Finding the Passage to the Quotient: Equivalence Relations steering the Abstraction Process from a high- to a low-frequency Harmonic

Motivated by the subjective definition of abstraction provided in Gilead et al. 2020, we illustrate here a universal abstraction process relying on Naive Set Theory. This concept, originating with the work of Dedekind, Frege, and Cantor in the second half of the nineteenth century, has been formalized in mathematics for some time and is based on the concept of equivalence relation leading to the passage to the quotient set. We then apply this precise mechanism to harmonics analysis of social cognition recently introduced in Maass et al. 2021. We finally observe that the family of equivalence relations is naturally endowed with a partial order providing a lattice structure. The well-known hierarchical tree-like structure induced by repeated passage to the quotient, see e.g. Gilead et al. 2020, Subsection 2.2.2., corresponds to an ascending path in the lattice.