The author says that his usual practice was to write down the answer first of all, and afterwards the question and its solution. His motive, he says, for publishing these problems was not from any desire to display his powers of mental calculation. Those who knew him will readily believe this, though they will hardly be inclined to accept his own modest estimate of those powers.
Still the book was intended, not for the select few who can scale the mountain heights of advanced mathematics, but for the much larger class of ordinary mathematicians, and they at least will be able to appreciate the gifted author, and to wonder how he could follow so clearly in his head the mental diagrams and intricate calculations involved in some of these "Pillow Problems."
His chief motive in publishing the book was to show how, by a little determination, the mind "can be made to concentrate itself on some intellectual subject (not necessarily mathematics), and thus banish those petty troubles and vexations which most people experience, and which—unless the mind be otherwise occupied—will persist in invading the hours of night." And this remedy, as he shows, serves a higher purpose still. In a paragraph which deserves quoting at length, as it gives us a momentary glimpse of his refined and beautiful character, he says:—
Perhaps I may venture for a moment to use a more serious tone, and to point out that there are mental troubles, much worse than mere worry, for which an absorbing object of thought may serve as a remedy. There are sceptical thoughts, which seem for the moment to uproot the firmest faith: there are blasphemous thoughts, which dart unbidden into the most reverent souls: there are unholy thoughts, which torture with their hateful presence the fancy that would fain be pure. Against all these some real mental work is a most helpful ally. That "unclean spirit" of the parable, who brought back with him seven others more wicked than himself, only did so because he found the chamber "swept and garnished," and its owner sitting with folded hands. Had he found it all alive with the "busy hum" of active work, there would have been scant welcome for him and his seven!
It would have robbed the book of its true character if Lewis Carroll had attempted to improve on the work done in his head, and consequently we have the solutions exactly as he worked them out before setting them down on paper. Of the Problems themselves there is not much to be said here; they are original, and some of them (e.g., No. 52) expressed in a style peculiarly the author's own. The subjects included in their range are Arithmetic, Algebra, Pure Geometry (Plane), Trigonometry, Algebraic Geometry, and Differential Calculus; and there is one Problem to which Mr. Dodgson says he "can proudly point," in "Transcendental Probabilities," which is here given: "A bag contains two counters, as to which nothing is known except that each is either black or white. Ascertain their colour without taking them out of the bag." The answer is, "One is black and the other white." For the solution the reader is referred to the book itself, a study of which will well repay him, apart from the chance he may have of discovering some mistake, and the consequent joy thereat!
A few extracts from the Diary follow, written during the early part of 1894:—
Feb. 1st.—Dies notandus. As Ragg was reading Prayers, and Bayne and I were the only M.A.'s in the stalls, I tried the experiment of going to the lectern and reading the lesson. I did not hesitate much, but feel it too great a strain on the nerves to be tried often. Then I went to the Latin Chapel for Holy Communion. Only Paget (Dean) and Dr. Huntley came: so, for the first time in my recollection, it had to be given up. Then I returned to my rooms, and found in The Standard the very important communication from Gladstone denying the rumour that he has decided upon resigning the Premiership, but admitting that, owing to failing powers, it may come at any moment. It will make a complete change in the position of politics! Then I got, from Cook Wilson, what I have been so long trying for—an accepted transcript of the fallacious argument over which we have had an (apparently) endless fight. I think the end is near, now.
Feb. 4th.—The idea occurred to me that it might be a pleasant variation in Backgammon to throw three dice, and choose any two of the three numbers. The average quality of the throws would be much raised. I reckon that the chance of "6, 6" would be about two and a half what it now is. It would also furnish a means, similar to giving points in billiards, for equalising players: the weaker might use three dice, the other using two. I think of calling it "Thirdie Backgammon."
March 31st.—Have just got printed, as a leaflet, "A Disputed Point in Logic"—the point Professor Wilson and I have been arguing so long. This paper is wholly in his own words, and puts the point very clearly. I think of submitting it to all my logical friends.
