Complete Works of Lewis Carroll

by Lewis Carroll

  Oct. 31st.—This morning, thinking over the problem of finding two squares whose sum is a square, I chanced on a theorem (which seems true, though I cannot prove it), that if x² + y² be even, its half is the sum of two squares. A kindred theorem, that 2(x² + y²) is always the sum of two squares, also seems true and unprovable.

  Nov. 5th.—I have now proved the above two theorems. Another pretty deduction from the theory of square numbers is, that any number whose square is the sum of two squares, is itself the sum of two squares.

  I have already mentioned Mr. Dodgson's habit of thinking out problems at night. Often new ideas would occur to him during hours of sleeplessness, and he had long wanted to hear of or invent some easy method of taking notes in the dark. At first he tried writing within oblongs cut out of cardboard, but the result was apt to be illegible. In 1891 he conceived the device of having a series of squares cut out in card, and inventing an alphabet, of which each letter was made of lines, which could be written along the edges of the squares, and dots, which could be marked at the corners. The thing worked well, and he named it the "Typhlograph," but, at the suggestion of one of his brother-students, this was subsequently changed into "Nyctograph."

  He spent the Long Vacation at Eastbourne, attending service every Sunday at Christ Church, according to his usual rule.

  Sept. 6, 1891.—At the evening service at Christ Church a curious thing happened, suggestive of telepathy. Before giving out the second hymn the curate read out some notices. Meanwhile I took my hymn-book, and said to myself (I have no idea why), "It will be hymn 416," and I turned to it. It was not one I recognised as having ever heard; and, on looking at it, I said, "It is very prosaic; it is a very unlikely one"—and it was really startling, the next minute, to hear the curate announce "Hymn 416."

  DR. LIDDELL.

  From a photograph

  by Hill & Saunders..

  In October it became generally known that Dean Liddell was going to resign at Christmas. This was a great blow to Mr. Dodgson, but little mitigated by the fact that the very man whom he himself would have chosen, Dr. Paget, was appointed to fill the vacant place. The old Dean was very popular in College; even the undergraduates, with whom he was seldom brought into contact, felt the magic of his commanding personality and the charm of his gracious, old-world manner. He was a man whom, once seen, it was almost impossible to forget.

  Shortly before the resignation of Dr. Liddell, the Duchess of Albany spent a few days at the Deanery. Mr. Dodgson was asked to meet her Royal Highness at luncheon, but was unable to go. Princess Alice and the little Duke of Albany, however, paid him a visit, and were initiated in the art of making paper pistols. He promised to send the Princess a copy of a book called "The Fairies," and the children, having spent a happy half-hour in his rooms, returned to the Deanery. This was one of the days which he "marked with a white stone." He sent a copy of "The Nursery 'Alice'" to the little Princess Alice, and received a note of thanks from her, and also a letter from her mother, in which she said that the book had taught the Princess to like reading, and to do it out of lesson-time. To the Duke he gave a copy of a book entitled "The Merry Elves." In his little note of thanks for this gift, the boy said, "Alice and I want you to love us both." Mr. Dodgson sent Princess Alice a puzzle, promising that if she found it out, he would give her a "golden chair from Wonderland."

  THE DEAN OF CHRIST CHURCH.

  From a photograph

  by Hill & Saunders..

  At the close of the year he wrote me a long letter, which I think worthy of reproducing here, for he spent a long time over it, and it contains excellent examples of his clear way of putting things.

  To S.D. Collingwood.

  Ch. Ch., Oxford, Dec. 29, 1891.

  My Dear Stuart,—(Rather a large note—sheet, isn't it? But they do differ in size, you know.) I fancy this book of science (which I have had a good while, without making any use of it), may prove of some use to you, with your boys. [I was a schoolmaster at that time.] Also this cycling-book (or whatever it is to be called) may be useful in putting down engagements, &c., besides telling you a lot about cycles. There was no use in sending it to me; my cycling days are over.

