Is Number a Causal Element?

[Eodnhoj7]

Is Number a Causal Element?

"The Neoplatonist Iamblichus…stated that the causal approach to nature consisted "in posting mathematical things as causes" from which the objects in the perceptible world arise. He subscribed to the Pythagorean belief that only what was possible in mathematics was possible in the structure of nature, and that nothing could exist that implied a mathematical impossibility." (Leonessi)

An extension of this dimension would be that logic is the symmetry to causality with only what as possible in logic is possible in the structure of nature, and that nothing can exist that implies a logical impossibility.

The question occurs however, as numbers and logistics propagate themselves into infinity what is not possible?

Another appropriate question would be to ask: If 1, the point, and the line are causal elements of logistics, Do they manifest as effectual elements (or complexes/approximates) that equivocate to n1n, the particle, and the wave?

"Nowadays, we think of number as a sign to denote a specific amount or quantity. We use numbers as tokens to represent things. The Pythagoreans saw number as a universal principle, such as light or electromagnetism or sound. As modern physics has
demonstrated, it is precisely the numeric, vibrational frequency or wavelength of electromagnetic energy that determines is particular manifestation." (Leonessi)

Can we not view logic in the same way as: “In the beginning was the Word, and the Word was with God, and the Word was God?” (AZ)

For what came first, the letter or the number?

[surreptitious57]

Equating numbers with electromagnetism is fundamentally wrong because they only exist as abstract entities where as electromagnetism is an observable phenomena. The frequency or wavelength of electromagnetic energy might be expressed in mathematical language but the energy
itself is still physical. All objects can be referenced mathematically but this does not make them mathematical in and of themselves since the
physical and the mathematical are completely separate categories. The Universe is not a mathematical construct like Max Tegmark thinks it is

[Eodnhoj7]

Equating numbers with electromagnetism is fundamentally wrong because they only exist as abstract entities where as electromagnetism is an observable phenomena.

Actually it is only observable through tools which approximates its nature. Putting two magnets together and pulling them apart so that they move back together only observes the movement of the magnets...you are not seeing the waves in and of themselves.



The frequency or wavelength of electromagnetic energy might be expressed in mathematical language but the energy
itself is still physical. All objects can be referenced mathematically but this does not make them mathematical in and of themselves since the
physical and the mathematical are completely separate categories.
What we understand of number manifests through empirical reality as much as abstract reality, and in these respect as a median it maintains a degree of physicality. Considering particle waves, at their root are composed of points and lines, to equate number (through dimensionality) as point and line implies a physical nature inherent within it.

You claim physical reality and mathematical realities are separate categories, but categories in themselves are abstract measurements and how can you equate physical reality to a category and deny the same for number?

The Universe is not a mathematical construct like Max Tegmark thinks it is
Prove it.

[osgart]

What about amorphous relationships and the rates of change in a given property of reality mathematically described?

Are there synergies?

Are there concepts in reality that don't have mathematical operators?

Everybody has seen math problems that where there is one true logical answer, people mess up the procedures, and get totally different wrong answers. Does nature always follow logic. Maybe nature can operate on those wrong answer ways.

Maybe where one would subtract nature throws it all in an opposing direction.

Anyway I'm dreaming.

[Eodnhoj7]

What about amorphous relationships and the rates of change in a given property of reality mathematically described?

Amorphous relationships, as a form of approximation, still observe specific characteristics in the respected that while the relationship may not be fully defined Point A is still connected to Point B, with both points still being the observable factors with the relationship.

With amorphous simply being the observation of something not "fully defined" there is still a degree of order, hence the approximate nature. All problems in these respects can be viewed as approximates, with the approximation merely being a connection between causes.





Are there synergies?

Well lets look at it this way.

We will equate all realities to be equivalent to 1d linear movements, with these movements in themselves being both composed of a particles and composing particles as further linear relations.

The 1d line exists as number inseparable from space, we observe this intuitively through 1, across many cultures, dependent on a linear mark.

So to begin our thought experiment.

