  Intelligence is a human construct to represent the ability to achieve goals.
Given this wide berth, intelligence has been defined countless times, studied
in a variety of ways and represented using numerous measures. Understanding
intelligence ultimately requires theory and quantification, both of which have
proved elusive. I develop a framework -- the Theory of Intelligences (TIS) --
that applies across all systems from physics, to biology, humans and AI. TIS
likens intelligence to a calculus, differentiating, correlating and integrating
information. Intelligence operates at many levels and scales and TIS distils
these into a parsimonious macroscopic framework centered on solving, planning
and their optimization to accomplish goals. Notably, intelligence can be
expressed in informational units or in units relative to goal difficulty, the
latter defined as complexity relative to system (individual or benchmarked)
ability. I present general equations for intelligence and its components, and a
simple expression for the evolution of intelligence traits. The measures
developed here could serve to gauge different facets of intelligence for any
step-wise transformation of information. I argue that proxies such as
environment, technology, society and collectives are essential to a general
theory of intelligence and to possible evolutionary transitions in
intelligence, particularly in humans. I conclude with testable predictions of
TIS and offer several speculations.
