Using an ideological GPS to navigate the pitfalls and molehills of politics and primaries requires an occasional pirouette. Candidates usually travel looking backward — looking at who’s behind them and how fast they are catching up. Occasionally, they also have to stop, climb a landmark, get themselves dirty in doing so, and check out the landscape in front of them.

Even those in second or third place — or fourth or fifth — move with a view to where they’ve been: Last month, less than 5 percent in the polls; two weeks ago, 9 percent; yesterday, 10 percent.

How often a candidate stops, turns around and checks the road ahead depends on the distance between the candidates just ahead and those just behind, as well as on how much farther it is to the journey’s end.

Yes, primaries are chaotic things, but this year’s Republican primary show seems more chaotic than normal. No wonder the candidates keep popping up and checking the landscape. How straight is the steering? Any U-turns or icy roads ahead? The volatility escalates day by day.

For some time it’s appeared that the Republican race would occur in two stages: Mitt vs. the anti-Mitts, and who’s the most anti-Mitt. The lead in the anti-Mitt race changed several times, and some fell so far behind as to be discounted, while others came out of nowhere. Going into South Carolina, there were four horses in the anti-Mitt race: Newt Gingrich, Ron Paul, Rick Perry and Rick Santorum.

Not anymore. Perry decided to return to Texas and tossed his miniature-sized hat to Newt. Gingrich is surging, and won South Carolina — the “kingmaker state.” (Republicans have their own Byzantine conventions: Iowa energizes the base, New Hampshire winnows the field, but for 30 years South Carolina has picked the nominee.)

No, wait — Santorum will win South Carolina because he retroactively won Iowa. (Retroactive wins are a Republican trademark. Must be a package deal with retrograde policies.)

Or Romney will win because he has the money and, like a caisson, he keeps rolling along.

Maybe the candidates — and the pundits who follow them, wearing embroidered lab coats and with magnifying glasses in hand — should stop, climb the ball (crystal or otherwise) and check out the volatile landscape.

Gingrich is known as a no-holds-barred, take-no-prisoners, ideological, truth-be-damned fighter. He’s taking it to Romney with his recent controversial ads. He took it to Fox News analyst Juan Williams. Williams, a prominent black political analyst, asked Gingrich to clarify his comments that “Poor kids lack a strong work ethic,” and Gingrich’s description of Obama as the “food stamp president.”

But Gingrich must now contend with his second wife, Marianne, who talked to ABC News about their failed marriage. Gingrich’s camp deferred to a statement by his two daughters about his past statement of regretting any pain he caused.

So, in Gingrich, conservatives get combative, but they also get racial innuendo and infidelity? Is this the real anti-Mitt?

Santorum has risen from Iowa, has new endorsements from the Christian evangelical movement, and speaks a perfect tea party. He may steer around Perry, but will it be enough? A third-place finish in South Carolina may be more troublesome than his fifth place in New Hampshire.

Paul keeps chugging along, more like the little engine that thought it could — third in Iowa, second in New Hampshire, was projected third in South Carolina. If the other anti-Mitts fall into a trap or a pitfall of their own making, he may yet be the slow and steady finisher. His supporters are extremely passionate about their guy.

Then there’s Romney himself. (Who may be the ultimate anti-Mitt.) His pyrrhic defeat in Iowa, his duh-triumph in New Hampshire, his money, his organization, his be-knighting by the pundit kingmakers, made his coronation — or nomination — seem inevitable.

But that’s just the sort of arrogance that turns off South Carolina voters.

Yet Romney has other problems. ABC News discovered 138 offshore tax havens for Bain Capital, Romney’s signature business.ùWhen one of his most ardent supporters, New Jersey Gov. Chris Christie, calls on him to clear the air and release his tax returns, it’s a sign of trouble.

But Gingrich isn’t the only combative conservative in the race. Romney also knows how to attack — witness some of his ads. And Romney’s made it clear that if you attack the way he made his wealth, you will be labeled as not only an enemy of free enterprise, but as undermining “One Nation, Under God.”

Yet what’s missing from the GOP’s looking glass is a way to see the direction that moves the country forward.