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There is a line segment A
There is a line segment that is one half of A as A1, the corresponding remainder of A is A2.
A1 is defined as A1 because of A2, A2 because of A1.
A1 and A2 are defined as A1 and A2 because of A, A is defined as A because of A1 and A2.
A is the relationship of the line segments it contains thus the whole is defined by the parts, A1 and A2 are defined by the relationship as A thus the parts are defined by the whole.
A1 is A at a micro scale, A is A1 at a macro scale; A2 and A follow this same nature.
A(n) is a context of itself thus is defined as self distinct by degree of its own nature.
A1 being 1/2 of A necessitates A as being 2 of A1; A(n) is its own ratio by degree of self-referentiality.
A1 is composed of A1.1 and A1.2 where A1.1 and A1.2 are relative 1/2 of A1 and A1 are 2 of A1.1 or A1.2.
A1.1 is 1/4 of A and A is 4 times A1.1, the line segment continues linearly at a fractal progession; this fractal progression is linear segment Aa.
The progression of Aa is a means of doubling and halving of line segments as a process where this ratio of 1/2 can be replaced with a linear progressive ratio of 1/3 and 2/3, 1/4 and 3/4, 1/5 and 4/5, so on an so fourth.
The progressive change in fractals resulting is in turn a fractal as 1 leads to 1/2 and 2 and 1/3 and 3 thus resulting in the line segment as a self-compounding fractal where the line segment is its own self-distinction at all levels.
The distinction of the line segment is the line segment, the distinction of 1 is by degree of 1; the point of the line segments is but the inversion of one line segment to another as the recursion of a 0d point.
The fractalization of the line segment in turn results in a rate which is in turn a fractal; this fractal is a linear space folding upon itself.
Each line segment is a relationship of line segments, each relationship of line segments is a new line segment; a relationship is composed of relationships, the relationships of relationships is a new relationship.
The line segment is but self-contained as self-distinction through the emergence of the 0d point as recursion by which the line is distinct by points and the points are distinct as the line.
Linear space corresponds to number, number corresponds to a fractal effect by degree of said linear space; fractals are self-contained contexts.
A line segment is a foundational distinction, a line segment observes the space between distinctions as a distinction itself.
The space between distinctions is their relationship, a relationship is a distinction within and of said distinctions as a line segment is a distinction as relationship.
The recursion of 0d points is a relationship of self contrast by which the line segment occurs as a distinction of said points.
All distinctions are composed of points and are a relative point dependent upon the framework of observation; an infinitely larg line segment is composed of points by degree of being composed of line segments, and infinitely small line segment is but a point.
The point is the means of change from one distinction into another; a point can be an abstract concept or empirical observation.
The rate of change for a line segement is a line segment less than or greater than the line segment that changes as rate is but a fractal and this fractal is rooted in being a line segment; albeit time.
One line segment greater than another is but the line segment as a fractal where 1 can be relative greater than 1 thus 1=/=1; yet 1=1 in the respect one line segment exists at all scales.
1 both is equal and unequal to itself, as equal is self-contained, as un-equal self-contrasts thus 1 is multivalently non-dual. 1 is a distinction, a variable is a distinction, 1 is a variable as many things equate to or are contained as 1.
The relation of a line segment is a pattern by degree of the line segments within and of a line segment as a degree of repetition.
All patterns are ratios of presence to absence relative to the degree of repetition by which a presence and absence alternate.
This repetition induces a scale invariance where a distinction occurs within one context and then repeats in another;
A1 and A2 are but A in different positions within itself where the position is but a self contrast that allows for a self scale by means of conditions as contexts that are a symmetry of inversion where one distinction is contained by another through the absence of one state within the other, this can be seen as A1 being the absence of A2 or A2 being the absence of A1;
this conditionality allows for a scale invariance by repetition of said distinction across contexts or rather a symmetry across contexts, this can be seen in A being repeated in A1 and A1 being repeated in A1.1, etc.;
said symmetry across contexts, as said distinction, results in a superpositioning of said distinction where said contexts are variations of how said distinction occurs, this can be seen in the repetition of A across A1 and A1.1 where each exists within the context of another (A1 relative to A2, A1.1 relative to A1.2 or A relative to B).
