The ancient historians are hopelessly unreliable when it comes to numbers

blood-letting of the American Civil War of 1861-65, in which 620,000 people were killed - more than in all the wars since waged by the USA

put together.

Historians in general do not pay enough attention to significant numbers. It is astonishing how many general histories there are extant that do not give the most basic numerical information needed to make informed judgments about the society in question. A recent general history of Byzantium never once gave the vital information that Constantinople at its apogee contained a population of one million. Conversely, professional historians like to swamp their learned journals with ''number-crunching'' of the most uninformative kind: how many indictments in the county of Middlesex in the eighteenth century resulted in ''guilty'' verdicts - that kind of thing - when what one wants is a reliable way to establish whether at any moment in time the true

rate of crime is rising, declining or holding steady.

The central paradox about significant numbers is that human beings are most careless in estimating the very thing that makes most impact on the imagination. The ancients, as is well known, were virtually innumerate, and from them we get our vague word ''myriad'' (from the Greek murio which could mean anything from a thousand to a hundred thousand). In the Iliad we are told off- handedly that Achilles and Hector slew thousands in a single day. In the Bible, we learn that Samson tied together the tails of 300 foxes (the exactitude of that ''300'' is peculiarly calculated to raise a smile in the modern reader) and killed 1000 men with the jawbone of an ass. The Psalms boast: ''Saul hath slain his thousands and David his 10,000s.'' Lest it be thought that this is mere poetic licence, it is worth establishing that the ancients always had an irritating habit of describing anything more numerous

than they could shake a stick at as ''10,000''.

We see this very clearly in the work of the historians of the Ancient World. Livy, Tacitus, Thucydides, Herodotus, and the others all have valuable things to tell us, some of which have been most surprisingly confirmed by modern archaeological research, but they are hopelessly unreliable when it comes to numbers.

In his classic account of the Persian War of BC 480-79, Herodotus tells us that Xerxes brought three million men from Persia to subdue Greece. The highest credible figure modern historians of the Ancient World can agree on for Xerxes's host, given the huge logistical problems involved in supplying such an army is 190,000. A German scholar of the nineteenth century once had fun with Herodotus's numbers, by ''factoring in'' the rate of march, the stopovers, the commissariat and the necessary bivouacs and billets required for an army of three million at the level of technology then prevailing.

He concluded that while the vanguard of the Persians was encountering Leonidas and his 300 Spartans at Thermopylae, the rearguard would still be trailing out of the Persian capital at Susa, 1500 miles away.

This tendency to overestimate numbers by an absurd margin continued through the medieval period. The Norman historian, Ordericus Vitalis, writing about the battle of Hastings in 1066, claimed that there were 100,000 combatants on either side, and that 15,000 Norman knights perished in a single incident when they tumbled into a deep ditch. In fact William the Conqueror assembled in France a total force of no more than 14,000. When we take off sailors, administrators and other non-combatants and deduct a further 2000 men for the troops William left in garrisons at Pevensey and Hastings after landing,

it is clear that on the day of the battle on October, 14, 1066, William had no more than 7500 combatants (his opponent Harold Godwinsson probably had about the same number).

If we zero in on the supply and logistical problems of the Norman army, we begin to appreciate the sheer absurdity of the ''myriads'' claimed by ancient and medieval historians. The Norman army was bivouacked at Dives on the Normandy coast for the month of August, 1066. Simply to keep this number of men sheltered and fed on a diet of bread and water required 1500 tents (the hides of 36,000 calves), 420,000 gallons of fresh water and 740 tons of wheat; in fact 1000 cart loads of wine were taken to Dives also, as well as vast amounts of meat. The 3000 warhorses were even more of a problem as they would have died off like flies unless supplied with a daily quota of water, grain, hay and straw.

Altogether at Dives, the horses consumed a million gallons of fresh water, 1600 tons of grain, 1500 tons of hay and 155 tons of straw. To keep this army required not just administrative talent of a high order but also host

of butchers, bakers, blacksmiths, tanners, leather workers, woodcutters, carters, carpenters, cooks, artisans, and sanitation engineers.

Every army faces the same logistical problems, mutatis mutandis, which was the main reason Napoleon's invasion of Russia in 1812 was such a fiasco. Used to commanding armies no larger than 90,000, he advanced into the Russian steppes without having thought through the commissariat problems of his unwieldly host and the uncertainties of the campaign. He planned for a 50-day campaign for 400,000 troops and in fact fought a five-month campaign with half as many men again. The huge size of the eventual front in Russia and the vast distances to be covered by supply wagons meant the commissariat details themselves consumed a third of the food they were taking to the combatants. Napoleon lost more men to starvation and disease on the way to Moscow because of his inadequate logistical grasp than to Cossacks, guerrilla bands and ''General Winter'' on the retreat.

This brief examination of the logistical problems of armies enables us to rule out as absurd the huge numbers described by ancient and medieval historians, even if we could not work it out by another method. It is usually considered that a nation can draft into armed services in wartime one-tenth of its total population, and of these in turn a tenth will actually see combat. Shakespeare put it well in Henry V on the eve of Agincourt: O! that we now

had here/But one ten thousand of those men in England/That do not work today.

