Friday, August 28, 2009

Middlemarch Revisited, Part V: On the Possibility of Dividing by Zero

And here I am naturally led to reflect on the means of elevating a low subject. Historical parallels are remarkably efficient in this way. The chief objection to them is, that the diligent narrator may lack space, or (what is often the same thing) may not be able to think of them with any degree of particularity, though he may have a philosophical confidence that if known they would be illustrative. It seems an easier and shorter way to dignity, to observe that-- since there never was a true story which could not be told in parables, where you might put a monkey for a margrave, and vice versa-- whatever has been or is to be narrated by me about low people, may be ennobled by being considered a parable; so that if any bad habits and ugly consequences are brought into view, the reader may have the relief of regarding them as not more than figuratively ungenteel, and may feel himself virtually in company with persons of some style. Thus while I tell the truth about loobies, my reader's imagination need not be entirely excluded from an occupation with lords; and the petty sums which any bankrupt of high standing would be sorry to retire upon, may be lifted to the level of high commercial transactions by the inexpensive addition of proportional ciphers (Middlemarch, chapter 35).
The funeral of Peter Featherstone has broken up and the will has been read—two wills, to be exact, the last of which leaves everything to the mysterious Mr. Joshua Rigg, on the condition that he adopt the name Featherstone. This leads Eliot “reflect on the means of elevating a low subject” by means of parables. If I tell a story about monkeys, it can be taken as a parable about margraves (i.e., princes). Or vice versa.

To make better sense of this passage, I turned a somewhat glazed eye to the critic J. Hillis Miller,* who reads it in the context of a discussion of the literary function of zero, and its association with irony and allegory (or “parable”). He points out the fascinating language of nullification in the passage—“not more than figuratively ungenteel,” “need not be entirely excluded”—and draws attention to the presence of zero at the end of the passage: “...and the petty sums which any bankrupt of high standing would be sorry to retire upon, may be lifted to the level of high commercial transactions by the inexpensive addition of proportional ciphers.”

Cipher, here, means “zero.” Any low number can be raised to a higher number by the addition of a 0. Thus, 1 can become 10 or 10,000, depending on how many zeros are added. The addition of a zero is “inexpensive” because a zero is, literally, nothing.

In the first will, Fred Vincy is left £10,000. In the second will, he receives nothing. Zero. Can it be that much of what distinguishes between individuals—measures of wealth, signifiers of class and rank, titles and names—is really nothing, an empty convention, a mere accumulation of zeros?

There is a fascinating kind of moral mathematics at work in Middlemarch. In chapter 18, when Dr. Lydgate enters the meeting at which the hospital chaplain is to be chosen, the voting has already reached a critical point. Bulstrode announces: “I perceive that that votes are equally divided at present” (216). The yeas and the nays cancel each other out, and in effect equal zero. Lydgate’s vote is now the only one that matters. His vote creates an immediate inequality: Tyke replaces Farebrother, and Farebrother—who has hitherto been working for nothing (zero)—loses a salary of £40.

Meanwhile, hapless Fred Vincy attempts to raise £160 to pay off a debt through some highly questionable transactions. Eliot writes: “Fred felt that he should have a present from his uncle, that he should jave a run of luck, that by dint of ‘swapping’ he should gradually metamorphose a horse worth forty pounds into a horse that would fetch a hundred at any moment—‘judgment’ being always equivalent to an unspecified sum in hard cash” (262). In Fred’s math, £40 seems to equal £100; he seems to think that his estimation of his own self-worth will have an equal value on the open market.

Earlier in the summer, while on vacation with my brother-in-law the mathematician, there was a long discussion about the impossibility of dividing by zero, a concept which I found difficult to understand. J. Hillis Miller seems to sympathize with my difficulties, saying that “zero plays havoc with meaning.” He then quotes Robert Kaplan, who explains the impossibility of dividing by zero in his book The Nothing That Is: A Natural History of Zero:
Experience tells us that 6 isn’t 17, for example (and experience or no, our minds jusrt seem to come with distinctions built in). But if you really could divide by zero, then all numbers would be the same. Why? ... [A]ny number times zero is zero—so that 6x0=0 and 17x0=0. If you could divide by 0, you’d get 8x0/0=17x0/0, the zeros would cancel out and 6 would equal 17. They aren’t equal, so you can’t legitimately divide by zero. It doesn’t mean anything.
But Eliot almost seems to be playing with a different kind of mathematics, in which all numbers are the same. The monkey equals the margrave. The lord equals the looby. Parable, allegory, metaphor, irony—the fictional art as George Eliot practices it—seems to be a kind of division by zero. “It doesn’t mean anything.” Or does it approach an infinity of meanings?

*J. Hillis Miller, “The History of 0,” Journal for Cultural Research 8.2 (2004), 123-139.

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