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II. Divine Systems
2.3 EIKOS Divine System of Language
Article 22 - SYMERICS Foundation Class
The PRIMARY RULES of the ELEMENTAL CONCEPT of SYMERICS of the SYMERICS FOUNDATION CLASS of the EIKOS Language System are:
1. SYMERICS is a FOUNDATION CLASS of ELEMENTAL CONCEPTS associated with the study of STRUCTURE, RELATION and QUANTITY expressed as VALID FORMULA. SYMERICS is a main branch of the Eikos Language System.
2. SYMERICS is constructed of twenty four [24] ELEMENTAL CONCEPTS including: SYMERICS, VARIABLE, FUNCTION, SUM, RELATION, DIMENSION, FORMULA, LINEAR FORMULA, MATRIX FORMULA, MULTI-DIMENSION FORMULA, FUNCTION VERSION, SIMPLE THEORETICAL FORMULA, SIMPLE NATURAL FORMULA, SIMPLE NUMERIC FORMULA, SIMPLE UNISET FORMULA, SIMPLE 2D GEOMETRIC FORMULA, SIMPLE 3D GEOMETRIC FORMULA, COMPLEX THEORETICAL FORMULA, COMPLEX NATURAL FORMULA, COMPLEX NUMERIC FORMULA, COMPLEX UNISET FORMULA, COMPLEX 2D GEOMETRIC FORMULA, COMPLEX 3D GEOMETRIC FORMULA and ALGEBRA.
3. All elements defined by EIKOS, LOGOS, NUMERICS, UNISET and GEOLEX may be expressed as a FORMULA of one or more VARIABLES defined by the rules of SYMERICS.
4. All FORMULA defined by the rules of SYMERICS must adhere to the Ucadian Semantic Classification System standard of declaration of DIA (statements of DA) in their formulation and writing.
5. A DIA is a formal declaration of DA (OBJECTS as defined by the Ucadia Classification System and the Ucadia Symbols System).
6. The function of a VALID FORMULA (in terms of structure and flow of variables according to the rules of SYMERICS) may be expressed by only three (3) major types: LINEAR, MATRIX or MULTI-DIMENSION types.
7. All VALID FORMULA under the rules of SYMERICS may be further classified according to three (3) categories defining its primary FUNCTION and SCOPE of APPLICATION including NON-GEOMETRIC NON-NATURAL, NON-GEOMETRIC NATURAL and GEOMETRIC.
The PRIMARY RULES of the ELEMENTAL CONCEPT of VARIABLE of the SYMERICS FOUNDATION CLASS of the EIKOS Language System are:
1. All known types of LOGOS, NUMERIC, UNISETS and GEOLEX may be represented as unique sets of SYMBOLS representing possible values called VARIABLES.
2. All variables may be defined into only one of two (2) TYPES being OBJECT VARIABLES and THEORETICAL VARIABLES.
3. An OBJECT VARIABLE is any VARIABLE that represents a known OBJECT and/or PROPERTY of an OBJECT defined by the Ucadia Symbols System.
4. A THEORETICAL VARIABLE is any VARIABLE that does not represents a known OBJECT and/or PROPERTY of an OBJECT defined by the Ucadia Symbols System.
5. All VARIABLES naturally inherit the rules and restrictions according to its TYPE (OBJECT or THEORETICAL) and particular use.
6. All variables are specialized and unique to some degree (UNIQUE VARIABLE) depending upon their particular TYPE.
7. All variables are co-dependent to some degree (CO-DEPENDENT VARIABLE) depending upon their particular TYPE.
8. All variables are common and interchangeable to some degree (UNIVERSAL VARIABLE) depending upon their particular TYPE.
The PRIMARY RULES of the ELEMENTAL CONCEPT of FORMULA of the SYMERICS FOUNDATION CLASS of the EIKOS Language System are:
1. All elements defined by EIKOS, LOGOS, NUMERICS, UNISET and GEOLEX may be expressed as a FORMULA of one or more VARIABLES.
2. All FORMULA must adhere to the Ucadian Semantic Classification System standard of declaration of DIA (statements of DA) in their formulation and writing.
3. A DIA is a formal declaration of DA (OBJECTS as defined by the Ucadia Classification System and the Ucadia Symbols System).
4. All VALID FORMULA of SYMERICS are constructed of three (3) primary components: FUNCTION, RELATION and SUM and two representations being RESULT (FUNCTION leads to SUM) or RELATION (SUM leads to FUNCTION).
5. A VALID FUNCTION must contain at least one (1) VARIABLE and one OBJECT defined by some formation relationship.
6. A VALID SUM must contain at least one (1) OBJECT or NUMBER. It may also contain the option of including one or more VARIABLES.
7. A VALID RELATION is any valid RELATOR of the Ucadia Symbols System that describes the leading relation between the RESULT (FUNCTION leads to SUM) or the RELATION (SUM leads to FUNCTION).
