Elliptic Curves and Hyperdeterminants in Quantum Gravity

Hyperdeterminants are generalizations of determinants from matrices to multi-dimensional hypermatrices. They were discovered in the 19th century by Arthur Cayley but were largely ignored over a period of 100 years before once again being recognised as important in algebraic geometry, physics and number theory. It is shown that a cubic elliptic curve whose Mordell-Weil group contains a Z2 x Z2 x Z subgroup can be transformed into the degree four hyperdeterminant on a 2x2x2 hypermatrix comprising its variables and coefficients. Furthermore, a multilinear problem defined on a 2x2x2x2 hypermatrix of coefficients can be reduced to a quartic elliptic curve whose J-invariant is expressed in terms of the hypermatrix and related invariants including the degree 24 hyperdeterminant. These connections between elliptic curves and hyperdeterminants may have applications in other areas including physics.Comment: 7 page

The Lebesgue Universal Covering Problem

In 1914 Lebesgue defined a "universal covering" to be a convex subset of the plane that contains an isometric copy of any subset of diameter 1. His challenge of finding a universal covering with the least possible area has been addressed by various mathematicians: Pal, Sprague and Hansen have each created a smaller universal covering by removing regions from those known before. However, Hansen's last reduction was microsopic: he claimed to remove an area of $6 \cdot 10^{-18}$, but we show that he actually removed an area of just $8 \cdot 10^{-21}$. In the following, with the help of Greg Egan, we find a new, smaller universal covering with area less than $0.8441153$. This reduces the area of the previous best universal covering by a whopping $2.2 \cdot 10^{-5}$.Comment: 11 pages, 5 jpeg figures, numerical errors correcte

Political discourse and religious narratives of Church and State in Papua New Guinea

In Papua New Guinea, attempts to keep religion and politics separate often meet with incomprehension and resistance on the part of the general populace, for in traditional Melanesian terms, religion has a political function: seen in the power to avert misfortune and ways to ensure prosperity and well being. This paper looks at how religious narrative plays a part in contemporary political discourse in Papua New Guinea. It will look first at the links between socio-political and religious institutions, and then will consider some of the ways religious values and symbols are used and exploited to legitimise political aspirations. In contemporary Papua New Guinea some leaders attempt to use Christian rhetoric and symbols to appeal to people’s religious sentiments and to promote nationalism, however, sometimes symbols apparently achieve the agent’s goal and at other times the symbol backfires on the user. How can we account for the selection, uses and effects of religious symbols in political discourse? The churches and Christian groups seeking not so much to gain political power as to control it, appear to be divided as to whether it is better to respond with a progressive social agenda or to control political power by means of spiritual power. Specific cases from contemporary national and local politics will be examined in detail, including events such as “operation brukim skru (operation bend the knee),” Archbishop Brian Barnes criticism of the government, and the debate over the cross on the top of the Parliament House. The goal of the paper is to provide an anthropological perspective on religion as a category ofconcern in the evolving political scene in contemporary Papua New Guinea.AusAI

Politics, Religion, and the Churches:The 2002 Election in Papua New Guinea

In Papua New Guinea in the immediate aftermath of the 2002 national election, many of more than two million potential voters looked for ways to express their feelings of anger, disappointment, and frustration. With 43 political parties and 2785 candidates vying for 109 seats in parliament, some hitches were predictable. However, no one expected the extent of the chaos and intimidation that was experienced in many parts of Papua New Guinea during June and July 2002. After having spent 29 years in Papua New Guinea, I am well aware of how foolhardy it is to try to generalize about the situation in that country but on this occasion there was a pervasive sense that something had gone terribly wrong. On the first day of polling, the Prime Minister, Sir Mekere Morauta, having had to wait for nearly five hours to cast his vote, was reported as saying, “This is more than a bungle. Someone should be hung for this” (Post-Courier, 18 June:1). That was on 17 June and the situation subsequently deteriorated. The Prime Minister was fortunate. Bishop Arnold Orowae, Catholic bishop in Enga Province, lined up in Wabag to cast his vote only to find that his name did not appear on the electoral roll. He left without voting and with a feeling of having been disenfranchised. In Port Moresby, 90 students at the Don Bosco Technical College were registered so that their names would be on the Common Roll but on voting day only five of their names appeared. The other 85 students were left disappointed and angry. This was a common experience. In the Highlands, what Bill Standish has called “gunpoint” democracy was rife with presiding officers being forced to sign ballot papers while facing down the barrel of a gun (Standish 1996).1 The police were outnumbered and outgunned and the army had to be called in to try to bring about a semblance of order in some provinces such as Southern Highlands and Enga Provinces. This paper discusses the present-day political significance of Christianity and the churches in Papua New Guinea against the background of political unrest and confusion in which the 2002 election was conducted.AusAI