The intuitions of higher dimensional algebra for the study of structured space

Higher dimensional algebra frees mathematics from the restriction to a purely linear notation, in order to improve the modelling of geometry and so obtain more understanding and more modes of computation. It gives new tools for noncommutative, higher dimensional, local to global problems, through the notion of «algebraic inverse to subdivision». We explain the way these ideas arose for the writters, in extending first the classical notion of abstract group to abstract groupoid, in which composition is only partially defined, as in composing journeys, and which brings a spatial component to the usual group theory: An example from knot theory is used to explain how such algebra can be used to describe some structure of a space. The extension to dimension 2 uses compositions of squares in two directions, and the richness of the resulting algebra is shown by some 2-dimensional calculations. The difficulty of the jump from dimension 1 to dimension 2 is also illustrated by the comparison of the commutative square with the commutative cube-discussion of the latter requires new ideas. The importance of category theory is explained, and a range of current and potential applications of higher dimensional algebra indicated.     

Marketplaces and Morality in Papua New Guinea: Place,Personhood and Exchange

In Papua New Guinea (PNG) more rural people, and especially rural women, earn cash from selling in marketplaces than from any other source. PNG's marketplaces are critical for food security, and for the redistribution of wealth. They are also important meeting places where people gather to see friends, hear the latest news, attend court cases, play cards and be entertained. This introduction to this special issue on ‘Marketplaces and Morality in Papua New Guinea’ reviews the history of PNG marketplaces and their contemporary forms. It charts their transformation from introduced colonial spaces into dynamic Melanesian places, which, as places to buy, sell and socialise, have become pervasive institutions in the lives of both urban and rural Papua New Guineans, and places where people interact with both known and unknown others. From this, marketplaces emerge as important spaces of moral evaluation and contestation in relation to what constitutes morally acceptable exchange and what practices are acceptable in these places. The paper demonstrates that exchange in the marketplace should not be reduced to commodity transactions, and questions assumptions about the types of people marketplaces create. It argues that the country's marketplaces are productive sites to consider ideas of exchange, social relations and social personhood, and that there is a critical need to understand the concrete details of what takes place in contemporary marketplaces.     

What really goes on in Silicon Valley? Spatial clustering and dispersal in modular production networks

Is the geographic trajectory of capitalism toward spatial clusteringor dispersal? Recent theoretical work in the stream of ‘relational’economic geography includes several dynamic elements that increasethe importance of spatial clustering over time. This paper developsthe concept of ‘modular production networks’ toshow that spatial clustering and dispersal can be compatible,mutually reinforcing trends. Modular production networks encompassnodes of tacit activity linked through the exchange of codifiedinformation to create global-scale production systems. In placeslike Silicon Valley, industry participants rely on the benefitsof proximity to help build and manage global-scale productionnetworks.     

Caddoan Area archaeology since 1990

This paper summarizes recent archaeological research efforts, and changing perspectives, about the native history of the Caddo peoples who lived in the Caddoan Archaeological Area, which centers on the Great Bend of the Red River in Oklahoma, Texas, Arkansas, and Louisiana. Of particular focus are the origins and early developments of the Caddoan tradition, regional diversity, subsistence changes and agricultural intensification, sociopolitical dynamics, and Caddoan-European interaction.