Under these terms the equation results:
A=((A1=(A2=/=A1))=/=A) → (A>A) = (A → A1 → A1.1 → … → (Ax/Ay) = (A=(A=/=A))
The nature of distinction is thus one of relationship as process where the only static state is void as 0d which is effectively superpositioned at all levels by degree of the potentiality by which a distinction, a line segment, occurs. The collapse of potentiality, a 0d point, is a self-referential self-contrast by degree of recursion as evidenced by the recursion of 0 dimensionality as the line segment itself.
All line segments are effectively holons as ratios and as such as rates of change by degree of contrast and in these respects the equation is the state of change by which emergence occurs as the collapse of 0d into the distinction of 0d.
The nature of the recursive point as a line segment results in a fixed point symmetry, due to scale invariance where the superpositioning of said distinctions is but a fixed context from which distinctions emerge and dissolve;
a reversible order occurs in respect to the nature of a colonic degree within distinction by which any dimension of point and line segment is but a dimension of itself thus is self contextualizing by nature of recursion thus leading to the recursion of distinction to be the superpositioning of distinctions as the whole of their relations and thus the simultaneous inversion unto another distinction as the collapse of the whole unto a distinct part or parts as further holon(s).
In these respects the fractal nature of the line segment is but the line segment as a holon where said holonic nature is but a state of recursion, inversion and superpositioning at once but each distinct within their own context. The line segment is thus trifold in nature where the fourth nature is the distinction of it itself.
By these degrees the further equations result:
A = ((A=A) = ((-A=-A) = (-A=-A)))
->
((A=A) = ((-A=-A) = (-A=-A))) =
(A=-A) = ((A=/=A) = (-A=/=-A))
->
{(A=A),(A=/=A),(-A=-A),(-A=/=-A)}
->
A= {A/(A>A),A>A/A}
↔ (A>A) = {A/(A+An),(A+An)/A}
->
(A = A>A = -A) = Aa
Equality as an operator is inseperable from 0. Recursive equality is recursive 0 as equality is zero difference thus the function of equality is the same as void or potentiality, equality necessitates an absence of difference and the absence of difference at the absolute level is 0, pure equality is nothingness or 0 or void.
=
== → =/=
(==)= → =
(==)== → =/=
…
The foundational nature of equations are rooted in recursive equality, recursive processes by which a relative static quantity or quality occurs by contrast.
Equality is a quantity of 0 thus the symbol effectively is an embedded number as an operator and the operator is a quantity.
Inequality, recursively, is the inverse as 1 given inequality results in a difference by which an assymetry occurs as a unified difference.
Identity derived from equality is identity derived from 0, 0 is the relationship of equality for the absence of difference is the unity of a thing.
Each distinction is the equality of a distinction to itself, a self-conditioning, for A=A there is only A as no space occurs for by which A is distinct but as its own condition, however this equality is also simultaneously the distinction of it for equality implies a relationship, thus in saying A=A there is emergent a duality of a self-conditioning and self-contrast.
Each individual A in A=A has a meta-identity of A1 and A2 where A1 derives its identity by contrast to A2 and vice versa thus leading to the further equations of {(A1=A1),(A2=A2)}. However these equations of (A1=A1) and (A2=A2) are structurally the same as (A=A) thus a self-conditioning occurs as (A=A) is both a fixed point symmetry, scale invariant, and a fractal, scale variants.
(A=A) is fixed point symmetry due to scale invariance of structure across (A1=A1) and (A2=A2) of the meta distinctions of each equations as (A1.1 = A1.1), (A1.2 = A1.2), (A2.1 = A2.1) and (A2.2 = A2.2) as all are fundamentally (A=A), the self contrast results in fractals by degree of scale variance in ratios where the scale of containment variates and yet is the same structure.
(A=A) is both scale invariant and scale variant, fixed point symmetry and fractal by nature, thus effectively is a superpositioned state, a paradox, until made distinct as paradox in which case a hyperdimensional form of recursion occurs where the paradox of (A=A) results in the paradox identified as (P=P) or “paradox equals paradox”, thus the nature of paradox becomes its own ratio of self-conditioning and self-contrast.
