8,988 research outputs found
A fast method for power spectrum and foreground analysis for 21 cm cosmology
No full textWe develop and demonstrate an acceleration of the Liu and Tegmark quadratic estimator formalism for inverse variance foreground subtraction and power spectrum estimation in 21 cm tomography from O(N[superscript 3]) to O(NlogN), where N is the number of voxels of data. This technique makes feasible the megavoxel scale analysis necessary for current and upcoming radio interferometers by making only moderately restrictive assumptions about foreground models and survey geometry. We exploit iterative and Monte Carlo techniques and the symmetries of the foreground covariance matrices to quickly estimate the 21 cm brightness temperature power spectrum, P(k[subscript ||],k[subscript ⊥]), the Fisher information matrix, the error bars, the window functions, and the bias. We also extend the Liu and Tegmark foreground model to include bright point sources with known positions in a way that scales as O[(NlogN)×(N point sources)]≤O(N[superscript 5]/[superscript 3]). As a first application of our method, we forecast error bars and window functions for the upcoming 128-tile deployment of the Murchinson Widefield Array, showing that 1000 hours of observation should prove sufficiently sensitive to detect the power spectrum signal from the Epoch of Reionization.National Science Foundation (U.S.) (Grant AST-1105835
Improved Measures of Integrated Information
No full textAlthough there is growing interest in measuring integrated information in computational and cognitive systems, current methods for doing so in practice are computationally unfeasible. Existing and novel integration measures are investigated and classified by various desirable properties. A simple taxonomy of Φ-measures is presented where they are each characterized by their choice of factorization method (5 options), choice of probability distributions to compare (3 × 4 options) and choice of measure for comparing probability distributions (7 options). When requiring the Φ-measures to satisfy a minimum of attractive properties, these hundreds of options reduce to a mere handful, some of which turn out to be identical. Useful exact and approximate formulas are derived that can be applied to real-world data from laboratory experiments without posing unreasonable computational demands.United States. Army Research Office (Grant W911NF-15-1-0300
Omniscopes: Large area telescope arrays with only N logN computational cost
No full textWe show that the class of antenna layouts for telescope arrays allowing cheap analysis hardware (with correlator cost scaling as Nlog N rather than N[superscript 2] with the number of antennas N) is encouragingly large, including not only previously discussed rectangular grids but also arbitrary hierarchies of such grids, with arbitrary rotations and shears at each level. We show that all correlations for such a 2D array with an n-level hierarchy can be efficiently computed via a fast Fourier transform in not two but 2n dimensions. This can allow major correlator cost reductions for science applications requiring exquisite sensitivity at widely separated angular scales, for example, 21 cm tomography (where short baselines are needed to probe the cosmological signal and long baselines are needed for point source removal), helping enable future 21 cm experiments with thousands or millions of cheap dipolelike antennas. Such hierarchical grids combine the angular resolution advantage of traditional array layouts with the cost advantage of a rectangular fast Fourier transform telescope. We also describe an algorithm for how a subclass of hierarchical arrays can efficiently use rotation synthesis to produce global sky maps with minimal noise and a well-characterized synthesized beam.United States. National Aeronautics and Space Administration (Grant NAG5-11099)United States. National Aeronautics and Space Administration (Grant NNG 05G40G)National Science Foundation (U.S.) (Grant AST-0607597)National Science Foundation (U.S.) (Grant AST-0708534)National Science Foundation (U.S.) (Grant AST-0908848)National Science Foundation (U.S.) (Grant PHY0855425)David & Lucile Packard Foundatio
Our mathematical universe: my quest for the ultimate nature of reality
No full textMax Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians
Critical Behavior in Physics and Probabilistic Formal Languages
No full textWe show that the mutual information between two symbols, as a function of the number of symbols between the two, decays exponentially in any probabilistic regular grammar, but can decay like a power law for a context-free grammar. This result about formal languages is closely related to a well-known result in classical statistical mechanics that there are no phase transitions in dimensions fewer than two. It is also related to the emergence of power law correlations in turbulence and cosmological inflation through recursive generative processes. We elucidate these physics connections and comment on potential applications of our results to machine learning tasks like training artificial recurrent neural networks. Along the way, we introduce a useful quantity, which we dub the rational mutual information, and discuss generalizations of our claims involving more complicated Bayesian networks. Keywords: formal languages; statistical mechanics; criticalit
Life 3.0 : being human in the age of artificial intelligence /
No full text"What jobs should be automated? How should our legal systems handle autonomous systems? How likely is the emergence of suprahuman intelligence? A.I. is the future of science, technology, and business--and there is no person better qualified or situated to explore that future than Max Tegmark. What has A.I. brought us? Where will it lead us? The story of A.I. is the story of intelligence--of life processes as they evolve from bacteria (1.0) to humans (2.0), where life processes define their own software, to technology (3.0), where life processes design both their hardware and software. We know that A.I. is transforming work, laws, and weapons, as well as the dark side of computing (hacking and viral sabotage), raising questions that we all need to address: What jobs should be automated? How should our legal systems handle autonomous systems? How likely is the emergence of suprahuman intelligence? Is it possible to control suprahuman intelligence? How do we ensure that the uses of A.I. remain beneficial? These are the issues at the heart of this book and its unique perspective, which seeks a ground apart from techno-skepticism and digital utopia"--"This is a Borzoi Book published by Alfred A. Knopf."Includes bibliographical references and index."What jobs should be automated? How should our legal systems handle autonomous systems? How likely is the emergence of suprahuman intelligence? A.I. is the future of science, technology, and business--and there is no person better qualified or situated to explore that future than Max Tegmark. What has A.I. brought us? Where will it lead us? The story of A.I. is the story of intelligence--of life processes as they evolve from bacteria (1.0) to humans (2.0), where life processes define their own software, to technology (3.0), where life processes design both their hardware and software. We know that A.I. is transforming work, laws, and weapons, as well as the dark side of computing (hacking and viral sabotage), raising questions that we all need to address: What jobs should be automated? How should our legal systems handle autonomous systems? How likely is the emergence of suprahuman intelligence? Is it possible to control suprahuman intelligence? How do we ensure that the uses of A.I. remain beneficial? These are the issues at the heart of this book and its unique perspective, which seeks a ground apart from techno-skepticism and digital utopia"-