"A Disputed Point in Logic" appeared also, I believe, in Mind, July, 1894.
This seems a fitting place in which to speak of a side of Mr. Dodgson's character of which he himself was naturally very reticent—his wonderful generosity. My own experience of him was of a man who was always ready to do one a kindness, even though it put him to great expense and inconvenience; but of course I did not know, during his lifetime, that my experience of him was the same as that of all his other friends. The income from his books and other sources, which might have been spent in a life of luxury and selfishness, he distributed lavishly where he saw it was needed, and in order to do this he always lived in the most simple way. To make others happy was the Golden Rule of his life. On August 31st he wrote, in a letter to a friend, Miss Mary Brown: "And now what am I to tell you about myself? To say I am quite well 'goes without saying' with me. In fact, my life is so strangely free from all trial and trouble that I cannot doubt my own happiness is one of the talents entrusted to me to 'occupy' with, till the Master shall return, by doing something to make other lives happy."
In several instances, where friends in needy circumstances have written to him for loans of money, he has answered them, "I will not lend, but I will give you the £100 you ask for." To help child-friends who wanted to go on the stage, or to take up music as a profession, he has introduced them to leading actors and actresses, paid for them having lessons in singing from the best masters, sent round circulars to his numerous acquaintances begging them to patronise the first concert or recital.
In writing his books he never attempted to win popularity by acceding to the prejudices and frailties of the age—his one object was to make his books useful and helpful and ennobling. Like the great Master, in whose steps he so earnestly strove to follow, he "went about doing good." And one is glad to think that even his memory is being made to serve the same purpose. The "Alice" cots are a worthy sequel to his generous life.
Even Mr. Dodgson, with all his boasted health, was not absolutely proof against disease, for on February 12, 1895, he writes:—
Tenth day of a rather bad attack of influenza of the ague type. Last night the fever rose to a great height, partly caused by a succession of five visitors. One, however, was of my own seeking—Dean Paget, to whom I was thankful to be able to tell all I have had in my mind for a year or more, as to our Chapel services not being as helpful as they could be made. The chief fault is extreme rapidity. I long ago gave up the attempt to say the Confession at that pace; and now I say it, and the Lord's Prayer, close together, and never hear a word of the Absolution. Also many of the Lessons are quite unedifying.
On July 11th he wrote to my brother on the subject of a paper about Eternal Punishment, which was to form the first of a series of essays on Religious Difficulties:—
I am sending you the article on "Eternal Punishment" as it is. There is plenty of matter for consideration, as to which I shall be glad to know your views.
Also if there are other points, connected with religion, where you feel that perplexing difficulties exist, I should be glad to know of them in order to see whether I can see my way to saying anything helpful.
But I had better add that I do not want to deal with any such difficulties, unless they tend to affect life. Speculative difficulties which do not affect conduct, and which come into collision with any of the principles whi
ch I intend to state as axioms, lie outside the scope of my book. These axioms are:—
(1) Human conduct is capable of being right, and of being wrong.
(2) I possess Free-Will, and am able to choose between right and wrong.
(3) I have in some cases chosen wrong.
(4) I am responsible for choosing wrong.
(5) I am responsible to a person.
(6) This person is perfectly good.
I call them axioms, because I have no proofs to offer for them. There will probably be others, but these are all I can think of just now.
The Rev. H. Hopley, Vicar of Westham, has sent me the following interesting account of a sermon Mr. Dodgson preached at his church:—
In the autumn of 1895 the Vicar of Eastbourne was to have preached my Harvest Sermon at Westham, a village five miles away; but something or other intervened, and in the middle of the week I learned he could not come. A mutual friend suggested my asking Mr. Dodgson, who was then in Eastbourne, to help me, and I went with him to his rooms. I was quite a stranger to Mr. Dodgson; but knowing from hearsay how reluctant he usually was to preach, I apologised and explained my position—with Sunday so near at hand. After a moment's hesitation he consented, and in a most genial manner made me feel quite at ease as to the abruptness of my petition. On the morrow he came over to my vicarage, and made friends with my daughters, teaching them some new manner of playing croquet [probably Castle Croquet], and writing out for them puzzles and anagrams that he had composed.
