title page:
		        Aesthetics: a wonderful mystery,
				   Vinyasi

				Contents

Acknowledgements
Preface(a commentary on this book)
Introduction(overview of sections and chapters)
Section 1: Discourse on Aesthetics
Section 2: Language Theory
Section 3: Hybrid Aesthetics
Section 4: Miscellaneous Math Ideas

	***************************************************************

		     Section 1: Discourse on Aesthetics

Chapter : Three Preliminary Definitions
Chapter : Aesthetic Theory
Chapter : The Ideal Class
Chapter : The Golden Class
Chapter : The Hybrid Group(Overview)
Chapter : Art
Chapter : Planetary Development

			Section 2: Language Theory

Chapter : The Language of Nature(Overview)
Chapter : Integrity
Chapter : Vibration
Chapter : Function

			Section 3: Hybrid Aesthetics

Chapter : Geometric
Chapter : Light Modeled
Chapter : Linear, Quadratic, Cubic, and Quartic+

?
Chapter : Stabilizing(Converging)
Chapter : The Gap(The Hole: Diverging)
Chapter : Dynamic(Fractal)
Chapter : Cyclic(Partly Fractal)
Chapter : Approximate

		     Section 4: Miscellaneous Math Ideas

Chapter :
Chapter :

	***************************************************************

Section 1: Aesthetic Approximation Theory:
Division By Zero.Subjective Math.Basic Approximation Theory.Ideal Numbers.Golden
Numbers.How Harmony Relates to Biology and Art in a Mathematical Sense.How Does
This Theory Fit Into the Scheme of Things.Art in Practice

(filenames: division.phi, divis1.phi, div2.phi-newest)
Chapter 1: Division by Zero:
Value.Sign.Modularity.Division.Algebra.Number Bases.Examples.Summary

old version: (filename: infinity.phi)
Chapter 1.1: Infinity Explained in Terms of the Relative:
Equivalence.Four Views of Infinity.The Definition of Division by Either Infinity
or Zero.Historical Perspective

(filename: humath.phi)
Chapter 1.2: The Humanization of Math: The Ten Processes of Binary Logical Math:
Dual-sign Math Systems are a Product of Four Logic Relations.
Addition as Discrimination.Negation as a Shift in Perspective.
Division as Parallelism, a Shift in Perspective, as well as the Simplification
of Units of Measurement Through Dominance.Multiplication as Polyglotism.
Summation of Squares as Making Distinctions Among Varied Self-Amplified Values.
Summation of Reciprocals as Making Distinctions Among Varied Values Whose
Orientation of Magnitude has been Switched from One Form of Infinity to Another.
Multiplation of Terms Involving Integer Exponentiation.Multiplation of Terms
Involving Exponents of Unit Fractions(1/a).
Summation of Terms Involving Integer Exponentiation.Summation of Terms Involving
Exponents of Unit Fractions(1/a).
Exterior to the System: Transcendental e: The System's Transcendental Function.

(filename: harmony.phi)
Chapter 1.3: Harmonic Systems:
Aesthetics is an Algebraic (Semantic) Inference From the Alphabetic Units of
Mathematical Thinking.
?Harmony as the Use of All Ten Processes Within a Unified System:
The Construction of Simple Polynomials in Multiple and Singular Unknowns.The
Unique Polynomial Qualities of an Algebraic Number.Substitution is an Assumed
Equivalence.Approximate Solutions of Simple Polynomials in One Unknown by Way
of: Partial Isolation of Terms.
Three Side-bars: The Degree of a Polynomial's "x" Term is Selective of a Root
During Self-Looping Partial Solution Methods by Way of the Root's Magnitude
and Sign.=
?Exponentiation Within the Context of Approximating Factors of a
Polynomial Gives Magnitude Towards Each Factor.Parallel Solutions as
a Function of Harmony: Integrity.Integrated Parallel Polynomial Functions in
Multiple Unknowns Approximating a Polynomial Function in One Unknown.

?How the Ten Math Functions Are Used

Overview of Some Binary Logic Aesthetic Classes

(filename: ideal.phi)
Chapter 1.4: The Ideal Class:
Definition.Generation.Uninacci.Fibonacci.Tribonacci.Multinacci.Infinacci.All-
Encompassing Unity of Growth and Simplicity of Form

