The six works presented in "Oulipoems" range from poems, to poetry games, to tools for writing poetry. They are inspired by the Oulipo movement, a French literary movement which combines writing and mathematics. Members of the Oulipo create works of literature that are governed by rules ("constraints"). For example, all words might have to contain only the vowel 'e' or words might be spelled phonetically. Members of the Ouliopo are also interested in algorithmically generated texts, including, especially, text-generating machines which can result in an infinite, or at least very large, number of different texts.
One famous Oulipo book is Raymond Queneau's Exercises de Style, which is a retelling of a very banal anecdote in many different styles and following many different constraints. This directly inspired "Morningside Vector Space," which retells a similarly banal story (based on my own experience) in a range of styles. The computer is central to the piece, however, because instead of having several static versions of the text, the text varies almost smoothly along two dimensions, controlled by the position of the mouse pointer in a colored square. The mathematical idea behind this is the notion of a vector space, in which each point (text) has a coordinate representing each basis vector (version of the text, or dimension along which the text can change).
Several of the other pieces also involve modifying a text via a specialized user interface, to generate either a small or large number of possible texts. In "No War," the text is on the soundtrack instead of in print. The mouse pointer position triggers a series of words in which each word has the same vowel sound but the order of the words is random. Some mouse positions also generate sound effects relating to war. The mathematics here are the idea of a random generator. The constraint that each word in a particular series must share a vowel sound is a typical Oulipo rule.
"Sundays in the Park" also involves variations on a text, but here, the number of texts that it is possible to generate is very large. The text as a whole has no definite meaning, but each group of words suggests the next by a process of punning or association. The groups can be displayed in several different ways, involving phonetic re-spellings, and the user cycles through the possibilities for each group by clicking on it. Phonetic spelling is an Oulipo procedure which was used in Queneau's book. The mathematics here are the combinatorics which tell you how many possible texts can be generated by this "text machine." The number of possibilities for each group ranges from 2 to 6, and there are 33 groups, so the number is between 2^33 and 6^33 =(2^33)(3^33), so this estimate is very inexact, as it varies by a factor of 3^33! I leave it to the user to calculate the exact number of possibilities.
"Headline News" introduces a new level of complexity. This piece is an analogue of the Rubik's cube, only it is presented in two dimensions. The puzzle is in the form of a grid in which the user can rotate the rows and columns independently to rearrange the texts. The piece can be used to compose texts that one is interested in, or it can be viewed as a mathematical puzzle in which the goal is to restore the initial configuration. There is a lot of math in this piece: Firstly, the game board is topologically a torus (because you get a torus if you take a square and glue together the opposite sides (to get a tube),and then glue together the ends of the tube. Secondly, there is also a lot of group theory in this puzzle. Each position can be seen as a permutation on all the squares = (8)(10) = 80 squares, so the group of moves G is a subset of the symmetric group S_80.
G is presumably a very complicated group. I have not figured out what group G is, but it has elements of many different orders. (In other words, there are moves which, if you repeat them a certain number of times, get you back where you started. The number of times you must repeat the move for this to happen is called the order of the move. Since each column has 8 elements, the move which rotates a column by one square has order 8. Likewise, the move rotating a row by one square has order 10. More complicated moves may have either smaller or bigger orders, depending on the move.) The texts themselves are alliterative (another constraint in the Oulipo sense of the word). By the way, the puzzle can always be solved. This doesn't mean that every arrangement of the texts is solvable (ie possible to manipulate so as to restore the initial configuration), but rather that the Scramble button scrambles by doing a series of legal moves, so that the moves could be undone if you could figure out how. I have not solved the puzzle (yet)...
"Poggle" returns us to the realm of easier games. Poggle is a version of the game Boggle, but the tiles have fragments of poetry on them instead of single letters. Like Boggle, the player has a time limit in which to select as many series of adjacent tiles as possible. But here, the goal is to create a good poem, not to score points.
Finally, with "The Electronic Muse," we are in the range of almost infinite possibilities. This program generates lines of poetry using the vocabularies of one of six different poets. The algorithm to generate the lines is based on the linguistics theory of Phrase Structure Grammar (developed by Chomsky). "The Electronic Muse" is a writing tool and not just a text generator, because the user can interact with it by editing the texts it generates. The user can also add words to the program's vocabulary. This piece is mathematical because of it's use of (mathematically inspired) linguistics. The texts it generates follow constraints since they use limited vocabularies and are generated according to rules.