Core books

“To know the world” - Homer
The present combinatorial hamiltonian theory of the world is based on a formal theory of knowledge. This is based, in turn, on formal scientific foundations laid down over the past 300 years by Newton, Leibniz, Euler, Hamilton, Boole, Peano, Galois, Gauss and many other abstract and physical scientists.

This fulfills the ancient goals of informal, literary thinkers, using natural language, who have also sought, with limited success, to know the world and to know what it means to know. These range from the early Greeks - Thales, Socrates and Aristotle, the 1st Western scientists - to 18th century workers, such as Locke, Kant, Marx, Freud, Heidegger, on to the moderns - Parsons, Adler, Pirsig, Wilson and others. For those who understand it, the world is now known.

Abstract: In this second of two Articles (SII), the ACHR Metatheory of Article I is used as a world program to combinatorially construct the four recursive systems of nature, each organized by the hamiltonian of Bellman-Pontryagin optimal control theory. In the 0-I recursion, physics bootstraps primordial substance and motion via the combinatorial Euler string-vortex equation with string constants, T, as representative of the world constant vector, c. This has a dual amplitude solution, A(, ), based on the function. This takes permutations, E, of nonintegers, E(NI), the NI representing relativistic substance, the modes of vibration corresponding to the elementary particle zoo.

Abstract: A lawful world must be a combinatorial or possibility-filling system generated by a combinatorial generating function in both the physical domain and the linguistic codomain. Such generating functions are identified as part of a theory of knowledge, that acts as a thought template or world program, which is used to construct both Universal Grammar and Universal Physics. Both of these are organized by a universal theory structure or story grammar called the hamiltonian. Since a transformation function converts the two, a combinatorial theory of the world results as Universal Science. This realizes the Minimalist Program as part of a far larger general theory of everything. A rigorous definition of ‘language’ emerges. The present program initiates computational grammar.

Abstract: We have elsewhere developed a mathematical theory of knowledge. This is also variously called cognitive structure, epistemology or a general theory of systems. We have then used it to generate alike the various specialty sciences. In this article, we summarize those results for sociology.

The individual personality is the unit of society. And a society is a combination and permutation (relation) of individuals in specified environments. Technically, we say that a society is a constrained combinatoric of individuals, where the constraints include both internal genetic and external environmental factors.

Department of Molecular Biology, Eastern Pa. Psychiatric Institute, Ret.
(Present address: 1B1 President Point Drive, Annapolis, MD 21403
Fax: 410-280-0727;

Abstract: From a World Axiom of lawfulness, four metatheorems are deduced comprising a mathematical metatheory (general theory of systems (GTS), world program, theory of knowledge, universals of the scientific method, cognitive structure, epistemology):

Donald O. Rudin spent his career in research seeking to discover what a man is that he can know and what knowledge is that a man can know it. This is the hardware and software of knowing. He and his colleagues hold pioneering patents on ultraselective ion-measuring electrodes and they synthesized the cell membrane structure and the nerve impulse. Nobelists Walter Brattain, co-inventor of the transistor, and Max Delbruck confirmed this work.

The Specialty Sciences in Standard and Unified Form

The key theories of the specialty sciences, from physics to sociology and grammar, are presented, when already available, as in physics and chemistry, in both their standard form and in the new unified hamiltonian form. Details of string theory and quantum gravity can be found the articles entitled Axiomatic Supertheory, I, II.

Featuring Omega-3 Recipes and Diets
by Donald O. Rudin
Core Books, Core Books for Core Education
ISBN 0-9664833-8-3 Pub. Date 2000

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My Recovery Form Schizophrenia On the First Omega-3 Trial
By Debi Erin with Clara Felix
Core Books, Core Books for Core Education
ISBN 0-929759-05-3 Pub. Date 2000

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The Four Cultures And Their Languages:
The Destiny of Man
by Donald O. Rudin
Core Books, Core Books for Core Education
ISBN 0-9664833-7-5 Pub. Date 2000