Competition of Languages and their Hamming Distance

We consider the spreading and competition of languages that are spoken by a population of individuals. The individuals can change their mother tongue during their lifespan, pass on their language to their offspring and finally die. The languages are described by bitstrings, their mutual difference is expressed in terms of their Hamming distance. Language evolution is determined by mutation and adaptation rates. In particular we consider the case where the replacement of a language by another one is determined by their mutual Hamming distance. As a function of the mutation rate we find a sharp transition between a scenario with one dominant language and fragmentation into many language clusters. The transition is also reflected in the Hamming distance between the two languages with the largest and second to largest number of speakers. We also consider the case where the population is localized on a square lattice and the interaction of individuals is restricted to a certain geometrical domain. Here it is again the Hamming distance that plays an essential role in the final fate of a language of either surviving or being extinct.Comment: 18 pages, 19 figure

Nested quasicrystalline discretisations of the line

One-dimensional cut-and-project point sets obtained from the square lattice in the plane are considered from a unifying point of view and in the perspective of aperiodic wavelet constructions. We successively examine their geometrical aspects, combinatorial properties from the point of view of the theory of languages, and self-similarity with algebraic scaling factor $\theta$. We explain the relation of the cut-and-project sets to non-standard numeration systems based on $\theta$. We finally examine the substitutivity, a weakened version of substitution invariance, which provides us with an algorithm for symbolic generation of cut-and-project sequences

The influence of geometrical and nongeometrical features on the use of the lexical concepts NEAR and FAR in English and Finnish

This paper investigates the impact of geometrical and nongeometrical features on the use of the lexical concepts NEAR and FAR in English and Finnish. Participants’ acceptability ratings for these concepts demonstrate that a bar in between a Figure and a Ground acts as a scale-setting object but not as a distance enhancing barrier, shows that the influence of the geometrical feature Figure–Ground distance exceeds the influence of several nongeometrical features, but most of all reveals that language specific lexical properties associated with NEAR and FAR predict language dependent effects for functional relatedness in interaction with Figure–Ground distance and bar presence

Differentiation with stratification: a principle of theoretical physics in the tradition of the memory art

The Art of Memory started with Aristotle's questions on memory. During its long evolution, it had important contributions from alchemist, was transformed by Ramon Llull and apparently ended with Giordano Bruno, who was considered the best known representative of this art. This tradition did not disappear, but lives in the formulations of our modern scientific theories. From its initial form as a method of keeping information via associations, it became a principle of classification and structuring of knowledge. This principle, which we here name {\it differentiation with stratification}, is a structural design behind classical mechanics. Integrating two different traditions of science in one structure, this physical theory became the modern paradigm of science. In this paper, we show that this principle can also be formulated as a set of questions. This is done via an analysis of theories, based on the epistemology of observational realism. A combination of Rudolph Carnap's concept of theory as a system of observational and theoretical languages, with a criterion for separating observational languages, based on analytical psychology, shapes this epistemology. The `nuclear' role of the observational laws and the differentiations from these nucleus, reproducing the general cases of phenomena, reveals the memory art's heritage in the theories. Here in this paper we argue that this design is also present in special relativity and in quantum mechanics.Comment: 6 pages, no figures; "Quantum theory from Problems to Advances", June 9-12, 2014, Linnaeus University, Vaxjo, Swede

Teaching linear algebra at university

Linear algebra represents, with calculus, the two main mathematical subjects taught in science universities. However this teaching has always been difficult. In the last two decades, it became an active area for research works in mathematics education in several countries. Our goal is to give a synthetic overview of the main results of these works focusing on the most recent developments. The main issues we will address concern: the epistemological specificity of linear algebra and the interaction with research in history of mathematics; the cognitive flexibility at stake in learning linear algebra; three principles for the teaching of linear algebra as postulated by G. Harel; the relation between geometry and linear algebra; an original teaching design experimented by M. Rogalsk

RUSSIAN VERBS OF SPATIAL ORIENTATION STAND, SIT, LIE

The semantics of Russian verbs of spatial orientation is far from being simple or trivial; complex spatial concepts categorized in these lexical items are based on a number of cognitive structures that emerge from different modes of man’s interaction with the environment