My research reflects my tendency to approach topics I’m interested in, even linguistics, through the lens of mathematics.
Early in my graduate career, I noticed a connection between the so-called X-bar schema and the famous Fibonacci numbers (1, 1, 2, 3, 5, 8,…). Following up on that observation led to the ideas described on this page: Fibonacci & L-grammars
Trying to motivate the claim that X-bar structure was optimal in some sense led me to the idea that syntax might be designed to minimize c-command relations, the topic of my dissertation. Such minimization would favor X-bar-like formats for phrase structure, and might go some way toward explaining the rather mysterious property of projection. I also explored the idea that syntactic movement was a mechanism to reduce c-command relations. That treatment of movement has some interesting consequences, including a possible explanation for the word order facts collected under Greenberg’s Universal 20 (and its modern refinements). This line of thought is detailed here: Economy of Command
In thinking about Universal 20, I noticed a connection with the Catalan numbers (1, 2, 5, 14, 42, …), another famous sequence. This numerical insight was the seed for my current project, ULTRA: the Universal Linear Transduction Reactive Automaton. While my earlier work was eccentric, it fit to a certain extent within the boundaries of existing syntactic inquiry. But ULTRA is a radical departure from current thinking, drawing together ideas from syntax, typology, computer science, psychology and psycholinguistics into a theory of universal-parser-as-universal-grammar. Among other affronts to modern sensibilities, ULTRA rejects the notion of Merge. Read more about it here: ULTRA