Holistic Computation Architecture & Hypercomputers

MetaCalculus is a higher-mathematical modeling paradigm and computation architecture which extends programming languages by adding a holon modeling template alphabet, which is used like the DNA alphabet to organize software holons into holarchies, congruent with Arthur Koestler's holarchy theory and Ken Wilber's Integral philosophy.

Automatic Differentiation Holons

Each holon is a context for automatic differentiation to support its solution process. It contains an operand model as a separate procedure, and a library solution engine (solver) which is called by the operator template. The template is therefore an interface between two levels of a holarchy. And the holon's model procedure may contain further operators invoking further holons.

Since holons can be nested, there are built-in mathematical transformations to propagate differentiation via variations of the chain-rule of differential calculus. These transformations are level-independent, therefore holarchy nesting is permitted to any depth. This simplifies modeling and programming in the manner of Simon's parable of the two watchmakers, but with additional self-organizing rules of an alphabet of mathematical closure (solvability) further governing holarchy structure.

Emulation Pseudo-Machine and Hardware Design

The semantic architecture of MetaCalculus is the holarchy emulation pseudo-machine, which is controlled by each iterative solver, performing automatic differentation and differential nesting propagation, all hidden from the application programmer. This emulation architecture motivated the design of two-generations of very-high-level language RISC computer architecture in the 1980s.

Today, with Moore's law being limited by the "power wall" we are interested in using these RISC designs as cores in multi-core RISC chips, allowing massively parallel optimization searching.