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:

You may tell me that by far the greater part of men are not concerned with these ultimate far goals of bewilderment and of despair to which the science of numbers will lead them out of their happy homes. I am not so sure. Nowadays when people are so fond of the word "sub-conscious" (and I have myself worked the animal as hard as was possible on meagre rations) we may drag it in here without extravagance. There is, I think, an instinct in men the least acquainted with mathematics that it is possible to push them too far; and though men begin to tremble long before the limits of human reason are reached—in fact, as a rule, they get the wind up before they reach the Calculi—yet a god tells them in what direction they are going, and warns them that too much curiosity is ill for man.