  You ask me if your last piece of "Meritt" printing is dark enough. I think not. I should say the rollers want fresh inking. As to the matter of your specimen—[it was a poor little essay on killing animals for the purpose of scientific recreations, e.g., collecting butterflies]—I think you cannot spend your time better than in trying to set down clearly, in that essay-form, your ideas on any subject that chances to interest you; and specially any theological subject that strikes you in the course of your reading for Holy Orders.

  It will be most excellent practice for you, against the time when you try to compose sermons, to try thus to realise exactly what it is you mean, and to express it clearly, and (a much harder matter) to get into proper shape the reasons of your opinions, and to see whether they do, or do not, tend to prove the conclusions you come to. You have never studied technical Logic, at all, I fancy. [I had, but I freely admit that the essay in question proved that I had not then learnt to apply my principles to practice.] It would have been a great help: but still it is not indispensable: after all, it is only the putting into rules of the way in which every mind proceeds, when it draws valid conclusions; and, by practice in careful thinking, you may get to know "fallacies" when you meet with them, without knowing the formal rules.

  At present, when you try to give reasons, you are in considerable danger of propounding fallacies. Instances occur in this little essay of yours; and I hope it won't offend your amour propre very much, if an old uncle, who has studied Logic for forty years, makes a few remarks on it.

  I am not going to enter at all on the subject-matter itself, or to say whether I agree, or not, with your conclusions : but merely to examine, from a logic-lecturer's point of view, your premisses as relating to them.

  (1) "As the lower animals do not appear to have personality or individual existence, I cannot see that any particular one's life can be very important," &c. The word "personality" is very vague: I don't know what you mean by it. If you were to ask yourself, "What test should I use in distinguishing what has, from what has not, personality?" you might perhaps be able to express your meaning more clearly. The phrase "individual existence" is clear enough, and is in direct logical contradiction to the phrase "particular one." To say, of anything, that it has not "individual existence," and yet that it is a "particular one," involves the logical fallacy called a "contradiction in terms."

  (2) "In both cases" (animal and plant) "death is only the conversion of matter from one form to another." The word "form" is very vague—I fancy you use it in a sort of chemical sense (like saying "sugar is starch in another form," where the change in nature is generally believed to be a rearrangement of the very same atoms). If you mean to assert that the difference between a live animal and a dead animal, i.e., between animate and sensitive matter, and the same matter when it becomes inanimate and insensitive, is a mere rearrangement of the same atoms, your premiss is intelligible. (It is a bolder one than any biologists have yet advanced. The most sceptical of them admits, I believe, that "vitality" is a thing per se. However, that is beside my present scope.) But this premiss is advanced to prove that it is of no "consequence" to kill an animal. But, granting that the conversion of sensitive into insensitive matter (and of course vice versa) is a mere change of "form," and therefore of no "consequence"; granting this, we cannot escape the including under this rule all similar cases. If the power of feeling pain, and the absence of that power, are only a difference of "form," the conclusion is inevitable that the feeling pain, and the not feeling it, are also only a difference in form, i.e., to convert matter, which is not feeling pain, into matter feeling pain, is only to change its "form," and, if the process of "changing form" is of no "consequence" in the case of sensitive and insensitive matter, we must admit that it is also of no "consequence" in the case of pain-feelin
g and not pain-feeling matter. This conclusion, I imagine, you neither intended nor foresaw. The premiss, which you use, involves the fallacy called "proving too much."

  The best advice that could be given to you, when you begin to compose sermons, would be what an old friend once gave to a young man who was going out to be an Indian judge (in India, it seems, the judge decides things, without a jury, like our County Court judges). "Give your decisions boldly and clearly; they will probably be right. But do not give your reasons: they will probably be wrong" If your lot in life is to be in a country parish, it will perhaps not matter much whether the reasons given in your sermons do or do not prove your conclusions. But even there you might meet, and in a town congregation you would be sure to meet, clever sceptics, who know well how to argue, who will detect your fallacies and point them out to those who are not yet troubled with doubts, and thus undermine all their confidence in your teaching.

