On

—with hosts of other lines which dignify the vast storehouse of the English lyric.

Of the modern masterpieces there is one—the best known of all, perhaps—where "and" does an enormous amount of work, which is the poem of Innisfree. It gives the rhythm as well as the mystery. I should like to see what the fools who are for cutting out "and" would make of that poem.

But the most sublime use of "and," alas! we have not. It is the "and" disjunctive; on which turned one of the great moments of history.

For you must know that when the second Council of Nicea finally condemned the monstrosities of the Iconoclasts, a saintly bishop from Cyprus wrote his opinion in Greek saying, "I revere, I embrace the sacred images, και [Greek: kai] I give worship to the Life-giving Trinity"—which is as much as to say, that he would be polite enough to an image, but his worship he reserved for the only true object of worship.

Now, this pronouncement was carried to a Council of the West, sitting at Frankfort, where there were bishops of the Pyrenees, of Gaul, of the Rhine Valley, of the Low Countries, of the Burgundian Hills, of the Swiss Mountains—indeed of all parts whatsoever that owed allegiance to Charlemagne.

At that moment Charlemagne was already wishing to be an emperor in the West. Those who served him were only too glad to find the Empire of the East—which claimed to be universal—making a howler. But the swarm of holy and unholy men at Frankfort were abominably ignorant of Greek. They did not understand the disjunctive value of και [Greek: kai]. They thought it a mere barbaric "and." They translated this famous phrase "I jumble up in one worship God and images." They rushed out with some fury against such a doctrine. They registered their hatred of it. On this point also Gibbon has (as one might expect) abominably falsified history.... But no matter.

The Bishops of Frankfort said what they had to say. In vain did those of Rome, who were acquainted with Greek, tell them that they had taken the sentence exactly upside down—that it meant "I do not worship the images. I distinguish the observance I give them from the worship I offer to That which alone is worthy of worship." They still clung to their primitive error. With difficulty were they led back into the right fold.

What great consequences their ignorance might have had! We might to-day be deprived of the Bambino. We might have lost Brou (but not Santiago, I think; for the Spaniards, and in particular the Galicians, are of a temper which will stand no nonsense. Though 1462 General Councils had condemned images, the Spaniard would have had them all the same: in which I praise him. Honour to the Pilar!).

Now, though it does not concern the little word "and," yet I am reminded (by this mention of the Second Council of Nicea) of a certain story which, as you may not previously have heard it, I will now proceed to relate. With that story I shall conclude; nor will your prayers and entreaties, however loud and passionate, move me to continue. I will tell you the story; then I will have done.

The story is this. As the Eastern bishops were travelling to the second Council of Nicea, the more worldly of them (these were the greater part) were very much disgusted to meet one particularly good bishop who had been bred a shepherd. He was poor. His manners were bad. He did not shave regularly. He was badly dressed. He was what they call in Birmingham "no class."

They jeered at him a little, but more than their jeering was their fear lest they should lost caste by entering the Imperial City in such company. So after this saintly man had made himself quite intolerable at dinner, they cast up a plot against him.

He had come with only one deacon, sitting each of them upon a mule, the one a brown mule, the other mottled. The mules were stabled in the great inn of the village where all were assembled. When the saintly, but not smart, bishop had gone to his rest, the smart bishops secretly sent a bravo into the stable to cut off the heads of the two mules. "In this way," said these wicked, worldly bishops, "we shall be spared the humiliating presence of the boor when we enter the imperial town; nor will men ever know that we kept such low company."

Long before it was dawn the poor Bishop's deacon, like a good deacon, a good rustic deacon, shook himself out of sleep. He went down to the stable with a lantern to get ready the beasts against the morning journey. With what horror did he not see there two heads lying upon the ground! The one was of his own mottled mule, the other of his master's brown mule. The mottled head lay severed upon the straw beside the brown head, the headless trunks leaning all collapsed against the stall sides.

The deacon, rushing up to his master, banged at the door, saying, "My Lord! My Lord! Evil men have cut off our mules' heads!" The Right Reverend, only half awake, said, "Sew them on again! When I wake I will attend to it."

