Webs of Lagrangian Tori in Projective Symplectic Manifolds

For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperk\"ahler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauville's. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt's theory of subnormal subgroups.Comment: 18 pages, minor latex problem fixe

Borel-Cantelli sequences

A sequence $\{x_{n}\}_1^\infty$ in $[0,1)$ is called Borel-Cantelli (BC) if for all non-increasing sequences of positive real numbers $\{a_n\}$ with $\underset{i=1}{\overset{\infty}{\sum}}a_i=\infty$ the set $$\underset{k=1}{\overset{\infty}{\cap}} \underset{n=k}{\overset{\infty}{\cup}} B(x_n, a_n))=\{x\in[0,1)\mid |x_n-x|<a_n \text{for} \infty \text{many}n\geq1\}$$ has full Lebesgue measure. (To put it informally, BC sequences are sequences for which a natural converse to the Borel-Cantelli Theorem holds). The notion of BC sequences is motivated by the Monotone Shrinking Target Property for dynamical systems, but our approach is from a geometric rather than dynamical perspective. A sufficient condition, a necessary condition and a necessary and sufficient condition for a sequence to be BC are established. A number of examples of BC and not BC sequences are presented. The property of a sequence to be BC is a delicate diophantine property. For example, the orbits of a pseudo-Anosoff IET (interval exchange transformation) are BC while the orbits of a "generic" IET are not. The notion of BC sequences is extended to more general spaces.Comment: 20 pages. Some proofs clarifie

Measuring Progress in Robotics: Benchmarking and the ‘Measure-Target Confusion’

While it is often said that in order to qualify as a true science robotics should aspire to reproducible and measurable results that allow benchmarking, I argue that a focus on benchmarking will be a hindrance for progress. Several academic disciplines that have been led into pursuing only reproducible and measurable ‘scientific’ results—robotics should be careful not to fall into that trap. Results that can be benchmarked must be specific and context-dependent, but robotics targets whole complex systems independently of a specific context—so working towards progress on the technical measure risks missing that target. It would constitute aiming for the measure rather than the target: what I call ‘measure-target confusion’. The role of benchmarking in robotics shows that the more general problem to measure progress towards more intelligent machines will not be solved by technical benchmarks; we need a balanced approach with technical benchmarks, real-life testing and qualitative judgment

Mineralogical Controls on the Ti Isotope Composition of Subduction Zone Magmas

The positive Ti isotope versus SiO2-content correlation in igneous rocks reflects the fractional crystallization of Ti-bearing oxide minerals. However, Ti isotope variations of subduction-related igneous rocks indicate that the Ti isotope compositions of their mantle sources are heterogeneous and additional mineral phases may promote Ti isotope fractionation. We have determined the Ti isotope composition of well-characterized subduction-related basalts, andesites and boninites. Samples from the Solomon Islands, the Troodos ophiolite in Cyprus, and Cape Vogel in Papua New Guinea show small but resolvable variations that may be related to differences in their mantle sources. Specifically, the δ49Ti of boninites (+0.109‰ to +0.168‰) is slightly higher than that of tholeiites (−0.027‰ to +0.111‰) from the same localities (Troodos in Cyprus and Cape Vogel in Papua New Guinea). Modeling suggests the partial melting of progressively depleted mantle sources where residual Cr-spinel plays a greater role in controlling the Ti budget during partial melting. More pronounced variations in δ49Ti are clearly linked to the fractional crystallization of Ti-oxides: Samples from Rabaul Volcanic Complex (New Britain, Papua New Guinea) show increasing δ49Ti (up to +0.373‰) with increasing Ti/V and decreasing Dy/Yb. Fractional crystallization models suggest that oxide minerals and amphibole are needed to sufficiently increase the δ49Ti of these magmas. Our study highlights that the combination of diagnostic trace element patterns and Ti isotope compositions in subduction-related igneous rocks can be a powerful tool to constrain petrogenetic processes and to discriminate between different crystallizing mineral phases

A better life through information technology? The techno-theological eschatology of posthuman speculative science

This is the pre-peer reviewed version of the article, published in Zygon 41(2) pp.267-288, which has been published in final form at http://www3.interscience.wiley.com/journal/118588124/issueThe depiction of human identity in the pop-science futurology of engineer/inventor Ray Kurzweil, the speculative-robotics of Carnegie Mellon roboticist Hans Moravec and the physics of Tulane University mathematics professor Frank Tipler elevate technology, especially information technology, to a point of ultimate significance. For these three figures, information technology offers the potential means by which the problem of human and cosmic finitude can be rectified. Although Moravec’s vision of intelligent robots, Kurzweil’s hope for immanent human immorality, and Tipler’s description of human-like von Neumann probe colonising the very material fabric of the universe, may all appear to be nothing more than science fictional musings, they raise genuine questions as to the relationship between science, technology, and religion as regards issues of personal and cosmic eschatology. In an attempt to correct what I see as the ‘cybernetic-totalism’ inherent in these ‘techno-theologies’, I will argue for a theology of technology, which seeks to interpret technology hermeneutically and grounds human creativity in the broader context of divine creative activity

