  Quantification starts with sum and product rules that express combination and
partition. These rules rest on elementary symmetries that have wide
applicability, which explains why arithmetical adding up and splitting into
proportions are ubiquitous. Specifically, measure theory formalises addition,
and probability theory formalises inference in terms of proportions. Quantum
theory rests on the same simple symmetries, but is formalised in two
dimensions, not just one, in order to track an object through its binary
interactions with other objects. The symmetries still require sum and product
rules (here known as the Feynman rules), but they apply to complex numbers
instead of real scalars, with observable probabilities being modulus-squared
(known as the Born rule). The standard quantum formalism follows. There is no
mystery or weirdness, just ordinary probabilistic inference.
