Topology and Verb Classes
Feature Column Archive
The web is rich in resources on verb classes in semantics and syntax (``verb classes'' in morphology, e.g. conjugation classes, are also documented). A nice general treatment is Verb Semantic Classes on the EAGLES website. Another survey is in Manfred Krifka's Lexicalische Semantik (PDF) notes. For verb classes in various languages: Hausa Tamil English French (PDF) Bangla, German, English and Korean (PDF). Levin's foundational work is not on the web but its index, containing her enumeration of classes, is available online.
On catastrophe theory: Lucien Dujardin's Catastrophe Teacher has two elegant applets illustrating the cusp and butterfly catastrophes. Sir Christopher Zeeman's Catastrophe Theory lectures are exciting but focus almost entirely on the cusp catastrophe. The Exploratorium's page on René Thom and Catastrophe Theory has a nice picture of Thom (see also Thom, Bahia, 1971). Robert Magnus' Mathematical Models and Catastrophes is the most complete survey on the web, but the figures are missing. Thom's works on the topic and additional resources in print are listed in the References.
A site related to the contents of this column is Franson D. Manjali's Dynamical Models in Semiotics/Semantics.
1. Natural languages, human thought and topology
In the December 2001 Scientific American Ian Tattersall (American Museum of Natural History) writes on the evolution of human intelligence. His main point is that consciousness as we experience it depends on language, but that the cerebral apparatus that handles language, as well as the vocal apparatus that mediates it, both are manifest in the fossil record and both predate by many millenia any evidence of conscious activity. Referring to language, Tattersall says: ``Exactly how this fateful novelty may have been invented is a ... question, upon which it is beyond my expertise to speculate.''
It has recently been recognized that all human tongues have such great similarities that, as Steven Pinker puts it, ``a visiting Martian scientist would surely conclude that aside from their mutually unintelligible vocabularies, Earthlings speak a single language.'' The similarities are structural, on several levels, but the basic structures are difficult to appreciate because we have nothing to compare them to. Given the evolutionary symbiosis between human language and human thought, it is structurally impossible for us to imagine a different kind of natural language.
Nevertheless we can ask whether there are specific aspects of life on this planet, or in this universe, which manifest themselves in the basic structure of our languages: why our languages are the way they are. The topologist René Thom in Topologie et linguistique (1970) proposed that the small number of elementary sentence types corresponds to the small number of topological structures underlying events in the exterior world.
In this column we will examine Thom's classification of these structures and the correspondence he finds between this set and the set of verb classes. This will be a truncated and schematic presentation of an admittedly approximate theory. But I believe Thom's work deserves our attention as a bold attempt to understand the topological underpinnings of human language, and of human thought.
Welcome to the
These web essays are designed for those who have already discovered the joys of mathematics as well as for those who may be uncomfortable with mathematics.
Read more . . .
Feature Column at a glance