The two most extravagant and improbable books in the world are Euclid and the Arabian Nights; but of the two by far the more improbable and extravagant is Euclid. Nay, it is flattery to say that Euclid is improbable; it is impossible.
For, consider; it is highly improbable, no doubt, that by rubbing a lamp you can summon a spirit, or jinn, who will build you a palace of incredible splendour in a night. This is most unlikely, I confess, but I cannot say that it is impossible, simply because neither I nor any one else can pretend to know all the laws of the universe. We are entitled to say that we have never come across the lamp, the genie or the palace; and that we have no intention of believing in the story till it be supported by strong evidence. We can say that, but we are really not entitled to say any more. We mustn’t even say ‘nonsense!’ or ‘rubbish!’ that is if we are cautious people. For — how long ago is it; twenty years, thirty years? — the state of a gentleman’s mind was once in some doubt. His relations were afraid that he was going mad, so they took out what Mr. Sampson Brass called a pretty little commission de lunatico. And a mental expert who gave evidence said that in his opinion Mr. X was mad, as mad as a hatter. The doctor had had a cosy little chat with Mr. X, and that gentleman had declared his belief in the possibility of dirigible flight. That was quite enough for the doctor. I don’t know whether the poor man was shut up. Possibly he is alive and in a madhouse to this day. He must find it highly amusing to watch the airplanes and airships soaring high above the asylum walls. Then the X-rays. I remember telling a friend about them in the ‘nineties; how some queer light had been found which would pierce through the solid walls of flesh and show, as in a photograph, every bone in your body. My friend laughed. He said that he did not believe everything that he saw in the papers. And then, you know, ‘wireless’: what would people have said to that? And wireless telephony: before long, they tell me, words uttered in London will be plainly audible in New York. Think of it, the human voice heard clearly across the Atlantic Ocean, as clearly and as easily as if the two speakers were talking to one another across the duck-pond in the farm-yard. It was utterly impossible according to all our notions and all our experience; but it has happened or soon will happen. So it doesn’t do to say that the highly improbable thing is therefore the impossible thing; Aladdin’s Lamp and the Genie and the Palace may yet come into experience.
Yet, as I say, I am willing to allow that the story of Aladdin and the Wonderful Lamp is, on the face of it, highly extravagant and improbable. But Euclid cannot be let down so easily as that. I remember little of that author, I am glad to say, but I shall never forget the astounding statements with which he opens his work. A point, he begins, with the calmness of the finished and shameless liar, has neither parts nor magnitude, but only position. A line, he goes on, is length without breadth. And a plane surface, so he declares, has length and breadth but no thickness. On such foundations does Euclid raise his system of Geometry. Let us consider a little. Euclid is not a theologian. He is not a metaphysician. He is not a spiritualist. He is not dealing with the world of mind, soul or spirit. He is occupied with the visible world that we know, the world of time, space, solidity and matter. And he declares that in this material world there is something existing called a point which has no size at all and no parts: a material thing without materiality. So with his line; it has length without breadth. Who has seen such a thing? Who can imagine the possibility of such a thing? And who can conceive a surface without depth? Aladdin is improbable; but Euclid is, in the strictest sense of the word, impossible. His definitions are contradictions. A man once asked me if I couldn’t think of the Euclidean surface as I thought of the surface of a perfectly still pool of water. Certainly I can; but I cannot think of water without depth; and that is the surface which Euclid propounds for our acceptance.
So, you see, geometry, a branch of pure mathematics, the most abstract of the sciences, the science which is supposed to convey necessary truth, which no discoveries can affect, which no experience can render invalid; this branch of science turns out to be founded on a series of absurdities and contradictions in terms. And arithmetic, again, another branch of pure mathematics; lucky is it for our poor little boys and girls as they get through the multiplication table, and advance by painful degrees to vulgar fractions; lucky is it for them that they do not dream of the nightmare country into which these studies inevitably lead. The Snark was a Boojum! There are worse Boojums than the Snark, as witness that notorious affair of the contest between Achilles and the Tortoise. It is well known that Achilles was the swiftest of all men; the champion sprinter, in fact. It is equally well known that the tortoise is one of the slowest of animals. So, oddly enough, their Managements met and arranged that the two should race each other. Naturally, it was a case for handicapping, and to make things simple it was agreed that Achilles ran a hundred times as quickly as the Tortoise, and therefore that Achilles must be scratch, and the animal have a hundred yards’ start. Very good. The race takes place. The swift-footed hero flies like light over the hundred yards which separate him from the Tortoise. But in that little space of time the Tortoise, a hundred times slower, has run a yard, and is still ahead. Achilles passes that yard, but the Tortoise has raced a hundredth of a yard and is still ahead. Then the thousandth part of a yard separates them; but the Tortoise by that much is still ahead — and will be ahead throughout all ages, if there be any truth in the science of arithmetic and in its doctrine of fractions. Solvitur ambulando: a practical experiment solves that puzzle, a philosopher said long ago; but as De Quincey notes, he was a foolish fellow, since the essence of the puzzle lies in the opposition between the known facts of the case and the teaching of science. We know that Achilles would pass the Tortoise in a flash; science tells us that the man must lag behind the reptile for ever.
Now then; to come to the practical application of all this. We have seen that science, in its most abstract mood; in those branches of it which are supposed to deal with necessary and unchanging truth, is founded on rank and preposterous absurdities. With its lines that are all length and no breadth, with its fraction dogmas that lead to the ridiculous; it is clearly nonsense. Very good; then do not let the doctor interfere with your dinner.