The deacon went down to the stable. With many tears he sewed on the two heads of the dead mules. The Bishop, when he had risen from sleep, said his prayers, came down into the stable, where, he having blessed the two mules, they came to life again in the most natural manner in the world. When he had breakfasted, he rejoined his deacon. Mounting the two beasts, they rode out into the break of the day. But, the light broadening as they approached the city gate, the crowd saw with astonishment a brown mule with a mottled head abreast of a mottled mule with a brown head, for the deacon, confused in the half darkness of the morning, had sewed the wrong heads to the wrong bodies.

Note the effect—as the veracious chronicler gives it. "Thus by that very action whereby these evil men had hoped to bring their companion to shame they did but the rather thrust him into glory; for their cruelty to the dumb beasts did but serve to heighten his holiness, making proof of God's power through him who could bring the dead to life."

Many are the morals of this tale, one of which is that it is silly to take more trouble than is necessary. For if the wicked Bishops had only drugged the mules instead of cutting their heads right off there would have been no miracle, nor glory to their despised colleague. Another is that if a thing is true you must believe it, however astonishing and unlikely it may sound in the ear of the unbeliever. Another is that a bishop has the right to get up rather later than the lower branches of the hierarchy. There are many other morals; but I will end. For if I go on I shall certainly bring "and" into my own sentences, which up to this point I have managed to avoid. "And" is not really necessary at all.

THE CAD'S ENCYCLOPÆDIA

I have a wealthy friend. He made his money by accident during the war. The Government owed him £500. A careless clerk (who was talking to a minx at the time) added three noughts without thinking, and on his modestly pointing out the error, the department wrote back to say they never made mistakes. And so it rested at that. After long hesitation how to get rid of all this money, he is at last engaged upon what I cannot but think a very useful work. I only wish that every rich man could be inspired by similarly valuable ideas, instead of frittering away money upon buying newspapers and souls and uneatable food in noisy restaurants.

This rich friend of mine had always had the idea, when he was poor, of getting together a Cad's Encyclopædia.

All the publishers whom he approached told him (with truth) that nothing is more venturesome than an Encyclopædia, and that even when one is pretty sure of a large public for one's subject the outlay is very heavy and the risk considerable.

My friend had—in the days of his poverty—prepared a detailed memorandum in which he urged the advantage of his scheme. He pointed out that there was an enormous number of Cads in the world, and that even those who read books and could afford to buy an Encyclopædia amounted to many millions. He urged the complete novelty of the scheme, the long-felt want, and all the rest of it. But they replied to him that a fatal drawback was the name.

"No doubt," said the head of one great firm, "there is a demand, and Cads naturally desire a book of reference of their own for their guidance and instruction; even those who are not Cads, but only interested in the subject of Cads, would also want it for making research. But few would buy it under that title because it is one which men avoid applying to themselves and dislike having applied to them by others. You will have noticed," said the great man genially, "that men are eager to ascribe to themselves ignorance, fatuous good nature, even appalling vices, but never Caddishness."

My friend could not but see the justice of the last remark, but he still maintained that a thing was more successful in the long run under its true name. He persisted in his idea, and when the accident of which I speak had suddenly made him rich he proceeded to realise it.

The first volume will be out next October. It will be privately published by a new firm created for the purpose. I hope I shall receive no correspondence upon it, because I cannot be bothered to negotiate its sale, but I shall give my friend the best advice as to how to put it upon the market in the unavoidable shyness of the usual agents.

This Encyclopædia was not an easy thing to get together, apart from the expense. First of all there was the difficulty of apportioning space. That is a difficulty attaching to all Encyclopædias, but particularly to an Encyclopædia on, and for the use of, and conveying information upon, Cads. In an Encyclopædia of Agriculture, for instance, the editors can make a fair guess as to what space will be wanted for each pest attaching to particular forms of vegetation, but it was difficult indeed to determine which habits of the Cad would require most description; what should be set aside for his house, what for his clothes, what for his manners; how many pages should be allowed to the Cad in Literature; how many inches to the more exotic types of Cad, such as the Negroid Cad, the Dago Cad, the International Wagon-lit Cad, and so on.