The following letter was forwarded on the Saturday:—
"7, Lushington Road, Eastbourne,
September 26, 1895.
Dear Mr. Hopley,—I think you will excuse the liberty I am taking in asking you to give me some food after the service on Sunday, so that I may have no need to catch the train, but can walk back at leisure. This will save me from the worry of trying to conclude at an exact minute, and you, perhaps, from the trouble of finding short hymns, to save time. It will not, I hope, cause your cook any trouble, as my regular rule here is cold dinner on Sundays. This not from any "Sabbatarian" theory, but from the wish to let our employés have the day wholly at their own disposal.
I beg Miss Hopley's acceptance of the enclosed papers— (puzzles and diagrams.)
Believe me, very truly yours,
C.L. Dodgson."
On Sunday our grand old church was crowded, and, although our villagers are mostly agricultural labourers, yet they breathlessly listened to a sermon forty minutes long, and apparently took in every word of it. It was quite extempore, in very simple words, and illustrated by some delightful and most touching stories of children. I only wish there had been a shorthand-writer there.
In the vestry after service, while he was signing his name in the Preachers' Book, a church officer handed him a bit of paper. "Mr. Dodgson, would you very kindly write your name on that?" "Sir!" drawing himself up sternly—"Sir, I never do that for any one"—and then, more kindly, "You see, if I did it for one, I must do it for all."
An amusing incident in Mr. Dodgson's life is connected with the well-known drama, "Two Little Vagabonds." I give the story as he wrote it in his Diary:—
Nov. 28th.—Matinée at the Princess's of "Two Little Vagabonds," a very sensational melodrama, capitally acted. "Dick" and "Wally" were played by Kate Tyndall and Sydney Fairbrother, whom I guess to be about fifteen and twelve. Both were excellent, and the latter remarkable for the perfect realism of her acting. There was some beautiful religious dialogue between "Wally" and a hospital nurse— most reverently spoken, and reverently received by the audience.
Dec. 17th.—I have given books to Kate Tyndall and Sydney Fairbrother, and have heard from them, and find I was entirely mistaken in taking them for children. Both are married women!
The following is an extract from a letter written in 1896 to one of his sisters, in allusion to a death which had recently occurred in the family:—
It is getting increasingly difficult now to remember which of one's friends remain alive, and which have gone "into the land of the great departed, into the silent land." Also, such news comes less and less as a shock, and more and more one realises that it is an experience each of us has to face before long. That fact is getting less dreamlike to me now, and I sometimes think what a grand thing it will be to be able to say to oneself, "Death is over now; there is not that experience to be faced again."
I am beginning to think that, if the books I am still hoping to write are to be done at all, they must be done now, and that I am meant thus to utilise the splendid health I have had, unbroken, for the last year and a half, and the working powers that are fully as great as, if not greater, than I have ever had. I brought with me here (this letter was written from Eastbourne) the MS., such as it is (very fragmentary and unarranged) for the book about religious difficulties, and I meant, when I came here, to devote myself to that, but I have changed my plan. It seems to me that that subject is one that hundreds of living men could do, if they would only try, much better than I could, whereas there is no living man who could (or at any rate who would take the trouble to) arrange and finish and publish the second part of the "Logic." Also, I have the Logic book in my head; it will only need three or four months to write out, and I have not got the other book in my head, and it might take years to think out. So I have decided to get Part ii. finished first, and I am working at it day and night. I have taken to early rising, and sometimes sit down to my work before seven, and have one and a half hours at it before breakfast. The book will be a great novelty, and will help, I fully believe, to make the study of Logic far easier than it now is. And it will, I also believe, be a help to religious thought by giving clearness of conception and of expression, which may enable many people to face, and conquer, many religious difficulties for themselves. So I do really regard it as work for God.
