Perspex machine XI: topology of the transreal numbers

The transreal numbers are a total number system in which even, arithmetical operation is well defined even-where. This has many benefits over the real numbers as a basis for computation and, possibly, for physical theories. We define the topology of the transreal numbers and show that it gives a more coherent interpretation of two's complement arithmetic than the conventional integer model. Trans-two's-complement arithmetic handles the infinities and 0/0 more coherently, and with very much less circuitry, than floating-point arithmetic. This reduction in circuitry is especially beneficial in parallel computers, such as the Perspex machine, and the increase in functionality makes Digital Signal Processing chips better suited to general computation.

A new governance perspective on port–hinterland relationships: the Port Hinterland Impact (PHI) matrix

We develop a new governance perspective on port–hinterland linkages and related port impacts. Many stakeholders in a port’s hinterland now demand tangible economic benefits from port activities, as a precondition for supporting port expansion and infrastructural investments. We use a governance lens to assess this farsighted contracting challenge. We find that most contemporary economic impact assessments of port investment projects pay scant attention to the contractual relationship challenges in port-hinterland relationships. In contrast, we focus explicitly on the spatial distribution of such impacts and the related contractual relationship issues facing port authorities or port users and their stakeholders in the port hinterland. We introduce a new concept, the Port Hinterland Impact (PHI) matrix, which focuses explicitly on the spatial distribution of port impacts and related contractual relationship challenges. The PHI matrix offers insight into port impacts using two dimensions: logistics dedicatedness, as an expression of Williamsonian asset specificity in the sphere of logistics contractual relationships, and geographic reach, with a longer reach typically reflecting the need for more complex contacting to overcome ‘distance’ challenges with external stakeholders. We use the PHI matrix in our empirical, governance-based analysis of contractual relationships between the port authorities in Antwerp and Zeebrugge, and their respective stakeholders.