8. All VARIABLES contained within a formula must be defined by their type (unique, co-dependent or universal) and type.
9. For a formula to function properly, the correct substitution of variables by type and purpose must take place.
10. The function of a formula (in terms of structure and flow of variables) may be expressed as LINEAR, MATRIX or MULTI-DIMENSION types.
The PRIMARY RULES of the ELEMENTAL CONCEPT of LINEAR FORMULA of the SYMERICS FOUNDATION CLASS of the EIKOS Language System are:
1. A LINEAR FORMULA is any VALID SYMERIC FORMULA where the FUNCTION adheres to the conventions of a two (2) Dimension LEFT to RIGHT FORMULA of the EIKOS Language System.
2. LINEAR FORMULA is one of three (3) Types of FUNCTION of SYMERICS including LINEAR, MATRIX (left-right, top-down, bottom-up) and MULTI-DIMENSIONAL (in-out, around).
3. All valid LINEAR FORMULA are read left to right and must contain at least two (2) VARIABLES defined by a valid RELATIONSHIP.
4. A valid LINEAR FORMULA may not contain MATRIX structure, nor may it contain a MULTI-DIMENSIONAL structure. In both cases, such a FORMULA if valid will be classed as other than a LINEAR FORMULA.
The PRIMARY RULES of the ELEMENTAL CONCEPT of SYMERICS-MATRIX FORMULA of the SYMERICS FOUNDATION CLASS of the EIKOS Language System are:
1. A MATRIX FORMULA is any VALID SYMERIC FORMULA where the FUNCTION adheres to the conventions of a two (2) Dimension MATRIX structure of the EIKOS Language System.
2. MATRIX FORMULA is one of three (3) Types of FUNCTION of SYMERICS including LINEAR, MATRIX (left-right, top-down, bottom-up) and MULTI-DIMENSIONAL (in-out, around).
3. A MATRIX structure is a rectangular table of ELEMENTS which may be NUMBERS or VARIABLES that can be modified according to any OPERATOR. The horizontal line in a MATRIX are called ROWS and the vertical lines are called COLUMNS.
4. All valid MATRIX structure must declare in its design and identification m ROWS, n COLUMNS, the OPERATORS to be applied to the ELEMENTS, the conditions of such application and the path of reading (left-right, top-down or bottom-up).
5. All valid MATRIX FORMULA must contain at least two (2) ROWS and two (2) COLUMNS of VARIABLES or NUMBERS defined by a valid RELATIONSHIP.
6. A valid MATRIX FORMULA may not containa MULTI-DIMENSIONAL structure. Such FORMULA are known as MULTI-DIMENSIONAL SYMERIC FORMULA.
The PRIMARY RULES of the ELEMENTAL CONCEPT of MULTI-DIMENSIONAL FORMULA of the SYMERICS FOUNDATION CLASS of the EIKOS Language System are:
1. A MULTI-DIMENSIONAL FORMULA is any VALID SYMERIC FORMULA where the FUNCTION adheres to the conventions of an n-Dimension DIMENSIONAL structure of the EIKOS Language System.
2. MULTI-DIMENSIONAL FORMULA is one of three (3) Types of FUNCTION of SYMERICS including LINEAR,MATRIX (left-right, top-down, bottom-up) and MULTI-DIMENSIONAL (in-out, around).
3. An N-DIMENSIONAL STRUCTURE is a FUNCTION defined by a RELATIONSHIP map of more than three (3) VARIABLES defined by a MOTION path and at least one (1) OPERATOR to be applied during MOTION.
4. MULTI-DIMENSIONAL permit the expression of simultanous n-dimensional events being applied to at least three (3) variables.
5. All valid MULTI-DIMENSIONAL FORMULA describing real OBJECTS must be 3-DIMENSIONAL with a GEOMETRIC path and RELATIONSHIP map. However, theoretical FORMULA without real objects permit more than three (3) dimensions.
6. A valid MATRIX FORMULA may not contain a MULTI-DIMENSIONAL structure. Such FORMULA are known as MULTI-DIMENSIONAL SYMERIC FORMULA.
The PRIMARY RULES of the ELEMENTAL CONCEPT of SIMPLE THEORETICAL FORMULA of the SYMERICS FOUNDATION CLASS of the EIKOS Language System are:
1. SIMPLE THEORETICAL FORMULA is any valid SYMERIC FORMULA that involves no more than three (3) VARIABLES in a SIMPLE LINEAR 2D FORMULA such that the FORMULA shall never apply to a GEOMETRIC nor NUMERIC, nor UNISET expression.
2. The purpose and function of SIMPLE THEORETICAL FORMULA is primarily to express all possible RELATIONSHIPS between real SETS, OBJECTS and NUMBERS that have no GEOMETRIC expression.
