  Our community has a deep and sophisticated understanding of phase transitions
and their universal scaling functions. We outline and advocate an ambitious
program to use this understanding as an anchor for describing the surrounding
phases. We explain how to use normal form theory to write universal scaling
functions in systems where the renormalization-group flows cannot be
linearized. We use the 2d Ising model to demonstrate how to calculate
high-precision implementations of universal scaling functions, and how to
extend them into a complete description of the surrounding phases. We discuss
prospects and challenges involved into extending these early successes to the
many other systems where the RG has successfully described emergent scale
invariance, making them invaluable tools for engineers, biologists, and social
scientists studying complex systems.
