Beyond Calculus Organization Alphabet

MetaCalculus emerged during the Apollo program as an organization paradigm of holistic mathematics and a computation pseudo-machine to implement it. It was congruent with Arthur Koestler's holarchy theory, also emergent at that time. Like DNA, it manifests as a very-high level alphabet each encapsulating a problem-part formulation of simultaneous equations and an iterative algorithmic solution process which solves these equations as a whole, yet this whole problem is a part which combines alphabetically as a unit of a higher whole problem. The alphabet consists of three types of holons (whole-parts):

Each holon is a context for automatic differentiation to support its solution process. The holon is dynamically created by a language operator macro-template (in parentheses). The created holon contains an operand model as a separate procedure, and 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.

Systems Engineering End-User Perspective

MetaCalculus is directly focused on application programming in science and engineering, where the end-user is a casual programmer who uses computers to solve sophisticated scientific problems, but is not necessarily a software expert, and doesn’t have time to become one. Yet the problems being addressed are systems-level inverse problems, involving simultaneous equations and multiple dimensions, as this is the way problems are apprehended in science—not the simple explicit structure of spreadsheets and ordinary programming languages. Yet the complexity of programming, is hardly more than what it takes to use a spreadsheet program. Compare this to what it is like to program in mainstream languages like Perl, Java, or C++, and ask yourself how one may go about programming these kinds applications in those languages!

The major lever for rapid prototyping is that in each holon of a program structure, the solver is interchangeable with other solvers in its class. Thus a user can experiment with solvers in the way he experiments with the multiple search-engines on the web. After all, that is what implicit solvers are—search engines. This facility dramatically reduces the time it takes to prototype a new application.