In these respects recursion of equality, at multiple levels gives the distinction of it. Visually this can be seen as a 0d point occuring recursively as the line segment. From equality identity both dissolves and collapses for what is assymetrical, odd, stands apart thus equality is unequal to itself when distinct and when indistinct is equal to itself and yet inequality is indistinct when equal to itself and distinct when unequal to itself. This can be seen as a line segment unequal to a point while being but a point when indistinct.
Pure equality is 0, there is no difference, thus is the same as void, 0d point, or pure potentiality as pure unactuality.
The nature of distinction is self embedded as what is beyond distinction is distinction as the distinction of beyond, what is beyond said distinction of beyond is the distinction from which said distinction is beyond thus making the original distinction beyond itself, further resulting in the nature of distinction being a process of self-embedding where said self-embedding effectively leaving it only as process that is both fixed point scale invariant symmetry and fractal scale variant symmetry where any assymtry is but the point of inversion from one symmetry to another by nature of the necessary contrast that allows said distinction to occur; this can be seen in the previously observed and emergent line segment mentioned prior.
The everpresent 0 dimensionality by which distinction emerges and dissolves necessitates that the foundational distinction is of said potentiality by which an inherent order, by means of duality of fixed point symmetry and fractal symmetry occurs, as the recursion of 0 dimensionality is the distinction of it by which pattern is by superpositioned cycles, loops or synonymous recursion thus necessitating 0 dimensionality, as distinct, is the process of self-embedding that effectively results in distinction being primarily foundational to both awareness and non-awareness, axiom and non-axiom, empirical and abstract, and experience and non-experience.
The nature of indistinction is effectively distinction distinct from itself thus is the contrast by which not only distinction occurs but effectively is the meta-distinction by the contained absence of distinction, through self-contextualization, in one respect while in a dual respect effectively results in the necessary self-contrast by which distinction is and is not and yet “is” and “is not” are subject to being distinction.
The nature of self-embedding results in any distinction of exterior effectively being the limit of the interior, that allows said interior to be distinct, while the distinction of interior being the limit of the exterior, that allows said exterior to be disstinct, thus the exterior is contained by the distinction of the interior, and vice versa, and what remains is but a holon that by nature reveals exterior and interior as but everpresent distinction as both process and limit where exterior and interior are not only contexts but effectively are and are not until emergence as the ratio of the distinctions themselves.
In these respects the distinction is a boundary of itself by which change occurs thus allows a distinction to be for without change there is no contrast and without contrast there is nothing and yet nothingness contains this change by degree of its potentiality to do so where what emerges is distinction and distinction to balance further distinction so that distinction remains.
As a boundary of itself there is only limit as change where what does not change is that there is distinction thus the question of the relative and absolute and static and flux are but fixed points of measurement by which further distinctions, from said foundations, are inherent ratios. The fundamental distinction, 1 dimensionality, observes this within the linesegment as the universal compression of any and all further dimensional objects. In these respects the line segment is the foundational dimension with the sphere being the result of infinite dimensions of 1 dimensional line segments; this sphere infinitelh contracts into a line segment and the line segment infinitely expands into a sphere where the everpresent medium is the 0d point and the fourth being the infinite variety of various forms and there said dimensions.
The practical medial measurement of PI effectively is a process of self-embedding fractals that reflects the order spontaneity of existence as each position within PI is a relative number that effectively is a holographic, fractal, emergence of 1 given each number is a holographic version of one as seen in each lines segment being a number on a number line which is a holographic nature of 1 as a single line segment.
The nature of PI is the distinction if the line segment and sphere effectively being one and the same where the fixed bounardies of the sphere result in the rate of change of the line segment and the inverse fixed nature of each calculation of pi being the change of the sphere thus observing the fixed and fluxing states are but contexts of distinction and the emphasis one one results in the other in a manner of inversion necessary for the distinction of each to occur and yet both are mediated by their emergence and dissolution into a 0d point.
