The (almost really) Complete Works of Lewis Carroll

To be Voted on in Congregation on Tuesday, Nov. 10, 1885

For two reasons I venture to trouble Members of Congregation with a few more printed remarks on this subject, instead of waiting till Tuesday: one is, that I am no orator; the other, that I doubt if any oration ever affects the voting to any appreciable extent. Men come with their minds already made up: they listen, with an ill-concealed impatience, to the debate, and then immediately vote, without the least regard to it, as their consciences, or their friends, have already dictated.

The main question to settle on Tuesday is, not which of the possible Cycles, that might be calculated, is the best—we shall have ample time, before 1889, to consider that question—but whether a Cycle of Simple Rotation is better (as its supporters believe) than any Cycle based on the relative sizes of Colleges.

And what I would urge is that almost any such Cycle would be more fair than the one now proposed.

Mr. Moore, in a paper put out in answer to mine, states that “the number of members of a College who are (practically) eligible as Proctor, depends not on the number of its Members of Convocation, but rather on the number of its educational staff, or perhaps of its Governing Body, or possibly, some might say, its Members of Congregation.” That may be. I only offered my Cycle, calculated on the numbers of Members of Convocation, as a specimen of a Proportionate Cycle. All these different ways would have to be fully considered, if (as I hope) Congregation rejects the “Simple Rotation” Cycle: and it would be well also to inquire on what priciple Cambridge, whose Cycle is, like our existing one, Proportionate, has calculated it.

Mr. Moore also thinks that a Proportionate Cycle would place at a disadvantage a Member of a College whose turn for electing a Proctor occurred at intervals of more than 11 years, because “it is well known that the eligibility of any person for the Proctorship is by Statute limited to a period of 11 years,” so that “some members of that College, however personally fitted for the office, will be excluded by standing from ever being elected by their own College.” Really, one is almost ashamed of having to refute so transparent a fallacy. A Proportionate Cycle is framed for the express purpose of giving to each man an equal chance of being elected, and a charge, of breaking down under so simple a test as this, is almost too absurd to discuss seriously. Let us, however, take a simple example: suppose two Colleges, one having 20 members eligible as Proctor, the other 10; and let the larger College have a turn once in 11 years, and therefore the other once in 22 years.

Any schoolboy could calculate the respective chances of election enjoyed by two members, one taken from each College. Suppose all the names on the books of the larger College during the next century could be put into a bag, and one drawn at random. What is his chance of being elected Proctor? There are only two elements to consider: one is, the chance that an election will occur during his statutable period of 11 years (which depends on the number of turns assigned to his College), the other, his chance, if an election does occur, of his being elected (which depends on the number of members in the College, as of course we must allow them all equal chances). Now, it is certain that an election will occur in his time: hence all we have to estimate is the second of these two elements: there are 20 competitors, so that his chance is 1-20th.

Now take a member of the small College: the chance of an election occurring in his time, is evidently one-half: and the chance that, if it does occur, he will be elected, is 1-10th: and one-half of 1-10th is (if I may be excused for mentioning so childish a truism) 1-20th. So that the member of the smaller College has exactly the same “expectation” as the member of the larger. It will indeed be a memorable day for Mr. Moore, if he ever succeeds in proving that one of the most elementary formulae in Algebra is incorrect! We shall next have him proving that the angles at the base of an isosceles triangle are not equal!

In contrast with the above illustration of the absolute justice of a Proportionate Cycle, let us consider an instance of the working of a Cycle of Simple Rotation. Observe these 40 men coming up High Street: the 20 on the one side are radiant with happiness—those on the other side are silent and gloomy. Why this difference? Let us accost the more cheerful company:

“We come,” they say, “straight from an interview with Mr. Moore. He has just told us that, as we happen to constitute two Colleges, ten in each College, we shall be called on to elect two Proctors in the next 11 years, so that two of us are secure of reaching that high office. ‘But you, O Unfortunate,’ he added (addressing those poor creatures on the opposite side), ‘since ye constitute but one College, know that but one of your number shall have a chance of the prize!’ Have we not, then, good cause to be jolly?” And this is Mr. Moore’s idea of even-handed justice!

Mr. Moore has one more objection to a Proportionate Cycle, viz. that “granting that it was approximately fair when first made out,” it “would almost certainly be far from corresponding with existing facts long before the Cycle of 30 years had run its course.” Now, I had said in my paper “it might be found necessary, in order to make due allowance for the varying numbers of members in Colleges, to make a fresh calculation at less intervals than 30 years, e. g. every five years.” At any rate, it would have run for centuries before it would be anything like so unfair as a Cycle of Simple Rotation!

Lastly, Mr. Moore states that the Cycle of Simple Rotation “has at least the merits of simplicity and permanence.” One can only admire the simplicity of a reader who finds any weight at all in such a plea. If a proposal be (as I contend his proposal is) radically unsound, its “simplicity” is a very doubtful recommendation, while its “permanence” only intensifies the evil. If you cut off a man’s nose, you undoubtedly simplify his features: and such an arrangement would most probably be permanent: still, were it proposed to apply the process to Mr. Moore himself, I feel no doubt that he would raise objections.

I trust that any Member of Congregation, who agrees with me as to the absolute unfairness of the scheme to be voted on next Tuesday, will take the trouble to come and vote against it, leaving the rival merits of the various possible Proportionate Cycles to be considered hereafter.

At least one may trust that no one will be led away by so flimsy a plea as that advanced by Mr. Pelham in the last debate—that “what is mathematically true is usually found to be practically false!” Does Mr. Pelham suppose that Architecture, Engineering, Insurance, Land-surveying, Navigation, are not “practical” Sciences? Would he willingly take his passage in a ship, whose captain adopted this wild theory in calculating his latitude and longitude? If Mr. Pelham ever undertakes the management of a large School, I presume he will make some such speech as this to his boys. “I have noticed, Boys, a great inequality in the distribution of food at dinner-time. The long table in the middle has four times as much as the end one, and each side-table has three times as much. This was so arranged, I believe, for the ridiculous reason that the one contains four times as many boys as the end-table, and the others three times as many. But this is merely a mathematical truth, Boys, and is therefore practically false. The new arrangement, which I am sure will commend itself to your common sense, will be that of delivering dishes to the separate tables in simple rotation. So remember, Boys, that in future the long table will not have its four dishes, and the side ones their three; but that there will be one leg of mutton for each table!” (Cheers?)