Dimensional Thinking Principles

1.1 - A definition determines the outline, magnitude, architecture and/or design of an object, such that any definition is distinct and unique from every other definition. (Definition)

a) An outline determines the external shape of an object. (Definition)
b) Magnitudes determine the measurable quantities of an object, relative to other magnitudes using the same standard of measurement. (Definition)
c) Architecture determines the construction, internal outlines and/or internal magnitudes of an object. (Definition)
d) A design determines the intended use of an object. (Definition)

2. Dimensions v1.1

2.1 - A dimension is a particular, uniquely definable element of an object’s outline, magnitude, architecture or design. (Definition)

2.2 - A dimension or collection of dimensions define an object. (Construction)

2.3 - Particular dimensions can be shared among multiple objects. (Construction)

2.4 - An idea is a unique definition of a perceivable dimension. (Construction)

2.5 - A context is a unique collection of ideas. (Definition)

2.6 - A mind is at least a collector and organizer of ideas and contexts. (Definition)

2.7 - Tangible dimensions are dimensions perceivable by the senses and which are ultimately capable of perception and definition by a mind. (Definition)

2.8 - Intangible dimensions are ultimately definable by an idea or context, and capable of collection by a mind. (Definition)

2.9 A valid idea definition must uniquely describe a perceivable dimension. (Definition)

3. Relationships v1.1

3.1 - A relationship is a framework for communication between two objects or among more than two objects. (Definition)

3.2 - A pathway is a circuit along which communication occurs. (Definition)

a) Pathways within a relationship consist of dimensions shared, directly or indirectly, between or among objects. (Construction)

3.3 - When a particular dimension is included in the construction an object, that dimension exists in a relationship with other dimensions used in the construction of the object. (Construction)

a) Particular dimensions can be shared among multiple objects. (Construction)
b) Objects directly sharing the same dimension do not directly share each and every other dimension within each and every object that shares that dimension, except in the case of identities. (Definition)
c) Dimensions not directly shared among objects that directly share at least one dimension are indirectly shared dimensions.(Definition)

3.4 - Objects are defined by their dimensions and the relationships among their dimensions. (Construction)

3.5 - Objects can exist in relationships with other objects. (Construction)

3.6 – Objects are composed of dimensions. (Construction)

3.7 – If Object A exists in a relationship with Object B, then the dimensions of Object A exist in a relationship with the dimensions of Object B. (Construction)

a) Objects in a relationship are dimensions of each other. (Construction)

3.8 - The alteration of any composing dimension changes an object’s definition. (Construction)

a) An object exists in a unique relationship with each of its composing dimensions. (Construction)

3.9 - The alteration of any relationship between or among an object’s composing dimensions changes an object’s definition. (Construction)

a) An object exists in a unique relationship with each of its composing relationships. (Construction)

3.10 - All modes of communication exist in this Universe and therefore all modes of communication are composed of energy.

3.11 - Influence is a communication of energy between two objects or among more than two objects. (Definition)

3.12 - For any entity to influence another entity, it must exist in a relationship with it. Construction)

a) Entities in a relationship influence each other. (Construction)

3.13 - For any idea to influence another idea, it must exist in a relationship with it. (Construction)

a) Ideas in a relationship influence each other. (Construction)

3.14 - For any entity to influence an idea, it must exist in a relationship with it. For any idea to influence an entity, it must exist in a relationship with it. (Construction)

a) Entities and ideas in a relationship can influence each other. (Construction)

3.15 - Perception is any relationship between or among objects. (Definition)

4. Existence and Perception v1.0

4.1 – Perception is any relationship between (1) the physical senses and/or (2) a mind and/or 3) any object. (Definition)

4.2 - Perception is a dimension of relationships. (Construction)

4.3 - Perception exists in this Universe. (Construction)

4.4 - Perception is composed of energy. (Construction)

4.5 - Perception is an object. (Construction)

4.6 - An object perceivable by the physical senses and/or by a mind must necessarily exist. (Definition)

4.7 - A dimension is a particular, uniquely definable element of an object’s outline, magnitude, architecture or design. (Definition)

4.8 - A dimension or collection of dimensions define an object. (Construction)

4.9 - Existence is a dimension of perception. (Construction)

a) Dimensions defining a perceivable object must necessarily exist.
b) A dimension or collection of dimensions define an object.
c) Perceivable objects must necessarily exist.

4.10 - An object not perceivable by a particular set of physical senses and/or a particular mind does not exist for those particular senses and/or that particular mind. (Construction)

a) Existence is a dimension of existence. (Construction)
b) Perception requires existence for its definition. (Construction)
c) Perception is an element of existence. (Construction)
d) There is no perception without existence.

4.11 - Existence is a dimension. (Construction)

4.12 - Existence is an object. (Construction)

4.13 - Perception is a dimension. (Construction)

4.14 - An entity is a particular object with the dimension of existence and at least one more dimension, such as height, depth, width, or mass. (Definition)

4.15 - Matter is an entity or collection of entities with the dimension of existence and at least one more dimension, such as height, depth, width, or mass. (Definition)

4.16 - An idea is a particular object with at least the dimension of existence. (Construction)

4.17 – Entities and ideas are objects that share the dimension of existence. (Construction)

4.18 - Objects that share the dimension of existence must necessarily share the dimension of perception. (Construction)

a) Entities and ideas are objects that share the dimension of perception. (Construction)

5. Shared Dimensions v1.1

5.1 - Mass is a measurement of a quantity of matter. (Definition)

5.2 – Mass is a dimension of matter. (Construction)

a) Mass and matter exist, therefore mass and matter are objects.
b) Objects are composed of dimensions.
c) Mass, as a dimension of matter, exists in a relationship with matter.
d) Objects in a relationship are dimensions of each other.
e) Mass is a dimension of matter.