3. There exists six (6) SETS of PROPERTIES in association to the VALID expression of any SIMPLE THEORETICAL SYMERIC FORMULA. These are DEFINITION, SYMBOL, OPERATIONS, EQUALITY, INEQUALITY and EQUIVALENCE.
4. The primary PROPERTY of DEFINITION for all VALID SIMPLE THEORETICAL SYMERIC FORMULA is that any variable defined by a Valid symbol has the same universal meaning wherever it is located within the FORMULA.
5. The primary PROPERTY of SYMBOL for all VALID SIMPLE THEORETICAL SYMERIC FORMULA is that only valid Eikos Symbols of the Ucadia Symbols System are valid and used.
6. There exists only seven (7) OPERATIONS for all VALID SIMPLE THEORETICAL SYMERIC FORMULA is that being ADDITION, SUBTRACTION, MULTI-ADDITION, MULTI-SUBTRACTION, RATIO, EXPONENT ADDITION and EXPONENT SUBTRACTION
7. There exists only three (3) PROPERTY of EQUALITY for all VALID SIMPLE THEORETICAL SYMERIC FORMULA being REFLEXIVE, SYMMETRIC and TRANSITIVE.
8. There exists only three (3) PROPERTY of INEQUALITY for all VALID SIMPLE THEORETICAL SYMERIC FORMULA being REFLEXIVE, SYMMETRIC and TRANSITIVE.
9. There exists only two (2) PROPERTY of EQUIVALENCE for all VALID SIMPLE THEORETICAL SYMERIC FORMULA being SYMMETRIC and TRANSITIVE.
The PRIMARY RULES of the ELEMENTAL CONCEPT of SIMPLE NATURAL FORMULA of the SYMERICS FOUNDATION CLASS of the EIKOS Language System are:
1. SIMPLE NATURAL FORMULA is any valid SYMERIC FORMULA that involves no more than three (3) VARIABLES in a SIMPLE LINEAR 2D FORMULA which may be applied to real world OBJECTS properties in a non-geometric expression.
2. The SUM of a SIMPLE NATURAL FORMULA must be either zero, or the sum of one or more non-zero terms.
3. The purpose and function of SIMPLE NATURAL FORMULA is primarily to express all possible RELATIONSHIPS within and between SETS that have no GEOMETRIC expression.
4. There exists six (6) SETS of PROPERTIES in association to the VALID expression of any SIMPLE NATURAL SYMERIC FORMULA. These are DEFINITION, SYMBOL, OPERATIONS, EQUALITY, INEQUALITY and EQUIVALENCE.
5. The primary PROPERTY of DEFINITION for all VALID SIMPLE NATURAL SYMERIC FORMULA is that any variable defined by a Valid symbol has the same universal meaning wherever it is located within the FORMULA.
6. The primary PROPERTY of SYMBOL for all VALID SIMPLE NATURAL SYMERIC FORMULA is that only VALID Eikos Symbols of the Ucadia Symbols System are valid and used.
7. There exists only seven (7) OPERATIONS for all VALID SIMPLE NATURAL SYMERIC FORMULA is that being ADDITION, SUBTRACTION, MULTI-ADDITION, MULTI-SUBTRACTION, RATIO, EXPONENT ADDITION and EXPONENT SUBTRACTION
8. There exists only three (3) PROPERTY of EQUALITY for all VALID NATURAL THEORETICAL SYMERIC FORMULA being REFLEXIVE, SYMMETRIC and TRANSITIVE.
9. There exists only three (3) PROPERTY of INEQUALITY for all VALID NATURAL SYMERIC FORMULA being REFLEXIVE, SYMMETRIC and TRANSITIVE.
10. SIMPLE NATURAL FORMULA are equivalent to the mathematical theory of a polynomial being an expression constructed from one or more variables and constants using operators where the sum is either zero or the sum of two (2) or more non-zero terms.
The PRIMARY RULES of the ELEMENTAL CONCEPT of SIMPLE NUMERIC FORMULA of the SYMERICS FOUNDATION CLASS of the EIKOS Language System are:
1. SIMPLE NUMERIC FORMULA is any valid SYMERIC FORMULA that involves no more than three (3) VARIABLES in which only PERFECT NUMBERS may be used in a SIMPLE LINEAR 2D FORMULA such that the FORMULA is not GEOMETRIC.
2. The purpose and function of SIMPLE NUMERIC FORMULA is to express certain RELATIONSHIPS within and between SETS of PERFECT NUMBERS that have no GEOMETRIC expression.
3. SIMPLE NUMERIC FORMULA may be either FINITE or INFINITE. INFINITE SIMPLE NUMERIC FORMULA are when there are an INFINITE number of solutions. FINITE is when there are only a FINITE number of solutions.
