Snowballs can also be studied numerically or mathematically. The following explanations are limited to snowballs de longueur. Figure 6 is a numerical representation of 55-word snowball. Incidentally, it is output of the first software program that I will present shortly, a T10 snowball de longueur.

Figure 6. A numerical representation of a 55-element, T₁₀ snowball de longueur

Exploring the numerical properties of this snowball leads to several interrelated characteristics. First, this snowball is a numerical figure known as a triangular number. In other words, it is a number that can be represented geometrically in the shape of a triangle. Pythagoras is credited with identifying the triangular numbers, which bolstered his and his followers’ beliefs that Nature is numerical and that the source of all meanings can be derived mathematically. In the following excerpt from her book, The Mystery of Numbers, Annemarie Schimmel offers the following context for their mathematical view of the cosmos:

everything seemed expressible in numbers. Observation of the regular movements of the sky led to the concept of a beautifully ordered harmony of the spheres. The evolution of the world was paralleled by that of numbers: unity can into existence from the void and the limit; out of the One the number appears, and out of the number comes the whole heaven, the entire universe.

Out of the one were the Pythagorean triangles, which grew equilaterally from a simple set of calculations.

The triangular numbers were identified by Pythagoras as a way to represent numerically geometrical shapes. Figure 7 is a sample of the first six triangles from Pythagoras’ study.

Figure 6. Figure 7. Illustration of the first six triangular numbers
from Lancelot Hogben’s Mathematics for the Million

The images are comprised of dots that are supposed to resemble the pebbles or stones that a follower of Pythagoras would have used to construct the figures. The method of arrangement was to add one more pebble to each subsequent row in order to construct the triangles. Figure 8 demonstrates how the rows are formed.

Figure 8. T₂ – T₆ with the rows outlined

For scholars in computers and writing, the numerical basis of this textual form is valuable for two reasons. First, it contributes to the cross-disciplinary approach to language and writing that Le Lionnais characterized as “dual citizenship” (see Part 1.iii). Second, it leads to new methods of writing in computational new media. Related to Manovich’s first principle of new media (see Part 1.iii), the ability to recognize the numerical character of a text is an essential step in the direction of new, experimental forms of writing, rhetoric, and textuality.

One intriguing characteristic of triangular numbers—and snowballs de longueur—is that they can be derived by adding up the consecutive integers that constitute their elements, which is a characteristic that will serve us well as we use AS3 to program our first snowball, which I’ll explain shortly when I discuss the importance of looping. This characteristic is represented in the parenthetical explanations in Figure 6. With Figure 6 in mind, Pythagoras' fourth triangle, T₄, which has a value of 10, is based on the addition of the numbers 1 – 4. Likewise, the value of T₆, which is 21, is derived by adding together the integers 1 – 6. The numerical representation of T₁₀ is the sum of 1 – 55, which is 1035.

Let’s dwell on this characteristic for a moment: the total number of elements in a triangular figure can be derived from the value of one of its sides. Let’s imagine that a creative writer has asked you to help h/er determine the number of words s/he will need to develop a 16-row snowball de longueur. What will be her total word count? Based on this characteristic of triangular numbers, you should be able to present h/er with an answer.

The answer is 136, and the solution can be reached in several different ways. Figure 9 depicts the three solutions presented in Brian Hayes essay titled “Gauss’s Day of Reckoning.”

Figure 9. Three solutions to the sum of an arithmetic progression presented by Brian Hayes

Hayes’ essay is an investigation of the historical accuracy of an anecdote about a young math prodigy named Carl Freidrich Gauss. As an adult, Gauss distinguished himself as one of the greatest mathematicians; as a child, his solution to a question posed by his school teacher echoes into the present. In the following excerpt from his essay, Hayes relays the story as it’s usually recounted:

In the 1780s a provincial German schoolmaster gave his class the tedious assignment of summing the first 100 integers. The teacher's aim was to keep the kids quiet for half an hour, but one young pupil almost immediately produced an answer: 1 + 2 + 3 + ... + 98 + 99 + 100 = 5,050. The smart aleck was Carl Friedrich Gauss, who would go on to join the short list of candidates for greatest mathematician ever. Gauss was not a calculating prodigy who added up all those numbers in his head. He had a deeper insight: If you "fold" the series of numbers in the middle and add them in pairs—1 + 100, 2 + 99, 3 + 98, and so on—all the pairs sum to 101. There are 50 such pairs, and so the grand total is simply 50×101. The more general formula, for a list of consecutive numbers from 1 through n, is n(n + 1)/2.

This description of Gauss’ solution troubles Hayes, because his research into the historical accuracy of the account is unfounded. Ultimately, noone knows which method the young Gauss used to solve the problem. In response to the three solutions that he presented in his essay (Fig. 9), Hayes writes, “Mathematically, its’ obvious they are equivalent. For the same value of n, they produce the same answer. But the computational details are different and, more important, so are the reasoning processes that lead to these formulas” (204).

My point in bring up this anecdote is two-fold. First, all three formulas lead to the same answer to our problem. If I want to determine the number of words in a 16-row snowball, I can use any one of the three methods.

The Oulipo were not Pythagoreans, but considering the fact that the snowball de longueur is a triangular figure, members of the research group might have been interested in its cross-disciplinary uses for invention. They may have been interested in the way that texts "constrained" by this mathematical structure are two-dimensional objects that have symmetrical or equilateral sides. They may have also been interested in the historical relevance of the triangle as it relates to Gauss’ solution to the question posed by his schoolmaster.

In sum, the triangular figure or snowball is is an object that represents a provocative blend of numerate, literate, and rhetorical methods of writing. It is a mathematically quantifiable object that can be generated computationally, it is an experimental form of writing that can be valued by poets and other creative writers, and it is a heuretic that can generate novel forms of textuality that represent visually schemes of amplification such as climax, hyperbole, and even the period.