For, note the difference between pure science and applied science. A line is always a line in all climates and all ages. Supposing there is such a thing at all, it is the same in Paris as in London, in Pekin as in Cape Town. If two and two make four, they have always made four, and make four as much for Smith as for Robinson. But with applied science the case is very different. Here you enter into a region of infinite doubts, difficulties, differences; differences of body, differences of mind, differences of climate, differences of custom, differences of disposition, differences of inheritance. To put it in a nutshell; I would as soon go to an astrologer as to a doctor, if I wanted an answer to the question: ‘Is beef bad for me?’ It is monstrous indeed that science, shown to be mad in the abstract, should presume to dictate to us in the concrete. Yet it does. Look at the solemn diets that are prescribed. I have known people who live — or think they live, for they are not alive — on nuts, carrots, bread and dates; with a little cheese as a perilous and doubtful indulgence, and with a glass of milk, if they are resolved to be dogs and devils. This diet, which is supposed to be a cure for rheumatism, forbids all wine, beer, spirits, all coffee, chocolate, cocoa, tea, all peas and beans, all meat, fish and eggs. If you wish to tread the narrow way you drink no milk and eat no cheese. I do not know whether it cures rheumatism, I do not know whether a wise man would not prefer to be rheumatic. But the worst of it is that the people who live in this ridiculous way, who follow the Vague Treatment, as it is called, affect airs of superiority. They look down on the people who eat chops and steaks and thank God for them. They watch each other. One of them records how, at afternoon tea, she occasionally takes half a cup to save trouble; and she complains mildly that through the Vague sect the rumour wildly runs: ‘Oh, Mrs. Blank has given up The Diet; she drinks tea!’ Then, there is the Bague diet. In this you eat no meat, of course not; but, furthermore, you must not have anything cooked. You may have peas and beans, but they must be raw; you revel on carrots and turnips, as they come from the field, save that they are finely shredded. Cooking, it appears, blasts the vitamines, it destroys the invaluable potassium salts; cooking is the cause of most of the deadly and awful diseases that waste the world. Can there be any more putrid silliness than this? Here is modern science advising us to go back to the wretched apish savages who were our remote ancestors, who grubbed for roots and climbed for nuts and devoured raw worms because they had not found out the secret of fire. Even supposing these pompous imbeciles are right — there is not the slightest reason to believe that they are right — is it not better to live like a man for fifty years on beefsteaks and vol-au-vents than to mop and mow for a hundred years like a monkey on chopped carrots? And then there is the milder but still abhorrent folly of the physician, the ‘well-known physician’ of the newspaper interview, who tells people that they eat far too much; the sort of man who advises, in print, a small portion of porridge for breakfast, a tomato and a bit of cheese for lunch, and half a sole and one slice of mutton for dinner. This fellow is everywhere; and I need scarcely say that he regards all the alcohols as deadly poison. He represents the almost universal concession to cant. Politicians, who love nothing better than a sound bottle of champagne opened at two o’clock in the morning, tell us that the State will rush down to ruin if we drink a glass of beer after ten p.m. So doctors, who can relish good meat and good drink with any man, tell the world through the newspaper that it ought to live in a manner that would make a riot in a monastery.
But the reductio ad absurdum— I remember that much Euclid — is quite delightful. For the last sixty or seventy years, this great bully, science, a sort of Gradgrind and Bounderby rolled into one, has been bragging and blustering and pretending to know everything and telling its grandmother how to suck eggs, and coming the most tremendous howlers on every possible subject. It has announced with a grin that would make an Earlswood idiot envious that it has been into the dissecting-room and hasn’t found the soul there. It tried a little Scripture History and announced, with a decision that the most dogmatic popes have been unable to command, that there are grave flaws in the story of Abraham, because writing is mentioned, and writing was unknown in the period at which Abraham is supposed to have lived. And this magnificent proclamation was made about a fortnight before certain inscribed tablets were found at Tel-el-Amarna; the characters having been formed 2,000 years at least before Abraham was born. Then a little profane history, for a change. You know about Homer and the Siege of Troy. Science laughed. There never was any Homer, there wasn’t any Troy, there wasn’t any Siege. The whole tale was a sun-myth. It was an account, in allegorical language, of the course of the sun over the heavens, from its rising to its setting. Then came Schliemann. He found Troy standing, what remained of it, in the place in which Homer said it stood. And, moreover, he found that it had been sacked, and that it had been burned, as Homer said it had been burnt. So sun-myths and sun-heroes went out of fashion, and in their place we have culture-gods and culture-heroes and culture-myths, and science is as happy as ever and as pleased as Punch, because it is quite sure that the Holy Grail was a saucepan used for cooking spring cabbage — as sure on this point as it was on the other point; that Achilles was the sun.
Very well, I have no objection. Fools must be fed with folly, and it seems the province of science to give fools their meat in due season. But I say to science: hands off my bill-of-fare! Conclude, if you like, that monkeys and anthropoid apes were the only people who knew how to order dinner. Discover, if you will, that the jackass is the supreme authority on diet, and that there is nothing like thistles. But let science keep its conclusions and discoveries to itself. I am going to have my dinner at the Café Royal.
Last updated Monday, December 22, 2014 at 10:53