A good friend (I am reconsidering that assessment after reading the article) sent me the link, below– With Category Theory, Mathematics Escapes From Equality, Wired Magazine. While the some of the ideas were hard for me to grasp, it is interesting on several levels:
- The article describes the dynamics around Lurie’s work as having some of the characteristics of The Structure of Scientific Revolutions or The Microbe Hunters in that it talks about the difficulties involved in introducing a new paradigm;
- It made me think that E.F. Codd might have jumped several generations (relational, object oriented and NoSQL) of database theory had he the tools that Lurie has developed. While Codd’s work (e.g., A Relational Model of Large Shared Data Banks; Communications of the ACM, 1970) focused on the structure of data (using set theory) and how manage (select, add, change, delete) data, Lurie’s modifications/extensions to set theory would seem to add a semantic dimension (based on information that seems to me would be implied by Lurie’s thinking) to both the entities and relationships defined in the database;
- But that would have assumed not only that Lurie’s work existed but also that it was as well understood as set theory. I say this because Codd’s work was pretty obtuse even though the theory behind it was pretty well understood. I imagine that work based on Lurie’s efforts would be impenetrable because the underlying theory is poorly understood (i.e. not accessible to most mortals) as Lurie’s work appears to be today;
- That said, I can imagine (and I don’t understand Lurie’s work on anything by a rank novices’ level) that his work could be the basis for some important breakthroughs in how we think about data.
Those are the reasons I thought you might find this introduction to Lurie’s work interesting.