Then there was a great debate between my friend and his sister on the vexed question of the She-Cad. I took part in this and strongly proclaimed my own opinion, which I have held for years after a very close examination of the matter, that there is no such thing as a She-Cad. A Cad is the opposite of a gentleman, just as a civilian is the opposite of a soldier, or a layman of a cleric. But there are no She-Gentlemen and therefore there are no She-Cads. To this it was objected by my friend's sister that she had personally known and handled several She-Cads, and she began to give examples. But I am glad to say my friend agreed with me that the type did not exist, and showed how every example his sister quoted was a false type and no more a She-Cad than the lemon sole is a sole, or margarine butter.

Under V. (a volume which we hope to reach—if the next great war can be staved off—round about 1930) we have, I am glad to say, a long and valuable article on the Virtues of Cads. This article is from various pens. All the introductory part has been written by an expert at party headquarters, and the diagrams have been drawn by a diner-out who has always got on well with Cads and has an exhaustive knowledge of their habits. There is a special division on the financial virtues of Cads by a banker and on the spiritual virtues of Cads by a divine of modernist complexion. But the subject is so large that we have a reference in small capitals at the end of the article to other special articles in the same department, and especially to what may be called the Calendar of Saints among Cads, that is, short biographies of Cads who have excelled in one or other of the virtues.

Among the special articles, that devoted to the Literary Cad is treated in two aspects—one by an opponent of such Cads, the other by an eminent writer who is himself a Cad. Under the same letter "L," we have a biography and bibliography of the Cad's Laureate who—thank Heaven—is still with us.

"C," which will appear in the second volume, due next December, will have under the heading "Candour" an article where the necessary presence of candour in Caddishness is developed in a masterly fashion by a psychological expert, and the fatal effect upon Caddishness of worldly wisdom and subtlety is conclusively proved by an aged novelist. No one can be a Cad (it is there clearly proved) who has not a simple heart. Under the same letter, at the word "Concert" we have "The Cads' Concert"; a full description, with a detailed bibliography of the latest development in Cad literature, which is the publication to the whole world of everything told one in private, and a great deal that has not been told one at all.

Under "I" there will be an equally interesting and lengthy article upon the Iconography of Cads, with a list of their principal portraits and busts, including public statues of London and other great cities; and under "T" a short, but very illuminating, essay upon the Theology of Cads, illustrated by experts from the whole range of apologetics, beginning with the opinions of the Early Fathers on the matter, and ending, at any rate for the moment, with those of Mr. Wells.

A number of details which would hardly occur to the general reader have been picked out with singular accuracy of judgment by my friend, whose industry and zeal I cannot over-praise. For instance, he himself deals, under "S," with the Cad and Spurs—showing why Cads hate Spurs when they do not wear them themselves, and why when they do wear them themselves they wear them too often and in incongruous surroundings.

Similarly we have the Cad and Checks—divided into cheques on a bank and checks which you wear, the latter coming first for alphabetical reasons. This should, perhaps, appear in the article on Cads and Apparel, under "A," but though the article "Apparel" is exhaustive in its way, readers are referred to special departments of this sort for more detailed acquaintance with their subject. Among other points the famous sentence: "In colour he affected the maroon, in pattern a quiet check," is exhaustively discussed by various hands and its disputed authorship finally established.

Under "A," by the way, we also have Cad's Architecture—a very difficult subject—and a more general psychological and medical heading of Animosity in Cads. The colouring of Cads, natural and artificial, we have, after some debate, put forward to the letter "P" under Pigment, because "C" was getting unwieldy. But Cad Catching or the art of hunting and tracking down a Cad will be included in its natural place with many diagrams and a list of the principal drugs, wines and tobaccos used in the trade.

Cad Curing, on the other hand—that is, the art of curing a Cad of his Caddishness—has been rejected from the heading "C" under the very just decision that it is a false category. There is, properly speaking, no curing of a Cad, because Caddishness is not a disease but a condition which we are perfectly open to accept and even to admire if we please. The whole subject has therefore been relegated to "E," where it is dealt with under the rubric "Elimination." It also appears in the first volume briefly by way of cross-reference under Auto-suggestion with formulæ for daily repetition, such as "Whatever else I am, I am a gentleman," or again, "It is all imagination. I didn't really offend them at all." In this department we have valuable exercises described, one of the most original of which is the setting apart of certain streets in London of a particular length (among others, Gower Street and the Cromwell Road) down which the patient is advised to walk at his ordinary gait, repeating the formula, over and over again just after he has paid a call at some house where he found himself coldly received.