5.3 - Energy is the object that produces or prevents motion, or has a tendency to do so. (Definition)

5.4 – Objects share the dimensions of existence, energy construction, matter and the constant speed of light. (Construction)

a) The Big Bang created a Universe constructed solely of energy;
b) Energy, in all its forms, is the sole substance of the known Universe;
c) Each object that exists must exist in this Universe of energy;
d) Objects existing in this Universe must be constructed of energy;
e) Via E=MCC, energy, matter, and the constant speed of light exist in a relationship with each other;
f) Objects in a relationship must share dimensions directly, or share dimensions indirectly via combinations of relationships. If dimensions are not directly or indirectly shared there is no framework for communication and therefore no relationship;
g) A dimension is a perceivable object. Perceivable objects must necessarily exist.
h) Entities and Ideas are perceivable objects, and must necessarily exist.
i) Via their energy construction, entities exist in a relationship with matter and the constant speed of light;
j) Via their energy construction, ideas exist in a relationship with matter and the constant speed of light;
k) Both entities and ideas exist in a relationship with energy, matter and the constant speed of light;
l) Entities and ideas exist in a relationship with each other via their shared dimensions.

6. Logic and Mathematics v1.1

6.1 – Logic and mathematics are objects. (Construction)

a) The Universe was created in a Big Bang of energy.
b) Every object in the Universe is composed of energy.
c) Energy obeys logical and mathematical laws.
d) Logical and mathematical laws exist in this Universe.
e) Logic and mathematics are composed of energy.
f) Logic and mathematics obey physical laws.
g) Logic and mathematics are objects.

6.2 - In a logical and mathematical Universe, all relationships are logical and mathematical. (Construction)

6.3 - Objects share the dimensions of existence, energy construction, matter and the constant speed of light. (Construction)

6.3 - Shared dimensions are the embodiment of logic and mathematics. (Definition)

6.4 - Logic and Mathematics embody the innate structure of the Universe. (Construction)

a) The Universe is composed solely of energy.
b) Energy completely obeys known laws.
c) Laws are structured as logical and/or mathematical objects.
d) Objects that obey laws have a logical or mathematical structure.
e) The Universe is composed of logical and mathematical objects.
f) Logic and Mathematics embody the innate structure of the Universe.

7. Physical Ideas v2.0

7.1 - Matter exists in a relationship with one or more dimensions such as height, width, depth or mass. (Definition)

7.2 - Matter is a perceivable object such that some or all of its dimensions can be touched, smelled, heard, seen or measured. (Definition)

7.3 - Objects whose dimensions can be touched, smelled, heard, seen or measured are physical objects. (Definition)

7.4 - Matter is a physical object. (Constructon)

7.5 – An Entity is a perceivable physical object with dimensions that can be touched, smelled, heard, seen or measured. (Definition)

7.6 – Entities exist in a relationship with matter. (Construction)

7.7 - Entities have a physical existence because they are composed of one or more dimensions such as height, width, depth or mass. (Construction)

7.8 - Ideas are composed of energy. (Construction)

7.9 - Energy is a perceivable object such that some or all of its dimensions can be touched, smelled, heard, seen or measured. (Definition)

7.10 - Ideas are perceivable objects. (Construction)

7.11 - Perceivable objects must necessarily exist. (Definition)

7.12 - Ideas are physical objects. (Construction)

a) Ideas are composed of energy and therefore exist in a relationship with energy;
b) Energy exists in a relationship with mass;
c) Mass exists in a relationship with matter;
d) Ideas exist in a relationship with mass via their relationship with energy;
e) Mass exists in a relationship with matter;
f) Ideas exist in a relationship with matter via their relationship with mass;
g) Matter exists in a relationship with one or more dimensions of height, width, depth and mass;
h) Ideas exist in a relationship with one or more dimensions of height, width, depth and mass;
i) Objects have a physical existence when they exist in a relationship with one or more dimensions of height, width, depth or mass;
j) Matter is a physical object;
k) An Idea is a physical object.

8. Geometric Architectures v2.0

8.1 - Height, width, depth, volume and mass are dimensions that can be logically and mathematically measured. (Definition)

8.2 - Measurable dimensions exist in a relationship with physical objects. (Construction)

8.3 - Measurable dimensions such as lengths and volumes depend on spatial distances or spatial densities relative to other spatial distances and spatial densities. (Construction)

8.4 - Physical objects are definable in all or in part by their measurable dimensions. (Construction)

8.5 - Measurable dimensions imply a physical shape. (Construction)

8.6 - Physical shapes imply a geometric outline. (Construction)

8.7 - Ideas are physical objects.

8.8 - Physical ideas assume a geometric form. (Construction)

8.9 – Physical ideas are composed of physical dimensions. (Construction)

8.10 – Grouped physical dimensions create a physical architecture. (Definition)

8.11 – A physical architecture implies a geometric architecture. (Definition)

8.12 – Physical ideas imply a Geometric Architecture. (Construction)

9. Contexts v2.0

9.1 - A context is equally an idea, or a collection of ideas. (Definition)

9.2 - Contexts assume a geometric form. (Construction)

9.3 – Any Idea or Entity with a geometric form is a Geometric Object. (Definition)

9.4 - Any dimension of an Idea is an object, therefore any dimension of a context is an object. (Construction)

10. Types of Contexts v3.0

10.1 - A context is equally an Idea, or a collection of Ideas.

