Dividing by Zero: Mathematics, Irony and Dialectic in Carlyle's "Fraction of Life" (1993)

Although Thomas Carlyle's correspondence often seems dismount the effect of his mathematical training on his later literary career, (1) some of his most famous images in works such as Sartor Resartus rely heavily on mathematical ideas. Often, however, Carlyle's use of mathematical imagery has been overlooked in the scholarship, (2) and when addressed, his attitude toward mathematics in general and his own mathematical training in specific has inspired more quest ions than answers. As Carlisle Moore and Frank M. Turner have observed, Carlyle's position toward in general, and mathematics in particular, is extremely problematic. Moore claims that Carlyle had might be called a love-hate interest in science (Torch 4-5), while Turner points out that Carlyle--although he was opposed many contemporary scientific theories--influenced many scientists and used scientific metaphors in an exact manner. One Carlylean passage in which the mathematical imagery is both particularly significant and complex is the famous fraction of passage from Sartor Resartus. In this excerpt from Yea, Teufelsdrockh, in discussing the deserts or average terrestrial lot that most people simply expect from life as their wages, claims: So true is it, what I then said, that the Fraction of Life can be increased in value not so much by increasing your Numerator as by lessening your Denominator. Nay unless my Algebra deceive me, Unity itself divided by Zero will give Infinity. Make thy claim of wages a zero, then; thou hast the world under thy feet. Well did the wisest of our time write: It is only with (Entsagen) that Life, properly speaking, can be said begin. (Works 1: 152-53) Although critics have commented on the use of mathematical imagery in addressing the passage, their conclusions have been of a general nature. Charles W. Schaefer comments that this excerpt shows that Carlyle had an enduring interest in the philosophy of mathematics (12), while Gerry H. Brookes remarks that the passage is an analogy arguing in support of the Everlasting Yea (110). Carlisle Moore is more explicit in the treatment of the mathematical content of the passage, noting that the imagery in the passage is drawn, interestingly, not from geometry but from the algebra, which [Carlyle] disliked (Torch 17). (3) Furthermore, Moore notes that Carlyle uses the passage in a serious manner to clarify and enforce the doctrine of Entsagen, the doctrine of Renunciation (Torch 17). However, even Moore's discussion of the passage raises important questions that have not been addressed. If the passage, as these critics assume, is affirmative in tone, why is it drawn from an area of mathematics that Carlyle presumably disliked? How do the complex and subtle mathematical ideas articulate the doctrine of entsagen, and why does Carlyle choose such a precisely mathematical image express it? Furthermore, these analyses of the fraction of omit an important fact, one that helps illuminate the nature of Carlyle's use of mathematical imagery in the passage. The fraction of image does not appear for the first time in Sartor Resartus, but in a journal that Carlyle kept in the late 1820s. If the journal entry was in roughly the same form as the later Sartor Resartus passage, then this discovery, although interesting in its own right, would not raise issues that alter the critical conversation on the image. However, a comparison of the two passages sheds new light on this famous excerpt of Sartor Resartus. In fact, the image evolved significantly from the early journal passage the corresponding extract of Sartor Resartus. This is a crucial revelation, since an examination of Carlyle's journal entries shows that he often experimented with passages that later became parts of his public writing. (4) Since Carlyle did not originally intend for his journals be published, (5) his initial, private formulation of images was most likely tentative and personal, rather than directed toward his public audience. …