Recent work has defended “Euclidean” theories of set size, in which Cantor’s Principle (two sets have equally many elements if and only if there is a one-toone correspondence between them) is abandoned in favor of the Part-Whole Principle (if A is a proper subset of B then A is smaller than B). It has also been suggested that Gödel’s argument for the unique correctness of Cantor’s Principle is ...

A general form of dynamical equations is obtained on the requirement of the superposition principle of quantum states; hence the constraints on the forms of the Lagrangians are acquired, under the assumption of correspondence between quantum states and field operators. It shows that the superposition principle requires the continuous transformation group of the Lagrangians to be compact, and th...

A general form of the dynamical equations is obtained on the requirement of the superposition principle of quantum states; hence the constraint on the forms of the Lagrangians is acquired under an assumption of correspondence between state and field operator. It shows that the superposition principle requires the continuous transformation group of the Lagrangians to be compact, and that the Lag...

Chaos dynamics, which characterizes biological information processing, generates information along the course of temporal development of the relevant system. In this system, the macroscopic uncertainty principle holds between observation time delta t and phase space volume delta omega determined by this observation. In other words delta t and delta omega cannot simultaneously be small. This pri...

We study classification of interacting fermionic symmetry-protected topological (SPT) phases with both rotation symmetry and Abelian internal symmetries in one, two, three dimensions. By working out this classification, on the one hand, we demonstrate recently proposed correspondence principle between crystalline those through explicit block-state constructions. find that for precise to hold it...

We review some aspects of the D1/D5 system of type IIB string theory and the associated five dimensional black hole. We include a pedagogical discussion of the construction of relevant classical solutions in supergravity. We discuss the gauge theory and the conformal field theory relevant to D-brane description of these systems. In order to discuss Hawking radiation we are automatically led to ...

The AdS/CFT correspondence realises the holographic principle where information in bulk of a space is encoded at its border. We are yet long way from full mathematical construction AdS/CFT, but toy models form quantum error correcting codes (HQECC) have replicated some interesting features correspondence. In this work we construct new HQECCs built random stabilizer tensors that describe duality...