The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning

An active area of research in the fields of machine learning and statistics is the development of causal discovery algorithms, the purpose of which is to infer the causal relations that hold among a set of variables from the correlations that these exhibit. We apply some of these algorithms to the correlations that arise for entangled quantum systems. We show that they cannot distinguish correlations that satisfy Bell inequalities from correlations that violate Bell inequalities, and consequently that they cannot do justice to the challenges of explaining certain quantum correlations causally. Nonetheless, by adapting the conceptual tools of causal inference, we can show that any attempt to provide a causal explanation of nonsignalling correlations that violate a Bell inequality must contradict a core principle of these algorithms, namely, that an observed statistical independence between variables should not be explained by fine-tuning of the causal parameters. In particular, we demonstrate the need for such fine-tuning for most of the causal mechanisms that have been proposed to underlie Bell correlations, including superluminal causal influences, superdeterminism (that is, a denial of freedom of choice of settings), and retrocausal influences which do not introduce causal cycles.Comment: 29 pages, 28 figs. New in v2: a section presenting in detail our characterization of Bell's theorem as a contradiction arising from (i) the framework of causal models, (ii) the principle of no fine-tuning, and (iii) certain operational features of quantum theory; a section explaining why a denial of hidden variables affords even fewer opportunities for causal explanations of quantum correlation

Description's Objects: Austrian Variations

What did Wittgenstein take description to involve ? What are the objects of his descriptions ? What did he think he was doing in and by describing what he described ? In order to answer these three questions it will be useful to appeal to an object of comparison. But which ? First we need an answer to another question

Towards a framework for investigating tangible environments for learning

External representations have been shown to play a key role in mediating cognition. Tangible environments offer the opportunity for novel representational formats and combinations, potentially increasing representational power for supporting learning. However, we currently know little about the specific learning benefits of tangible environments, and have no established framework within which to analyse the ways that external representations work in tangible environments to support learning. Taking external representation as the central focus, this paper proposes a framework for investigating the effect of tangible technologies on interaction and cognition. Key artefact-action-representation relationships are identified, and classified to form a structure for investigating the differential cognitive effects of these features. An example scenario from our current research is presented to illustrate how the framework can be used as a method for investigating the effectiveness of differential designs for supporting science learning

Half century of black-hole theory: from physicists' purgatory to mathematicians' paradise

Although implicit in the discovery of the Schwarzschild solution 40 years earlier, the issues raised by the theory of what are now known as black holes were so unsettling to physicists of Einstein's generation that the subject remained in a state of semiclandestine gestation until his demise. That turning point -- just half a century after Einstein's original foundation of relativity theory, and just half a century ago today -- can be considered to mark the birth of black hole theory as a subject of systematic development by physicists of a new and less inhibited generation, whose enthusastic investigations have revealed structures of unforeseen mathematical beauty, even though questions about the physical significance of the concomitant singularities remain controversial.Comment: 30 pages latex. Contrib. to Encuentros Relativistas Espanoles: A Century of Relativity Theory, Oviedo, 2005 (ed. L. Mornas