Sunday, March 17, 2013

A Boolean View into Nested Structured~Duality

Thanks to Verna Muitt's recent mention of interests in George Boole (jcs-online), I was fascinated to read through the wikipedia summary of his life and contributions.
(See: )

Some selected quotes...

"this [Boole] identity play an important role in the theory of the Hilbert transform"

"Boole's initial involvement in logic was prompted by a current debate on quantification, between Sir William Hamilton who supported the theory of "quantification of the predicate", and Boole's supporter Augustus De Morgan who advanced a version of De Morgan duality, as it is now called. Boole's approach was ultimately much further reaching than either sides' in the controversy.[19] It founded what was first known as the "algebra of logic" tradition."

"By 1 (unity) Boole denoted the "universe of thinkable objects"; literal symbols, such as x, y, z, v, u, etc., were used with the "elective" meaning attaching to adjectives and nouns of natural language. Thus, if x = horned and y = sheep, then the successive acts of election (i.e. choice) represented by x and y, if performed on unity, give the class "horned sheep". Thus, (1 – x) would represent the operation of selecting all things in the world except horned things, that is, all not horned things, and (1 – x) (1 – y) would give all things neither horned nor sheep."

"In 1937 [Claude] Shannon went on to write a master's thesis, at the Massachusetts Institute of Technology, in which he showed how Boolean algebra could optimise the design of systems of electromechanical relays then used in telephone routing switches. He also proved that circuits with relays could solve Boolean algebra problems. Employing the properties of electrical switches to process logic is the basic concept that underlies all modern electronic digital computers."

"Hence Boolean algebra [algebra of logic, ca. 1847] became the foundation of practical digital circuit design; and Boole, via Shannon [1937] and Shestakov [1935], provided the theoretical grounding for the Digital Age"

The wiki account also references Boole owing his mature works as stemming from a mystical experience at age 17.

This is an important string of tidbits for all of us who now live, work and  communicate via computers and the Internet within the digital age.

The trial theory I am advocating can readily be seen as an extension or  yet another nested level of developments along Boole's line of thought and work. However, instead of developing  an abstract 'algebra of logic', what we face in this transition is grasping how we CAN develop and create any 'algebra of logic', 'algebras of algebras of algebras of logics'  -- or representations of essentially anything and everything else.

Instead of the ~Boolean 2^n digital coding and relay switching in energized semi-conductor devices, in the trial theory I am advocating selected facets of the basic magnetic tetrahedral analog mathematics expose our inherent, creative 6^n structural coding within our own nested (biochemical) structural energetics.  The 2^n expressions arise from the internal 6^n expressions.

Following this analog math trade route, any student can acquire the requisite nested fields within nested fields large-scale orientation and physical intuition first, and quiite directly,  continuing along as in the initial phase of the Faraday-Maxwell transtion.

The enfolding and transcendent  understanding thus firmly established, then when one looks back through to the structural coding in the hydrogen bonding layer, one can see that ALL of our various protein-foldings, say, in our various native tongues and linguistic expressions, including those in the handy abstract pure and applied mathematics, differ slightly  from one another due to historical or contextual qualifications or 'contamination'. However,  ALL of these variants also have their common roots of meaning within the internal 6^n ~binary tetrahedral analog mathematics. By viewing the system through the shortcut of the analog math lens, we are able to solve the n-equations with m-unknowns in just a couple of steps.

Call it 'internal 6^n ~binary tetrahedral analog mathematics', or call it nested Boolean algebra; it still comes dome down to picking a structure and then picking a duality and then building outward to the limits of the initial procedural choices.

Best regards,
Ralph Frost

With joy you will draw water
from the wells of salvation.  Isaiah 12:3

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