Axiomatic World Theory Based on Universal System Theory

Donald O.Rudin

International Institute for Advanced Studies

208 Victor Pkwy, #3G, Annapolis, MD 21403, USA

 

A Theory of the World is developed. This starts by constructing a theory of knowledge, also variously known as general systems or optimal control theory, epistemology or the universal strategy of the scientific method. The theory of knowledge acts as a World Program. It processes a database of world constants, c, into a recursive or hierarchical chain of four systems comprising the world. All systems are formed by combinatorial principles and have identical hamiltonian structures.

The world constants, c, characterize the quantities and qualities of primordial motion—a universal combinator—and also the quantities and qualities of a primordial substance—a universal combinatee. Motion drives the substance into all possible flow-wave structures, as outcomes of the world fluid computer. Its states comprise the events of history.       A lawful world has only five foundational concepts, both abstract and physical:

quantity, 1, and quality, MLT, of combinatees, X (= Sx_i,) and combinators, NOR (= NOT + OR), subject to constraints, c.

The ordered informal mnemonic is <qq;cc,c>, here called the Informal Leibnizian Alphabet. About 1700, Leibniz said, "I have found a way, by the Ars Combinatoria, to construct all things in the world, with their theorems, as from an alphabet."

We transform these terms into the Formal Leibnizian Alphabet, as follows: The universal quantity is the number 1. The universal Boolean conjunctions or operators, NOR, are defined as NOT + OR, where NOT takes things apart and OR (inclusive) puts them together. In mathematics, MINUS and PLUS replace NOR. In geometry, NOR becomes CUT and JOIN. Applying NOR or " to the universal number 1 generates all other numbers. This is the combinatorial form of Peano's postulates.

Applying NOR to the universal qualities of mass, length and time, MLT, generates abstract compound qualities. For example, n(ML²T^-2)_LT, is a thought or emotion, having a number, n, of energy, nerve impulses, ML²T^-2, distributed in neural nets in space-time, LT.

Hence, <qq;cc,c> h <1, MLT; X, NOR, c>, where X is any noun defined by a set of adjectives, Sx_i, obtained from 1 and MLT. In standard reaction or program form, this is:

 

ACHR-HC World Program            or Reaction

Products are the 4 recursive ham. systems of world theory

Database, c, characterizes the properties of combinatee and combinator world reactants

    

                                     

 

Hence, the combinatorial world reactants, c, are processed by a world program or reaction, denoted by the mnemonic ACHR-HC (ah'-ker-h-c), into world theory, which is a chain of 4 successive products called systems, produced alike by combinatorics and having identical hamiltonian structures. When c is given physical values, an Euler-Veneziano string-vortex equation results related to Prigogine vortex mechanics, with 2nd order rim perturbations (flow-wave structures of the world computer) producing elementary particles.

The ACHR-HC World Program stands for:

Axiomatic: Everything follows from a pair of first principles or axioms, considered below.

Combinatorial: Combinatorics supplies a universal system formation principle.

Hamiltonian: Ultimately from Newton, provides a universal system organizing principle.

Recursive: The four systems are hierarchical, with intersystem mechanics to be developed,

Harmonic stability conditions hold for each system. Finally, we must specify

Completion and/or Incompletion conditions.