(filename: golden.phi)
Chapter 1.5: The Golden Class as Defined by Two Qualities Applied to Two Fields:
Modularity and Substitution in Relation to Algebra and Geometry:
and Two Approaches of Generation:
The Modularity of Golden Numbers: Algebraic Beauty and Geometric Beauty with
Power.
The Algebraic Approach:
A Simple Cascading Pattern to Modular Summation.Modular Subtraction.
The Golden Pattern Determines the Golden Outcome.Integration of Subtotals to
Produce Approximations of Golden Ratios.
Sandwiched-Glass-Panes-and-Reflecting-Light Model.Honeybee Genealogy Model.
Review of Fibonacci's Bunny Model.The Ideal and Golden Classes'
Reciprocal Limits of Magnitude.
The Geometric Approach:
Formulated in Euclidean Geometric Terms.Non-Euclidean Formulation of Angular
Classes.
Two Types of Substitution: Telescoping and Reformulation.
Algebraic Telescoping Substitution: Integrated Parallel Computation.
?(doesnt serve the same function as Alg. Subs.: approximation):
Geometric Telescoping Substitution: Regular and Stellated Polygons.
Algebraic Reformulative Substitution: Serial Block Computation of Golden and
Quadratic Polynomials.

Linear Aesthetic Relations Within the Plane.
Expanded and Modified Greatest Common Divisor Algorithm.

(filename: planet.phi)
Chapter 1.6: Planetary Development:
DNA as a Function of the Four Logic Relations.
Occurrence of Traditional Aesthetic Values on Earth (Geology, Biology,
?Neurology, Architecture).The Fibonacci Series.The Lucas Series.The Ptah Series:
Its Postulated Use in Egyptian Mathematics.
Geometric Hybridization of Golden Values.
The Pell Series.
The Modified Pell Series.
A Bubble Universe.
Maldek.Venus, or Life in a Sulfate World.?Life on a Cubic
(or Higher) World.Conclusion

(filename: mathart.phi)
Chapter 1.7: The Mathematical Basis For Art Derived From Aesthetics:
The Units of Art: Relations of Angle or Length.Vibrational Art: Music, Magnetic
Fields, Painting and Graphics.Structural Art: Painting, Sculpture and Architec-
ture.Movement Art: Dance.Holographic Art

(filename: makemuse.phi)
Chapter 1.8: The Making of Vibrational Art, An Example From Music:
Synopsis.Linear Versus Irrational Music.Pure Versus Equal Temperment.Pure
Temperment Chromatic Scale Building.Approximating Pure Temperment With the Use
of Equal Temperment.The Coexistence(?Comingling) of Both.Melody Building.
Evaluating the Roots of a Polynomial: The ?<Radical> Method.Creating Series Sets----The Geometric Method.

(filename: melody.phi)
Chapter 1.9: Aesthetic Constructs:
(From Music): Melody Construction.

(filename:
Chapter 1.10: The Making of Angular Art, An Example From ?:

(filename: langnatr.phi)
Chapter 1.11: The Language of Aesthetics (From Where Does It Come?):
Speculating on the Nature of Higher Forms of Aesthetics:
The Two Raised to the Tenth Power(Thousand+) Views of Reality Simplified to Just Four: The Undefinable
[Transcendental], The Finite Capacity of an Individual System to Embody
Essential Qualities[Idealism], The Dynamics of Vibrancy(Systems of Vibration as
a Means for Evolving Consciousness)[Subjectivity], The Form of Function(Science
as a Means for Expressing Soul Character)[Objectivity].
The Four Linguistic Sets: The Transcendental Set.The Diety Set.The Vibrational
(Tonal) Set.The Functional(Logic/Math) Set.Our View of Each Set Determines The
Scope and Structure of The Next Operative Set.Each Set Contributes Toward the
Building of An Aesthetic Scale: Agreement Among Differing World Views Spawns a
Usefull System.
Chakras: Modes(Scales) of Consciousness.Octaves:
States of Consciousness.Zodiacal Keynotes: Planets of Influencial Dharma:
Nature's
Support For Right Action.The Median Consciousness of a Planet's Seasons: The
Evolution of the Piano
Keyboard.The Growth of Logic: Higher Mathematics For Higher Artistic Develope-
ment.One Result: One More Definition of Imaginary Numbers.The Inherent Self-
Sufficiency of Mathematical Systems.

Digital Logic at the Heart of Math.Dimensional Logic.
The Previous Form(see end of ch.3).The Next Higher Form.The Limitations of
Higher Dimensions.Planar Relations of Beauty.

	***************************************************************

Section 2: Additional Math:
All of the Basic Math Ideas Not Covered in the Previous Section, But Related in
an Indirect Way as Background Material:
Overview of Approximation Methods.
The Structure of a Polynomial as the Basis for Infinitely Many Quadratic or
Golden Methods:
The Alternating Incremental Method.
The Quadratic Fibonacci and Lucas Functions.
Summation of Paired Multipliers.
Collapsed Polynomials (a*x^degree + b*x^0), Two Methods:
Calculating the Roots of Numbers Using Only a Credit Card Calculator.
Historical Perspective: Self-Looping Approximation According to Newton.
Filling in Self-Looping Gaps (the Holes): Newton's Method for Best Fit of a
Polynomial's Roots.
The Quadratic Euclidean Algorythm.
The Calculator Version for The Euclidean Algorythm.
The Polynomial Euclidean Algorythm.
The Expanded Greatest Common Divisor Algorythm.
How to Test Continued Fractions for Accuracy.
An Improvement on Gauss's Approximation of Pi as a Continued Fraction.