Everything we understand of time is rooted in a 1d line (1) extending into a 0d space (0) ad-infinitum. Now the 1d line cannot extending into a 0 space ad-infinitum considering there is nowhere to go. So the line, if it is to extend ad-infinitum, must fold in upon itself in order to relate. The 1d folds upon itself, through the 0d space, with this folding creating two lines.

Now this folding, resulting in two lines (as an angle), are simply lines connected through a 0d point which we observe as the apex of the angle. In these respects the 0d point is strictly and an extension of the 0d field and what we observe as points in turn exist as fields.

Now these two lines, considering they must extend ad-finitum continually fold (or halve) themselves perpetually.

This is considering the zero dimensional point, which connects them acts simultaneously as a field much in the first manner we see in the first line.

These lines continually halve through the 0d point which is a common mediator amidst all the lines. Time and Size begin to take place as these linear relations form the foundation of time as the relation of movements and size following the same format. Time does not exist unless observing the relation of movements. Size cannot be observed unless one thing is relative to another, with both "things" in themselves constantly moving. So time and size are inseparable in these respects.

Now, as we progress further through the movements, we observe a branching effect of linear relations with these branches "appearing" to extend further and further away from eachother in one respect. While one branch, "A", maybe seperated from another branch "E", because of branches "B","C" and "D", in reality they are not. This is considering both "A" and "E" are connected through the same "0d" point-field that causes their individuation to begin with.

"A" and "E" may be proportional through the inherent number of seperations, through the 0d point, with this number of seperations being the foundation for there relative size and qualitative proportional nature. Because "A" and "E" are proportional, through the 0d point, what may happen to "A" must also happen to "E" through the 0d point-field.

So while we observe "A" and think it is not only alone, but also amorphous relative to "B" and "C", in reality we cannot observe "E". "E" being proportional due to the linear "halving" in itself extending to a further linear dimension which forms the branches themselves as extending only linearly relative to other branches. In simpler terms, what we observe as non-linear movements, are linear movements relative to other dimensions...and the halving process continues while maintain a connection through the 0d point field.


These branches as composed of continual halving through a "Y" effect, provides the foundation for frequencies as multiple angles (relating 1d lines) when observed from a perspective linear relations. Take for example observing a tree, we see this "Y" effect form in an apparently curved or "circular" fashion when we take into account all the branches relative to eachother. However if we walk through an orchard, these "curves" actually form a lines as one tree then another then another.

If we take all these "Y"'s which composed the foundation for the branches and viewed them in 1 dimensional line, we observe "frequency" as a byproduct with the dualistic alternating 1d lines (with alternation being a form of halving through folding we see in the example of the original line) being the foundation of movement seperating the 1d space into +2d space as movement. This may appear confusing, so in simpler terms:

The frequencies, or even "strings" if you want to call them that, are composed of 1d lines (number as space) continually folding and halving through a 0d point-field in which 1 as a 1d line as unit, must relate to further 1d lines as units, in order to exist in the 0d field.



With the invention of quantum computing, I believe we are inevitably stuck with defined numbers not only in spatial terms but fundamentally as extensions of space itself. In memory serves correctly, and you may want to do the research for yourself, certain physicists, mathematician/logician and computer engineers are looking for physical constructs (ie, frequencies) which are inseperable from number.

Research this fact for yourself however, I am going off of memory. However the logic seems sound as if number is rooted in dimensions (such as thought or consciousness being a dimension of both physical reality and/or a higher dimension, spiritual one) number may be a multi-dimensional entity.

Are there concepts in reality that don't have mathematical operators?

Considering the premise of a reality summating itself (addition) in a unity or being seperating (subtraction, multiplication, division) into units and these operators of arithmetic are the premise for all further mathematical operators can they be entirely seperated?

Everybody has seen math problems that where there is one true logical answer, people mess up the procedures, and get totally different wrong answers. Does nature always follow logic. Maybe nature can operate on those wrong answer ways.



If you look at where the "step" was messed up, you can also observe the equation branching to another answer that while "wrong" relative to the original premise may follow a another like of logic starting with the "mess up". In these respects the beginning "change", ie "mess up", acts as a causal point for further logistic structure.