The Encyclopædia can be bought at a reduction of 20 per cent. by those who pay for the whole twelve volumes in advance. My friend, who has already learned the elements of finance (he got his fortune a full six years ago), has calculated that at the present rate of 7 per cent. which any fool can obtain upon good security to-day, he is up about 13s. 2d. a copy on each subscriber who falls into the trap. He is preparing a cheaper edition to appear immediately after the lists of the first expensive edition are closed. This cheaper edition will consist of the unsold sheets of the first, cut down and put into new cases. I forgot to add that there are a certain number of coloured plates in each volume and a very thorough and exhaustive index, on the new American system, known technically as "The Labyrinth." There is also a number of very handsome maps showing the geographical distribution of Cads and elaborate curves, giving their vital statistics, growth and decay. Every set has attached to it a general "All In" policy of insurance with two new clauses specially drawn up, one for the use of Cads threatened by the various dangers peculiar to their rank, and the other for Non-Cads, ensuring them against the various dangers peculiar to the Cad's approach and neighbourhood. All this insurance is free.

ON THE MELTING OF THE ICE

I wish I had been there when the ice melted; in the days when the great river valleys were formed, when the rich meadows were laid down from the mud of the flooded rivers, and when the gravels were rolled along, forming beaches one below the other as the waters subsided, when Northern Europe was carved.

Men were there and saw it. Some say it was so little a while ago that the great monarchies of the hot places, Egypt and Assyria, were in their splendour, and there is something to be said for that saying.

It was an Englishman, spontaneous, individual, but at the same time exact, who started that hare. And the hare may be more than a phantasm. When you read the arguments it looks as though he were right. And if he were right, what an explanation of history!... The Ice Melting but 5 or 6,000 years ago.

Then indeed could we explain how it is that the North was unheard of during all these early centuries, and how it was that an increasing field increasingly breeding men, expanded towards the North, and how it is that you have no records of the North before the first movements of tribes 3,000 years ago, and their greater movement 2,000 years ago, and then at last the very late story of the brief Scandinavian adventure with its marvellous epics. And it would explain also the very small numbers of the North and the way in which the North got its language so largely from the South—for what we call the "Teutonic languages" to-day (of which we have no appreciable record till about Charlemagne's time), turn out to be for half their matter at least (and research will increase the proportion) built up of words from the Mediterranean. [Read Wiener, his revolutionary book and the collapse of the "Early Gothic" fraud.]

But apart from what it would explain in history, what a vision it must have been whenever it took place! For the melting of the ice was very rapid. The geologists do not always use their eyes. Look at those great scoops in the chalk hills shorn out by the water as it swung from left to right through the valleys, and see those enormous floods racing down.

See how those huge stones were rolled along which form the gravels of the higher levels, and ask yourselves in what a current they drove! Or wonder at the great sawings through the rock which unite and drain the old lakes of the Pyrenees! That was a sight to see! It is just possible that some one recorded it. Some traveller thrust up northward by exile or by avarice may have come with his slaves and his retinue to the edges of the enormous thing. He may have seen the Rhone tumbling like a sea released through the gap of the Jura. Or he may have seen the white seething at the mouths of the river which laid down the Camargue.

We see no such things nowadays.

Imagine yourself in a galley bowling westward under the Levanter compelled to go further north than you had wished: the wind dropping. Then your hanging about all night off the coast of what is now the Stes. Maries, and then at morning hearing with fright, but with wonder, on your starboard beam to the North, the enormous noise of waters, and seeing the flecks of foam go by you, and catching on the horizon a sort of low tumble or cataract or flood reaching the sea over twenty miles of beach and carrying with it half a county of stones from the hills. There the stones are to this day—a vast plain of sterile pebbles from a fist to a pea. The ancients said that Hercules once passed that way.

Or think what it must have been to stand on the Ventoux and see the melting of the ice from Auvergne. Or to stand driven upward on to the hills of the Artois, and to see the waters rising in the Dover strait below.

For the thing went very quickly, make no doubt of that.