10.2 - Ideas are composed of dimensions.

10.3 - Contexts are composed of dimensions. (Construction)

10.4 - A contextual filter is a logical or mathematical law that associates or disassociates dimensions from each other. By so doing, contextual filters associate particular dimensions to contexts, and disassociate particular dimensions from contexts. (Definition)

10.5 - A Base Geometric Architecture (BGA) is a self-consistent logical island of ideas. (Definition)

10.6 - A Point of View (POV) Context is one or more Base Geometric Architectures logically connected and used as the primary contextual filter for other ideas. (Definition)

10.7 - Any Base Geometric Architecture composing a POV Context may itself be a POV Context when associated with a different pool of perceivable contexts. (Construction)

10.8 - Point of View Contexts are either objective (scientific) or personal. (Definition)

a) Objective Base Geometric Architectures (OBGA) are composed of standardized sets of dimensions and rules arranged in a particular design. (Definition)
b) Personal Base Geometric Architectures (PBGA) are composed of non-standardized dimensions and rules arranged in a particular design. (Definition)

10.9 - Objective Base Geometric Architecture (OBGA) and Personal Base Geometric Architectures (PBGA) are logical or mathematical groupings of GAs. (Definition)

10.10 - Objective Points of View (OPOV) create Objective Base Geometric Architectures (OBGA).

10.11 - Personal Points of View (PPOV) create Personal Base Geometric Architectures (PBGA).

11. Rules and Levels v2.5

11.1 – A rule is a logical or mathematical law that embodies a relationship between or among particular dimensions in any pool of perceivable dimensions. (Definition)

a) Each rule is a unique context defined by a logical or mathematical law. (Construction)
b) Each rule is a unique idea structure defined by a logical or mathematical law. (Construction)

11.2 – Organized objects are objects that exist in logical or mathematical relationships with each other. (Definition)

11.3 - The Ideas composing a context are organized by a rule. (Construction)

11.4 - Ideas are logically organized when they are physically grouped by a physical rule. (Construction)

11.5 - Every rule defines a context. (Construction)

11.6 – Different rules can be logically or mathematically combined via shared dimensions. to form complex contexts. (Construction)

11.7 - A complex context is the logical or mathematical combination of two or more rules. (Definition)

11.8 - A level can be one context organized by one predominant rule. (Definition)

11.9 – A level can be multiple contexts related to each other by a more inclusive, encompassing rule. (Definition)

11.10 - Each context in a complex context is a level of the complex context. (Construction)

12. Truth, Dominant Rules and Recessive Rules v2.0

12.1 - A context is said to be completely truthful when its composing dimensions are exactly defined and completely consistent with the rule or rules used to build the context. (Definition)

12.2 - A context is said to be completely truthful when it is reproducible using exactly defined dimensions operated on in the same way by exactly the same rules. (Definition)

12.3 - If all the dimensions composing a context are not completely consistent with the rule or rules governing the context, but some are consistent while others are not, then that context is partially true and partially false. (Definition)

12.4 - If each dimension composing a context is not uniquely and exactly defined, then the context is partially true and partially false. (Definition)

12.5 - POV contexts are filters used to associate and disassociate dimensions. (Construction)

12.6 – Every complex context has a Dominant Rule (DR) context that associates and disassociates contexts to the complex context. (Definition)

a) Dominant Rules are Point Of View Filters (Construction)

12.7 - The Dominant Rule of a truthful context must include all the dimensions in the perceivable pool of dimensions consistent with the logical or mathematical law of the rule. (Definition)

12.8 – Recessive Rules are contexts in a complex context other than the Dominant Rule. (Definition)

a) Recessive Rules may be Dominant Rules in other contexts. (Construction)

12.9 - A Paradox is a context with two contradictory Dominant Rules. (Definition)

12.10 - A Dilemma is a context with two or more contradictory Recessive Rules. (Definition)

12.11 - A First Level dimension is a dimension physically shared by a rule, Dominant and/or Recessive, and a dimension in the perceivable pool of dimensions. (Definition)

12.13 – An incomplete idea structure is a partially true and partially false context. (Definition)

13. A New Definition of Physical Existence v2.0

13.1 - A mathematical point has no dimensions. (Definition)

a) A point has no width, length, or depth. (Definition)

13.2 - A mathematical line has one dimension. A line has the dimension of length, but no width or depth. (Definition)

13.3 - A mathematical plane has two dimensions. A plane has length and width, but no depth. (Definition)

13.4 – The definition of points, lines and planes are perceivable by a mind. (Construction)

13.5 - Objects perceivable by a mind are mental objects. (Definition)

13.6 – Definitions are contexts. (Construction)

13.7 – Contexts are objects. (Construction)

13.8 - Perceivable objects exist. (Definition)

13.9 - Objects that exist are composed of energy. (Construction)

13.10 - Energy exists in a relationship with matter. (Construction)

13.11 - Points, lines and planes are mental objects that exist in a relationship with matter. (Construction)

13.12 - Mental objects are Ideas. (Definition)

13.13 - Points, lines and planes are Ideas with a mathematical, logical and physical existence. (Definition)

14. Maps and Territories v2.0

14.1 - A map is a mental object. (Definition)

14.2 - A territory is at least a three-dimensional object. (Definition)

14.3 - A map defines a territory or another map. (Definition)

14.4 – A map is a context. (Construction)

14.5 - When a map defines another map, it is equivalent to a rule defining a level. (Definition)

14.6 - When a map defines a three-dimensional object, it is equivalent to a rule defining a territory. (Definition)

14.7 - The definition of “Nothingness” is a territory with no dimensions. (Definition)

14.8 - The context “Nothingness” exists as a map, but does not define a three-dimensional territory. (Construction)

a) An object not perceivable by a particular set of physical senses and/or a particular mind does not exist for those particular senses and that particular mind. (Construction)
b) Objects without dimensions are not perceivable. (Construction)
c) “Nothingness” does not exist as a territory. (Construction)
d) “Nothingness” exists only as a mental object. (Construction)

14.9 - Maps and territories exist in a relationship with each other, but they are not dimensionally equivalent.

