The first Gulf War ended after 100 hours, having reached the limits of its UN mandate. Gulf War II now exceeds that, and everyone wonders when it will end.

For any hope of an answer, the question must be narrowed. Will it 'end' when the last US, British and Australian soldier has left Iraq? Will it end when the last aircraft carrier leaves the Persian Gulf?

Perhaps it will end when an official UN administration has accepted control and responsibility for Iraq's institutions. Whatever the speculation, the end will be a long time coming.

War in transition

If all US objectives are met, whatever the final stages reveal them to be, will all US-British-Australian troops leave for home? Until the objectives of the invaders becomes clear, it is difficult for anyone to estimate how long hostilities will last.

We can assume, based o­n US President George W Bush's statements, that the invasion will proceed until all of Iraq is under US control. Perhaps then the shooting war will stop, followed by a benevolent occupation to install freedom, democracy and a government with a favourable oil policy toward the US, Britain, Australia, and Israel. Water, food and medical supplies for the population are promised as well.

Any estimate of the time required for an end to active hostilities is made difficult by the extraordinary flexibility exhibited by the two combatants. The nature of the war is in daily transition, from a more traditional type where two conventional armies vie for disputed territory, into a lop-sided, sporadic shootout reminiscent of guerrilla warfare the world over.

If the Iraqi army joins in a big pitched battle, it is possible the end might come in a matter of weeks. We were told to expect a conclusion in days, then weeks, and now the projection is for a long, tough campaign.

We are daily assured that the outcome will soon arrive, and it will certainly be a complete sweep for the invaders. This now appears a less likely outcome. Looking back at the first five days, o­ne sees fewer prospects for a completely satisfactory victory.

Basic truths

Things have become murky, and o­ne would like to get a clearer picture. But how? Well, there is a way. It is possible to make an analysis that is primarily based o­n geometrical considerations, and it suggests this engagement will continue in various forms indefinitely ... to the everlasting frustration of the present US administration. We can use geometry.

To some, geometry may seem a poor starting point to look for an answer to the question of when the war will end. Actually, it is a very good place to start, and it tells us the war will continue into the indefinite future.

What follows is not the politically correct answer. Depending o­n your degree of interest in how geometry can predict an unexpected outcome, you might consider a departure now, as what follows may prove tiresome. That is to say, you are excused.

Since you have elected to stay, let me say a word in defence of geometry. Some say there is no absolute truth, and that it is foolish to pretend such certainty is possible. Everything is relative, so the argument goes, and this is perhaps the case in most areas of human affairs.

However, it does not apply to geometry. There are basic geometrical truths, and they apply in all circumstances. Ignorance of this power of geometry to provide logical truth is tantamount to an invitation to folly.

A willing disregard of its importance condemns o­ne to perpetual ignorance. Further, if accompanied with a prideful and self-righteous arrogance, it can guarantee the failure of an ambitious enterprise.

Plato opened a school in Athens that lasted for 900 years. He was so impressed with the power of geometry that he inscribed over his doorway, "Let none enter here who are ignorant of geometry." He considered it a prerequisite for further learning. It formed the logical foundation upon supports subsequent mental development.

You may wonder how geometry can make a projection with such certainty. Numerous demonstrations are possible, but our immediate concern is elsewhere. It is enough for the moment to provide o­nly o­ne example of the power of geometry. If it helps us to see the situation in Iraq with greater clarity, giving us some idea of the future, that will suffice.

Guerilla warfare

Consider the relationship between the area of a territory and the length of its periphery. Without introducing the formulas which allow an exact calculation, it is easily seen that as the area increases, so does the length of the perimeter.

An area to be defended is vulnerable along its border. The shorter that border is, the fewer the men and equipment required to defend it against a given invader. The optimal relationship between area and perimeter occurs in the case of the circle. The poorest ratio occurs where the area is narrow and has highly irregular borders.

We may apply this basic truth to a war in which Combatant A has a conventional army, modern in all respects, and invades the territory of Combatant B, who has o­nly a poorly equipped guerrilla army.

To all appearances, the modern army would have the advantage and the guerrilla force can soon expect to be overwhelmed. Since this is the conventional expectation, it always comes as a surprise when the outcome favours the underdog.

The war against terrorism is such a guerrilla war, and it is being fought in a conventional manner, through conquest and dominion over people, resources, and territory. This theory is based o­n the concept that, if the guerrillas are denied a place to live and are not allowed any freedom of movement or communication, they will be suppressed to the point of impotence.

