My first critical awareness of the tensions between different methodologies arose 5 years ago when preparing the materials for two undergraduate courses: ‘Operations Management’ and ‘Strategy’. The former was concerned with explanation in which there is the assumption of causality; the operations environment could be designed in an optimal manner with predictable behaviour—the domain of those f...

Recall that hyperbolic 3-manifolds M and N are said to be commensurable if they have a common finite sheeted covering. This is equivalent to the fundamental groups having subgroups of finite index which are conjugate in PSL(2,C). In general it is very difficult to determine if two manifolds are commensurable or not, once the most obvious invariants of commensurability (for example, the invarian...

I would say that if you are interested in the philosophical, technical underpinnings of knowledge systems and of the Semantic Web and semantic technologies generally, this is a good book to have due to the chapters by Magee. (I found his chapter “On commensurability” to be something of a tour de force summary of some main currents of the past fifty years of both Anglophone and Continental philo...

We investigate an imbalanced mixture composed of two-color fermions and scalar bosons in the hard-core limit, considering repulsive attractive interspecies intraspecies interactions. The interplay between commensurability, interactions imbalance generates three insulating phases: a mixed Mott state two spin-selective insulators characterized by commensurability relations $\rho_B+\rho^{\uparrow,...

Our main result is that for any positive real number x0, the set of commensurability classes of arithmetic hyperbolic 2– or 3–manifolds with fixed invariant trace field k and systole bounded below by x0 has density one within the set of all commensurability classes of arithmetic hyperbolic 2– or 3–manifolds with invariant trace field k. The proof relies upon bounds for the absolute logarithmic ...

This sharpens [10], where it was shown that the complex length spectrum of M determines its commensurability class. Suppose M ′ is an arithmetic hyperbolic 3-manifold which is not commensurable to M . Theorem 1.1 implies QL(M) 6= QL(M ′), though by Example 2.1 below it is possible that one of QL(M ′) or QL(M) contains the other. By the length formulas recalled in §2.1 and §2.2, each element of ...