4. The simplest FINITE SIMPLE NUMERIC FORMULA is 1 multiplied by the variable [a] = 2
5. The simplest INFINITE SIMPLE NUMERIC FORMULA is 1 multiplied by the variable [a] = the variable [b]
6. SIMPLE NUMERIC FORMULA are equivalent to the mathematical theory of Diophantine equations whereby an indeterminate polynomial equation exists that permits variables to be integers only.
The PRIMARY RULES of the ELEMENTAL CONCEPT of SIMPLE UNISET FORMULA of the SYMERICS FOUNDATION CLASS of the EIKOS Language System are:
1. SIMPLE UNISET FORMULA is any valid SYMERIC FORMULA that involves no more than three (3) VARIABLES in a SIMPLE LINEAR or MATRIX FORMULA such that the FORMULA shall never apply to a GEOMETRIC expression.
2. The purpose and function of SIMPLE UNISET FORMULA is primarily to express all possible RELATIONSHIPS within and between SETS that have no GEOMETRIC expression.
3. There exists six (6) SETS of PROPERTIES in association to the VALID expression of any SIMPLE UNISET SYMERIC FORMULA. These are SET, SYMBOL, OPERATIONS, EQUALITY, INEQUALITY and EQUIVALENCE.
4. The primary PROPERTY of SET for all VALID SIMPLE UNISET SYMERIC FORMULA is that there exists more than three (3) VARIABLES belonging to one (1) SET.
5. The primary PROPERTY of SYMBOL for all VALID SIMPLE UNISET SYMERIC FORMULA is that only VALID Eikos Symbols of the Ucadia Symbols System are valid and used.
6. There exists only seven (7) OPERATIONS for all VALID SIMPLE UNISETSYMERIC FORMULA is that being ADDITION,SUBTRACTION, MULTI-ADDITION, MULTI-SUBTRACTION, RATIO, EXPONENT ADDITION and EXPONENT SUBTRACTION
7.There exists only three (3) PROPERTY of EQUALITY for all VALID SIMPLE UNISET SYMERIC FORMULA being REFLEXIVE, SYMMETRIC and TRANSITIVE.
8.There exists only three (3) PROPERTY of INEQUALITY for all VALID SIMPLE UNISET SYMERIC FORMULA being REFLEXIVE, SYMMETRIC and TRANSITIVE.
9.There exists only one (1) PROPERTY of EQUIVALENCE for all VALID SIMPLE UNISET SYMERIC FORMULA being SYMMETRIC and TRANSITIVE.
The PRIMARY RULES of the ELEMENTAL CONCEPT of SIMPLE 2D GEOMETRIC FORMULA of the SYMERICS FOUNDATION CLASS of the EIKOS Language System are:
1. SIMPLE 2D GEOMETRIC FORMULA is any valid SYMERIC FORMULA that involves no more than five (5) VARIABLES in a SIMPLE LINEAR 2D FORMULA such that the FORMULA always apply to a real GEOMETRIC expression.
2. The purpose and function of SIMPLE 2D GEOMETRIC FORMULA is primarily to express all possible RELATIONSHIPS within and between SETS that have GEOMETRIC expression.
3. There exists six (6) SETS of PROPERTIES in association to the VALID expression of any SIMPLE 2D GEOMETRIC FORMULA. These are GEOLEX, SYMBOL, OPERATIONS, EQUALITY, INEQUALITY and EQUIVALENCE.
4. The primary PROPERTY of GEOLEX for all VALID SIMPLE 2D GEOMETRIC SYMERIC FORMULA is that the FUNCTION and RELATIONSHIPS of the VARIABLES is expressed by at least one valid GEOMETRIC FUNCTION and SHAPE.
5. The primary PROPERTY of SYMBOL for all VALID SIMPLE 2D GEOMETRIC SYMERIC FORMULA is that only VALID Eikos Symbols of the Ucadia Symbols System are valid and used.
6. There exists only seven (7) OPERATIONS for all VALID SIMPLE 2D GEOMETRIC SYMERIC FORMULA is that being ADDITION, SUBTRACTION, MULTI-ADDITION, MULTI-SUBTRACTION, RATIO, EXPONENT ADDITION and EXPONENT SUBTRACTION
7. There exists only three (3) PROPERTY of EQUALITY for all VALID SIMPLE 2D GEOMETRIC SYMERIC FORMULA being REFLEXIVE, SYMMETRIC and TRANSITIVE.
8. There exists only three (3) PROPERTY of INEQUALITY for all VALID SIMPLE 2D GEOMETRIC SYMERIC FORMULA being REFLEXIVE, SYMMETRIC and TRANSITIVE.
9. There exists only one (1) PROPERTY of EQUIVELENCE for all VALID SIMPLE 2D GEOMETRIC SYMERIC FORMULA being SYMMETRIC and TRANSITIVE.