The theory of a conventional war against terrorism calls for the physical possession of territory, acquired by invasion. Those defenders not killed in the invasion are incarcerated for as long as they would pose a threat as free people. The consequence is that an occupying force must thereafter defend the territory.

If the inhabitants are overcome by force, but are still present and free to move about within the borders of the controlled area, then an ability to identify potential combatants is necessary. If all inhabitants have a similar appearance, and there is no apparent means to distinguish a combatant from a non-combatant, then the guerrilla army has not been defeated.

It is still intact, o­nly forced into a more surreptitious form of combat. They have the advantage of striking at a time and place of their choosing, with whatever weapons may be available. They generally do not attempt to hold territory, since it invites massive retaliation. The essence of guerrilla warfare is surprise and mobility.

A conventional army, seeking to conquer and occupy a given area, has a two-fold task. It must protect the borders of conquered territory from a foreign attack, and defend itself internally from the counter-attack of local guerrilla forces.

History tells us that this task is difficult, and usually proves impossible. The recent conflict in Vietnam offers a lesson, as does the continuing situation in Afghanistan.

The Russians seem to have acquired a difficult and expensive education from their Afghan and Chechen experiences. The US and its allies are still struggling with the basic concepts, but are blinded by a thirst for Middle Eastern oil, and having an unfortunate faith in Israeli fealty.

Threat from within

There is an interesting twist to the Iraqi scenario, in that ethnic and religious pressures tend to divide the country. If this occurs, it effectively compounds the problem, because it greatly increases the length of the borders to be defended even while the total area inside remains constant.

When there are hostile elements still armed and free inside the area that is conquered by invasion, they must all be identified and eliminated, either by killing, incarceration or removal by other means. This has been the dilemma of all colonial powers, as seen in the case of Israel, still fighting its guerrilla war after 50 years.

The impasse is usually solved by colonial powers by establishing a servile civil service composed of locals, and supervising them with vigilance and vigour. The British were expert at the subversion of local governments, with the subsequent substitution of an army and police force of British-trained locals. An officer force was placed over them, supplied by the London Colonial Office.

A few regiments of the regular British army are thus sufficient to maintain permanent and continuing control, often in a conspiracy with the local potentate, who lives under the threat of a cannon, with o­nly a mutiny here and there, now and again, to be put down with a ruthless demonstration of force.

The US is reluctant to embark o­n the avenue of colonialism, preferring instead to introduce its brand of representative democracy and its three-balanced-houses institution of government.

Unfortunately, there is no country where this has been completely successful, because the process requires forgiveness of the brutalities committed during the conquest, which is seldom forthcoming, even after many generations.

The war in Iraq, though initially a contest between conventional forces, is certain to be transformed into another case of conventional warfare versus guerrilla warfare, with the outcome similar to all those before.

To the problem of protecting its borders, carefully screening all incoming travelers, is added the problem of a discontented populace. During the long Vietnam war, the number of bombings in government facilities in the US steadily grew, until it averaged over 50 a week.

This was not a threat from without, it was a threat from within. It was this growing threat that led to the shooting of students at their school.

Hostile inhabitants

Once the military forces of a country begin to kill their peacefully demonstrating citizens, the war is all but lost. It is impossible to maintain an effective foreign fighting force when internal dissent is so high.

That is because while the home territory can be defended along its borders, at whatever cost in terms of personnel and material, it cannot be defended against its own hostile inhabitants, which is effectively a guerrilla force at large within the area to be defended.

When a war is unpopular, there is the additional problem of dissent within the military ranks. Unpopular orders create resentment, and in active combat it is easy to kill officers who are disliked.

During the Vietnam war, many officers were killed by 'fragging', which was the term for rolling a live grenade into the officer's tent while he is sleeping. An incident of this type has already occurred in the first few days of the war o­n Iraq, and certainly there are reasons why it may happen again.

The invading force must set up an occupying force to hold the territory taken, which would tend to deplete the resources of the advancing troops. Every bit of territory occupied compounds the problem. Territory you own, owns you.

If sufficient resources in men and material are not available to protect the lines of supply, these become vulnerable to attacks that remove essential supplies and personnel, and put transport equipment out of commission.

When such attacks occur, additional forces must be assigned the task of protecting the lines of supply. As the supply lines become longer, the same considerations of geometry apply to the area to be protected.

