Non-power positional number representation systems, bijective numeration, and the Mesoamerican discovery of zero

Pre-Columbian Mesoamerica was a fertile crescent for the development of number systems. A form of vigesimal system seems to have been present from the first Olmec civilization on wards, to which succeeding peoples made contributions. We discuss the Maya use of the representational redundancy present in their Long Count calendar, a non-power positional number representation system with multipliers 1, 20, 18 x 20, ..., 18 x 20(n). We demonstrate that the Mesoamericans did not need to invent positional notation and discover zero at the same time because they were not afraid of using a number system in which the same number can be written indifferent ways. A Long Count number system with digits from 0 to 20 is seen later to pass to one using digits 0 to 19, which leads us to propose that even earlier there may have been an initial zeroless bijective numeration system whose digits ran from 1 to 20. Mesoamerica was able to make this conceptual leap to the concept of a cardinal zero to perform arithmetic owing to a familiarity with multiple and redundant number representation systems

Fundamentos de la utilidad de un análisis no-lineal en el sistema climático

Taking into account that the Climate System is the result of a series of complex interactions between all the subsystems that comprise it, it is necessary to regard the importance of the use of non-linear analysis tounderstand climate variability and the phenomena derived from this. Throughout this work, a compilation was made on the most important methods used for the study of climate. The usefulness of linear analysis is pointed out, arguing at the same time, the relevance of combining the latter with a non-linear approach, since only with the union of these two will it be possible to more accurately predict the behavior of the climate system.To illustrate this, temperature series are analyzed in Antofagasta, located in the southern hemisphere, which has fewer and shorter records compared to the northern hemisphere.Tomando en cuenta que el Sistema Climático es el resultado de una serie de interacciones complejas entre todos los susbsistemas que lo conforman, es necesario considerar la importancia del uso del análisis no-lineal para entender la varibilidad climática y los fenómenos que se derivan de ésta. A lo largo de este trabajo se hizo una recopilación sobre los métodos más importantes que se utilizan para el estudio del clima. Se puntualiza la utilidad del análisis lineal, argumentando al mismo tiempo, la relevancia de juntar este último con un enfoque no-lineal, ya que sólo con la unión de estos dos será posible predecir de manera más certera el comportamiento del sistema climático. Para ilustrar esto se analizan series de temperatura en Antofagasta, localizada en el hemisferio sur que cuenta con menos registros y más cortos en comparación al hemisferio norte

Chaos and periodicities in a climatic time series of the Iberian Margin

We analyze the time series of the temperature of the sedimentary core MD01-2443 originating from the Iberian Margin with a duration of 420\u2009kyr. The series has been tested for unit-root and a long term trend is estimated. We identify four significant periodicities together with a low climatic activity every 100\u2009kyr, and these were associated with internal and external forcings. Also, we identify a high-frequency fast component that acts on top of a nonlinear, irreversible slow-changing dynamics. We find the presence of chaos in the climate of the Iberian Margin by means of a neural network asymptotic test on the largest Lyapunov exponent. The analysis suggests that the chaotic dynamics is associated with the fast high-frequency component. We also carry out a statistical analysis of the dimensionality of the attractor. Our results confirm the possibility that periodic behavior and chaos may coexist on different time scales. This could lead to different degrees of predictability in the climate system according to the characteristic time scales and/or phase-space locations