There is a superstition for the moment in favour of slow, very slow, changes in the affairs of this earth. I think that superstition has arisen from a muddle-headed hope that slow work can exclude a Creator and Will. At any rate there is no proof for it. Some of the processes have been very slow (they are exceedingly slow to-day), but some jerks have been rapid enough: revolutionary: catastrophic: and the last melting of the ice was of these.

And what do you suppose happened in the splendid valleys of Norway? To-day they are drowned. What recession of the ice filled them more full? How did man come to occupy the land released? During what intermission of time, during what generations (few and creative) did the tall fair race, for a moment wanderers, build their little simple structure of a religion which we know so little (because what we have of it is wholly intermixed with the Roman) and of a language which we know still less (for that also is mixed with the South), but at any rate of a special culture common to but a few thousands of men. How came these Scandinavians to copy Roman ships? It all came after the melting of the ice.

Then I ask myself what men saw, and what they felt as they saw, the waterfalls. For those marked all Europe also. Glaciers we know to-day. We have but to imagine them expanded, and the landscape is the same. Stand on the Maladetta and conceive the field of ice holding not only the shoulder of the mountain but all the valley below and out to the plain of France, and you only have the replica of what a man may see from Mont Blanc. Or stand on an Alpine peak and imagine the sheets of ice and snow below you, spread, covering every rock for as far as the eye can reach, and you only have a repetition of what men still see in Greenland. But we have no modern parallel (save in perhaps half a dozen places on the whole earth) by which to reconstruct the enormity of the waterfalls of those days.

For there were not only these swirling waters carving out the great valleys, there was the thundering of water down over the ledges, thousand upon thousand. Perhaps they helped to scoop out the smaller lakes more than did the ice before them. There must have been some such sight above Grenoble when the great lake which burst seven hundred years ago was forming. For in the beginning that lake basin in which Bourg d'Oisans now stands must have been a mass of ice, and then as the ice melted and as the glacier above it melted all the way up to La Grave, up to the very shoulders of the Pelvoux, what mighty armies of water must have roared down to the trench of the Isere! And wherever there is to-day a gorge (or, at least, in the most of these cuttings) you must have had the same sight. Their little dwindling descendants now and then show a trickle of water for our amusement and we are still astonished. But the grandfathers of these were giants!

They say also that the sea rose. It may have done so. Perhaps it must have done so. And if it did so what a sight must that also not have been: the cutting of the straits.

I have read of but one part of the world in which a tradition remains of such a change, and in that case it may have been an earthquake rather than a rising of the waters: I mean the Straits of Messina. Of the water flooding in here there is a legend; but there is none remaining of the cutting of the chalk between Kent and the Artois; or of the flooding, if it were flooded, of the channel between the Pillars of Hercules; or of the slower lap which gradually just covered the entrances of the Baltic—a fresh-water lake.

And by the way, what made that most amazing issue whereby the Black Sea feeds the Eastern Mediterranean with a continuous stream? I have read so many guesses, and they have not satisfied me. It is so long, so narrow, so artificial, and double at that. Very changed would the history of the world have been—of the modern world—if Nature had played some freak of the same sort to join the central Atlantic and the central Pacific Seas, or if the low sand between the Red Sea and the Mediterranean had not run dry, or if by some shock the Mediterranean had poured into the Jordan valley.

There is much else in the melting of the ice. Was it then that Northern Africa dried up? Was it then that the old watercourses which are now desert and in which you can still find proof of the habitations of men, and the stranded beasts and fishes of old rivers, were in full spate?

Who lived there? What did they in the story of mankind? And did Egypt when it was already able to build and to carve men out of stone, look out from the head of the Delta upon a shallow sea?

I think the greater part of the story of the world's landscape has been lost to us for ever.

ON THE HATRED OF NUMBERS

I knew a man once who was the head of his college and very famous as a scholar; because, although he had no learning, he was very kind and witty. But this man had one thing upon which he never jested, and that was his hatred (which he pretended to be a contempt) of numbers.

He would say, not as a curiosity, still less as an apology, that he was quite incapable of "doing sums"; and as I met him in early youth the example has influenced the whole of my life. I have known all my life what I think many people do not know, or at least not many people of those engaged in exposition, that a large part of educated people feel thus about numbers. They neglect them, or hate them, or despise them, and in any case cannot and will not deal with them.