Maybe where one would subtract nature throws it all in an opposing direction.
Anyway I'm dreaming.

[osgart]

So everything passes through a point of a field, 0d. And this 1d linear is relative motion to the point. A B C D and E are instantiations that together through the point constitute time elapsing.

Perhaps I'm not understanding what you mean by dimensionality. How many total dimensions are there, and how do they differ?

It's almost as if you are inventing space itself, how everything takes on new dimension through the 0d. With your folding process and how it summates new dimensions. And everything is relative with respect to the linear.

I'm not sure if I am to take this as abstract or tangible.

When I see 3 dimensional space , I perceive nothing takes on tangibility without the third dimension. Like writing on a piece of paper is mostly 2d, except for the thickness of the ink and paper, making it tangible with the third dimension.

[Eodnhoj7]

So everything passes through a point of a field, 0d. And this 1d linear is relative motion to the point. A B C D and E are instantiations that together through the point constitute time elapsing.

Perhaps I'm not understanding what you mean by dimensionality. How many total dimensions are there, and how do they differ?
Totally? Infinite as extensions of a 1d space in which everything is viewed as one moment. In these respects both 1 and infinity are proportional, however I still developing the math for it.

Infinity would exist not only as a preliminary space that provides the foundation for "unit as never changing consistency" but from a perspective of 1d perspective also acts as another "field" in which pure 1d space acts as a point (which in itself has an inseperable role as a field also.

You have to keep in mind, and you can observe this in the single geometric circle as strictly being a point mirroring itself through linear dimensions, that each dimension as an extension of 1 it itself is conducive to 1. In simpler terms the "point" as pure space, acts like a glue conducive to an ether.

Temporally however? I am in agreement with the string theorists, from a seperate angle (or perspective), that at minimum it is 10. Most likely 12 to 13. However time, considering it is founded in alternation linear dimensions conducive to a circularity, must cycle through itself. In simpler terms, time zones as what the ancients might call "ages" must circulate through themselves and cancel themselves out. This canceling, in turn creates the necessary vaccum for another time zone to appear. These time zones, in theory, would have their own physics each time and in theory each 'cycle" would have its own new "physics" which may change only by a fraction of 1/n→∞ .

Their may in theory, and this is the most logical answer I can observe as of yet, may be infinite number of time zones.

Think of time cycle, or age, like a grape on a vine in the middle of a vine field.


It's almost as if you are inventing space itself, how everything takes on new dimension through the 0d. With your folding process and how it summates new dimensions. And everything is relative with respect to the linear.

I'm not sure if I am to take this as abstract or tangible.

Both, considering what we understand of the "line" as a phenomena cannot be seperated from either. Remember, space is a binding median between dimensions...even imaginary ones of "physical" and "abstract".

When I see 3 dimensional space , I perceive nothing takes on tangibility without the third dimension. Like writing on a piece of paper is mostly 2d, except for the thickness of the ink and paper, making it tangible with the third dimension.

[odysseus]

Of course number is a causal element. The question is, what is causality? Once you realize you don't know this, then this obviates mind body matters altogether. Such questions manufacture issues out of nothing since they presuppose conditions that are ill defined in the first place.

[Eodnhoj7]

Of course number is a causal element. The question is, what is causality? Once you realize you don't know this, then this obviates mind body matters altogether. Such questions manufacture issues out of nothing since they presuppose conditions that are ill defined in the first place.

What we understand of causality is strictly structure where A leading to B leading to C, observes that A is the cause for B and exists through B as an effect. B as the cause for C, is an effect in itself, and what we observe of as "C" exists through A as cause mirroring through B as effect.

What we understand of cause and effect is cause mirroring itself through effect, with effect being an approximate cause, yet a cause in itself. In these respects what we understand of causality is the observation of structure.

[odysseus]

Eodnhoj7
What we understand of causality is strictly structure where A leading to B leading to C, observes that A is the cause for B and exists through B as an effect. B as the cause for C, is an effect in itself, and what we observe of as "C" exists through A as cause mirroring through B as effect.

What we understand of cause and effect is cause mirroring itself through effect, with effect being an approximate cause, yet a cause in itself. In these respects what we understand of causality is the observation of structure.

