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"

Sunday, March 10, 2013

Lines -- News from the front

[jsc-online 3/10/2013]

Dear Verna,

Pardon me, but hoping on grace on a Sunday afternoon,  I will breech the limit you requested in asking for replies from those who know a lot about perception, particularly along the lines of Arnold's or others' similar, interesting and useful, but still  rather only visually oriented models.  Hopefully you will get ample replies of the kind you seek from the knowledgeable respondents.

I don't know a lot about such visually oriented models but I rather ~see the terrain more in terms of the visual and other senses all being or reducing down to being in terms of an underlying, I guess my option is to call it a primary tactile sense.

In this alternate storyline, for instance,  pardon my hunter-gatherer hypersensitivities, but if you set up an "observer focal point" (OFP) say, within one's gut, heart or head, and then if the wind comes toward the front heart-side of the body conveying a particular scent, or a distinctive  noise, or even a pressure or other *feel*,  if the sense or recognition is attractive or repulsive various optimal "lines" are clearly defined, actually, quite naturally,  just in terms  of minimizing energy use, or maximizing energy conservation.

Or, one hears a strange branch break unexpectedly which establishes a "line" and then one turns her gaze in