Now when one learns a thing like that early in life, when one early discovers that a thing apparently ridiculous is quite common, the mind sets to work at once to try and find out an explanation. For a very long time I could pretend to none, but I think I am at last beginning to see my way in the matter and to grasp why it is that so many people avoid the prime measure of reality.

On the face of it one would say that the thing was impossible, for one can do nothing without numbers. The human life is distinguished from the bestial chiefly by the use and knowledge of numbers. Which reminds me that I once went to see in Berlin a horse of which it was said by its owner that it could count up to ten. This was before the war. I do not know what may have happened since. It was all nonsense; the horse could not count up to ten. What it could do was to move its foot round, tapping it along a row of large numbers, and when it got to the number which the owner wanted it to indicate he spoke to the horse and the horse stopped moving. But to return from Berlin.

Everything done by a human being all day long, even sleeping, is based upon numbers: all his observation and all his action. To be the enemy of numbers is like being the enemy of the air one breathes or of the necessity of human speech. Why, then, is it that this enmity arises, or at any rate has arisen to-day, rather late perhaps in modern history, and especially here in England?

I think it is due to the convergence of a great number of tendencies.

In the first place, numbers always involve some act of thought, just as progress always involves some action of the body. And people fight shy of numbers just as they tend to fight shy of exertion. If you have four people to dinner, and you ask three more, that makes seven. It is quite a little sum, and may be compared to the exertion of crossing a room. Still, very often one does not like even to cross the room, but prefers sitting in one's chair to getting up to take a book.

If you are rich enough to be overdrawn at the bank, and then lucky enough to get a sum of money larger than your overdraft, and then honest enough to pay it in, it is your duty to make a little calculation on the back of the counterfoil, turning a minus into a plus, and you have to carry pence into shillings and shillings into pounds. It is quite a little exertion, like going up a flight of stairs.... I fancy that more than half the people who have bank accounts shirk that duty. Yet it is a plain duty, for if you do not know your balance at the bank you may inadvertently smash a stumer, si j'ose m'exprimer ainsi.

There is another cause for this fear of numbers, and that is their absolute quality. They have no penumbra. You cannot play the fool with words when they refer to numbers as you can in matters where measure is not exact. You cannot combine a part of reality with a part of illusion, which is the very essence of æsthetic enjoyment. Numbers are thus heartless, and the heart loves to ignore them. If your country is losing population but gaining trade you may boycott the population statistics and dwell lovingly upon the trade statistics. But it is more comfortable still to indulge in a vague vision of your country thoroughly prosperous all round and happy. You see this cause of the hatred of numbers coming out very strongly in the case of people who are losing money. Either they stop keeping accounts or they falsify the accounts by hiding sheer loss under some fancy name, such as Goodwill, or Office Furniture, or "Estimated Value." That is an extreme case, but I am sure that in all cases a part of the dislike of numbers comes from this absolute, bullying quality they have.

Nor is it wholly an unreasonable attitude, for the functions of the mind not only include appreciations and creative acts which escape rigid measure, but indeed those acts are the most important.

For instance, the ratio one to the square root of two is the most perfect proportion for the dividing of a window, as with a mullion; for it represents to the eye, and through the eye to the soul, that great principle of the Mean which governs harmony throughout the world. It was a proportion which they loved in the true Middle Ages, and I will show it to you combined with the simple proportions of one to two, one to three, etc., in many and many a window of the thirteenth and early fourteenth centuries, in the time when men were still simple. Nevertheless, an artist may quite justly say that in a particular case this rigid rule would bind him too much. Something in the way the light falls, something in the thickness of the walls, or even in the outlook from the window, makes it fail. It is not to the eye what it is to the measurement upon the plan, and so the artist is perfectly right to say that he will here not be bound by an exact framework of number. It only needs a little exaggeration of such an experience or a little repetition of it to make a weak mind abjure measure in art altogether. And there must have been a lot of that abjuration lately to judge by the funny things one sees.

Numbers also disappoint and annoy in another fashion, which is that men read into them more than they say and then blame the numbers for misleading them.