Chapter 2.1: Overview of Methods Not Covered In Section One
The Mechanics and Limitations of Each Method.

	***************************************************************

Section 3:
A More Indepth Study of Beauty Via Golden Beauty's Source, Hybrid Beauty,
Derived From Geometry, Polynomials, and a Light Model:

Chapter 3.?: Linear Relations of Aesthetics and the Parallel Method For Categorizing
Beauty:
The Logical Difference Between Polynomials in One Versus Multiple Unknowns.
Numbers Are a By-Product of Polynomials in One Unknown(A Base).Polynomials in
One Unknown Are a Way of Creating and Defining Irrational Numbers.Polynomials in
One Unknown Can Be Approximated Using Sets Of Polynomials in Multiple Unknowns
Calculated in Parallel.
Their Limitations.

Continued Fractions of Polynomials.Their Extensions From Lower to Higher
Degrees.Limitations.The Creation of Alternate Forms of Beauty:
Simple(Linear), Straightforward(Quadratic), Transformational(Cubic), Approximate
(Quartic+)], Unclassified General, Golden, Hybrid: [Stabilizing
(Converging), Dynamic(Fractal), Cyclic(Partly Fractal)].

		Hybrid
			Geometric
			Algebraic (Polynometric)
				Linear, Quadratic, Cubic, and Quartic+
				Stabilizing(Converging)
				The Gap(The Hole: Diverging)
				Dynamic(Fractal)
				Cyclic(Partly Fractal)
				Approximate
			Light Modeled
Extention of the Golden Algebraic Method.Adjusted Multiplication of the Roots.
Derivation of the Coefficients From Partial Quotients.The Transformation of
One Set of Coefficients Into Another.Relations Within A Set.Integration Within
The Quadratic Parallel Method.The Quadratic Quality to Any Polynomial With It's
Location in Polygons

	***************************************************************

Abbreviations and Notations
Glossary
References
Index

			      Abbreviations

EuA: Euclidean Algorithm
gcf, gcd: greatist common factor(divisor)
lcm: least common multiple
q1, q2, q3, etc.: partial quotients of the Euclidean algorithm and parallel
	computation of infinite set series

and:				Notations

	     <> IS NOT EQUAL TO	        =: IS APPROXIMATELY EQUAL TO

	     ^ EXPONENTIATION		<RADICAL BRACKETS>, where:

	   		<SQUARE ROOT OF...>, or:

<ROOT OF...>R, where R = the fractional exponent of a radical, either as:

R=an integer, the reciprocal of a unit fraction(1/integer); or as,

R=a non-unit fraction(integer/integer)

{THE TAKING OF ANY ROOT OF A NUMBER WITHOUT THE NEED FOR SPECIFYING WHICH ROOT}
			      X	= {Y}^(1/Z)

	     (EUCLIDEAN ALGORITHM PERFORMED ON A SET OF ANY SIZE)

	(FIRST ORDER PARANTHESIS)	     [SECOND ORDER PARANTHESIS]

[PARTIAL QUOTIENTS OF A CONTINUED FRACTION: q1, q2, q3,...; OR..., q1, q2;...]

			       &  INFINITY

			       >>>>  ARROWS; LEADS TO...


move to back of text:		Glossary

Aesthetics: the study of harmonic relations in any field of inquiry
 Harmonic Systems(of dual sign mathematic systems): approximation methods
 	generating ?logarithmic scales of relations from simple polynomials in
	one unknown--relations may be angular, phasic, linear, vibrational, or
	molecularly weighted
Euclidean geometry: realistic
 Non-Euclidean geometry: surrealistic; not unreal, but outside the fringe of
 	normal reality; sometimes the equivalent of the real, but stated in
	simpler terms
Beauty; Charm; Nourishment
 Power; Purification (Destruction when in excess)
Golden: Pure-Bred; conventionally it refers only to Golden Beauty, but now it
	also includes Golden Power
 Semi-Golden: sometimes used to refer to Golden Power
 Hybrid: Quasi-golden; makes use of Golden's conceptual framework, but minus its
         symmetry
Ideal: the highest form that aesthetics can take within our style of thinking
Multiplicative Series: coventionally known as a geometric series
 Additive Series: a progression of numbers stemming from the process of addition
 Algebraic Series: a combination of the above, plus exponentiation
Summation: accumulative addition; potentially infinite
 Multiplation: accumulative multiplication; potentially infinite


				References

Cayce, Edgar; Life and Medical Readings; Association for Research and
Enlightenment; Virginia Beach, Virginia, 19??-19??

