Since at least 1676, when Sir William Petty, previously a professor of anatomy and music, wrote Political Arithmetick, scholars have aspired to a physics of politics. While we have discovered some science in politics during the intervening 331 years, physics has come a lot further since Sir Isaac Newton wrote about gravity, a decade after Petty penned his volume.

Nevertheless, allow me to don the garb of physics to consider some axioms that may help decipher the primary process. I start with conclusions from earlier columns but dress them up as axioms to avoid repeating evidence adduced previously and to project an air of certainty where none actually exists.

To win his or her party’s nomination, a candidate must win either Iowa or New Hampshire.

Axiom 2: A candidate who wins both Iowa and New Hampshire will win his or her party’s nomination.

Axiom 3: If Iowa and New Hampshire produce a split decision, the contender with the greatest resources going into Feb. 5 will win the nomination.

Lemma 1: (OK, it’s not really a Lemma, but it extends the gimmick and, anyway, the axioms aren’t really axioms, either.) If Rudy Giuliani skips both Iowa and New Hampshire, as some of his advisers are reportedly urging, he will not win the nomination. Months ago, when most still derided his quest as an impossible dream, I urged Giuliani be considered the Republican front-runner. Since then, though, he has made one error after another and by Mellman’s 1st Axiom, skipping the two early states will doom his candidacy.

Lemma 2: If Giuliani abandons Iowa, John McCain, Mitt Romney and Fred Thompson will be locked in a death struggle there. If either McCain or Romney wins Iowa, he is almost guaranteed the New Hampshire victory and therefore, by Mellman’s 2nd Axiom, the nomination. Winning Iowa does not assure Thompson a New Hampshire first, but he cannot allow Romney or McCain to win Iowa, or his prospects fall to near-zero.

Lemma 3: Iowa is the whole ball game for John Edwards. The strong impression he left there in 2000, combined with his effective courtship of the state’s voters in the years since, catapulted him into first place there, for now. If he wins Iowa, Edwards will be a giant-killer, having felled both Hillary Clinton and Barack Obama. The momentum that generates, and the negative press that will attach to the giants he slew, gives him the chance to take New Hampshire, Nevada or South Carolina and go on to win on Feb. 5. If Edwards loses Iowa, he will not win New Hampshire and his chances of securing the nomination plummet.

Lemma 4: Hillary Clinton or Barack Obama can effectively end the battle for the nomination in Iowa. If either of them wins in Iowa, they will win in New Hampshire and, by Axiom 2, will secure the nomination then and there. Of course, the shouting will continue, along with intense battles, and maybe even some wins by other candidates, but the race will effectively be over. If Obama concludes he cannot emerge victorious in Iowa, it will be in his interest to forge a tacit alliance with Edwards to prevent a Clinton win — risky, but better than letting Clinton win the nomination in Iowa.

Lemma 5: Iowa and Nevada are critical for the second-tier candidates. They cannot hope to jump-start their campaigns after New Hampshire, and they will not win New Hampshire without victories in either Iowa or Nevada.

Some will complain that I have vastly oversimplified the process. They are correct — but I’ll bet I’m right. Let’s see whether I do Sir William proud.

Mellman is president of The Mellman Group and has worked for Democratic candidates and causes since 1982. Current clients include the majority leaders of both the House and Senate.