‘‘Defining’’ Our Future by ‘‘Defining’’ Ourselves

Teaching/Communication/Extension/Profession,

On defining irreducibility

We show that irreducibility is not a first-order definable property of real algebraic varieties. The proof is based on the recent o-minimality result for the exponential function. We conjecture that irreducibility is not a definable property of complex algebraic varieties

Defining Original Presentism

It is surprisingly hard to define presentism. Traditional definitions of the view, in terms of tensed existence statements, have turned out not to to be capable of convincingly distinguishing presentism from eternalism. Picking up on a recent proposal by Tallant, I suggest that we need to locate the break between eternalism and presentism on a much more fundamental level. The problem is that presentists have tried to express their view within a framework that is inherently eternalist. I call that framework the Fregean nexus, as it is defined by Frege’s atemporal understanding of predication. In particular, I show that the tense-logical understanding of tense which is treated as common ground in the debate rests on this very same Fregean nexus, and is thus inadequate for a proper definition of presentism. I contrast the Fregean nexus with what I call the original temporal nexus, which is based on an alternative, inherently temporal form of predication. Finally, I propose to define presentism in terms of the original temporal nexus, yielding original presentism. According to original presentism, temporal propositions are distinguished from atemporal ones not by aspects of their content, as they are on views based on the Fregean nexus, but by their form—in particular, by their form of predication

Defining Regional Boundaries

The purpose of this resource is to identify a reqion for study as a system, and to establish a list of characteristics and features useful for determining the boundaries of regional systems. Students discuss their current understanding of what Earth systems are and how they work, and consider how to identify the boundaries of a region for Earth system study. In small groups, they select a region for recommendation to the class, and they make a list of characteristics and features that can mark the boundaries of regional systems. After presentations by each group, the class chooses one region for study as an Earth system. Then they mark the boundaries of their chosen region on their Landsat image, topographic map, or other map. Educational levels: Middle school, High school

Deconstructing and defining EULEX

Hailed as the greatest European Security and Defence Policy (ESDP) mission to date, the European Rule of Law Mission in Kosovo (EULEX) has been oscillating between fulfilling its mission statement crafted in Brussels, while managing the controversial ethnic expectations of the local population in Kosovo. Because of its imposed “status neutral,” in its three years of deployment in Kosovo, EULEX is considered to have been preoccupied with keeping a low profile, remaining invisible and not taking stances in an otherwise politically unsettled territorial entity amid acute ethnic cleavages. While it is considered as an important example to test the EU’s vertical and horizontal consistencies, EULEX’s ambiguous legal status has had its own implications; how EULEX seeks to maintain its coherence within Kosovo with its headquarters in Brussels. With most of its work dedicated to its Press and Information Office, in articulating and setting forward communication in three different languages and aiming three different (to say the least) audiences, its journey is still that of seeking legitimacy and popular support. This work examines EULEX from a critical perspective

Equations Defining Toric Varieties

This article will appear in the proceedings of the AMS Summer Institute in Algebraic Geometry at Santa Cruz, July 1995. The topic is toric ideals, by which I mean the defining ideals of subvarieties of affine or projective space which are parametrized by monomials. Numerous open problems are given.Comment: AMS-Tex, 13 page

Polynomials defining distinguished varieties

Using a sums of squares formula for two variable polynomials with no zeros on the bidisk, we are able to give a new proof of a representation for distinguished varieties. For distinguished varieties with no singularities on the two-torus, we are able to provide extra details about the representation formula and use this to prove a bounded extension theorem.Comment: 26 page