A nineteenth century mathematician, Carl Jacobi, solved an important problem that had bewildered Legendre, one of the near all time greats, for a quarter of a century. Jacobi attributed his success to his reversal of a conventional approach, of inverting an orthodox attack. Thus his motto became: invert, always invert.

If the word ever got out how successful this method is outside of mathematics, teaching inversion would certainly become part of the core curriculum.

For example, two physicists (Urbain Le Verrier and John Couch Adams) discovered a new planet (Neptune) by looking at an old one (Uranus).

And the chemist, Mendeleev, also predicted three new elements by carefully ordering the old ones.

And a biologist who followed Jacobi's advice would have been the first to discover a retrovirus which reverses the role of message and messenger and could very well become the Rosetta stone of the genome.

A Rosetta stone in the field of therapy is called flooding or paradoxical intent. If a patient is afraid of elevators, he is made to spend a weekend riding elevators until his brain literally grows bored receiving the same messages of alarm, the same cries of wolf, until it elects to ignore them – rather like a human thing.

This reminds me vaguely of the time my hard drive crashed. I was choking back the tears until a technician was able to get my computer to reboot one last time by turning it upside down. When my deliverer saw me blinking stupidly, he mumbled, "If you feel faint, pal, put your head down." Whatever doubts I had about machines having a psychology were forevermore resolved.

Money also has a perverse psychology. Economists have their Laffer curve. Under some circumstances revenue can actually increase when tax rates are cut.

And box office receipts also increased when a good musical in the Sixties was renamed The Roar of the Greasepaint, the Smell of the Crowd.

Invert, always invert.

Sun Tzu counseled us to get ready for war during peace and peace during war.

And Liddel-Hart advised us to use an opponent's own effort to overthrow him (as in ju jit-su). I suspect that after a review of the cod wars between England and Iceland, the old strategist would have – with good outcome – fruitfully taken the side of the fish.

We enter the future backwards, Paul Valery shrewdly observed.

So when we remember that the prophets of Israel who denounced most deftly really didn't want to be prophets, that Joel and Moses certainly didn't want the job and that Jonah ran for his life – then, we, as Jacobians, will at once understand the secret of choosing a leader: you simply select someone who doesn't like to lead.

Claudius, for example, was an above average Rome Emperor – he was elevated as a joke by the Praetorian Guard. There were only two truly great popes, Gregory and Hildebrand, and each left Rome when he was elected. And if we were to seek a truly majestic king, such as the first and greatest of the Plantagenet, we might not find him on his throne, but we could very well find him on his knees being whipped by monks. Some good presidents have been dark horses. And the only good businessmen I have personally known – in the sense of being both ethical and successful – have been widows. So the lesson of history could not be more clear: if you ever serve on a search committee, crown a shepherd boy king.

But admittedly choosing military leaders requires a trickier kind of inversion: you should choose the best of the worse (NCO's such as U. Grant or N. Green, our modern centurions) of the worst of the best (the goats of West Point such as A. Custer or J. McLain). But in a pinch, choose the first style of savagery, since you tend to find the authentic demons reigning in hell rather than serving in heaven.

What then would a Jacobian do in Iraq? In view of the fact that U.S. policy is violent and ineffective, then would not an inversion of U.S. strategy be both nonviolent and effective?

Christopher Hitchens describes a scene in his book, The Elgin Marbles: Should They be Returned to Greece?, in which Greek soldiers at one point actually offer to supply their Turkish enemies with ammunition to shoot at them if only the Turks will shoot at just them and not the Acropolis. The message for us here is that reverence can be used as leverage, especially in matters of life and death simply because reverence has to do with the meaning of life and the meaning of death.

The U.S. policy in Iraq is to kill terrorists and protect the shrines. Clearly we should stop killing terrorists and start pulling down the shrines.

We should do this and do it very quickly because something really, really bad is coming down the pike. The insurgents have already shot women. Soon they will axe them. And it is only a matter of time before Jewish children are beheaded on the net and beheaded as slowly as humanly possible. Once a terrorist threat is made to do this, American troops should immediately follow Lord Elgin's shining example and rush out to hack off a something holy. A counter threat should then be made. The captured shrine will be blown to bits if some insurgent savage proceeds with his awful plan. That's the stick. And the shrine will be returned if the child is released and the kidnapper turned over – no questions asked. That's the carrot.

Needless to say, the Islamic extremists would react with a pure, purple rage. And they would certainly attack the Vatican.

Well, okay. Fine.

While they're doing that, they won't be shooting toddlers in the back in Beslen.

Victor Davis Hanson cites a successful precedent to this approach in The Soul of Battle. Sherman defeated the South not by destroying Southern armies but by destroying the reason Southern armies fought, by ripping apart the social structure of the South – by torching their plantations, their holy shrines.

Whether this solution appeals to you depends on what your answer would be to the old ethical question: in a fire, would you save a Rembrandt or a cat?