Another letter, written a few months later to Miss Dora Abdy, deals with the subject of "Reverence," which Mr. Dodgson considered a virtue not held in sufficient esteem nowadays:—
My Dear Dora,—In correcting the proofs of "Through the Looking-Glass" (which is to have "An Easter Greeting" inserted at the end), I am reminded that in that letter (I enclose a copy), I had tried to express my thoughts on the very subject we talked about last night—the relation of laughter to religious thought. One of the hardest things in the world is to convey a meaning accurately from one mind to another, but the sort of meaning I want to convey to other minds is that while the laughter of joy is in full harmony with our deeper life, the laughter of amusement should be kept apart from it. The danger is too great of thus learning to look at solemn things in a spirit of mockery, and to seek in them opportunities for exercising wit. That is the spirit which has spoiled, for me, the beauty of some of the Bible. Surely there is a deep meaning in our prayer, "Give us an heart to love and dread Thee." We do not mean terror: but a dread that will harmonise with love; "respect" we should call it as towards a human being, "reverence" as towards God and all religious things.
Yours affectionately,
C.L. Dodgson.
In his "Game of Logic" Lewis Carroll introduced an original method of working logical problems by means of diagrams; this method he superseded in after years for a much simpler one, the method of "Subscripts."
In "Symbolic Logic, Part i." (London: Macmillan, 1896) he employed both methods. The Introduction is specially addressed "to Learners," whom Lewis Carroll advises to read the book straight through, without dipping.
This Rule [he says] is very desirable with other kinds of books—such as novels, for instance, where you may easily spoil much of the enjoyment you would otherwise get from the story by dipping into it further on, so that what the author meant to be a pleasant surprise comes to you as a matter of course. Some people, I know, make a practice of looking into vol. iii. first, just to see how the story ends; and perhaps it is as well just to know that all ends happily—that the much persecuted lovers do marry after all, that he is proved to be quite
innocent of the murder, that the wicked cousin is completely foiled in his plot, and gets the punishment he deserves, and that the rich uncle in India (Qu. Why in India ? Ans. Because, somehow, uncles never can get rich anywhere else) dies at exactly the right moment—before taking the trouble to read vol i. This, I say, is just permissible with a novel, where vol. iii. has a meaning, even for those who have not read the earlier part of the story; but with a scientific book, it is sheer insanity. You will find the latter part hopelessly unintelligible, if you read it before reaching it in regular course.
CHAPTER IX
(1897—1898)
Logic-lectures—Irreverent anecdotes—Tolerance of his religious views—A mathematical discovery—"The Little Minister" Sir George Baden-Powell—Last illness—"Thy will be done"—"Wonderland" at last!—Letters from friends "Three Sunsets"—"Of such is the kingdom of Heaven."
The year 1897, the last complete year which he was destined to spend, began for Mr. Dodgson at Guildford. On January 3rd he preached in the morning at the beautiful old church of S. Mary's, the church which he always attended when he was staying with his sisters at the Chestnuts.
On the 5th he began a course of Logic Lectures at Abbot's Hospital. The Rev. A. Kingston, late curate of Holy Trinity and S. Mary's Parishes, Guildford, had requested him to do this, and he had given his promise if as many as six people could be got together to hear him. Mr. Kingston canvassed the town so well that an audience of about thirty attended the first lecture.
LEWIS CARROLL.
A long Sunday walk was always a feature of Mr. Dodgson's life in the vacations. In earlier years the late Mr. W. Watson was his usual companion at Guildford. The two men were in some respects very much alike; a peculiar gentleness of character, a winning charm of manner which no one could resist, distinguished them both. After Mr. Watson's death his companion was usually one of the following Guildford clergymen: the Rev. J.H. Robson, LL.D., the Rev. H.R. Ware, and the Rev. A. Kingston.
Complete Works of Lewis Carroll Page 144
