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.