult. Have you noticed that just about the only representatives courageous enough to speak truthfully are the ones who’ve decided not to run for reelection?

The problem is also that nearly everyone talks about “working across the aisle” to reach reasonable compromises, but then they either don’t really mean it or find that they can’t without being branded RINOs or socialists and being shunned by their parties.

As I said, though, a critical mass of even 12 people of goodwill working together might tip the scales and cause more and more of their colleagues to join this independent, centrist coalition. And then a breath of fresh air might actually begin to blow some of the hot air, blatant lies and obstructive rhetoric out of our legislative chambers.

Things couldn’t really get much worse, so there’s nothing meaningful to lose — and something valuable perhaps to gain.

L. Phillips Runyon III has practiced law in Peterborough for 50 years and was the presiding justice of the 8th Circuit Court for 27 years.