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 space-time dimensions. The result is that it seems we live in an El Naschie's E-infinity Cantorian space-time; 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.
Complex problems need interdisciplinary approaches. Thinking in an interdisciplinary way asks for changes in learning and teaching and hence in our views on pedagogical problems. An interdisciplinary approach could provide a new framework also for dealing with disciplinary didactical problems. In this paper, we propose a methodology which we call globally interdisciplinary laboratories as an effective way to practice interdisciplinary teaching at the high school level. We discuss the possibility of applying this methodology to the learning and teaching of mathematics. Globally interdisciplinary laboratories are designed by a pool of researchers in collaboration with high school teachers of several disciplines and they are delivered in the classroom by a pool of teachers in co-presence. This has been experimented in Italy in many classes which are part of a national educational project called Liceo matematico. In this paper, we discuss the general design principle of a GIL and exemplify the methodology by considering the one we have called educate the sight, which aims at stimulating, within an interdisciplinary framework, intellectual curiosity, the ability to spot the prominent features of a problem and, in mathematics, the ability of conjecturing, which should be one of the fundamental concerns of mathematical teaching, according to Polya's decalogue for mathematics teachers (POLYA, 1981).
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