I don't see the purpose of calling it a mirroring. The metaphor simply presents the idea that what is transmitted in a causal event from the causal agency to the effected one bears something of the character of the material nature of the former, as in a hard and unyielding pool ball denting the my skull with a round impression.
Anyway, the extraordinary thing about causality is that it is apriori, which means it describes the necessity of having a causal agency present to make motion possible in the effect. Can't have an effect without a cause. Impossible. And the reason I say numbers belong to causality is that to say otherwise either means to place numbers outside of the causal world in a sort of non causal ontology, which I can't even imagine, or fit them in this world and just call them non causal, which I can't even imagine. Talk about something not being caused yet still a kind of entity is nonsense.

[Eodnhoj7]

Eodnhoj7
What we understand of causality is strictly structure where A leading to B leading to C, observes that A is the cause for B and exists through B as an effect. B as the cause for C, is an effect in itself, and what we observe of as "C" exists through A as cause mirroring through B as effect.

What we understand of cause and effect is cause mirroring itself through effect, with effect being an approximate cause, yet a cause in itself. In these respects what we understand of causality is the observation of structure.

I don't see the purpose of calling it a mirroring.
Propogation and manifestation of symmetry, as dimension, which is conducive to structure...what we understand of order is structure...structure and causality in these respects are inseperable.

The metaphor simply presents the idea that what is transmitted in a causal event from the causal agency to the effected one bears something of the character of the material nature of the former, as in a hard and unyielding pool ball denting the my skull with a round impression.

But is it symmetry none the less for both the pool ball and round indentation are approximations of a constant spherical spatial "cause".


Anyway, the extraordinary thing about causality is that it is apriori, which means it describes the necessity of having a causal agency present to make motion possible in the effect. Can't have an effect without a cause. Impossible.
Nor effect without cause, hence we can observe effect as approximate cause with randomness being the limit of this structure as absence of structure.

And the reason I say numbers belong to causality is that to say otherwise either means to place numbers outside of the causal world in a sort of non causal ontology, which I can't even imagine, or fit them in this world and just call them non causal, which I can't even imagine.
How can number be placed outside a causal world, when numbers as "effects" of the material world are causes in themselves? This is considering effect as approximate cause, hence cause in itself, is merely an approximation of order?

Talk about something not being caused yet still a kind of entity is nonsense.

What if number, as premised in space it based upon an intradimensional point where it mirrors itself ad-infinitum as both limit (direction of space through intradimensionality) and no-limit (infinity as the 1d point is pure direction?)

[odysseus]

Eodnhoj7
What if number, as premised in space it based upon an intradimensional point where it mirrors itself ad-infinitum as both limit (direction of space through intradimensionality) and no-limit (infinity as the 1d point is pure direction?)

I would probably ask you, what do you mean by "intradimensional point"? What do you mean by a one dimensional point? And so on. Such things likely belong to science fiction rather than meaningful utterances. You would need to shoe why I should take these seriously.

[Eodnhoj7]

Eodnhoj7
What if number, as premised in space it based upon an intradimensional point where it mirrors itself ad-infinitum as both limit (direction of space through intradimensionality) and no-limit (infinity as the 1d point is pure direction?)

I would probably ask you, what do you mean by "intradimensional point"? What do you mean by a one dimensional point? And so on. Such things likely belong to science fiction rather than meaningful utterances. You would need to shoe why I should take these seriously.

The paradox of point division is one example:

http://www.sciencechatforum.com/viewtop ... 65&t=34194


And another argument as an excerpt from part of a paper I am working on...the whole argument is not presented but should give you a based idea:


The first axiom of the argument is a simple one: what we understand of all phenomena, at minimum, is strictly an observation of space. It is the one universal axiom which exists as the limits that give structural boundaries to reality. In a separate and simultaneous respect, it is absent of the very same definition as no-limit. Space observes a dualistic nature of limit and no-limit.

