Researcher of mathematical biology and wearer of false moustaches. My interests include:
Why do some species (including the human one) exponentiate and become pests? Why do other species collapse? How can we use ecological methods to intervene to tame pests and rescue species on the verge of extinction? Read all about my work with a species of giant carnivorous landsnail here here
The ecological dynamics of invasion, persistence and extinction,
A strange fact has been observed by biologists, species in diverse ecological communities (e.g. rainforests) are far more likely to survive the invasion of competitors or predators than those in less diverse communities. One has to wonder why this is, and how these diverse and stable communities develop over time.
The biological mechanisms of hypertrophy,
Muscle cells are unlike ay other cell in your bodies. Numerous theories on which kind of exercise or nutrition is best for their growth exist, however much of the biological complexity of the cells themselves is not understood. Quite clearly what is needed is a theory that connects our understanding of the cells on a small scale, with our large scale theories on sports, nutrition and exercise, so we can better evaluate the science involved.
Number theory and Category theory (topics in pure mathematics, the philosophy of pure mathematics and abstract logic)
Are all statements true or false, and if not what other categories exist? If such categories exist, how can we build a framework to compare them? If they exist are there statements that remain the same regardless of how we formulate our categories? Are their links between ideas expressed in alternate forms of logic?
Beyond simple logic, are there statements that move from provable to unprovable in different systems? Are there logical systems where current unsolved problems become soluble (e.g. the Reimann hypothesis)? Are there statements that fail to be provable in any logical system? Moreover, what should the effect of the potential unprovability of many statements have on mathematics and science in general?
Mathematical and logical approaches to ethics, meta-ethics and philosophy
In ethics we ask what makes an action, or a person good. In Meta ethics we ask whether or not any ethical statements regarding good and evil are true, or if in fact all are false or their truth values are unknowable.
Can we use approaches from game theory to determine which actions are best in a given circumstance, or even which ethical rules provide the best action in a variety of circumstances. Can we define sets of actions and investigate concepts of ethical commutitavity (whether the ordering of a set of actions is important) and dominance(whether in a group of ethical theories one action is always preferable to another)? As a result can we create new meta ethical theories from a reductionist view of the interaction of ethical theories?
Cliodynamics and mathematical approaches to sociology
What aspects of history and sociology can be modelled with dynamical systems? Can we look at the propogation of a set of genes, an ideology or a set of memes through time? How have differing social circumstances altered this propagation?
For example how have changing attitudes towards homosexuality affected the propagation of genes associated with it? How have changing economic circumstances influenced the attitudes of different religious groups towards birth control?
Network theory approaches to Textual criticism
Shakespear is taught in every english high school, but many academics doubt whether he was the author of some of his best known plays. Christianity and Judaism are is two of the worlds main religons, but many doubt whether Moses wrote the pentateuch, or whether any of the prophets or apostles wrote the books bearing their names.
The kind of literary theory that is relied upon to give us insights into these problems does not currently have any basis in statistics or empirical evidence. A generalised form of these theories is that there are a number of original authors, each with individual characteristics, and distinctive language, ideas and techniques, and these authors retain these identifying marks throughout their work, and that these characteristics can be used by a trained reader to identify the work of different authors. Statistics could be used to cluster these characteristics, and evaluate the significance of this kind of clustering, allowing us a qualitative way of comparing different theories of compilation, and avoiding the effects of confirmation bias on the part of the modern analyst.