Most fruitful method to formulate a perfect theory should start from induction and via deduction lead to reduction if necessary. To eliminate the dichotomy of infinity i.e. the infinity understood as both a simple continuum without any boundaries or the ever-increasing sequence, we must introduce pieces of space. Infinity as a number has no sense and leads to incoherent theories. Applied mathematics should be defined as mathematical methods starting from pieces of space placed in the infinite nothingness. Since in such theory, information is not lost so such theory is mathematically coherent, simple and reversible. There do not appear physical singularities and infinities. Our cosmos, and many others, appeared due to inelastic collision of two or more very big pieces of space composed of smaller pieces. Only granular/discrete and kinetic geometry can be the foundations of coherent description of Nature. Here are formulated the fundamental axioms as the foundations of ontology. Entanglement of the Einstein-spacetime components leads to both psychology and particle physics. Due to the very different properties of fields associated with Gravity and Standard-Model/Quantum-Physics, unification of these two basic theories within the same methods is impossible.