Observing the definition of space, within any given dictionary source, one is placed into a paradox. A whole host of definitions are given, which include but are not limited to: “area” “volume”, “dimension”, and “limit” These definitions,summated under the last definition as “limit”, reflect back upon the process of definition as a form of limit in itself by which a phenomena exists through the inherent limits which form it. Space as limit is limit through space, with the observation of any dictionary definition resulting in a dualistic circular and linear form of reasoning where one definition leads to another while simultaneously circling back to the original. Under these terms circular rational is justified through inherent linear elements and vice versa while observing, under certain degrees, Mirimanoff’s concept of “wellfoundedness” in which the definition as a set of information contains no infinite descension further implying an original source.

This dualism of progressive linear and circular definition provides a limit in itself through a process of mirroring in which the further corresponding definitions in turn follow this same process. The axiom of space follows this definition process in which a limit reflects itself through a further limit, rationally in both form and function as circular, and reflects further limits, rationally in both form and function as linear, in which an observation of no-limit occurs. This observation of “no-limit” is founded inherent within the dictionary definitions of space in an immediate respect within the aforementioned definition itself. In a separate respect, function follows form where these definitions reflect through further definition ad-infinitum in a dual circular and linear regressive/progressive manner. Limit and No-Limit are dependent on a dual form of circular and linear reasoning that simultaneously manifests further definition while maintaining there own under spatial terms.

This dualistic understanding of space can further be observed in many of the works of the pre-socratic including but not limited to the Pythagoreans and Anaximander. The Pythagorean Philolaus observed “that all things in the universe result from a combination of the unlimited and the limiting; for if all things had been unlimited, nothing could have been the object of cognizance.” Aristotle observed “[the Pythagoreans] plainly say that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be drawn in and limited by the limit.” He further implied that the Pythagorean teaching of the limit and no-limit were direct results of the philosopher Anaximander who argued “(that which is) unlimited”, “boundless”, “infinite”, or “indefinite” as “Apeiron” and “peras” as “end, limit, boundary”.

Modern philosophical instinct and training implies the definition of space as limit and no-limit in dual linear and circular terms questionable considering one is presented with two perspectives: They are an empirical contradiction or a transcendental paradox in the respect that logic either nullifies itself or transcends pasts its origins. (quote) Neither school of thought gives any real justification as they manifest a dualism in which one perspective attempts to wrestle over the other, resulting in a Neitschian view of force embodied as “perspectivism” , Pythagorean definition where duality is conduce to change, or the problem of Wittgenstein where “[a]ll the propositions of logic are generalizations of tautologies and all generalizations of tautologies are generalizations of logic. There are no other logical propositions.”

Paradoxically, the western empirical linearism and eastern transcendental circular forms of logic, both need eachother as one exists as the “limit” which defines the other. The western laws of logic observe the “fallacy of circularity” as a justification for linearism. The eastern views observe the deficiencies of individuative linearism promote holistic circularity. In a separate respect both observe a nature of “no-limit” through western regressive and progressive rationality dependent to a degree on infinitism and eastern circularity dependent on holisitic centering and rotation as absent of limit.

The problem occurs in the respect that we are constantly limited to dualisms, and the problems of logic and definition are reduced to ones of dimension. These dualisms create a problem of definition dependent upon polarity, observed in the hermetic philosophy as the “Principle of Polarity”. One polarity defines the other while simultaneously causing a perpetual sense of definition between the two. Polarity can be viewed as a contradiction of force under the Nietzschean metaphors of Apollo and Dionysus , an absence of structure as the Pythagorean Dyad , and an alternation of definition through the hermetic “Principle of Frequency” . Or it may simply just be observed as a problem in the same manner of Cartesian Dualism and Platonic Dualism leading to the competing substance, property, and predicate dualistic perspectives that provides for the universal means of division in philosophy between materialism and idealism .

A third more rational approach must be taken in order to deal with the multiple dualisms inherent through the limit and no-limit definitive nature of space in both form and function, quantity and quality, circularity and linearism, and western empirical and eastern transcendental logic. Without a solution to these reoccurring duals a process of fracturing takes place in which each definition is dependent on an infinite linear regression, circular justification or simply an acceptance of the axioms without any observable definition, all of which are observed in the Munchausen Trilemma .
This fracturing can be implied as a form of logistic Atomism, observed by the more modern philosophers Russel, Wittgenstein and Carnap and stemming from the pre-Socratic philosophers Leucippus and Democritus of Abdera , in which the linear regressive separation, circular definition, and axioms can be observed as individual units in themselves that must relate through a process of continual change. Hence it may be implied that dualisms are dependent on relativistic logistic unit-particles that exist through continual individuation as a form of definition.