Masculinidades Cuánticas:Haciendo Género con la Hipótesis del Universo Matemático de Max Tegmark
No full textIn his book Our Mathematical Universe, Max Tegmark proposes a way of viewing “reality” as a multiverse of parallel universes governed by mathematics. In this article we take a few of Tegmark’s more accessible ideas and combine them with the study of masculinities to form “quantum masculinities.” Specifically, we use Tegmark’s presentation of the multiverse and the quantum state of superposition as a thinking tool for imagining not just multiple masculinities but infinite and contradictory masculinities. We then mobilize this newly proposed concept of quantum masculinities in two contexts. First, we put quantum masculinities in dialogue with Judith Butler’s theory of gender performativity to question to what degree gender performance requires an observer. Second, we explore how far quantum masculinities are reconcilable with The Five Stages of Masculinity. We conclude with some discussion about the categories of “I” and “we” in imagining the self, as well as how the study of masculinities might evolve.En su libro Our Mathematical Universe, Max Tegmark propone una forma de ver la "realidad" como un multiverso de universos paralelos gobernados por las matemáticas. En este artículo tomamos algunas de las ideas más accesibles de Tegmark y las combinamos con el estudio de las masculinidades para formar las "masculinidades cuánticas". Específicamente, utilizamos la presentación de Tegmark del multiverso y el estado cuántico de superposición como una herramienta de pensamiento para imaginar, no solo masculinidades múltiples, sino que masculinidades infinitas y contradictorias. Después vamos más allá y planteamos este nuevo concepto de masculinidades cuánticas en dos contextos. En primer lugar, ponemos en contacto las masculinidades cuánticas con la teoría de la performatividad de género de Judith Butler para preguntarnos en qué medida el desempeño de género requiere una persona observadora. En segundo lugar, exploramos hasta qué punto las masculinidades cuánticas son reconciliables con Las Cinco Etapas de la Masculinidad. Concluimos con una discusión sobre las categorías de "yo" y "nosotros" al imaginarnos a nosotros mismos, y sobre cómo podría evolucionar el estudio de las masculinidades
Born in an infinite universe: A cosmological interpretation of quantum mechanics
No full textWe study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for calculating probabilities must be supplemented by estimates of relative frequencies of observers. We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantum measurement in different regions, with relative frequencies given by the square of the wave-function amplitudes. Our formal argument hinges on properties of what we term the quantum confusion operator, which projects onto the Hilbert subspace where the Born rule fails, and we comment on its relation to the oft-discussed quantum frequency operator. This analysis unifies the classical and quantum levels of parallel universes that have been discussed in the literature, and has implications for several issues in quantum measurement theory. Replacing the standard hypothetical ensemble of measurements repeated ad infinitum by a concrete decohered spatial collection of experiments carried out in different distant regions of space provides a natural context for a statistical interpretation of quantum mechanics. It also shows how, even for a single measurement, probabilities may be interpreted as relative frequencies in unitary (Everettian) quantum mechanics. We also argue that after discarding a zero-norm part of the wave function, the remainder consists of a superposition of indistinguishable terms, so that arguably “collapse” of the wave function is irrelevant, and the “many worlds” of Everett’s interpretation are unified into one. Finally, the analysis suggests a “cosmological interpretation” of quantum theory in which the wave function describes the actual spatial collection of identical quantum systems, and quantum uncertainty is attributable to the observer’s inability to self-locate in this collection.United States. National Aeronautics and Space Administration (Grant No. NAG5-11099)United States. National Aeronautics and Space Administration (Grant No. NNG 05G40G)National Science Foundation (U.S.) (Grant No. AST-0607597)National Science Foundation (U.S.) (Grant No. AST-0708534)National Science Foundation (U.S.) (Grant No. AST-0908848)National Science Foundation (U.S.) (Grant No. PHY-0855425)National Science Foundation (U.S.) (Grant No. PHY-0757912)Templeton Foundation (Foundational Questions in Physics and Cosmology grant)David & Lucile Packard FoundationResearch Corporatio
Life 3.0
No full textHow will Artificial Intelligence affect crime, war, justice, jobs, society and our very sense of being human? The rise of AI has the potential to transform our future more than any other technology—and there’s nobody better qualified or situated to explore that future than Max Tegmark, an MIT professor who’s helped mainstream research on how to keep AI beneficial. How can we grow our prosperity through automation without leaving people lacking income or purpose? What career advice should we give today’s kids? How can we make future AI systems more robust, so that they do what we want without crashing, malfunctioning or getting hacked? Should we fear an arms race in lethal autonomous weapons? Will machines eventually outsmart us at all tasks, replacing humans on the job market and perhaps altogether? Will AI help life flourish like never before or give us more power than we can handle? What sort of future do you want? This book empowers you to join what may be the most important conversation of our time. It doesn’t shy away from the full range of viewpoints or from the most controversial issues—from superintelligence to meaning, consciousness and the ultimate physical limits on life in the cosmos
- …
