There seems to actually be real momentum behind this attempt as reviving Less Wrong. One of the oldest issues on LW has been the lack of content. For this reason, I thought that it might be worthwhile opening a thread where people can suggest how we can expand the scope of what people write about in order for us to have sufficient content.
Does anyone have any ideas about which areas of rationality are underexplored? Please only list one area per comment.
Is there a single book or resource you would recommend for learning how group theory/symmetry can be used to develop theories and models?
I work in fluid dynamics, and I've mainly seen group theory/symmetry mentioned when forming simplifying coordinate transformations. Fluid dynamicists call these "dimensionless parameters" or "similarity variables". I am certain other fields use different terminology.
See my response below to WhySpace on getting started with group theory through category theory. For any space-oriented field, I also recommend looking at the topological definition of a space. Also, for any calculus-heavy field, I recommend meditating on the Method of Lagrange Multipliers if you don't already have a visual grasp of it.
I don't know of any resource that tackles the problem of developing models via group theory. Developing models is a problem of stating and applying analogies, which is a problem in category theory. If you want to understand t... (read more)