A holon is a boundary of inversion between part and whole, it is the recursive limit by which it contains itself as further parts and wholes, as further holons, this the holon is the point of potentiality from which it emerges as the distinction of itself. In these degrees the holon is a variable as super positioned holons while dually being a relative fixed point of change.
All distinctions are holons by nature with the fundamental distinction of the line segment and sphere being the fundamental holon from which various other forms and dimensional degrees of forms occur.
As both a wave, field, point excitation and n-dimensional forms it is effectively grades of the dualism of the foundational distinction of line segment and sphere as the unified distinction of pi itself.
The wave is but the alternation of the distinction as recursion of specific qualities and the inverse space where said qualities exist anti-thetically. These qualities are effectively forms or limits. A wave effectively is alternation, inversion of states, the repeats as recursion.
The field is the distinction as a context where the field contains both relations and potential relations as a whole set conducive to how the relations change as one distinction.
The point excitation is but the emergence or a distinction within the field of relative distinctions as a relative part by which the emergence results in the change of the field.
N-dimensional forms are but the repetition of a specific form as a frequency, a wave, the set of relations of distinctions, the field, and the emergence and dissolution of parts as a change in the field, the point excitation.
In these respects all distinctions are spatially: waves, fields, point excitations and n-dimensional forms as the intersection.
The fourfold nature can be seen within any distinction:
1. The wave can be seen as the pulsing emergence and dissolution of a distinction where it alternates between occuring and not occuring. This wave is the occurence of distinction.
2. The field can be seen as the context of the distinction itself being the potentiality of further distinctions emerging and dissolving from it. This field is the relation of one distinction to another.
3. The point excitation can be observed as the changes which emerge and dissolve from the field. This point excitation is the relationship of distinctions as a new distinction.
4. The n-dimensional form is the culmination of wave, field and point represented by the variety of forms which occur. This is the transformation of the distinction by degree of generative emptiness.
This fourfold nature compresses into a 1 dimensional line segment as the reduction of dimensions of expression inevitably resorts to one, and the expansion of dimensions from 1 effectively is the line segment occuring holographically. Any n-dimensional form effectively is the holographic compounding of 1 dimensional space, any reduction of a n-dimensional form effectively results in a 1 dimensional space.
An n-dimensional form effectively is a 1 dimensional linear lattice that contains itself. All dimensions are recursion of 0 thus effectively the base recursion of 0, or 0d point, results in all dimensions and meta-dimensions being rooted in the base distinction of 0 as 1 distinction by means of recursion thus 1 dimensionality is embedded within all degrees of dimensional forms as the recursion of 0 reflects a self-embedding of distinction at all levels where the primary distinction of 0 is superimposed as the void from which distinction emerges and dissolves as the distinction of the void itself.
Distinction is but a ratio of spaces, by degree of being limits, folded upon itself within the context of another space, another limit, and as the context of another thus effectively distinction is spatial folding, limit folding, where what is considering static is a fixed point of reference relative to another and what is considered change is but a ratio of spaces, limits; time is a distinction.
The definitions of words, the distinction of symbols, are but the ratio of words by which one word is contained by others and others by one, and the context of the word determines which definition arises thus effectively leaving a word as but a ratio of words, both one and many or whole and part as a holon. This is akin to the line segment containing line segments. The definition of a word is but its collapse of potential meanings relative to an applied word as relative context.
This collapse of potential meaning unto actual meaning relegates the choice of the observer as but superimposed possibilities by which pattern contextualizes the superpositioned state by instigating collapse through an applied pattern, the perspective, where said pattern induces symmetry by means of isomorphically inducing the actual meaning from said potentiality of the words meaning through underlying symmetry across the words. Choice effectively is the collapse of potential distinction unto actual distinction by degree of attention contained through perspective. This perspective is the recursion of symbols, forms, by which a pattern through which distinctions emerge and dissolve. In geometric terms the point of awareness is akin to void, 0d, as observation of observation reveals void, the persective is the sphere of distinctions that determines how the point of awareness is contained and the changes said awareness induces to said perspective as awareness is the point of change and the sphere contains said change by containing patterns. Words, symbols, are the primary distinctions and what constitutes a symbol or word is but the distinction directs change as by applied a limit conducive to a set.
