On the symbiosis of law and truth in Christian theology: Reconciling universal and particular through the Pauline law of love

This article argues that the secular liberal and positivist foundations of the modern Western legal system render it violent. In particular, the liberal exclusion of faith and subjectivity in favour of abstract and universal reason in conjunction with its privileging of individual autonomy at the expense of the community leads to alienation of the individual from the community. Similarly, the positivist exclusion of faith and theology from law, with its enforced conformity to the posited law, also results in this violence of alienation. In response, this article proposes a new foundation for law, a natural law based in the truth of Trinitarian theology articulated by John Milbank. In the Trinity, the members exist as a perfect unity in diversity, providing a model for the reconciliation of the legal individual and community: the law of love. Through the law of love as the basic norm, individuals love their neighbours as themselves, reconciling the particular and the universal, and providing a community of peace rather than violence.

Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal Sampling

In this paper we have used simulations to make a conjecture about the coverage of a t-dimensional subspace of a d-dimensional parameter space of size n when performing k trials of Latin Hypercube sampling. This takes the form P(k,n,d,t) = 1 - e^(-k/n^(t-1)). We suggest that this coverage formula is independent of d and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the t-dimensional subspace at the sub-block size level. These ideas have particular relevance when attempting to perform uncertainty quantification and sensitivity analyses.