On Fragments and Geometry: The International Legal Order as Metaphor and How it Matters

This article engages the narrative of fragmentation in international law by asserting that legal academics and professionals have failed to probe more deeply into ‘fragmentation’ as a concept and, more specifically, as a spatial metaphor. The contention here is that however central fragmentation has been to analyses of contemporary international law, this notion has been conceptually assumed, ahistorically accepted and philosophically under-examined. The ‘fragment’ metaphor is tied historically to a cartographic rationality – and thus ‘reality’ – of all social space being reducible to a geometric object and, correspondingly, a planimetric map. The purpose of this article is to generate an appreciation among international lawyers that the problem of ‘fragmentation’ is more deeply rooted in epistemology and conceptual history. This requires an explanation of how the conflation of social space with planimetric reduction came to be constructed historically and used politically, and how that model informs representations of legal practices and perceptions of ‘international legal order’ as an inherently absolute and geometric. This implies the need to dig up and expose background assumptions that have been working to precondition a ‘fragmented’ characterization of worldly space. With the metaphor of ‘digging’ in mind, I draw upon Michel Foucault’s ‘archaeology of knowledge’ and, specifically, his assertion that epochal ideas are grounded by layers of ‘obscure knowledge’ that initially seem unrelated to a discourse. In the case of the fragmentation narrative, I argue obscure but key layers can be found in the Cartesian paradigm of space as a geometric object and the modern States’ imperative to assert (geographic) jurisdiction. To support this claim, I attempt to excavate the fragment metaphor by discussing key developments that led to the production and projection of geometric and planimetric reality since the 16th century

Quantifying Self-Organization with Optimal Wavelets

The optimal wavelet basis is used to develop quantitative, experimentally applicable criteria for self-organization. The choice of the optimal wavelet is based on the model of self-organization in the wavelet tree. The framework of the model is founded on the wavelet-domain hidden Markov model and the optimal wavelet basis criterion for self-organization which assumes inherent increase in statistical complexity, the information content necessary for maximally accurate prediction of the system's dynamics. At the same time the method, presented here for the one-dimensional data of any type, performs superior denoising and may be easily generalized to higher dimensions.Comment: 12 pages, 3 figure

One Dimensional Asynchronous Cooperative Parrondo's Games

An analytical result and an algorithm are derived for the probability distribution of the one-dimensional cooperative Parrondo's games. We show that winning and the occurrence of the paradox depends on the number of players. Analytical results are compared to the results of the computer simulation and to the results based on the mean-field approach.Comment: 10 pages, 4 figures, submitted to Fluctuations and Noise Letter

Cooperative Parrondo's Games on a Two-dimensional Lattice

Cooperative Parrondo's games on a regular two dimensional lattice are analyzed based on the computer simulations and on the discrete-time Markov chain model with exact transition probabilities. The paradox appears in the vicinity of the probabilites characterisitic of the "voter model", suggesting practical applications. As in the one-dimensional case, winning and the occurrence of the paradox depends on the number of players.Comment: Presented at the 3rd Int. Conference NEXT-SigmaPhi; Figures not include