The problem occurs in the respect that the very problem of definition we seek to avoid, change, appears to be one of the very foundations for this very act of definition. We can simply observe this as relativity merely being individuative limits and no-limits that exist as spatial dimensions of change as unit-particulate. This provides the foundation for not only materialistic change as a refutation of idealism observed by Kant , further evidenced by physics dependence on Principle of Locality in the Principle of Relativity, but further change in abstract logistic structures such as moral relativism, truth and cultural relativism , methodological relativism, relationalism and dialectic materialism . However, the observation of change as a constant, through logisitic unit-particulate, observes a consistency which further results in another dualism of change and no-change, which is further exacerbated by the number of aforementioned dualities premised in spatial limit and no-limit.

The question is what is the unifying median of all these definitions? Again intuition and reason leads one to the first axiom of geometry: “the point” which is again inherent within the question itself. Space as a unifying medial point which acts as a common bond gives a starting definition as to the nature of space itself. And what is this starting definition? Space begins with the “point”. Viewing this foundation of space through the standard Euclidian definition, or even non-Euclidian, as a 0d entity would be instinctive from the standard academic school of thought, however a few problems occur based upon this simple premise.
Our observation of the 0d point is strictly the observation of an individuator which divides and multiplies 1d lines, at minimum. It observes a degree of unity as “part”, “particulate” or “unit” but not “unity” itself. This is considering the 0d point lacks dimensionality and depends on the dimensionality of the 1d line ??and other dimensional spatial structures?? in order to be observed. Absent of the dimension, the 0d point acts as an individuator which relates through 1d lines. These 1d lines exist as extradimensional entities, which continually project past their origins of the 0d point. However when strictly relative to the 0d point, they project nowhere as observed ((((in the Aristotelian argument of movement in a void))). The 1d line must relate to other 1d lines, through the 0d point, in an equal manner to which a unit (or particulate) must relate to further units (or particulate in order to exist. In these respects, the 0d point as an individuator of units or particulate is dependent upon an extradimensionality which projects pasts its origins. In these regards extradimensionality is synonymous to individuation as relation through 0d.
So what to do? How can a unity be observed through space when the 0d point/1d line dualism itself cannot be a “unity”, but rather a “unit”, because of it’s inherent Extradimensional nature being a cause of individuation. We see this intuitively within various cultures which used and still use the line as a marker for “unit.”

What if the 0d point is inverted into an intradimensional entity as the 1d point? The problem occurs that in the foundations of Euclidian and Non-Euclidian geometry no 1d point occurs, it is not even a concept. As a matter of fact, according to modern instinct, it appears neither as a contradiction or paradox as it is not even a concept. But is it really a concept we have not fully dealt with or categorized? Intuitively the 0d point is quantified into units of 1, in various phases of measurement, yet the multiplication or division of zero, with this individuation being the foundations of measurement, cannot occur as 0 can neither be multiplied or divided without resulting in zero. To observe 0 as 1 unit is to equate it to a unit which can be multiplied or divided, and yet current mathematics does not allow for this function. Contradictory it is often times quantified and qualified in such terms.

However if we look at the point as intradimensional, or directed into itself, what we get is a new entity that acts as unified totality that exists on its own terms and is purely axiomatic both qualitatively and quantitatively. In one respect the point as intradimensional is directed into itself, with the point being a center that allows for infinity, or absence of limit. The point as both center to other centers and center to its own center, maintains an spatial dimensionality of “no-limit” as a center contains no limit. We can observe this within transcendental qualities and quantities such as Pi.(quote) In these respects the center exists as its own axiom, through the point, and holds the definition of space as “no-limit”.
However, the problem occurs in regards to this definition of “no-limit”: Can the point mediate between “no-limit” and “limit”? The solution appears to exist within the concept of intradimensionality. The 1d point, as intradimensional, maintains itself as a “limit” through dimensionality with dimension merely being space as direction. In simpler terms dimensionality is merely space as direction. We can observe this in the previously mentioned extradimensional space, in which dimensions must progress past their origins through relations with further dimensions, i.e the 1d line relative to the 1d line through the 0d point. Dimension in these respects, appears to exists as a boundary in itself as the relation of dimensions is strictly the relations of “direction”.

