The extensions of Boltzmann-Gibbs classical entropic form are presented. The focus is on the thermodynamical entropies which do not obey classical definition of additivity and extensity with main motivation coming from the gravitational systems admitting long-range interactions both in astrophysics (black holes) and in cosmology. Horizon entropies are the main concern. In the paper, the plethora of non-Boltzmann-Gibbs entropies are studied and the comparative analysis of their properties with respect to additivity and extensivity is presented.

We present a brief history of the construction of models of the universe, followed by calculations of quantitative characteristics of basic geometric and kinematic properties of the Standard Cosmological Model ($\Lambda$CDM). Using the Friedmann equations of uniform space, we derive equations characterizing a $\Lambda$CDM model that describes a universe corresponding to current observational data. The equations take into account the effects of radiation and ultra-relativistic neutrinos. It is shown that the universe at very early and late stages can be described to sufficient accuracy by simple formulas. Certain important moments of cosmic evolution are determined: the times when densities of the gravitational components of the universe become equal, when they contribute equally to the gravitational force, when the accelerating expansion of space begins, and several others. The dependences of different distances on redshift and the scale factor of space are derived. The distance to the sphere that expands with the speed of light (the Hubble distance), and its current and future acceleration, are found. Concepts of a horizon, second inflation, and second horizon are discussed. We consider the remote future of the universe and the opportunity, in principle, of connection with extraterrestrial civilizations.

This qualitative study conducted at St. Michael's College explores the integration of philosophical dimensions in arts and sciences education and its implications for pedagogy and student learning. Drawing on three theoretical framework informed by Piaget, Sartre, and Vigotsky, the study examines the perspectives of 30 participants, including teachers and students, through semi-structured interviews. The findings reveal diverse viewpoints, with some participants emphasizing disciplinary specialization for focused skill development, while others advocate for integrating philosophical dimensions to enhance critical thinking, interdisciplinary connections, and ethical awareness. The implications highlight the importance of balancing disciplinary depth with interdisciplinary exploration in arts and sciences education. Educators are encouraged to recognize the value of disciplinary specialization while integrating philosophical dimensions to foster critical thinking skills, interdisciplinary connections, and ethical awareness among students. Recommendations include providing professional development opportunities for educators, incorporating philosophical perspectives in curriculum frameworks, and exploring the long-term impact of integrating philosophical dimensions on student learning outcomes. Future research should investigate specific pedagogical approaches, consider cultural and contextual factors, and further explore the impact of integrating philosophical horizons to advance educational practices. By embracing the integration of philosophical dimensions, educators can create meaningful learning experiences that promote critical thinking, interdisciplinary connections, and ethical awareness in arts and sciences education.