Robot rights? Towards a social-relational justification of moral consideration \ud

Should we grant rights to artificially intelligent robots? Most current and near-future robots do not meet the hard criteria set by deontological and utilitarian theory. Virtue ethics can avoid this problem with its indirect approach. However, both direct and indirect arguments for moral consideration rest on ontological features of entities, an approach which incurs several problems. In response to these difficulties, this paper taps into a different conceptual resource in order to be able to grant some degree of moral consideration to some intelligent social robots: it sketches a novel argument for moral consideration based on social relations. It is shown that to further develop this argument we need to revise our existing ontological and social-political frameworks. It is suggested that we need a social ecology, which may be developed by engaging with Western ecology and Eastern worldviews. Although this relational turn raises many difficult issues and requires more work, this paper provides a rough outline of an alternative approach to moral consideration that can assist us in shaping our relations to intelligent robots and, by extension, to all artificial and biological entities that appear to us as more than instruments for our human purpose

SIC~POVMs and Clifford groups in prime dimensions

We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence, two SIC~POVMs covariant with respect to the HW group are unitarily or antiunitarily equivalent if and only if they are on the same orbit of the extended Clifford group. In dimension three, each group covariant SIC~POVM may be covariant with respect to three or nine HW groups, and the symmetry group of the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW groups respectively. There may exist two or three orbits of equivalent SIC~POVMs for each group covariant SIC~POVM, depending on the order of its symmetry group. We then establish a complete equivalence relation among group covariant SIC~POVMs in dimension three, and classify inequivalent ones according to the geometric phases associated with fiducial vectors. Finally, we uncover additional SIC~POVMs by regrouping of the fiducial vectors from different SIC~POVMs which may or may not be on the same orbit of the extended Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J. Phys. A: Math. Theor. 43, 305305 (2010

The Mathematical Universe

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.Comment: Replaced to match accepted Found. Phys. version, 31 pages, 5 figs; more details at http://space.mit.edu/home/tegmark/toe.htm

The Web will kill them all: new media, digital utopia, and political struggle in the Italian 5-Star Movement

This article examines the role of discourses about new media technology and the Web in the rise of the 5-Star Movement (Movimento 5 Stelle, or M5S) in Italy. Founded by comedian and activist Beppe Grillo and Web entrepreneur Gianrobe rto Casaleggio in 2009, this movement succeeded in becoming the second largest party at t he 2013 national elections in Italy. This article aims to discuss how elements of digital uto pia and Web-centric discourses have been inserted into the movement’s political message, and how the construction of the Web as a myth has shaped the movement’s discourse and political p ractice. The 5-Star Movement is compared and contrasted with other social and political move ments in Western countries which have displayed a similar emphasis on new media, such as the Occupy movement, the Indignados movement, and the Pirate Parties in Sweden and Germ any. By adopting and mutating cyber- utopian discourses from the so-called Californian i deology, the movement symbolically identifies itself with the Web. The traditional political esta blishment is associated with “old” media (television, radio, and the printed press), and rep resented as a “walking dead,” doomed to be superseded and buried by a Web-based direct democra cy

The Social and Ethical Acceptability of NBICs for Purposes of Human Enhancement: Why Does the Debate Remain Mired in Impasse?

The emergence and development of convergent technologies for the purpose of improving human performance, including nanotechnology, biotechnology, information sciences, and cognitive science (NBICs), open up new horizons in the debates and moral arguments that must be engaged by philosophers who hope to take seriously the question of the ethical and social acceptability of these technologies. This article advances an analysis of the factors that contribute to confusion and discord on the topic, in order to help in understanding why arguments that form a part of the debate between transhumanism and humanism result in a philosophical and ethical impasse: 1. The lack of clarity that emerges from the fact that any given argument deployed (arguments based on nature and human nature, dignity, the good life) can serve as the basis for both the positive and the negative evaluation of NBICs. 2. The impossibility of providing these arguments with foundations that will enable others to deem them acceptable. 3. The difficulty of applying these same arguments to a specific situation. 4. The ineffectiveness of moral argument in a democratic society. The present effort at communication about the difficulties of the argumentation process is intended as a necessary first step towards developing an interdisciplinary response to those difficulties