Después de haber analizado las razones que indujeron a las antiguas matemáticas griegas y de que Aristóteles sólo admitiera una débil forma de lo infinito (el potencial), se explora una ampliación de este concepto más allá de sus referencias numéricas y geométricas. El infinito puede expresar la “inagotable” riqueza ontológica de los atributos de las entidades individuales o, en otro sentido, el infinito puede ser entendido como aquello “ilimitado”. En este segundo sentido la “negación” (de las limitaciones) se presenta como una fuerza positiva en la formación del sentido ontológico de lo infinito.

Ontología, homonimia y explicación reductiva en Aristóteles. II Homonimia en la Física. III. Homonimia y explicación reductiva en el tratamiento de espacio, infinito y tiempo en Física III-IV. IV. Consideraciones finales.

El objetivo de este artículo es explicar las características básicas de la concepción aristotélica de la continuidad sostenida a lo largo de su Física. Tal como intentaré mostrar, es imposible comprender realmente qué entiende Aristóteles por “continuidad” si no se comienza por dilucidar la particular posición que tiene la continuidad junto a otros términos, dentro del marco de su teoría física, tales como “sucesión”, contigüidad” y “contacto”. En este punto, mostraré cómo una correcta aproximación a la noción de “continuidad” exige especificar la relación, así como también la diferencia, entre “continuidad” y “contigüidad”, ya que no es del todo claro cómo debemos entender esta diferencia terminológica al interior de la física aristotélica. Luego, y finalmente, mi análisis se concentrará en examinar qué afirma Aristóteles en relación a la “continuidad” propiamente tal. Éste análisis, a su vez, aborda los conceptos más importantes de la teoría aristotélica de la continuidad y aborda, a su vez, el llamado carácter operativo de la concepción aristotélica del continuum.

This paper analyzes two different proposals, one by Ellis and Brundrit, based on classical relativistic cosmology, the other by Garriga and Vilenkin, based on the DH interpretation of quantum mechanics, both of which conclude that, in an infinite universe, planets and living beings must be repeated an infinite number of times. We point to some possible shortcomings in the arguments of these authors. We conclude that the idea of an infinite repetition of histories in space cannot be considered strictly speaking a consequence of current physics and cosmology. Such ideas should be seen rather as examples of {\guillemotleft}ironic science{\guillemotright} in the terminology of John Horgan.

“The Center is Everywhere” is a sculpture by Josiah McElheny, currently (through October 14, 2012) on exhibit at the Institute of Contemporary Art, Boston. The sculpture is based on data from the Sloan Digital Sky Survey (SDSS), using hundreds of glass crystals and lamps suspended from brass rods to represent the three-dimensional structure mapped by the SDSS through one of its 2000+ spectroscopic plugplates. This article describes the scientific ideas behind this sculpture, emphasizing the principle of the statistical homogeneity of cosmic structure in the presence of local complexity. The title of the sculpture is inspired by the work of the French revolutionary Louis Auguste Blanqui, whose 1872 book “Eternity Through The Stars: An Astronomical Hypothesis” was the first to raise the spectre of the infinite replicas expected in an infinite, statistically homogeneous universe. Puzzles of infinities, probabilities, and replicas continue to haunt modern fiction and contemporary discussions of inflationary cosmology.

The Riemann Hypothesis has been of central interest to mathematicians for a long time and many unsuccessful attempts have been made to either prove or disprove it. Since the Riemann zeta function is defined as a sum of the infinite number of items, in this paper, we look at the Riemann Hypothesis using a new applied approach to infinity allowing one to easily execute numerical computations with various infinite and infinitesimal numbers in accordance with the principle `The part is less than the whole’ observed in the physical world around us. The new approach allows one to work with functions and derivatives that can assume not only finite but also infinite and infinitesimal values and this possibility is used to study properties of the Riemann zeta function and the Dirichlet eta function. A new computational approach allowing one to evaluate these functions at certain points is proposed. Numerical examples are given. It is emphasized that different mathematical languages can be used to describe mathematical objects with different accuracies. The traditional and the new approaches are compared with respect to their application to the Riemann zeta function and the Dirichlet eta function. The accuracy of the obtained results is discussed in detail.

Today, Yaroslav Sergeyev, a mathematician at the University of Calabria in Italy solves this problem (and the analogous three dimensional version called Menger’s sponge). For the last few years, Sergeyev has been championing a new type of mathematics called infinity computing. The basic idea is to replace the notion of infinity with a new number that Sergeyev calls grossone. Sergeyev begins by adding a new axiom to the axiom of real numbers, which he calls the infinite unit axiom. This introduces grossone–the infinite unit. Because it is governed by the other axioms of real numbers, grossone behaves much like one too. So it’s possible to multiply grossone, divide it, add to it and subtract from it, just as is possible with other real numbers. That suddenly makes working at infinity much easier by using a computing process that Sergeyev calls the infinity computer, which has the additional axiom built in. “The introduction of grossone gives a possibility to work with finite, infinite and infinitesimal quantities numerically,” he says. To show off its power, he works through the Sierpinski carpet examples given above, revealing how it’s possible to keep track of the number of iterations at infinity simply by adding or subtracting real numbers from grossone. If a square can created in grossone steps, a square doughnut can be created in -grossone minus 1- steps. In this way, it’s a simple matter to differentiate between any of the shapes in carpet sequence. That looks handy. The inability to keep track of mathematical processes at or close to infinity in a consistent fashion has frustrated mathematicians and physicists for centuries. So if Sergeyev has found a way round this that works, that’s clearly a highly significant advance.