One vs. two non-symbolic numerical systems? Looking to the ATOM theory for clues to the mystery

An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers:  n, l, ml, and...

The Greek philosopher Democritus proposed that everything on Earth is made up of tiny particles called atomos, Greek for "indivisible," from which the modern term "atom" is derived. In the 19th century, John Dalton proposed the atomic theory that is still largely correct today. He put forth five postulates to explain how atoms made up the world around us. (1) All matter is composed of infinitely small particles or atoms. (2) All atoms of a given element are identical to one another and (3) are...

Overview

Dalton was only partially correct about the particles that make up matter. All matter is composed of atoms, and atoms are composed of three smaller subatomic particles: protons, neutrons, and electrons. These three particles account for the mass and the charge of an atom.

The number of protons in the nucleus of an atom is its atomic number (Z). This is the defining trait of an element. Its value determines the identity of the atom. For example, any atom that contains six protons is the element carbon and has the atomic number 6, regardless of how many neutrons or electrons it may have. A neutral atom must contain the same number of positive and negative charges, so the number of protons equals the number of electrons. This means that the atomic number also...

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information: