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| "One important
characteristic of
a body of knowledge is that it is
conveyed through a rather specialized
language, by which we mean that words are used in certain special senses
and that certain concepts and categories are treated as fundamental to an
understanding of the subject. This aspect of a body of knowledge is its
language or vocabulary. To a large extent, any specialized language represents
an artificial creation
because it is self-consciously constructed to express meanings and definitions
as precisely as possible." - Sheldon S. Wolin, Politics and
Vision |
Trivium
Trivium means "the place where three roads meet".
The
subjects of the trivium are the foundation for the quadrivium, the upper
division of the medieval education in the liberal arts, which comprised
arithmetic (number), geometry
(number in space), music (number in
time), and astronomy (number in space and time).
Educationally, the
trivium and the quadrivium imparted to the student the seven liberal arts of
classical antiquity.
Grammar teaches the mechanics
of language to the student.
This is the step where the student "comes
to terms," defining the objects and
information perceived by the five senses.
Hence, the
Law of Identity: a
tree is a
tree, and not a
cat.
Logic (also dialectic)
is the "mechanics" of thought and of analysis:
process of
identifying fallacious arguments
and statements by
systematically
removing contradictions, thus producing
trusted knowledge.
Rhetoric is the application
of language in order to instruct and to persuade the listener and the reader.
Knowledge (grammar), understood, (logic) transmitted as wisdom
(rhetoric).
A Diophantine equation is a polynomial equation, involving
two or more unknowns, such that the only solutions of interest are the integer
ones (an integer solution is such that all the unknowns take integer values).
A linear Diophantine equation equates to a constant the sum of two or
more monomials, each of degree one.
The simplest linear Diophantine
equation takes the form ax + by = c, where a, b and c are given integers.
An exponential Diophantine equation is one in which unknowns can appear
in exponents - am + bn =
ck.
Diophantine problems have fewer equations than unknowns
and involve finding integers that solve simultaneously all equations.
As such systems of equations define algebraic curves, algebraic
surfaces, or, more generally, algebraic sets, their study is a part of
algebraic geometry that is called Diophantine geometry.
The word
Diophantine refers to the Hellenistic mathematician of the 3rd century,
Diophantus of Alexandria, who made a study of such equations and was one of the
first mathematicians to introduce symbolism into algebra.
The
mathematical study of Diophantine problems that Diophantus initiated is now
called Diophantine analysis.
While individual equations present a kind
of puzzle and have been considered throughout history, the formulation of
general theories of Diophantine equations (beyond the case of linear and
quadratic equations) was an achievement of the twentieth century.
A
homogeneous Diophantine equation is a Diophantine equation that is defined by a
homogeneous polynomial. A typical such equation is the equation of Fermat's
Last Theorem x d + y d - z d =
0.
An example of an infinite diophantine equation is: n = a2
+ 2b2 + 3c2 + 4d2 + 5e2 + …,
which can be expressed as "How many ways can a given integer n be written as
the sum of a square plus twice a square plus thrice a square and so on?"
The number of ways this can be done for each n forms an integer
sequence.
Infinite Diophantine
equations are related to theta functions and
infinite dimensional
lattices.
In mathematics, theta functions are special functions of
several complex variables.
The most common form of theta function is
that occurring in the theory of elliptic functions.
With respect to one
of the complex variables (conventionally called z), a theta function has a
property expressing its behavior with respect to the addition of a period of
the associated elliptic functions, making it a quasiperiodic
function.
In the abstract theory this quasiperiodicity comes from the
cohomology class of a line bundle on a complex torus, a condition of
descent.
Quadrivium
The quadrivium consists of arithmetic, geometry, music and
astronomy.
These stand on the
trivium, consisting of grammar,
logic and
rhetoric.
A quadrivium
plinth is required for the study of
philosophy and
theology.
In the liberal arts as
curriculum in universities the quadrivium is typically considered to be
the study of number and its
relationship to space or time.
"Azazel taught men to make
swords, and knives, and shields, and breastplates, and made known to them the
metals of the earth and the art of working them, and bracelets, and ornaments,
and the use of antimony, and the beautifying of the eyelids, and all kinds of
costly stones, and all colouring tinctures.
There arose much
godlessness, and they committed fornication, and they were led astray, and
became corrupt in all their ways.
Semjaza taught enchantments, and
root-cuttings, 'Armaros the resolving of enchantments, Baraqijal astrology,
Kokabel the constellations, Ezeqeel the knowledge of the clouds, Araqiel the
signs of the earth, Shamsiel the signs of the sun, and Sariel the course of the
moon." - Enoch 8 |
Gödel's incompleteness theoremsThere
will always be questions that cannot be answered, using a given set of
axioms;
You cannot prove that a given system of axioms is consistent,
unless you use a different set of axioms.
Every formal system is either
incomplete or inconsistent.
Tarski's undefinability theoremGiven a formal arithmetic system, the concept of truth in that
system is not definable using only those formal arithmetic
expressions.
Chaos Theory:
Chaos theory is focused on the deterministic laws of underlying
patterns of highly sensitive dynamic systems where conditions initially thought
stable deteriorate rapidly into random states of chaotic disorder and
irregularities.
Theories are said to be commensurable if they
can be discussed
using a shared nomenclature
revealing
a recognizable
conceptual structure that allows direct comparison of foundational
elements.
Theories are incommensurable if they are embedded in
starkly contrasting conceptual
frameworks whose symbolic
languages do not overlap sufficiently to
permit a direct
comparison of foundational
elements.
Incommensurability results when individuals "talk past each other"
and comparison becomes muddled by confusion about
context and labels.
Theories are
speculative
conjectures using
abstract reasoning.
Theories require a
basic philosophical understanding of
phenomena.
Theories involve
rational assumptions
based on limited knowledge.
Shaping
principles define comprehension and
methods of analysis.
Sets of theorems constitute systemically
unifying perspectives.
Theory of Property
Supremacy:
James McGill Buchanan saw society as a cutthroat realm
of makers (entrepreneurs) constantly under siege by takers (everybody
else).
His own language was often more stark, warning the alleged
“prey” of “parasites” and “predators” out to
fleece them.
Colgate Darden, who had married into the DuPont family,
found Buchanan’s ideas to be spot on.
In nurturing a new
intelligentsia to commit to his values, Buchanan stated that he needed a
“gravy train,” and with backers like Charles Koch and conservative
foundations like the Scaife Family Charitable Trusts, others hopped aboard.
Money, Buchanan knew, can be a persuasive tool in
academia.
Buchanan advised proponents of Reagan Revolution in their
quest to unleash markets and posit government as the “problem” rather
than the “solution.”
Concepts
are tangible mental images formed
in the mind.
Concept and
perception are entwined
like vines enwrapping each other.
The process of
conceptualization is an activity of
interpreting
perceptions.
Conceptualization is a cognitive process using
modes of
consciousness to frame something
incomprehensible making
it understandable.
Concepts
are inferred or
derived through
induction or
deduction.
Every concept rests on a
foundation of configurations of
relationships.
Taken together
conceptual images constitute
an intelligible
world.
There are two basic kinds of concepts =
theoretical and
empirical.
Empirical
concepts relate to tangible
activities of the sensory domain.
Theoretical concepts use
abstraction to make the
mystifying
comprehensible.
A theoretical concept is an
abstraction.
To abstract
means to draw or derive from.
Abstraction has
no concrete tangible existence in and of
itself.
Theoretical concepts
work in tandem with empirical concepts.
A concept is mental model built in order to
grasp something intangible.
The
theoretical concept of
patriotism stirs emotional implants deep in the
subconscious playing back
images and symbols of tangible activities.
You can be
patriotic, but you
cannot see,
touch, or
taste
patriotism.
Terrorist supression
involves eyes and ears
and boots on the
ground.
Sporting events
inculcate a sense of
patriotism.
If you
see something say something.
Those sincerely
committed to self-knowledge,
in all its complexity, refuse to be
manipulated by the deceitful
patriotic propaganda and religious
rhetoric.
Theoretical
concepts have the potential to deeply influence subconscious
understanding of reality
without conscious
awareness.
Delusions of grandeur
use magical rhetoric
to artificially program the
gullible human subconscous into believing
Hiroshima was
necessary.
Axiomatic concepts,
fundamental precepts, are implicit in every perception as they are the
foundation of all other
concepts.
Axiomatic concepts include:
existence,
identity,
consciousness.
To perceive a
thing is to perceive that it exists.
To perceive a thing is to
perceive that it is something.
To perceive a thing is to perceive that one is
conscious.
Axiomatic
concepts cannot be defined in terms of other concepts as foundational concepts
are logically prior to all other concepts.
No proof can be offered for
axiomatic concepts, nor is any needed:
it is
self-contradictory to deny
them, for they must be accepted and used in every such
denial as they are
self-evident. |
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This web site is not a commercial web site and
is presented for educational purposes only.
This website defines a
new perspective
with which to engage reality to which its author adheres. The author feels that
the falsification of reality outside personal experience has forged a populace
unable to discern propaganda from reality and that this has been done
purposefully by an international corporate cartel through their agents who wish
to foist a corrupt version of reality on the human race. Religious intolerance
occurs when any group refuses to tolerate religious practices, religious
beliefs or persons due to their religious ideology. This web site marks the
founding of a system of philosophy named The Truth of the Way of the
Lumière Infinie - a rational
gnostic mystery
religion based on reason which requires no leap of faith, accepts no
tithes, has no supreme leader, no church buildings and in which each and every
individual is encouraged to develop a personal relation with the Creator and
Sustainer through the pursuit of the knowledge of reality in the hope of curing
the spiritual corruption that has enveloped the human spirit. The tenets of The
Truth of the Way of the Lumière Infinie are spelled out in detail on
this web site by the author. Violent acts against individuals due to their
religious beliefs in America is considered a "hate crime."
This web site
in no way condones violence. To the contrary the intent here is to reduce the
violence that is already occurring due to the international corporate cartels
desire to control the human race. The international corporate cartel already
controls the world economic system, corporate media worldwide, the global
industrial military entertainment complex and is responsible for the collapse
of morals, the elevation of self-centered behavior and the destruction of
global ecosystems. Civilization is based on coöperation. Coöperation
does not occur at the point of a gun.
American social mores and values
have declined precipitously over the last century as the corrupt international
cartel has garnered more and more power. This power rests in the ability to
deceive the populace in general through corporate media by pressing emotional
buttons which have been preprogrammed into the population through prior mass
media psychological operations. The results have been the destruction of the
family and the destruction of social structures that do not adhere to the
corrupt international elites vision of
a perfect world. Through
distraction and coercion the direction of thought of the bulk of the population
has been directed toward solutions proposed by the corrupt international elite
that further consolidates their power and which further their purposes.
All views and opinions presented on this web site are the views and
opinions of individual human men and women that, through their writings, showed
the capacity for intelligent, reasonable, rational, insightful and unpopular
thought. All factual information presented on this web site is believed to be
true and accurate and is presented as originally presented in print media which
may or may not have originally presented the facts truthfully.
Opinion and thoughts have
been adapted, edited, corrected, redacted, combined, added to, re-edited and
re-corrected as nearly all opinion and thought has been throughout time but has
been done so in the spirit of the original writer with the intent of making his
or her thoughts and opinions clearer and relevant to the reader in the present
time.
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 Copyright
© Lawrence Turner
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