14.10 - Maps and territories exist in a relationship with each other, but intervening levels may be required to complete the relationship.

15. Power Relationships v2.0

15.1 - A relationship is a framework for communication between two objects or among more than two objects. (Definition)

15.2 - All modes of communication exist in this Universe and therefore all modes of communication are composed of energy. (Construction)

15.3 - Influence is a communication of energy between two objects or among more than two objects. (Definition)

15.4 - Entities in a relationship influence each other. (Construction)

a) Entities can influence each other equally. (Construction)
b) Entities can influence each other unequally. (Construction)

15.5 - Contexts are composed of energy. (Construction)

15.6 - Influence can express itself as a transfer of contexts. (Construction)

15.7 - Power is the capacity for and measure of energy transfer. (Definition)

15.8 - The object with greater influence in a relationship has a position of greater power in that relationship. (Definition)

15.9 - A pathway is a circuit along which communication occurs. Pathways within a relationship consist of dimensions shared between or among objects. (Definition)

15.10 - Entities with different Points of View share fewer dimensions than entities with identical or similar Points of View. (Construction)

a) Entities with different Points of View share fewer pathways of communication. (Construction)

15.11 - Entities with different Points of View influence each other less than entities with identical or similar Points of View. (Construction)

16. The Rules of Power Relationships v2.5

16.1 - Contexts can be constructed of one dimension, or they can be constructed of more than one dimension. (Definition)

16.2 - When a context is constructed of one dimension, it is defined by that dimension. (Definition)

16.3 - When a context is constructed of more than one dimension, all the dimensions used in its construction are related by a rule. That rule is a context defined by its dimensions. (Definition)

16.4 - Contexts can enter relationships with other Geometric Architectures by sharing dimensions with those contexts. (Construction)

16.5 – Contexts can break existing relationships with other contexts by disassociating themselves from the dimensions shared with the other contexts. (Construction)

a) Changing one dimension of a context changes the definition of the context. (Construction)
b) In any context, associated dimensions can only be disassociated by a change in the definition of the context. (Construction)

16.6 - When a new shared dimension is added to a context, the original rule that related the original dimensions undergoes a change in definition to include the additional dimension. (Definition)

16.7- Addition is a rule that combines two or more contexts by introducing a shared dimension to the pool of available dimensions. (Definition)
16.8 - Multiplication is rule that combines two or more contexts by introducing a shared dimension multiple times to the pool of available dimensions. (Definition)

16.9 - Subtraction is a rule that disassociates a shared dimension from a context, creating a new unique definition of that context. (Definition)

16.10 - Division is a rule that disassociates multiple identical shared dimensions from a context, creating a new unique definition of that context. (Definition)

16.13- Identity Rule: For any uniquely defined context A, A = A (Definition)

16.14 – Inequality Rule: A ≠ B (Definition)

17. Contextual Relationships v2.5

17.1 – Rules are logical or mathematical processes that identify relationships between or among particular dimensions in any pool of perceivable dimensions. (Definition)

17.2 - Geometric Architectures are composed of dimensions related by a Dominant Rule. (Construction)

17.3 - Contexts are Geometric Architectures composed of dimensions related by a rule. (Construction)

17.4 – The Dominant Rule of a context is its Point of View. (Definition)

17.5 – Complex contexts are composed of one Dominant Rule, also known as a Point of View, and one or more Recessive Rules. (Definition)

a) Each rule defines a level of the complex context. (Construction)

17.6 - Contexts are necessarily unique in any pool of dimensions because the Dominant Rule organizing the context’s dimensions is unique to any particular pool of dimensions. (Definition)

a) Contexts with identical DRs are identities, one and the same, in any particular pool of dimensions. (Construction)

17.7 – Complex contexts are composed of a Dominant Rule and one or more Recessive Rules. (Definition)

a) Complex contexts with identical DRs and RRs in the same pool of perceivable dimensions are identities. (Construction)

17.8 – Recessive Rules are not unique to any particular context. (Definition)

17.9 - Complex contexts with different Dominant Rules may have identical RRs in their structure. (Construction)

17.10 - Recessive Rules in one context may be Dominant Rules in other contexts. (Construction)

17.11 – A First Level relationship is formed when one or more contexts with different Dominant Rules form relationships by directly sharing one or more dimensions. (Definition)

17.12 – Contexts in relationships with other contexts form complex contexts. (Definition)

17.13 – From the Point of View of context “A”, the Dominant Rule of “A” remains unchanged in the formation of complex contexts. (Definition)

17.14 - From the Point of View of context “A”, the Dominant Rules of other contexts in a complex context become Recessive Rules for “A”. (Construction)

17.15 – Second, Third, and Fourth Level relationships are formed between the Dominant Rule and Recessive Rules in complex contexts when dimensions within Recessive Rules (and not shared with the Dominant Rule) form First Level relationships. (Definition)

17.16 - In the case of Second, Third and Fourth Level relationships, the DR indirectly shares the First Level relationships between RRs via the DR’s directly shared dimensions with the RRs. (Construction)

17.17 - Analogy is a logical process whose basic mechanism is used in different degrees by all forms of comparing and contrasting contexts. (Definition)

a) Metaphor
b) Simile
c) Comparison
d) Exemplification
e) Allegories
f) Parables

17.18 - Paradoxes and Dilemmas are complex contexts with conflicting Recessive Rules in their structure.

18. Feelings, Thinking and the Self Image v2.0

18.1 - The Dominant Rule of a Self Context (SC) is “All My Beliefs Are Right”. (Definition)

18.2 - The Self Context (SC) is the sum of interactions between a Dominant Rule “All My Beliefs Are Right” and all the Recessive Rules composing the SC. (Definition)

18.3 - The Self Context defines an Identity Point of View (IPOV). (Definition)

18.4 - A Rule is a Point of View. (Construction)

18.5 - Power is the capacity for, and measure of, energy transfer. (Definition)

18.6 - Feelings are the relationships between an Identity Point of View and its Recessive Rules. (Definition)

18.7 – Feelings are relative states of power as viewed from the Identity Point Of View. (Definition)

18.8 – Thinking is the comparing and contrasting of Recessive Rules relative to the Identity Point of View. (Definition)

18.9 - Ideal love is the equal influence of perceivable energy, in both measure and kind, between and among objects. (Definition)

18.10 - War is an unequal influence of perceivable energy, in both measure and kind, between or among objects. (Definition)

Part 2 - FIRST LEVEL APPLICATIONS

19. The Physical Mechanics of Logic and Mathematics v2.5

19.1 – An “object” is any unique entity or any unique Idea.

19.2 – Perceivable objects must necessarily exist.

a) Entities and Ideas are perceivable, and therefore entities and Ideas exist.

19.3 – The Big Bang theory postulates a Universe composed solely of energy.

19.4 – Objects that exist in the Universe are composed solely of energy.

a) Entities and Ideas are composed of energy.

19.5 – An object is said to be in a relationship with another object when one or more of its composing dimensions is identical to one or more dimensions composing a second object. (Definition)

19.6 - An object is said to be in a relationship with another object when one or more of its composing dimensions is logically related to one or more dimensions composing a second object. (Definition)

19.7 - An object is said to “obey” a logical or mathematical law when one or more of its composing dimensions is identical to the composing dimensions of a logical or mathematical rule. (Definition)

19.8 – Via E=MCC, entities exist in a relationship with energy, mass and the constant speed of light.

19.9 – Objects can be viewed as energy, mass or the constant speed of light, depending on the Point Of View used.

19.10 – Mass is a measurement of a quantity of matter.

19.11 - A dimension is a particular element of an object’s outline, magnitude, architecture or design.

a) A dimension or collection of dimensions define an object.
b) Mass requires matter for its definition, and matter requires mass for its definition.
c) Mass is a dimension of matter, and matter is a dimension of mass.

19.12 – Dimensions in a definition are related by a logical or mathematical rule.

a) Mass exists in a relationship with matter, and matter exists in a relationship with mass.

19.13 - Matter exists in a relationship with one or more dimensions such as height, width, depth or mass.

19.14 – Objects have a physical existence when they exist in a relationship with one or more dimensions of height, width, depth and mass.

a) Ideas, which are composed of energy, can be viewed as massive objects.
b) As objects with mass, Ideas can be viewed as matter.
c) Ideas are physical entities.

19.15 – Energy, in all its forms, can be defined with logical and mathematical laws.

a) Energy, in all its forms, exists in a relationship with logical and mathematical laws.
b) In a Universe composed solely of energy, relationships are either logical or mathematical.

19.16 - Definitions and relationships, composed solely of energy, must necessarily also exist in a physical form.

a) Logical and mathematical definitions can be viewed as physical relationships.
b) Logical and mathematical definitions can be viewed as physical constructions.
c) Logical and mathematical relationships can be viewed as physical relationships.
d) Logical and mathematical relationships can be viewed as physical constructions.

20. First Level GO Mechanics v2.5

20.1 - Geometric Architectures (GAs) are contexts constructed of dimensions organized by a rule.

20.2 - Points of View, Dominant Rules and Recessive Rules are all rules capable of organizing dimensions into GAs.

20.3 - A First Level contextual relationship is created between two Geometric Architectures when one or more dimensions in the construction of one GA exist identically in the construction of another GA. (Definition)

a) A GA is a First Level dimension of every uniquely defined entity. A GA adds a dimension of formal structure to every uniquely defined entity.

20.4 The contexts joined in a First Level relationship are an identity if all perceivable dimensions of their composing GAs are identical, indicating all perceivable dimensions are shared. (Definition)

20.5 - Point of View Contexts are either objective (scientific) or personal.

20.6 - Objective Base Geometric Architectures (OBGA) and Personal Base Geometric Architectures (PBGA) are logical groupings of GAs.

20.7 - Objective Points of View (OPOV) are entirely dependent on unique definitions that include all dimensions in the perceivable pool of related dimensions. (Definition)

20.8 - Personal Points of View (PPOV) are entirely dependent on unique definitions that do not include all dimensions in the perceivable pool of related dimensions. (Definition)

20.9 - A fact is an object entirely dependent on a unique definition that includes all the dimensions in the perceivable pool of dimensions. Facts are entirely dependent on an Objective Point Of View. (Definition)

20.10 - Objective Truth is an object entirely dependent on a unique definition that includes all the dimensions in the perceivable pool of dimensions. Objective Truth is entirely dependent on an Objective Point Of View. (Definition)

20.11- Hints, clues, indications, opinions and guesses are objects entirely dependent on a unique definition that does not include all the dimensions in the perceivable pool of dimensions. Hints, clues, indications, opinions and guesses are entirely dependent on a Personal Point Of View. (Definition)

Part 3 - MULTIPLE LEVEL APPLICATIONS

21. The Relative Framework of the Dimensional Nexus v2.5

21.1 - An Idea is a perceivable object, composed of energy, and therefore capable of being viewed as energy, mass, matter and speed, or any combination or proportions of energy, mass, matter and speed.

a) Matter has a physical structure and can be defined at least by the Geometric Architecture of that physical structure.
b) Ideas can be viewed as matter.
c) Unique Ideas can be defined at least by their Geometric Architecture.
d) A Geometric Architecture defines a unique Idea.
e) Every Geometric Architecture can be viewed as an Idea.
f) Ideas can be viewed as energy, mass, matter or speed, or any combination or proportions of energy, mass, matter and speed. Therefore, energy, mass, matter and speed are logically related to all Ideas.
g) The logical relationships among energy, matter, mass, speed, and Ideas define a logical island of Ideas.
h) A Base Geometric Architecture is a self-contained logical island of ideas.
I) All Ideas can be viewed as Base Geometric Architectures.

21.2 – A dimension is a perceivable object, composed of energy, and therefore capable of being viewed as energy, mass, matter and speed, or any combination or proportions of energy, mass, matter and speed.

a) Matter has a physical structure and can be defined at least by the Geometric Architecture of that physical structure.
b) Dimensions can be viewed as matter.
c) Unique dimensions can be defined at least by their Geometric Architecture.
d) A Geometric Architecture defines a unique dimension.
e) Every Geometric Architecture can be viewed as a dimension.
f) Dimensions can be viewed as energy, mass, matter or speed, or any combination or proportions of energy, mass, matter and speed. Therefore, energy, mass, matter and speed are logically related to all dimensions.
g) The logical relationships among energy, matter, mass, speed, and dimensions define a logical island of Ideas.
h) A Base Geometric Architecture is a self-contained logical island of ideas.
I) All dimensions can be viewed as Base Geometric Architectures.

21.3 – Contexts and Rules are composed of Ideas and Dimensions

a) A context is a logical or mathematical organization of Ideas.
b) A rule is a logical or mathematical organization of dimensions.
c) An idea is an object composed of one or more dimensions.
d) A context is a logical or mathematical organization of dimensions.
e) A rule is a logical or mathematical organization of ideas.
f) Ideas and dimensions can be defined at least by their Geometric Architectures.
g) A Geometric Architecture defines a unique Idea. Put another way, a Geometric Architecture defines a unique dimension.
h) A Base Geometric Architecture is a self-contained logical island of ideas.
i) A Point Of View is one or more Base Geometric Architectures logically related and used as the primary filter for newly introduced Ideas.
j) Contexts are Base Geometric Architectures composed of dimensions related by a logical rule. Both a context and the GA of that context include the same defining dimensions.
k) Dimensions related by a logical rule form a self-contained logical island of ideas.
l) Every rule defines a context. (Definition)
m) Every context defines a rule. (Definition)
n) Rules, contexts and Points Of View can be viewed as Base Geometric Architectures

21.4 - A law is a logical or mathematical rule. A rule defines a context, therefore a law is a context.

a) An object exists in a relationship with another object when one or more of its composing dimensions is identical to one or more dimensions composing the other object. (Definition)
b) An object exists in a relationship with another object when one or more of its composing dimensions is logically related to one or more dimensions composing the other object. (Definition)
c) - An object is said to “obey” a logical or mathematical law when one or more of its composing dimensions is identical to the composing dimensions of a logical or mathematical rule. (Definition)
d) Matter obeys logical and mathematical laws.
e) Ideas can be viewed as matter.
f) Ideas obey logical and mathematical laws.
g) Ideas are said to be logically organized when they are physically grouped by a physical law.

21.5 – Complex contexts consist of two or more contexts organized by different rules.

a) A Base Geometric Architecture is a self consistent logical island of ideas. Put another way, a BGA is a logical grouping of Geometric Architectures.
b) Every rule is a BGA.
c) Every rule defines a context.
d) Rules can be combined to form complex contexts.e) Complex contexts consist of a Dominant Rule and one or more Recessive Rules.
f) Each context in a complex context is a level of the complex context, where a level is defined as one context organized by one rule, or multiple contexts related to each other by a more inclusive, encompassing rule.

21.6 – A Geometric Architecture defines a unique Idea. Put another way, a Geometric Architecture defines a unique dimension.

a) Any unique object is composed of at least one dimension.
b) Any unique dimension is an object.
c) One or more dimensions define an object.
d) Every unique dimension must be uniquely defined.
e) A definition determines the Architecture, magnitude, architecture and/or design of an object, such that any definition is distinct and unique from every other definition. (Definition)
f) For any definition to be unique and distinct from any other definition, it must be logically compared or contrasted with every other definition to determine its uniqueness.
g) A dimension must exist in a logical relationship with another dimension to determine its uniqueness versus the other dimension.
h) A dimension defines an Idea.
i) A Base Geometric Architecture is a self contained logical island of Ideas.
j) A structure that compares or contrasts two dimensions is a self contained logical island of Ideas.
k) A definition is a Base Geometric Architecture.

21.7 - Any particular dimension is an Idea, a Geometric Architecture, a rule, a context, a law, a definition, a Base Geometric Architecture and a Point Of View. Its function in a context depends on the context in which it is viewed. (Definition)

22. Logic and Mathematics Are Pathways In The Dimensional Nexus v1.0

22.1 - The Dimensional Nexus is the sum total of dimensions and relationships in the Universe.

22.2 - The Dimensional Nexus is composed of energy.

22.3 - Energy obeys logical and mathematical laws.

22.4 - An object is said to “obey” a logical or mathematical law when one or more of its composing dimensions is identical to the composing dimensions of a logical or mathematical rule.

22.5 - Objects that obey a logical or mathematical law exist in a relationship with that law via their shared dimension.

22.6 - Shared dimensions are pathways between objects and the laws they obey.

22.7 – Logic and mathematics are pathways in the Dimensional Nexus.

23. Multiple Level GO Mechanics v2.5

23.1 - A First Level contextual relationship is formed between two Geometric Architectures when one or more dimensions in the construction of one GA exist identically in the construction of another GA.

a) A First Level relationship is formed when contexts organized by different rules form relationships by directly sharing one or more dimensions via valence.

23.2 – A rule is a unique logical or mathematical structure of dimensions.

a) Every rule is a unique structure defined by the logical or mathematical relationships of its composing dimensions.
b) The physical structure of a dimension is defined at least by its Geometric Architecture.
c) Every rule is composed of Geometric Architectures.

23.3 - An Idea is a perceivable object, composed of energy, and therefore capable of being viewed as energy, mass, matter and speed, or any combination or proportions of energy, mass, matter and speed.

a) Matter has a physical structure and can be defined at least by the Geometric Architecture of that physical structure.
b) Ideas can be viewed as matter.
c) Unique Ideas can be defined at least by their Geometric Architecture.
d) A Geometric Architecture defines a unique Idea.
e) Every Geometric Architecture can be viewed as an Idea.

23.4 – A context is a logical or mathematical organization of Ideas.

a) Every rule is composed of Geometric Architectures.
b) A Geometric Architecture defines a unique Idea.
c) A Base Geometric Architecture is a self-contained logical island of ideas.
d) Contexts are Base Geometric Architectures composed of dimensions related by a logical or mathematical rule. Both a context and the GA of that context include the same defining dimensions.
e) Every rule defines a context. (Definition)
f) Every context defines a rule. (Definition)

23.5 - A law is a logical or mathematical rule.

a) Matter “obeys” logical and mathematical laws.
b) Ideas can be viewed as matter.
c) Ideas obey logical and mathematical laws.
d) Ideas are said to be logically organized when they are physically grouped by a physical law.

23.6 - A rule is a self consistent logical island of Ideas.

a) Every rule defines a context.
b) Rules can be combined to form complex contexts.
c) Complex contexts consist of a Dominant Rule and one or more Recessive Rules.
d) Each context in a complex context is a level of the complex context, where a level is defined as one context organized by one rule, or multiple contexts related to each other by a more inclusive, encompassing rule.

23.7 - A filter associates or disassociates dimensions based on the logical or mathematical laws organizing the filter. By so doing, filters associate or disassociate contexts, and associate or disassociate Ideas.

a) A Dominant Focal Geometric Architecture (DFGA) is the GA within any context to which other GAs in the context refer. The DFGA is the core physical structure to which other GAs in the context attach. (Definition)

b) A Point of View (POV) is one or more Base Geometric Architectures logically connected and used as the primary filter for other ideas. Like the subject of a sentence, the focal point of the Point Of View is its DFGA.

23.8 - A Second Level contextual relationship is created between two Base Geometric Architectures when at least one dimension of each BGA is related by a rule independent of the rules organizing the first two Base Geometric Architectures; that is, by a single mathematical or logical rule separate and different from the logical and mathematical rules organizing the first two Base Geometric Architectures. The Second Level related dimensions are never identical to the shared dimension or dimensions creating the First Level contextual relationship.

a) Every rule defines a context.
b) Rules can be combined to form complex contexts.
c) Complex contexts consist of a Dominant Rule and one or more Recessive Rules.
d) The logical and mathematical operations of the Dominant Rule are the primary filter in any complex context.
e) The logical and mathematical operations of Recessive Rules in a complex context are filtered through the logical and mathematical operations of the Dominant Rule.
f) Dominant Rules and Recessive Rules are composed of dimensions.
g) In a Second Level contextual relationship at least two dimensions are related by a rule different from the DR and RR in a complex context. This new rule becomes an additional RR in the complex context. Those dimensions are never directly shared by valence between the DR and the original RR.

23.9 - A Third Level contextual relationship is created among the Dominant Rule and two Recessive Rules of a complex context when dimensions within Recessive Rules (and not within the Dominant Rule) form one or more First Level relationships. In these cases the DR indirectly shares dimensions with both the RRs via its directly shared dimension(s) with one or both of the RRs.

23.10 - Individual GAs in a container object must share one identified dimension with all the other GAs in the container, but they may also share additional dimensions with one or more other GAs in the container.

a) The Dominant and Recessive Rules of numerical container objects, also know as sets, are always the product of an Objective Point Of View. (Definition)
b) The Dominant and Recessive Rules of non-numerical container objects, also know as sets, can be the product of either an Objective Point Of View or a Personal Point Of View. (Definition)

23.11 – Logic and Mathematics associate dimensions by assembling physical dimensions into physical form factors.

23.12 – Logic and Mathematics are the basis of both “hard” sciences like Physics and Chemistry, and also of “soft” sciences like Sociology and Psychology.

a) The dimensions of “soft” sciences are physical dimensions.
b) Physical dimensions obey physical laws.
c) The dimensions of soft sciences must obey physical laws, just as do the dimensions of hard sciences.

24. The Mechanics of Perception v1.0

24.1 - A complex context is a set of dimensions organized by a Dominant Rule and one or more Recessive Rules.

24.2 – The structure of a complex context can be changed by the addition of subtraction of new dimensions.

24.3 – New dimensions are sourced from the physical senses, and from the nexus of dimensions both directly related and indirectly related to the existing dimensions in a complex context.

24.4 – The flow of new dimensions through Dominant and Recessive Rules are the mechanics of perception.

a) The integration of new dimensions into a context changes the definition of the context, and may change the Point Of View of the context.

24.5 - Contextual constructions are the logical and mathematical machines of understanding and meaning.

24.6 – New dimensions entering a context are equivalent to energy flowing into a context.

25. Shared Dimensions Define the Physical Structure of Logic and Mathematics v2.0

25.1 – A context is composed of logically or mathematically related Geometric Architectures.

a) The mechanical processes of logical operations and the mechanical processes of mathematical operations are indistinguishable from each other. Any logical operation can be executed and described mathematically, and vice versa.

25.2 - Geometric Architectures are entirely composed of dimensions. Dimensions are composed of energy. Geometric Architectures are therefore entirely composed of energy.

a) Via the big Bang Theory, this Universe was created in a burst of energy, and everything in the Universe is necessarily composed of energy.
b) Perceivable objects necessarily exist. Objects that exist must exist in this Universe of energy. Perceivable objects are therefore composed of energy.
c) Dimensions are perceivable. Therefore they exist and they are composed of energy.
d) Geometric Architectures are entirely composed of dimensions, therefore Geometric Architectures are entirely composed of energy.

25.3 – A relationship is a framework for communication between two objects or among more than two objects.

a) A pathway is a circuit along which communication occurs. Pathways within a relationship consist of dimensions shared, directly or indirectly, between or among objects.

25.4 - A dimension can be viewed as a Base Geometric Architecture, a logical island of Ideas.

a) Ideas require dimensions for their definition.
b) Dimensions are perceivable objects, and therefore dimensions necessarily exist.
c) Objects that exist in this Universe are composed of energy.
d) Via E=MCC, energy, mass and the speed of light squared are logically and mathematically related to each other.
e) Energy, mass and the speed of light squared are ideas.
f) A dimension is a logical island of Ideas.

25.5 - Communication requires 1) a physical medium that is, or contains, the message, and 2) a physical pathway that directs the medium.

a) Via the big Bang Theory, this Universe was created in a burst of energy, and everything in the Universe is necessarily composed of energy.
b) All modes of communication existing in this Universe must necessarily be composed of energy.

25.6 – Influence is a communication of energy between two objects or among more than two objects.

a) For any object to influence another object, it must exist in a relationship with it. Therefore objects in a relationship can influence each other.

25.7 - Logical and mathematical laws and processes have a physical structure.

a) Via the Big Bang Theory, this Universe was created in a burst of energy, and everything in the Universe is necessarily composed of energy.
b) Energy has a mass component, and mass is a measure of a quantity of matter. Mass therefore requires matter for its definition. Energy therefore has a matter component.
c) Energy and matter share the dimension mass in their definitions.
d) Energy is logically and mathematically related to mass via E=MCC.
e) Mass is logically and mathematically related to matter via the definition of mass as a quantity of matter.
f) Energy is logically and mathematically related to matter via their shared dimension mass.
g) Matter is a physical entity.
h) Logical and mathematical processes exist in the Universe and therefore are composed of energy and have a physical existence.
i) Logical and mathematical processes have a physical existence, and therefore a physical structure.

25.8 - Logical and mathematical laws and processes influence physical objects.

a) Influence is a communication of energy between two objects or among more than two objects.
b) For any object to influence another object, it must exist in a relationship with it. Therefore objects in a relationship can influence each other.
c) Logical and mathematical processes exist in a relationship with physical objects.
d) Logical and mathematical processes influence physical objects.

25.9 Shared dimensions define the physical structure of logic and mathematics.

a) Logical and mathematical processes influence physical objects.
b) Communication requires a physical medium that is, or contains, the message and a physical pathway that directs the medium.
c) A shared dimension is a physical pathway between Geometric Architectures.
d) Contexts are Geometric Architectures composed of dimensions related by a logical or mathematical rule. A rule is a logical or mathematical process, and therefore a rule is a physical structure.
e) Shared dimensions provide physical pathways within logical or mathematical structures.

25.10 The mechanics of meaning is the flow of energy – the flow of dimensions – across shared dimensions.

Part 4 - CONCLUSIONS

26.1 Physical Ideas and Dimensional Logic

26.2 Godel's Incompleteness Theorem and Dimensional Logic

a) Godel's Theorem
b) Linear Logic vs Dimensional Logic
c) Introducing Hierarchies into Typographical Number Theory
d) Dimensional Mathematical Axioms

26.3 Dimensional Thinking and the Levels of Logic

26.4 The Function of Perception

a) Arguments Supporting Non-Physical Ideas
b) An Argument Supporting Physical Ideas
c) The Mesh of Physicality
4) A Definition of Perception
5) The Function of Perception

END