  At Eastbourne, last summer, I heard a preacher advance the astounding argument, "We believe that the Bible is true, because our holy Mother, the Church, tells us it is." I pity that unfortunate clergyman if ever he is bold enough to enter any Young Men's Debating Club where there is some clear-headed sceptic who has heard, or heard of, that sermon. I can fancy how the young man would rub his hands, in delight, and would say to himself, "Just see me get him into a corner, and convict him of arguing in a circle!"

  The bad logic that occurs in many and many a well-meant sermon, is a real danger to modern Christianity. When detected, it may seriously injure many believers, and fill them with miserable doubts. So my advice to you, as a young theological student, is "Sift your reasons well , and, before you offer them to others, make sure that they prove your conclusions."

  I hope you won't give this letter of mine (which it has cost me some time and thought to write) just a single reading and then burn it; but that you will lay it aside. Perhaps, even years hence, it may be of some use to you to read it again.

  Believe me always

  Your affectionate Uncle,

  C. L. Dodgson.

  CHAPTER VIII

  (1892—1896)

  Mr. Dodgson resigns the Curatorship—Bazaars—He lectures to children—A mechanical "Humpty Dumpty"—A logical controversy—Albert Chevalier—"Sylvie and Bruno Concluded"—"Pillow Problems"—Mr. Dodgson's generosity—College services—Religious difficulties—A village sermon—Plans for the future—Reverence—"Symbolic Logic."

  At Christ Church, as at other Colleges, the Common Room is an important feature. Open from eight in the morning until ten at night, it takes the place of a club, where the "dons" may see the newspapers, talk, write letters, or enjoy a cup of tea. After dinner, members of High Table, with their guests if any are present, usually adjourn to the Common Room for wine and dessert, while there is a smoking-room hard by for those who do not despise the harmless but unnecessary weed, and below are cellars, with a goodly store of choice old wines.

  The Curator's duties were therefore sufficiently onerous. They were doubly so in Mr. Dodgson's case, for his love of minute accuracy greatly increased the amount of work he had to do. It was his office to select and purchase wines, to keep accounts, to adjust selling price to cost price, to see that the two Common Room servants performed their duties, and generally to look after the comfort and convenience of the members.

  "Having heard," he wrote near the end of the year 1892, "that Strong was willing to be elected (as Curator), and Common Room willing to elect him, I most gladly resigned. The sense of relief at being free from the burdensome office, which has cost me a large amount of time and trouble, is very delightful. I was made Curator, December 8, 1882, so that I have held the office more than nine years."

  The literary results of his Curatorship were three very interesting little pamphlets, "Twelve Months in a Curatorship, by One who has tried it"; "Three years in a Curatorship, by One whom it has tried"; and "Curiosissima Curatoria, by 'Rude Donatus,'" all printed for private circulation, and couched in the same serio-comic vein. As a logician he naturally liked to see his thoughts in print, for, just as the mathematical mind craves for a black-board and a piece of chalk, so the logical mind must have its paper and printing-press wherewith to set forth its deductions effectively.

  A few extracts must suffice to show the style of these pamphlets, and the opportunity offered for the display of humour.

  In the arrangement of the prices at which wines were to be sold to members of Common Room, he found a fine scope for the exercise of his mathematical talents and his sense of proportion. In one of the pamphlets he takes old Port and Chablis as illustrations.

  The original cost of each is about 3s. a bottle; but the present value of the old Port is about 11s. a bottle. Let us suppose, then, that we have to sell to Common Room one bottle of old Port and three of Chablis, the original cost of the whole being 12s., and the present value 20s. These are our data. We have now two questions to answer. First, what sum shall we ask for the whole? Secondly, how shall we apportion that sum between the two kinds of wine?