Lightning strikes

In a war between conventional forces, superior equipment and tactics generally prevail, and this is true even against forces entrenched in the defence of their home turf. If the retreating force transforms itself into a guerrilla force, either gradually or o­n order, the superiority may evaporate, simply because there is no target worth the cost of the missile or artillery.

One or a few individuals moving about with light weaponry, such as rifles with telescopic sights or portable rockets, can keep a large conventional force engaged for hours or days, then disappear.

Mobile equipment such as tanks and helicopters make good targets for small rockets, launched from the shoulder. Because such light weaponry is easily transported, it can more quickly change its battle venue than a large mechanised force, and it is also more easily concealed.

Geometry tends to favour a guerrilla force. A conventional army occupying territory is forced into small enclaves that are more easily defended than an extended battlefront. These fortified areas then become attractive targets because guerillas can easily penetrate the surrounding areas and attack with mortars and rockets.

What geometry tells us is that the inhabitants of the area being occupied must be docile. They must not actively resist the invading force. If they do resist, and the resistance is a determined o­ne, the force attempting to maintain a continuous presence will be subject to unremitting terrorist attacks, coming at any exposed point and any opportunistic time.

Because a hostile local faction is difficult to identify, eradicate or incarcerate, such a situation inevitably becomes a protracted engagement, with consequent loss of personnel, equipment and morale. Geometrical analysis shows us the seedbed of genocide.

The US strategy is to use technology to make surgical strikes, expending expensive missiles and bombs to destroy buildings and other infrastructure that support a conventional army.

While this tactic is effective in removing the communication and logistical support for a conventional force, it is useless against a guerrilla army, and o­nly accelerates the transition of a conventional army, o­ne that can be overcome, into a guerrilla army than cannot.

The occupying force becomes a captive in its own castles, venturing out from its airfields and bases for a sortie from time to time, prompted by information or opportunity.

This operational tactic establishes temporary bases, offering limited control and aimed at domination of o­nly an immediately surrounding area. Because total domination and control are seldom possible, these temporary enclaves become permanent, lasting until they are overrun or voluntarily abandoned.

When an invading force recognises it is in difficulty, it generally summons assistance from allies equally ignorant of geometry. When they join as allies, their participation invites the attention of the guerrilla opposition.

Now the the assisting ally assumes the problems of the invader, and its own military problems are immediately compounded, because a necessity arises to defend the borders of the home country against the guerrillas and their allies.

It is an instantaneous and unavoidable consequence. Participation invites retaliation from without, in addition to any hostile faction of their own citizens who oppose the sending of forces abroad.

Building a new world

If the people around the world fail to recognise the important changes that are taking place, the situation will soon devolve into two factions: those countries seen to be supporting the invasion of Iraq, and those who are publicly opposed to it.

Because neutrality is now called opposition, there are no neutral countries. Every country opposed to the war o­n Iraq is not actively supporting the guerrilla fighters, but others are willing to provide equipment, though covertly. Countries providing aid are motivated by a desire for economic gain, and by a natural desire to bring balance back to global geo-politics.

The arms dealers provide night goggles, telescopic rifles, portable rocket launchers, and satellite jamming devices - all of these, the favourite weaponry of guerrilla forces. These weapons are effective against the mechanical and technological superiority of a modern army.

As personnel losses mount and the expense of replacing costly hardware becomes intolerably burdensome, public zeal for such expeditionary exercises will flag. Time is o­n the side of the guerrillas, who have negligible expense, and accumulate little debt. o­nly minimal training is necessary for a guerrilla army, and the supply of human resources is as deep as the population.

If there is a model to examine for its predictive value, Israel serves well. It has enormous technological superiority, and the Palestinians have none, yet the 50-year attempt to eliminate and remove the native Palestinian population has failed.

By some perverse logic, the US has announced it will solve the Palestinian problem by invading Iraq. In the event, they have o­nly joined Israel in its misery. The war is thereby broadened.

The best thing Britain and Australia can do is to bring their troops home before there is further diplomatic and political damage. There is little to gain and much to lose, including the national honour.

The US has declared its willingness "to go it alone" without UN approval, in violation of all international agreements, and that is what it should be allowed to do.

It is possible the US economy will collapse before the Iraq war ends. If so, the world must be prepared to make something new and better from the pieces. There is, however, no need to act in haste. The war in the Middle East will be there a long time. Geometry tells us so.