I had a good deal of experience of that during the last two years of the war. People had got fidgety under the strain, and they did not want to watch the rate of progress made in wearing down the besieged Boche. Sometimes they would angrily deny those numbers altogether. So a man getting into a train for Edinburgh and foolishly expecting it would take him three hours would after, say, the fifth hour get very much annoyed with a companion who should be perpetually pulling out a map and a watch and telling him exactly how far they had come. I remember that this was particularly the case with the rate of German casualty.

There was nothing very mysterious about this; there was a certain known margin of error, and therefore a certain known maximum and minimum. For instance, it could be calculated from all sorts of sources which confirmed each other—prisoners' reports, published lists, rolls of honour, the rate of retirement of divisions, the analogy of known losses upon our side, and so on. But there came a time after which people were impatient and preferred to believe the whole thing to be fantastic guesswork, because they were in a hurry, and at the same time half despairing. There were hundreds and perhaps thousands of expert soldiers up and down Europe engaged in arriving at these numbers, their conclusions were centralised in the various staffs; and it was surprising to see by how little the various estimates differed. I remember once at Chantilly comparing a set of figures arrived at by one of the national staffs with another set of figures based upon different national methods, and remarking that there was not five per cent difference between them. Yet the ordinary member of the public had by that time become completely suspicious of all figures.

The German casualties on the Somme are a good example. We do not know them to a single unit, and shall never so know them. But we know them within a certain margin of error, and we knew them shortly after the cessation of the battle within a rather larger margin of error. But the ordinary member of the public at home was not in a mood for them, and would not follow them. I got shoals of insulting letters about them from honest people who were disappointed of a miracle. Yet these numbers were of supreme importance. For it was the usury of the Somme, coming after that of Verdun, which began the process of decline upon the enemy's side, politically and morally even more than militarily. The plain man could only see that the Somme had not succeeded in breaking the German line; his expectation was disappointed; he thought all this talk of numbers beside the mark, and his annoyance with it took the natural though very illogical form of belabouring the poor dumb figures that had done him no harm.

I remember very well how, after I had published the approximate figure of enemy losses of 1916 in "Land and Water" (supplied of course from Staff figures), the Harmsworth Press fully persuaded the mass of Englishmen that the German recruitment was inexhaustible. The figures showed a loss of about one-sixth of the total enemy recruiting power. The general reader could not be bothered with anything so precise. First he thought I had said the enemy were all gone, then he thought that the enemy never could be worn down. He disliked numbers, did the general reader, and every demagogue will do well to play upon that dislike of numbers. It is one of the main ways of deceiving the silly populace.

After all these more or less disreputable reasons for the dislike of numbers one comes to a series of much better reasons, and first among these undoubtedly is the truth expressed in the epigram, "Lies, Damned Lies, and Statistics." You can prove anything almost by Statistics, and therefore if one lives in a time when statistics are a plague (because there is such facility for gathering them under our modern system of arbitrary, all-powerful and highly-centralised government) one comes to suspect their use and even to detest it. Now that suspicion and that detestation are well founded.

The reason they are well founded is this.

Judgment, the most valuable of all the rational qualities, is essentially an integration of an almost infinite number of differentials. The mind is seized with a very large number, an almost infinite number (or, as mathematicians would say, an indefinitely large number) of impressions which it combines, and on the combined effect of which it bases certitude. I have no doubt of an oak tree when I see it, although I do not look at each leaf nor measure the exact outline even of one leaf to note within what margin of error it conforms to the type or form of an oak-leaf. I recognise a voice or a face by integrating a vast number of small differentials, and no amount of mathematical or mechanical argument drawn from impressions far less numerous and not combined by a human mind at all would convince me of error. That is why we say that a good portrait is always better than a photograph, and that is why we often say of a photograph that it is not like the original at all. A photograph is only the record of one selected, very limited set of impressions, highly restricted in number and in time, which cannot compare in value with the general conclusion of an observer using all the human faculties over a considerable time, and endowed with the organic power of unification.

In the same way a piece of statistics, however accurate, concerns only one of an infinite number of factors. You get nearer the truth as you combine one set of statistics with a second, a third, a fourth; but though you were to have a thousand sets they would not outweigh your general judgment based on observation.