A good rule of thumb, then, is: discover the population of a society, divide by 100 and you will have the number of battlefield effectives.

That would mean that the Roman empire at its height, with a population of some 70 million, could

probably put into the field, at a maximum effort, and in all fronts

simultaneously, three-quarters of a million troops.

Yet even Napoleon, a great mathematician and universally recognised as a military genius, found the control and supply of half a million men beyond him. The tendency, therefore, with modern historians, has been to play safe and always to accept the lowest possible estimate of populations, armies and battle casualties, Unfortunately, this methodology produces its own absurdities. All the best estimates concur that the population of pre-Columbian America north of Mexico was about 14 million, and of Mexico itself about 25 million.

It is also well known that the arrival of the conquistadors in the Americas devastated the indigenous peoples through the introduction of killer epidemics such as smallpox, measles, tuberculosis, influenza, malaria, and typhoid, and that the continent thus lost about 90% of its population. Yet we can still find a well-known historian like Sir Martin Gilbert (in The Routledge Atlas of American History) quoting the pre-Columbian population for North America as ''approximately one million Indians''.

What is going on here? Is this just the ''swing of the pendulum'' and are modern historians simply introducing their own distortions by ''downsizing'' all statistics in a reaction against the excesses of earlier eras? I would like to suggest that there is more to it than that, and that we are faced with a manifestation of human nature. If we are ashamed or horrified by the scale of casualties we ourselves have inflicted, if national pride is involved, or if we are unwilling to concede the talent, heroism, and sacrifice of other nations, the natural tendency is to belittle the extent of their losses. Conversely, if we are defeated

as a nation, it is always because we were betrayed or the enemy was vastly superior in manpower.

When the flower of Christian chivalry was destroyed in Hungary and Poland in 1240-42, during the brilliant campaign fought by the Mongol generals Batu and Subudei, the cry immediately went up that the soldiers of Christ had been overwhelmed by ant-like hordes; in fact the Mongols were numerically inferior in this campaign.

There was an echo of this in the way every victory won in the Korean war by the Chinese Red Army was attributed to a massive superiority in numbers, and every battle won by the UN was due to the military genius of

Douglas MacArthur.

It seems clear that the West has used the hyperbole of the ancient historians to mask or obfuscate its own acts of barbarism or to play down the fatal impact of European exploration on what is now called the Third World. To take the example of pre-Columbian America, it makes a great difference to the human imagination which of the figures we choose, the probable one or Gilbert's fantasy. Ninety per cent of one million would produce 900,000 dead, but this pales beside the more plausible 12 million. Yet the guilt or shame need not only be about the Third World. During the Thirty Years War (1618-1648) the population of Germany declined from 21 million to 13 million.

For a long time historians refused to accept these figures, using Xenophon's ''myriads'' as cover. We see the tendency to downsize through guilt every day, whether through nitpicking over the exact casualties sustained at Hiroshima, Nagasaki, and Dresden (unacknowledged Western war crimes) or in the absurd pretence that only 5000 and not the true figure of 30,000 ''disappeared'' in Argentina during the Army regimes of the 1970s. In western accounts the lowest figure for these casualties will always be the one accepted.

The Anglo-Saxon nations of the West have never liked to admit the huge contribution made by the Soviet armies to the defeat of Hitler in 1941-45, nor fully acknowledge the sacrifice of the Russian

people. During the 1950s the conventional figure for Russian dead in the ''Great Patriotic War'' was 12 million; this was taken up as a kind of mandarin's mantra and nobody thought to examine the provenance of the statistic. Then in 1963, during a speech in Washington, President Kennedy revealed that according to the best CIA data, the true figure was 20 million dead. Recently, as the old Soviet archives have been opened and reputable scholars have examined the records, it has been discovered that the true figure is nearer 50 million - a quarter of the total population and an almost incomprehensible catastrophe for any society.

Why the reluctance to acknowledge this unparalleled tragedy? Partly it is national chauvinism - that regrettable reflex which makes it front-page ''news'' if 100 Britons die in a plane crash, but a page-two filler if 100 Columbians or Arabs do so. As Sir Robert Walpole cynically told Queen Caroline in 1734: ''Madam, there are 50 thousand slain this year in Europe, and not one Englishman.'' Partly it is entrenched Cold War dislike of the Russians, the post-1945 revulsion against Stalin, who during the Second World War was regarded as benign old Uncle Joe, and the

''Eng-er-land'' mentality which continues to insist that El Alamein was as significant as Stalingrad.

A final thought. Why do the police always scale down the numbers of protesters so that their figures for the numbers attending demonstrations are always much less than those of the organisers? Is this again the desire to diminish the achievement of those against whom one has some grudge?

In 1960, the organisers of the campaign for Nuclear Disarmament claimed to have had 100,000 supporters in Trafalgar Square at the end of the Aldermaston March. Piqued by police claims that the true number was 60,000, the organisers in 1961 hired a group of professional tellers to estimate the final tally. They made it 80,000, but once again the police came up with a significantly lower estimate - 50,000. Perhaps the answer, for those who cannot stomach the scale of

Soviet losses in 1941-45, is to hire the Met to conduct their own audit on the newly-opened Russian archives.

n Frank McLynn is a Visiting Professor at Strathclyde University.