The nature of word is thus reduced to a line segment, both in form, but effectively function as a string of words are but superimposed segments of meaning as a new string as the assertion itself.
This can be seen where x = (a,b,c) as
x/(a,b,c) and a = (x,y,z) as a/(x,y,z) where x is a relative line of meaning that contains further lines as relative ratios and (x=a) ↔ l or (x=b) ↔ m or
(x=c) ↔ n. Given meaning is directive of meaning the nature of language, through the word is akin to a line segment intuitively. In these respects a word or symbol is but the containment of potential meanings that are collapsed in the context of the word or symbol that is relative to it. Each word is but a point of potentiality by which meaning is derived by relation akin to points that become distinct through their relationship as the line segment.
The nature of language is effectively the application of distinction by which language becomes a topological event f induced limits by which the inevitable nature of a ratio, as rationality, occurs thus effectively resulting in the word and symbol being holons that have a nature isomorphic to the line segment itself as a unified hyper-dimensional linear lattice.
A word or symbol is the direction of change and as such the nature of the line segment, as a lattice, is superimposed. By change there is the emergence and dissolution of distinction and by this emergence and dissolution as a distinction the nature of distinction is embedded in itself where the nature of axiom and non-axiom are transcended by the event of distinction itself.
Distinction is further fourfold:
1. There is distinction.
2. There is the relations of distinctions.
3. This relation is a distinction.
4. The distinction is empty in itself thus generative.
This can be seen in the linear lattice as a 1 dimensional state of hyper-dimensions:
1. There is a line segment.
2. There is a line segment relative to another line segment.
3. This relation is a line segment.
4. The line segment is empty, as composed of a 0d point, yet is generative by degree of the recursion of this 0d point.
The point is generative of itself by degree of its distinction, as recursion, for the self-containment as self-contrast is but the inversion of the indistinct as the distinction by means of potentiality which is distinct as potentiality by means of its containment of the actual, through the potentiality of potentiality from which potentiality is everpresent and yet collapses unto the actual through which this further potentiality is contained as distinction. The line segment is the containment of potentiality as the self-containment of the 0d point by degree of its distinction.
If all distinctions occur by the recursion of potentiality, as the 0d point or void, and the potentiality mediates all things by evidence of change, thus is ever-present as all process, then it contains itself through the distinction of itself, in infinite distinctions, thus the 0d point as void or potentiality, is boundless and effectively unknowable but by its distinction as the recursion itself from which it is the inversion of itself by degree of the distinction of it as emergent. In these respects the point contains infinite points and is unified as distinct as a point.
In these respects distinction is the void mirroring itself. A simple equation of (n>0) is untrue in the context of the distinction of zero as one (0)1 as no number can be greater or lesser than zero as there is nothing to be greater or less than as nothing is there until made distinction and with said distinction to argue one distinction as greater than another is an application of relative scale as multiple distinctions require distinction to be a holography of itself.
In shorter terms to have a distinction be greater or lesser requires another distinction by which to compare. If 0 is nothing than being cannot be greator or less than nothing as being can only be compared to being if only being exists. The distinction of nothing effectively results in a relative contextualizing of potentiality within a given context. 1 cannot be greater than 0 as 0 does not exist, but if zero does exists as a distinction than effectively 1 is the distinction of it. If 1>0 than it is equivalenr to saying a distinction is greater than an absence of distinction but a paradox occurs as an absence of distinction is distinct from the presence of distinction thus is a distinction embedded within a distinction as a self-contrast that allows distinction to occur. Effectively is 0 is a distinction that contains itself than 0 is self embedding of distinction, self embedding of one as a fractal, that effectively is infinite, so in one context 1<0 due to zero being infinite compression of expressions of one and in another context 1>0 as a collapse of the infinite into a distinct boundary.
Nothingness is potentiality as a thing can only change is there is nothing in the way of said change thus by nature the change that constitutes reality necessitates nothingness as potentiality. This nothingness is the emergence and dissolution of a distinction as change itself. For change to occur there must be an absence of said thing for a thing cannot change if it already exists within the space from which it emerges and dissolves.
