A last point more or less separates the place where the modular calculus separates off from the modular algebra: Suppose, by considering the sentence as a set of letters, we finally found a list of relationships that would completely describe it, such as:
1) Three a’$ must be separated by, respectively, seven letters and two spaces, and one letter and one space.
2) Two ra’s must be separated by no letters and no spaces.
3 ) One m must follow one a.
Et cetera ...
Even though, at the end, we have a list of relationships that completely describes the sentence (so that, say, a computer could translate our list into the matrix form of a flash-display, i.e., a list of numbers), still no relation, or even consecutive group of relations in our list, can be said to stand for any thing, attitude, or relation in the situation which the sentence models. Yet the sentence is completely described by this list.
Notice also: The list of numbers for the matrix display also completely describes the sentence. Yet here, some consecutive groups of numbers can be said to stand for things, attitudes, and relations in the situation—since certain groups of numbers each of which is given a number, then your minimum list of things and relations (minimum because some letters can be made in two forms:
stand for certain words and certain word groups. Notice as well that, while in this list there will be a consecutive group of numbers that stands for the relationship of the and hammer, and a and nail, there is no consecutive group that stands only for the relation of hammer, hit, and naiclass="underline" because the numbers standing for the second a in the sentence will be in the way.
We can call the computer matrix display a modular description because it preserves some of the modular properties of the sentence in a list that describes the sentence.
We can call the list of letters in relation to each other a nonmodular description because it preserves none of the modular relations of the sentence in a list that describes the sentence.
As we have seen, with our computer example, complete descriptions of models can be translated from nonmodular descriptions into modular ones and back again and remain both complete and intact. The first useful thing the modular calculus yields us is the following information:
Consider language a list of relationships between sounds that model the various ways sounds may relate to one another—or, if you will, a list of sentences about how to put together sentences, i.e., a grammar. The modular calculus lets us know, in no uncertain terms, that even if such a list were complete, it would still be a nonmodular description. It has the same modular order (the proof is not difficult) as our description of the sentence The hammer hit a nail as a set of letters precisely spaced and divided.
The calculus also gives us tools to begin to translate such a list into a modular description.
Now the advantages of a modular description of either a modeling object, like a sentence, or a modeling process, like a language, are obvious vis-a-vis a nonmodular description. A modular description allows us reference routes back to the elements in the situation which is being modeled. A nonmodular description is nonmodular precisely because, complete or incomplete as it may be, it destroys those reference routes: it is, in effect, a cipher.
The problem that still remains to the calculus, despite my work, and that will be discussed in the later lectures, is the generation of formal algorithms for distinguishing incoherent modular descriptive systems from coherent modular descriptive systems. Indeed, the calculus has already given us partial descriptions of many such algorithms, as well as generating ones for determining completeness, partiality, coherence, and incoherence—processes which till now had to be considered, as in literature which so much of this at a distance resembles, matters of taste. But their discussion must be left for the last lecture.
About The Author
“Samuel R. Delany is the most interesting author of science fiction writing in English today,” said The New York Times Book Review. He was born in New York City in 1942. His acclaimed science fiction novels include Babel-17 and The Einstein Intersection, both winners of the Nebula Award for best science fiction novel. He has also written Nova, Triton, the best selling Dhalgren and the Neveryon fantasy series, Tales of Neveryon, Neverydna and Flight from Neveryon. Stars in My Pocket like Grains of Sand is the first volume of a science fiction diptych which will conclude with The Splendor and Misery of Bodies, of Cities, to be published by Bantam Spectra Books in 1986. Also a critic of science fiction, he has published two essay collections on the field, The Jewel-Hinged Jaw and Starboard Wine, as well as The American Shore, a book-length semiotic study of the science fiction short story “Angoul-eme” by Thomas M. Disch.
Called “the most interesting author of science fiction writing in English today” by The New York Times Book Review, Samuel R. Delany is the author of more than a dozen acclaimed science fiction and fantasy novels including BABEL-17 and THE EINSTEIN INTERSECTION (both winners of the Nebula Award for best novel), NOVA, DHALGREN, THE FALL OF THE TOWERS and NEVERYON trilogies, and STARS IN MY POCKET LIKE GRAINS OF SAND, the first volume in a science fiction diptych which will conclude with THE SPLENDOR AND MISERY OF BODIES, OF CITIES, to be published in 1986 as a Bantam Spectra Book.