Darwin, Charles; The Origin of the Species;

?Jet Propulsion Laboratory's Updated Information on Venus Flyby

?Holden, Alan and Morrison, Phylis; Crystals and Crystal Growing; The MIT Press;
Cambridge, Mass.; 1995

Lutes, Charlie; Lectures

Mahesh Yogi, Maharishi; Science of Creative Intelligence, Lesson ?; ?; ?; 1972?


Ogilvy, C. Stanley, and Anderson, John T., Excursions In Number Theory, Oxford
University Press, New York, 1966

Staff of Research and Education Association, Dr. M. Fogel, Director, Handbook of
Mathematical, Scientific, and Engineering Formulas, Tables, Functions, Graphs,
Transforms, , Piscataway, NJ, 1994

Tynne, Anne G., Geometric Extensions of Consciousness, Zodiac 19, 1969
---------, Simultaneous Randomness and Order: The Fibonacci Divine Proportion
As a Universal Forming Principle, Ph.D Thesis, Ann Arbor, MI: Univ. Microfilms
Int., 1975

The Urantia Book, The Urantia Foundation?, Chicago, IL, 1934

Van Nostram's Scientific Encyclopedia,

Watts, Donald J. and Carol M., A Roman Apartment Complex, Sci. Am., Vol. 255,
no. 6, 132-140, Dec. 1986

			      Acknowledgements

	I wish to thank the patience of close friends and relatives for making
me possible.
	California State University at Northridge has my thanks for the use of
their library, computers, classes, and teachers.
	And You, for your time and consideration of this material.


				  Preface
		   (a commentary on the writing of this book)



				Introduction

	We will never know completely the full scoop about anything so long as
we are human. We usually count three sources for our information: knowledge
about our own, or someone else's experience, reason, and intuition. We and
society will never live long enough to know everything---how long is eternity?
Reason always requires the full picture to be accurate---are you God? Intuition,
no matter how accurate, is ephemeral---can you prove or disprove what lies
beyond akasha (the holy ghost of eastern thinking)? Maybe as suprahumans it is
more expedient to create knowledge to satisfy the requirement at hand, rather
than be subservient to fulfill knowledge by having to learn it. Who should be
the master? (I am using knowledge as a much more broad term here to designate
reality just before it manifests.) But that is the prerogative of the Almighty-
--something to look forward to. In the mean time, we will just have to make do-
--but don't take my word for it.

	This study is both theoretical and applied with most of its emphasis on
subjective interpretation. I have tried to be both self and conventionally
consistent, but have taken liberties with nomenclature whenever it appears to
help organize concepts.
	Section One is an introduction to aesthetic theory.It uses a minimum of
math for understanding this subject.
	Section Two discusses a special but necessary adjunct to the general
theory. It is extremely difficult to comprehend (or write about), so take it
easy. It gives an indepth look into the possible consequences of some of these
basic ideas when taken to extreme.
	Section Three brings into focus some general understanding of background
material not covered in either sections one or two.
	Section Four is a hands-on approach to making all of this mumbo jumbo
practical. It speculates: "as above, so below"---what we do is also done by the
gods.
	Speculation is offered at the end of Section One as to how this topic
developes within the scheme of things. Other speculations are also offered
(especially concerning planetary developement, although this whole book is a
speculation) that at times may strain your patience. I regret if this is the
case. I wouldn't feel the text complete if any idea relating to the topic were
left out.
	Enjoy this, if you can!

Normally, new ideas within the realm of pure
mathematics must be first postulated as a hypothesis and then proven logically
before ever being stated as theoretical fact. New ideas in the applied sciences,
however, such as astronomy, may be theorized if there is sufficient data that
consistently agrees with itself to date and is agreed upon my most observers.
The difference between a hypothesis and a theory is that a theory is recognized
as a valid statement about nature within the limitations of human understanding,
while a hypothesis is a proposed idea in need of substantiation before
professional opinion puts its good housekeeping seal of approval on it. In the
applied sciences, observation is the hypothesis("Do I see what I think I see?"),
while in theoretical endeavors, speculation is the hypothesis(even if it is
conjectured logically, since it takes multiple views to double-check accuracy:
is it conjectured out of context?, how large is the context?; what does the
context include?, what does it exclude?).


quotation page:

	    Ars Longa, Vita Brevis:     Art (is) long, life (is) short.

Latin, pronounciation: (arz longa, veeta brevis)


section title page:
Section 1: Aesthetic Approximation Theory