Francesco Saverio Tortoriello

Stochastic self-similar and fractal universe

The structures formation of the Universe appears as if it were a classically self-similar random process at all astrophysical scales. An agreement is demonstrated for the present hypotheses of segregation with a size of astrophysical structures by using a comparison between quantum quantities and astrophysical ones. We present the observed segregated Universe as the result of a fundamental self-similar law, which generalizes the Compton wavelength relation. It appears that the Universe has a memory of its quantum origin as suggested by R.Penrose with respect to quasi-crystal. A more accurate analysis shows that the present theory can be extended from the astrophysical to the nuclear scale by using generalized (stochastically) self-similar random process. This transition is connected to the relevant presence of the electromagnetic and nuclear interactions inside the matter. In this sense, the presented rule is correct from a subatomic scale to an astrophysical one. We discuss the near full agreement at organic cell scale and human scale too. Consequently the Universe, with its structures at all scales (atomic nucleus, organic cell, human, planet, solar system, galaxy, clusters of galaxy, super clusters of galaxy), could have a fundamental quantum reason. In conclusion, we analyze the spatial dimensions of the objects in the Universe as well as spacetime dimensions. The result is that it seems we live in an El Naschies E infinity Cantorian spacetime; so we must seriously start considering fractal geometry as the geometry of nature, a type of arena where the laws of physics appear at each scale in a self--similar way as advocated long ago by the Swedish school of astrophysics.

Un’esperienza didattica half-flipped in un ambiente di apprendimento SCALE-UP

Abstract – In this paper we describe a teaching experiment with a “blended” approach based on the integration of frontal lessons, flipped learning, Peer Discussion, Just in Time teaching and e-learning, also carried out using the social platform Edmodo and a Facebook group. The development of the students’ skills was monitored by means of three tests administered within the experiment; in parallel, we monitored the motivation level and the attitude towards the discipline through an affect test and a satisfaction survey. Some students had two additional hours per week based on cooperative learning in a SCALE UP learning environment. The research methodology falls within the Educational Reconstruction framework, that allowed us to investigate didactical phenomena, designing and creating learning environment, artefacts, teaching and learning sequences in authentic educational contexts. The results of the affect test showed a better attitude towards the discipline; from the satisfaction survey it emerged that most of the students liked the use of alternative methodologies. The results of our experimentation were analysed also from the point of view of disciplinary learning, comparing the students’ performances with the results of a test of a previous cohort of students who attended the same course. Riassunto – In questo articolo, viene riportata la sperimentazione di un approccio didattico di tipo “blended” integrando lezioni tradizionali, flipped learning, Peer Discussion, Just in Time Teaching e e-learning, con l’ausilio della piattaforma sociale Edmodo e un gruppo Facebook. Lo sviluppo di competenze degli studenti e stato monitorato attraverso tre prove intercorso; parallelamente, e stato monitorato il loro livello di motivazione allo studio della disciplina attraverso un test affect e un test di gradimento. Alcuni studenti hanno integrato lo studio con due ore settimanali aggiuntive di lezioni gestite utilizzando il coperative learning in un ambiente di apprendimento SCALE-UP. La metodologia di ricerca attuata rientra nel quadro della Educational Reconstruction, che ha permesso di studiare i fenomeni didattici progettando e realizzando ambienti di apprendimento, artefatti, sequenze di insegnamento/apprendimento che il ricercatore ha sperimentato in contesti educativi autentici. Dai risultati del test affect, sembra emergere una migliore predisposizione allo studio della disciplina; dal test di gradimento emerge, per la maggior parte degli studenti, l’apprezzamento dell’utilizzo di metodologie didattiche alternative. I risultati della sperimentazione sono stati analizzati anche dal punto di vista dell’apprendimento confrontando i risultati ottenuti dagli studenti con quelli degli studenti della coorte precedente che hanno frequentato lo stesso corso. Keywords – flipped learning, peer discussion, Just in Time teaching, SCALE-UP Parole chiave – Insegnamento capovolto, discussione tra pari, insegnamento Just in Time, SCALE-UP

On an assumption of geometric foundation of numbers

In line with the latest positions of Gottlob Frege, this article puts forward the hypothesis that the cognitive bases of mathematics are geometric in nature. Starting from the geometry axioms of the Elements of Euclid, we introduce a geometric theory of proportions along the lines of the one introduced by Grassmann in Ausdehnungslehre in 1844. Assuming as axioms, the cognitive contents of the theorems of Pappus and Desargues, through their configurations, in an Euclidean plane a natural field structure can be identified that reveals the purely geometric nature of complex numbers. Reasoning based on figures is becoming a growing interdisciplinary field in logic, philosophy and cognitive sciences, and is also of considerable interest in the field of education, moreover, recently, it has been emphasized that the mutual assistance that geometry and complex numbers give is poorly pointed out in teaching and that a unitary vision of geometrical aspects and calculation can be clarifying.