Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our texbook “An Introduction to Kolmogorov Complexity and Its Applications” (M. Li and P. Vitanyi), 2nd Ed., Springer-Verlag, 1997.

Uncovering the structure of socioeconomic systems and timely estimation of socioeconomic status are significant for economic development. The understanding of socioeconomic processes provides foundations to quantify global economic development, to map regional industrial structure, and to infer individual socioeconomic status. In this review, we will make a brief manifesto about a new interdisciplinary research field named Computational Socioeconomics, followed by detailed introduction about data resources, computational tools, data-driven methods, theoretical models and novel applications at multiple resolutions, including the quantification of global economic inequality and complexity, the map of regional industrial structure and urban perception, the estimation of individual socioeconomic status and demographic, and the real-time monitoring of emergent events.

El presente artículo se interroga por el lugar que ocupa lo social al interior de la teoría sobre la existencia humana que Sartre desarrolla en El ser y la nada: Ensayo de ontología fenomenológica (1943). Con ese fin se analizan paso a paso los principales argumentos y conceptos sartreanos referidos a la existencia del otro, la relación fundamental con el otro, las relaciones concretas con el otro y, finalmente, la experiencia del nosotros.

These remarks take up the reflexive problematics of Being and Nothingness and related texts from a metalogical perspective. A mutually illuminating translation is posited between, on the one hand, Sartre’s theory of pure reflection, the linchpin of the works of Sartre’s early period and the site of their greatest difficulties, and, on the other hand, the quasi-formalism of diagonalization, the engine of the classical theorems of Cantor, Gödel, Tarski, Turing, etc. Surprisingly, the dialectic of mathematical logic from its inception through the discovery of the diagonal theorems can be recognized as a particularly clear instance of the drama of reflection according to Sartre, especially in the positing and overcoming of its proper valueideal, viz. the synthesis of consistency and completeness.

We review attempts by Pascual Jordan and other researchers, most notably Lawrence Biedenharn to generalize quantum mechanics by passing from associative matrix or operator algebras to non-associative algebras. We start with Jordan’s work from the early 1930ies leading to Jordan algebras and the first attempt to incorporate the alternative ring of octonions into physics. Jordan’s work on the octonions from 1932 till 1952 will be covered, discussing aspects of the exceptional Jordan algebra and how to express probabilities when working with the octonions and the exceptional Jordan algebra.

We formulate a quantum theory of the Universe based on Bayesian probability. In this theory, the probability of the Universe is not a frequency probability, which can be obtained by observing experimental results several times, but is a Bayesian probability, which can define a probability of an event that occurs just once. As an example, by applying the quantum theory of the Universe to an action of a scalar field theory in the four dimensions as a toy model for the theory of the Universe, we explicitly obtain the probability of the Universe and the action of matters in the Universe.

Para Alexandr Dugin [1] toda teoría política se fundamente en un sujeto: el individuo en el liberalismo, la clase social en el marxismo, y el Estado o la raza en el fascismo. En su propuesta de una Cuarta Teoría Política (en adelante CTP) nos habla del Dasein como sujeto de esta teoría. El Dasein o ser-ahí es un concepto fundamental de la filosofía de Martin Heidegger. En este artículo intentaremos aclarar que significa exactamente el concepto de Dasein y de qué manera se relaciona con las tesis de Dugin.

We explore the different meanings of “quantum uncertainty” contained in Heisenberg’s seminal paper from 1927, and also some of the precise definitions that were explored later. We recount the controversy about “Anschaulichkeit”, visualizability of the theory, which Heisenberg claims to resolve. Moreover, we consider Heisenberg’s programme of operational analysis of concepts, in which he sees himself as following Einstein. Heisenberg’s work is marked by the tensions between semiclassical arguments and the emerging modern quantum theory, between intuition and rigour, and between shaky arguments and overarching claims.

Postulo que es posible un realismo no estándar, un realismo que se coloque más allá de la representación y la predicción, centrándose en la experimentación. Y reconozco como ejemplo el realismo «materialista» del nuevo experimentalismo de Ian Hacking y de la teoría del cierre categoríal de Gustavo Bueno, ampliamente desarrollados en el último capítulo de la tesis. Estos dos filósofos marcan un nuevo rumbo en filosofía de la ciencia: «los filósofos de la ciencia se han limitado a pensar la ciencia como representación o predicción, pero de lo que se trata es de pensarla como transformación (construcción e intervención)». En cualquier caso, de cara al futuro, no cabe sino reconocer que la mayor o menor potencia de una teoría de la ciencia se va a medir por su capacidad para estar al tanto del funcionamiento de las ciencias modernas, como la física cuántica o la física del caos

In the theory of conditional sets, many classical theorems from áreas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or optimization. The frequent experience that such theorems can be proved by ‘conditionalizations’ of the classical proofs suggests that a general transfer principle is in the background, and that formulating and proving such a transfer principle would yield a wealth of useful further conditional versions of classical results, in addition to providing a uniform approach to the results already known. In this paper, we formulate and prove such a transfer principle based on second order arithmetic, which, by the results of reverse mathematics, suffices for the bulk of classical mathematics, including real analysis, measure theory and countable algebra, and excluding only more remote realms like category theory, set theoretical topology or uncountable set theory, see eg the introduction of Simpson