The fantasies of Lewis Carroll, Alice’s Adventures in Wonderland and Through the Looking Glass, have been rightly admired by millions of readers. One of those admirers is said to have been Queen Victoria. According to legend, when the Queen read Alice, she was so delighted by it that she requested Carroll to dedicate his next book to her. Imagine her surprise when his next book turned out to be a mathematical tome entitled An Elementary Treatise on Determinants!
Carroll himself denounced this anecdote as “an absolute fiction,” but literary buffs continue to tell it because it amusingly illustrates the contrast between Carroll’s diverse writings. In the Treatise, for example, mathematics is a straightforward, thoroughly logical process.
If there be given n Equations, not all homogeneous, containing Variables: a test for their being consistent is that either, first, there is one of them such that, when it is taken along with each of the remaining Equations successively, each pair of Equations, so formed, has its B-Block evanescent; or secondly, there are m of them, where m is one of the numbers 2…..n, which contain at least m variables, and have their V-Block not evanescent, and are such that, when they are taken along with each of the remaining Equations successively, each set of Equations, so formed, has its B-Block evanescent.[i]
But in Through the Looking Glass, mathematics becomes something else again.
“Try another Subtraction sum. Take a bone from a dog: what remains?”
Alice considered. “The bone wouldn’t remain, of course, if I took it—and the dog wouldn’t remain: it would come to bite me—and I’m sure I shouldn’t remain!”
“Then you think nothing would remain?” said the Red Queen.
“I think that’s the answer.”
“Wrong, as usual,” said the Red Queen: “the dog’s temper would remain.”
“But I don’t see how—“
“Why, look here!” the Red Queen cried. “The dog would lose its temper, wouldn’t it?”
“Perhaps it would,” Alice replied cautiously.
“Then if the dog went away, its temper would remain!” the Queen exclaimed triumphantly.
Alice said, as gravely as she could, “They might go different ways.” But she couldn’t help thinking to herself, “What dreadful nonsense we are talking!”[ii]
Nonsense indeed. If we had no objective evidence about Lewis Carroll outside of these two works, if the only information we had about him was the information that could be gleaned from the Treatise and from Looking Glass, it would be easy to believe that they were written by two different authors. The styles of the two works are completely different. The Treatise is a somber and stilted exposition of technical truths. Looking Glass is a wonderfully witty work of nonsense. The Treatise was written in the precise prose of the thesis. Looking Glass was written in the fluid prose of fiction. Even the title pages of the two books bear the names of two different authors: the author of Looking Glass was Lewis Carroll, but the author of the Treatise was Charles Lutwidge Dodgson!
Fortunately, we do have objective evidence about Carroll, and this evidence confirms that Dodgson was Carroll’s real name and that Dodgson did write both books. He is therefore one of the best proofs that a single author can change his style.
The Reasons for Changing Styles
The documentarians argue that there is only one explanation for a change in style: a change in authors—which is one reason why they assign these two passages from the Pentateuch to two different authors:
And Yahweh spoke to Moses, saying, “…These are the feasts of Yahweh, holy convocations which you shall proclaim at their appointed times. On the fourteenth day of the first month at twilight is Yahweh’s Passover. And on the fifteenth day of the same month is the Feast of Unleavened Bread to Yahweh; seven days you must eat unleavened bread. On the first day you shall have a holy convocation; you shall do no customary work on it. But you shall offer an offering made by fire to Yahweh for seven days. The seventh day shall be a holy convocation; you shall do no customary work on it.”
Lev. 23:1, 4-8
“Observe the month of Abib, and keep the Passover to Yahweh your God, for in the month of Abib Yahweh your God brought you out of Egypt by night…. You shall eat no leavened bread with it; seven days you shall eat unleavened bread with it, that is, the bread of affliction (for you came out of the land of Egypt in haste), that you may remember the day in which you came out of the land of Egypt all the days of your life…. Six days you shall eat unleavened bread, and on the seventh day there shall be a sacred assembly to Yahweh your God. You shall do no work on it.”
Deut. 16:1, 3, 8
But the real explanation is that Moses has simply changed his style from one passage to the other—and for some very good reasons…..
[i] Charles Lutwidge Dodgson, An Elementary Treatise on Determinants (London: Macmillan, 1867), 61 as quoted in Francine F. Abeles, The Mathematical Pamphlets of Charles Lutwidge Dodgson and Related Pieces, Vol. 2 of The Pamphlets of Lewis Carroll, edited by Stan Marx and Edward Guiliano (Charlottesville, Virginia: University Press of Virginia, 1994), 158-159.
[ii] Lewis Carroll, Alice’s Adventures in Wonderland and Through the Looking Glass (N.Y.: Airmont Publishing Company, Inc., 1965), 237-238.