Nothingness, void, potentiality, 0 dimensional point(s), 0 and space are all synonymous terms. The term ● will be used to represent all of these terms. ● is all things for if not ● would have something beyond ● thus effectively is not all things, but given a thing requires contrast so to be a thing then all things is effectively ●. One thing is effectively nothing in itself as infinite configurations of it existing all at once would leave ●. To visualize this one can imagine a circle with infinite circles within and without it with infinite circles between these circles. The circle is always present and yet there is only ● as percievable.
The nature of inference, or the direction of one distinction to another as A → B, effectively is the means of inversion of potentiality, contained within one distinct state, by which said potentiality collapses by means of the distinction itself as the limiting pattern from which potentiality is shaped. A → B requires that A contains the potential state of (B, B1, B2…Bx) within it from which the collapse of A into B(x) requires a context beyond A which directs said collapse as the direction of A is determined by the context in which it is contained. Thus the linear stream of A → B(x) requires A as being contained by context Z in such a manner to direct its collapse thus A → B requires an expression of context beyond it.
Inversely the collapse of A into B requires that B effectively allows A to be distinct as B is the distinction of the potentiality of A thus further requiring that B produces A in the respect that the potentiality of A, as B, allows for A to exist as a distinct state for A contrasts to B in one respect while dually, in another respect the collapse potentiality of A as B allows A to occur as distinct through a self-conditioning. The collapse of A into B, relative to its potential as B(x), being determined by context Z effectively observes that Z is contained, self-conditionally as the sequence which is A → B which in turn results in the distinction of Z. In these respects each distinction contains a sequence of distinctions as the distinction of the context itself.
In these respect Z is the relationship of A and B that effectively follows the same nature of A → B as Z has potentiality that results in the statement Z → Zn where the collapse of Z to Zn is in turn defined by the potentiality of Z as the sequences of A->B, A1->B1, Ax → Bx thus any distinction is effectively the distinction of many potentialities that are each dimensions by nature. The collapse of potentiality into one distinction, Z, is the collapse into another A → B, where the collapse of potential states into distinction results in patterns across sequences, or rather dimensions, thus show a level of recursive potentiality across dimensions.
The recursion of A → B and Z → Zn effectively results in a unilateral degree of recursions of recursions across a series of sequences. In a linear 1 dimensional latice than can be see as the line segment Z leading to another line segment Zn, as a new line segment, where line segment Z is composed of line segments A and B where effectively each distinct line segment is a spatial ratio that is synonymous to number. So while A → B is line segment Z, as two line segments, the nature of Z → Zn is effectively another line segment as Q which in turn follows the same nature, thus the collapse of potentiality in A as B, through Z in turn reflects the collapse of potentiality of Q into Qn as Q → Qn. Recursion does not only happen in a linear sequence but effectively vertically in dimensions as Q may be relatively larger than A but effectively Q and Qn can be the same ratio as A and B, so while scale may very the invariance of ratios allows a superpositioning of ratios.
While recursion may occur infinitely this infinite nature is collapse by degree of the dimensionality itself for while A->B->C->… the nature of it being a limited dimension as Z effectively sets a finite bounds to it where this finite bounds, as Z, is akin to an actual rate of change that effectively constitutes as a form. This can be view dualistically as:
1. A line segment being finite and yet composed of infinite line segments.
2. An infinite line being composed of fractal line segments where any progress along infinity maintains the same fractal line segment.
The unification of this duality is infinite progressive finite line segments, as fractals, with each line segment containing infinite line segments.
In these respects the line segment A contains A1 → An where the line segment A is the superimposed state of infinite line segments that collapse unto a finite number upon collapse where any irrational number is essentially the rate of fractal line segments infinitely emerging within finite segment A. Given the line segments are emerging infinitely as fractals that have a dual nature of both multiplying the line segment A, fractally, and dividing it, fractally this infinite emergence is a self sustained loop as line segment A. A, in these respects, becomes a self-generating loop as the multiplication of line segments within A is the simultaneous division of them thus effectively resulting in the irrationality of A as a self-sustained recursion loop that inverts itself. In these respects the form of A is synonymous to a process that effectively is self-contained as self generative or rather auto-poietic.