  The sum to be asked for the whole he decides, following precedent, is to be the present market-value of the wine; as to the second question, he goes on to say—

  We have, as so often happens in the lives of distinguished premiers, three courses before us: (1) to charge the present value for each kind of wine; (2) to put on a certain percentage to the original value of each kind; (3) to make a compromise between these two courses.

  Course 1 seems to me perfectly reasonable; but a very plausible objection has been made to it—that it puts a prohibitory price on the valuable wines, and that they would remain unconsumed. This would not, however, involve any loss to our finances; we could obviously realise the enhanced values of the old wines by selling them to outsiders, if the members of Common Room would not buy them. But I do not advocate this course.

  Course 2 would lead to charging 5s. a bottle for Port and Chablis alike. The Port-drinker would be "in clover," while the Chablis-drinker would probably begin getting his wine direct from the merchant instead of from the Common Room cellar, which would be a reductio ad absurdum of the tariff. Yet I have heard this course advocated, repeatedly, as an abstract principle. "You ought to consider the original value only," I have been told. "You ought to regard the Port-drinker as a private individual, who has laid the wine in for himself, and who ought to have all the advantages of its enhanced value. You cannot fairly ask him for more than what you need to refill the bins with Port, plus the percentage thereon needed to meet the contingent expenses." I have listened to such arguments, but have never been convinced that the course is just. It seems to me that the 8s. additional value which the bottle of Port has acquired, is the property of Common Room, and that Common Room has the power to give it to whom it chooses; and it does not seem to me fair to give it all to the Port-drinker. What merit is there in preferring Port to Chablis, that could justify our selling the Port-drinker his wine at less than half what he would have to give outside, and charging the Chablis-drinker five-thirds of what he would have to give outside? At all events, I, as a Port-drinker, do not wish to absorb the whole advantage, and would gladly share it with the Chablis-drinker. The course I recommend is

  Course 3, which is a compromise between 1 and 2, its essential principle being to sell the new wines above their value, in order to be able to sell the old below their value. And it is clearly desirable, as far as possible, to make the reductions where they will be felt, and the additions where they will not be felt. Moreover it seems to me that reduction is most felt where it goes down to the next round sum, and an addition in the reverse case, i.e., when it starts from a round sum. Thus, if we were to take 2d. off a 5s. 8d. wine, and add it to a 4s. 4d.—thus selling them at 5s. 6d. and 4s. 6d. the reduction would be welcomed, and the addition unnoticed; and the change would be a popular one.

  The next extract shows with what light-hearted frivolity he could approach this tremendous subject of wine:—

  The consumpt
ion of Madeira (B) has been during the past year, zero. After careful calculation I estimate that, if this rate of consumption be steadily maintained, our present stock will last us an infinite number of years. And although there may be something monotonous and dreary in the prospect of such vast cycles spent in drinking second-class Madeira, we may yet cheer ourselves with the thought of how economically it can be done.

  To assist the Curator in the discharge of his duties, there was a Wine Committee, and for its guidance a series of rules was drawn up. The first runs as follows: "There shall be a Wine Committee, consisting of five persons, including the Curator, whose duty it shall be to assist the Curator in the management of the cellar." "Hence," wrote Mr. Dodgson, "logically it is the bounden duty of the Curator 'to assist himself.' I decline to say whether this clause has ever brightened existence for me—or whether, in the shades of evening, I may ever have been observed leaving the Common Room cellars with a small but suspicious-looking bundle, and murmuring, 'Assist thyself, assist thyself!'"

  Every Christmas at Christ Church the children of the College servants have a party in the Hall. This year he was asked to entertain them, and gladly consented to do so. He hired a magic lantern and a large number of slides, and with their help told the children the three following stories: (1) "The Epiphany"; (2) "The Children Lost in the Bush"; (3) "Bruno's Picnic."