From this premise the question occurs as to how the point, as intradimensional, can have direction if direction implies an extradimensional spatial relation in which something is directed towards something? In simpler terms dimension unavoidably requires relation with relation as the observation of an inherent unit-particulate separation to some degree. If the 1d point is directed into itself, where would it move? The 1d point cannot be empty otherwise it requires the 0d point to exist inside it as a separate dimension, or maybe better put “absence” of dimension. If this is the case the 1d point is no longer a point but rather a circle or sphere. The “center” nature of the 1d point justifies its nature of “no-limit” as the intradimensional nature is without limit through the “no-limit” of the center. In simpler terms, because the point is “center” it is directed into itself without limit.
This nature of center as “no-limit” simultaneously justifies the intradimensional nature of the point as “limit”. Considering dimension exists as directional space which forms limit and boundary, the infinite intradimensional nature of the 1d point, observes the unlimited direction of space as unlimited “limit”. “Limit” in turn exists on its own terms as ever-present through the 1d point. The 1d point is infinite on its own terms and exists as a medial unifying space qualitatively as “limitless limit” and quantitatively as “numberless number” (quote).

The 1d point directed into itself, observes space as direction existing ad-infinitum as not the movement towards a center but rather the center itself being pure unified direction which moves itself paradoxically into non-movement or stability. As the 1d point alone exists, it has nowhere to move except to itself, and in these respects the rate of movement exists ad-infinitum. To illustrate this point, take for example a spinning wheel. When the wheel spins slowly, the movement can be observed through the various senses especially sight and sound. As the movement increases the change in sensual perception occurs as the speed causes a distortion in the original appearance of the wheel, while the squeaking tones increase to a higher pitch. The increase in speed causes an increase in sound pitch and observable movement. Eventually the rate, in this case infinity, causes the wheel not only to cease what appears as movement but the pitch reaches a frequency which cannot be heard let alone identified. Movement ad-infinitum paradoxically results in an absence of movement as infinite movement can go nowhere except to itself as infinity. Considering infinity exists through, but is not limited to all existence, the 1d points contains all phenomena as 1 eternal ever-present moment.

[odysseus]

Eodnhoj7
The first axiom of the argument is a simple one: what we understand of all phenomena, at minimum, is strictly an observation of space. It is the one universal axiom which exists as the limits that give structural boundaries to reality. In a separate and simultaneous respect, it is absent of the very same definition as no-limit. Space observes a dualistic nature of limit and no-limit.

Okay, I read it all. I can't respond to it all, but I can make interpretative observations.

One might argue that time is more fundamental than space because time encompasses both spatial and temporal principles of thought, or, "limit". After all, when I "observe" a number, I do so in time, but is this a spatial event?
But there is also the position that takes our spatial understanding of all phenomena, and reduces it to the pragmatic functions of the language and logic "about" some transcendental feature of the presence of things. Talk about things as if talk, thought, logic were some mirror of nature is what Kant called dogmatic metaphysics. If your are going to make an apriori argument about what is the case that has no observable features, then you are going have to explain how language can produce what is real by argument alone.

Observing the definition of space, within any given dictionary source, one is placed into a paradox. A whole host of definitions are given, which include but are not limited to: “area” “volume”, “dimension”, and “limit” These definitions,summated under the last definition as “limit”, reflect back upon the process of definition as a form of limit in itself by which a phenomena exists through the inherent limits which form it. Space as limit is limit through space, with the observation of any dictionary definition resulting in a dualistic circular and linear form of reasoning where one definition leads to another while simultaneously circling back to the original. Under these terms circular rational is justified through inherent linear elements and vice versa while observing, under certain degrees, Mirimanoff’s concept of “wellfoundedness” in which the definition as a set of information contains no infinite descension further implying an original source.