For instance, a man knows perfectly well what he means by a wet day. Your statistician may come along with his figures of rainfall and may prove by them that a very fine day was a wet one. He says, "Half an inch of rain fell in twenty-four hours." But if the half-inch of rain all fell in one hour just before the dawn of a hot and cloudless summer's day he is wrong and you are right. To give even a rough impression through mere statistics of what common sense calls "a wet day" you would have to compare many sets of figures. There would be first of all the inches of rainfall, then the number of hours during which perceptible rain was falling, then the number of hours during which the sky was overcast, then the rate of evaporation, then figures showing what proportion of rainfall came in the waking and in the sleeping hours, then a table showing how far the rain was intermittent, for a day during which you have rainfall in the first half and none in the second is not at all the same thing as a day in which rain falls every half-hour. And even when you had all those statistics combined, no sane man would accept them against his own general impression.

There is a parallel here with the very legitimate suspicion people are beginning to feel toward what is called "scientific" argument in social and domestic matters. If a man has worked hard all the morning in the open air and is very hungry he looks forward to a beefsteak and a pint of beer at luncheon, and if some science fellow comes along with a tabloid and a little water out of a tank it is no good telling the man that such a meal will be "scientifically the equivalent" of what he was expecting. He knows very well that the word "equivalent" here is a lie; and it is hard lines that the noble title of Science should have been degraded as it has been in our generation by nonsense of this sort. They are still at it, but I do not think it will last long, for it is provoking anger. There are people who come and tell country folk that the rooms in which they sleep must have a certain "cubical capacity," so that a great healthy man as strong as an ox and sleeping as no townsman can sleep is "scientifically" proved to be in a very parlous way when he lives as his English fathers have lived before him for a thousand years. And "I with these mine eyes have seen" an inspector insisting that the window-space of a room should be not less than one-tenth or one-quarter or whatever it was of the floor-space, without noting that the window in one case looked on to a blank wall, and in another on to the infinite spaces of the sea.

The use of statistics in argument is essentially deduction from insufficient premises, and though the mass of men who are getting more and more exasperated with the results of such argument are not yet conscious of the flaw in their oppressors' reasoning, they only know instinctively that it is bad reasoning—and they are right.

The whole argument against the abuse of statistics is summed up in the story of the man who explained what an average was. "If you were struck dead by lightning at my side and I remained safe and sound, we should both be on the average half dead."

But there is a deeper final cause for the suspicion of numbers on which one must touch very carefully, because though it has led to the wildest extravagance in philosophy, and has weakened the use of the human reason in modern times, it none the less has a basis of truth.

Numbers, absolute though they be, and the expression of the human mind's divine capacity for measure, escape us in their ultimate use. The science of numbers, when you have pursued it far enough, lands you where every human analysis lands you—in a contradiction or a mystery. On this account it is that men have been tempted of late to a monstrous denial of mathematical truth, and that as a part of their general revolt against reason. But it is true that you approach regions beyond which what had hitherto been the necessary laws of number cease to stand. You have it wherever there is a sudden passage from an indefinitely increasing number to an indefinitely small one; a sudden passage through what we call "the infinite" to "Zero." And you get it in the "limit" of any mathematical process.

For instance, as you stretch out an ellipse it ought to get more and more like a parabola, at any rate at the business end, if I may so express myself; and it ought gradually at the end of the process to merge into a parabola. Then, as you go on tilting your plane, you ought logically to be able to follow the process of the parabola turning into an hyperbola. Well, the thing does not happen that way. The ellipse remains an ellipse though its foci get farther and farther apart. It remains an ellipse right up to the critical moment, when the distant focus vanishes into infinity, and, then, suddenly, the curve becomes a parabola, and then in a flash, it turns inside out, splits into two, and is an hyperbola. And no one will ever be able to tell you what happened out in the infinities, where the transmogrification took place.

There is a lot more.... Every operation of subtraction, or of the addition of opposite signs, is a mystery; for the conception of the negative in mathematics is a mystery. As for imaginaries, and the dear old root of minus one, you may call it a convention if you like, but it cannot be altogether a convention since it is a necessary basis for arriving at a truth; nor is it a lie, though it certainly dresses up like one. Its name is iota and I loved it long ago. One might quote of this formidable being what I think St. Augustine said of some Bible-story: