Language as Geometric

[Eodnhoj7]

The Geometric Nature of Language can be observed through the "Prime-Triadic Laws of the Axiom" observed below or the following thread:

viewtopic.php?f=5&t=25507


The nature of language is determined not just by its self-evident under axioms, but how these axioms exist in accords to language as an "axiom" in itself. While these laws are not limited strictly to language, they exist through them, and hence are laws of language and logic as well.


1. All axioms are points of origin; hence all axioms as progressive linear definition and circularity are points of origins. The point of origin progresses to another point of origin through point 2 and cycles back to itself through point 3 with this linear progression and circularity originating from themselves, through eachother and point 1.

Point 1 is original and exists through points 2 and 3 as points 2 and 3.

As original Points 1,2,3 are extension of eachother as one axiom, while simultaneously being nothing in themselves as points of origin that invert to further axioms respectively; hence originate as 1 and 3 through 1 and 3 as 1 and 3 laws



If I look at the sentence:

"The dog ate the cat." These words are inhernent axioms as points of origin in themselves and effectively exist as point space.

Using "(x)∙" as a symbol for point space, which as an axiom is in itself a point of reference to the observer denoting that these laws are not just limited to language but language as symbolism is not just limited to the written word but thoughts within the observer, the sentence can be observed geometrically as:

(The)∙ (dog)∙ (ate)∙ (the)∙ (cat)∙



This sentence in itself is an axiom as a point of origin and can be observed as:

((The)∙ (dog)∙ (ate)∙ (the)∙ (cat)∙)∙



While the same applies to the letters which form the sentence:

(((T)∙(h)∙(e)∙)∙ ((d)∙(o)∙(g)∙)∙ ((a)∙(t)∙(e)∙)∙ ((t)∙(h)∙(e)∙)∙ ((c)∙(a)∙(t)∙)∙)∙


And The paragraphs, pages, etc. as well (this will not be observed for brevity).












2. All axioms are progressive linear definition; point 1 and 3 progress to point 2 as respective points of origin observed in point 1 while this linear progression from one to another through alternation and exists as circulation between points 1 and 3 to point 2 and point 2 progressing to points 1 and 3.

Point 2 is definitive and defines points 1 and 3 with points 1 and 3 defining point 2.

As definitive Points 1,2,3 progress from one to another and are inherently seperate. As seperating one from another they are connected under a common function of "seperation"; hence are defined as 1 and 3 through 1 and 3 as 1 and 3 laws.



If I look at the sentence:

"The dog ate the cat." These words are inhernent axioms as lines of definition in themselves and effectively exist as linear space.

Using "(x)∙→" as a symbol for projective linear space and "(x)∙⇄" as a symbol for connective linear space,


which as an axiom is directed to and from the observer, while connected with the observe from a difference reference point, denoting that these laws are not just limited to language but language as symbolism is not just limited to the written word but thoughts within the observer, the sentence can be observed geometrically as:

(The)∙→ (dog)∙→ (ate)∙→ (the)∙→ (cat)∙

(The)∙⇄ (dog)∙⇄ (ate)∙⇄ (the)∙⇄ (cat)∙



This sentence in itself is an axiom as a projective/connection and can be observed as:

((The)∙→ (dog)∙→ (ate)∙→ (the)∙→ (cat)∙→)∙→ (Y)∙
((The)∙⇄ (dog)∙⇄ (ate)∙⇄ (the)∙⇄ (cat)∙⇄)∙⇄ (Y)∙

(Y)∙ = next sentence.



While the same applies to the letters which form the sentence:

(((T)∙→(h)∙→(e)∙)∙→ ((d)∙→(o)∙→(g)∙)∙→ ((a)∙→(t)∙→(e)∙)∙→ ((t)∙→(h)∙→(e)∙)∙→ ((c)∙→(a)∙→(t)∙→)∙)∙→ (Y)∙
(((T)∙⇄(h)∙⇄(e)∙)∙⇄ ((d)∙⇄(o)∙⇄(g)∙)∙→ ((a)∙⇄(t)∙⇄(e)∙)∙⇄ ((t)∙⇄(h)∙⇄(e)∙)∙⇄ ((c)∙⇄(a)∙⇄(t)∙⇄)∙)∙⇄ (Y)∙

And The paragraphs, pages, etc. as well (this will not be observed for brevity).








3. All axioms are maintain through a circularity, as linear alternation through point 2, and points of origin as point 1, with point 1 and 2 circulating through each other as point three while circulating through themselves as each other. Point 3 maintains itself as circular and maintains points 1 and 2 as circular while points 1,2 and 3 circulating through eachother maintain eachother.

Point 3 is circular and exists through 1 and 2 as 1 and 2.

As circular Points 1,2,3 are maintained through eachother as eachother as one axiom, while simultaneously dissolving into further axioms as eachother; hence they circulate as 1 and 3 through 1 and 3 as 1 and 3 laws.



Considering the sentence, is dependent upon the projective nature in which it is written and read, the nature of the circularity in sentences observes certain inherent characteristics:


It observes the maintenance, or inseparability of certain axioms, where descriptors cycle with the quality being described:

Example:

The brown dog ate the yellow cat.
((The)∙→ ((brown)∙ ⟲ (dog)∙)∙→ (ate)∙→ (the)∙→ ((yellow)∙ ⟲(cat)∙)∙)∙→ (Y)∙



These order of these descriptors changes relative to language as the descriptor may be equally involved in form the quality, and the quality may be equally observed as forming the descriptor. For example in English "Good Man" may be observed in Hebrew as "Man Good".

It also observes that the sentence does not necessarily have to be observed in the same order to have the same meaning.





Observing each progression of one axiom to another, other this circularity in a different manner where a sentence can be arranged in many different ways and yet mean the same thing.

The brown dog ate the yellow cat.

(((The)∙→((Brown)∙⟲(Dog)∙)∙)∙→(Ate)∙⟲ (The)∙→((Yellow)∙⟲(Cat)∙)∙)∙⟲)∙→ (Y)∙

[Impenitent]

mathematics is nothing but language

-Imp

[-1-]

mathematics is nothing but language

-Imp

I used to think, or they told us in school, that language is a symbolic representation of reality. It is one level removed from reality.

I then thought, and this was not told to us, that math is a representation of language, one level removed from it. Not all language is represented by math, but all math is a representation of one part or another of language. Not pure math, but applied math, like the one where the numbers represent numbers of units of a measure.

I then thought that learning a foreign language is also a representation of language, of one's first language. It is also one level removed from the mother tongue.

[Eodnhoj7]

mathematics is nothing but language

-Imp

And language is nothing but directed movement, or "limits", which not just construct reality but exist through and stem from the same limits they are describing in infinite variations.