This sounds like this postmodern alternative: we are faced in our intuitions about the world a paradox of infinity and finitude. Acknowledging a phenomenon is inherently limiting, for the nature of an affirmation is to set something off from something else. Affirmations are inherently "difference" that is a "deference" to the body of terminology that surrounds the term. There are no affirmations that are "stand alone" and this is the circularity of which you speak. A coherence of self referential thought, the "well foundedness" of which refers to pragmatic application. Just as the hammer makes its way to the nail successfully, and consummates its journey, so does language in conversation, in empirical examination. Limitation is the parameters of what a hammer does, what language does, in its execution. But then comes the paradox: infinity, the terminus of language, yet a presence nevertheless. Why space? Being possesses space.

This dualism of progressive linear and circular definition provides a limit in itself through a process of mirroring in which the further corresponding definitions in turn follow this same process. The axiom of space follows this definition process in which a limit reflects itself through a further limit, rationally in both form and function as circular, and reflects further limits, rationally in both form and function as linear, in which an observation of no-limit occurs. This observation of “no-limit” is founded inherent within the dictionary definitions of space in an immediate respect within the aforementioned definition itself. In a separate respect, function follows form where these definitions reflect through further definition ad-infinitum in a dual circular and linear regressive/progressive manner. Limit and No-Limit are dependent on a dual form of circular and linear reasoning that simultaneously manifests further definition while maintaining there own under spatial terms.

Now, this sounds like the infinite question begging of terms, for a term is inherently limiting, and circular, being part of a self referential system of logic and language. The observation of no limit is qualified by limit; after all, to give it utterance is to contain it and reduce it to the "same", that is, to the closed, finite body of disclosing terminology.
Let's see, the limit is circular, the No-limit is linear. But then, how does the No-limit makes its way into meaningful thought? Once it is received, it is an interpretative entity. Unless you making an intuitive claim: Infinity is intuited, acknowldged in the finitude of human possibilities, but registered as infinity apriori.

This dualistic understanding of space can further be observed in many of the works of the pre-socratic including but not limited to the Pythagoreans and Anaximander. The Pythagorean Philolaus observed “that all things in the universe result from a combination of the unlimited and the limiting; for if all things had been unlimited, nothing could have been the object of cognizance.” Aristotle observed “[the Pythagoreans] plainly say that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be drawn in and limited by the limit.” He further implied that the Pythagorean teaching of the limit and no-limit were direct results of the philosopher Anaximander who argued “(that which is) unlimited”, “boundless”, “infinite”, or “indefinite” as “Apeiron” and “peras” as “end, limit, boundary”

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The presocratics are not helpful. I mean, I see why you refer to them, but they do not adjust for the idealism of finitude.

Modern philosophical instinct and training implies the definition of space as limit and no-limit in dual linear and circular terms questionable considering one is presented with two perspectives: They are an empirical contradiction or a transcendental paradox in the respect that logic either nullifies itself or transcends pasts its origins. (quote) Neither school of thought gives any real justification as they manifest a dualism in which one perspective attempts to wrestle over the other, resulting in a Neitschian view of force embodied as “perspectivism” , Pythagorean definition where duality is conduce to change, or the problem of Wittgenstein where “[a]ll the propositions of logic are generalizations of tautologies and all generalizations of tautologies are generalizations of logic. There are no other logical propositions.”

This paradox is best taken up by Kant, Husserl, Levinas, and others, by my thinking. I believe the contradictions of finitude and infinity that tell us, for example: Being here cannot truly be, being here, given that 'here' is a local concept embedded in infinity in the last spatial analysis of being here, all finite terms yield to this one infinity; are signs of the end of philosophy. The terminus is without meaning, an empty spinning of wheels, because here is must be realized that what all the fuss was about, was really about value. Time for Zen.

[odysseus]

No time for the rest. Not a fan of Nietzsche. Wrote a paper on The Birth of Tragedy once. Don't see how you make much use of it here, though.