### The Paradox of Point Division and a Theoretical 1d Point?

Posted:

**March 3rd, 2018, 12:53 pm**The Paradox of Point Division x/y → (1+y)*x = z

Presented argument:

What we understand of the point as a 0d entity causes problems when we refer to it as a unit of measurement. For example if a line is divided by three points we intuitively quantify 0 into a unit conducive to "1".

The problem occurs in the act of quantifying 0 we inherently view it as a unit in itself, however a unit (as a part or piece of something greater, usually another unit) relies on some inherent degree of dimensionsality. This dimensionality, often defined as the minimum number of coordinates or something conducive to a spatial property in itself, is dependent upon viewing space in directional terms (premised often times in the 1d line).

The problem occurs in the respect we can only view the extradimensional line in terms of relation, it must relate to other lines in order to exist. This can be observed through angles.

Standard division observes the individuation of a unit into parts, with the original unit being the potential relation of those parts with the parts themselves being the actual relations as ω/φ.

In these respects what we understand of division is actually an observation of particulation as change through actual and potential relations.

The question occurs as to what happens when we view the unit, in this case "1", as a point in itself? How can a point be divided into anything less than a point?

Now the point as "1" appears to form somewhat of a contradiction considering we view it, in standard academic terms, as a 0 dimensional entity. The problem of point division seems, in these respects, to end in a contradiction as 0/x always results in 0. Viewing the point as 1 would require it to contain dimensionality with this dimensionality fundamentally being intradimensional in nature. In simple terms, the point folding into itself ad-infinitum to form the foundation of dimension as "direction" through an intradimensional nature.

So where the 1d line as a spatial "unit" is dependent upon an infinite extradimensionality, the 1d point would be dependent upon infinite intradimensionality as spatial "unity".

Observing the point in these terms, as intradimensional with the 0d point being a dual "non-being", what we observe as division fundamentally changes reflective of the premises.

A point divided through 1 line of negative dimension results in the point as “2”.

This can be observed from a simple mental exercise where one imagines a point with a line halving it. The point is "halved", however considering the point is still a point, this results in the 1 point turning into two points. A positive 1d point, with positive equated to "summation as unity" similar to how we view addition as a summative process resulting in unity, mirroring a divisive -1d dimensional line, with negative dimensionality being synonymous to both an imaginary unit and one of "deficiency" or "absence", results in the divisive -1d line halving the point. The -1d line is not a dimension in itself but rather an approximation between the point as point, considering the point can only be observed approximately and not as a whole.

Considering a point cannot be halved, as the division of a point still results in the point, what we observe is a form of multiplication.

Take for another example the biological cell. When it splits to reproduce, does it divide itself or multiply itself? Or both? Either way we see a process of individuation.

Furthermore, a point divided through the mirroring of divisive 2, in which -1 dimensional line “halves” the point 2 times, results in the point as three. Where the standard act of division results in a fraction of the original, what we observe here is an approximation of 1 point through multiplicity. This approximation observes these parts in themselves as extension of a point as points.

In these respects the divisive value merely acts as a set of-1d lines connecting multiple points.

It is in this understanding of point division that the algebraic expression of standard division “x/y” is equivalent to “(1+y)*x = z” in which “y” equals the number of divisive -1d lines, “x” equals the number of sets connected by these lines and “z” equals the total number of points.

In these respects a point divided is actually a point multiplied as the point itself remains as a point. Multiplication and division are identical duals relative to the point as "1".

Agree/Disagree Why?

Presented argument:

What we understand of the point as a 0d entity causes problems when we refer to it as a unit of measurement. For example if a line is divided by three points we intuitively quantify 0 into a unit conducive to "1".

The problem occurs in the act of quantifying 0 we inherently view it as a unit in itself, however a unit (as a part or piece of something greater, usually another unit) relies on some inherent degree of dimensionsality. This dimensionality, often defined as the minimum number of coordinates or something conducive to a spatial property in itself, is dependent upon viewing space in directional terms (premised often times in the 1d line).

The problem occurs in the respect we can only view the extradimensional line in terms of relation, it must relate to other lines in order to exist. This can be observed through angles.

Standard division observes the individuation of a unit into parts, with the original unit being the potential relation of those parts with the parts themselves being the actual relations as ω/φ.

In these respects what we understand of division is actually an observation of particulation as change through actual and potential relations.

The question occurs as to what happens when we view the unit, in this case "1", as a point in itself? How can a point be divided into anything less than a point?

Now the point as "1" appears to form somewhat of a contradiction considering we view it, in standard academic terms, as a 0 dimensional entity. The problem of point division seems, in these respects, to end in a contradiction as 0/x always results in 0. Viewing the point as 1 would require it to contain dimensionality with this dimensionality fundamentally being intradimensional in nature. In simple terms, the point folding into itself ad-infinitum to form the foundation of dimension as "direction" through an intradimensional nature.

So where the 1d line as a spatial "unit" is dependent upon an infinite extradimensionality, the 1d point would be dependent upon infinite intradimensionality as spatial "unity".

Observing the point in these terms, as intradimensional with the 0d point being a dual "non-being", what we observe as division fundamentally changes reflective of the premises.

A point divided through 1 line of negative dimension results in the point as “2”.

This can be observed from a simple mental exercise where one imagines a point with a line halving it. The point is "halved", however considering the point is still a point, this results in the 1 point turning into two points. A positive 1d point, with positive equated to "summation as unity" similar to how we view addition as a summative process resulting in unity, mirroring a divisive -1d dimensional line, with negative dimensionality being synonymous to both an imaginary unit and one of "deficiency" or "absence", results in the divisive -1d line halving the point. The -1d line is not a dimension in itself but rather an approximation between the point as point, considering the point can only be observed approximately and not as a whole.

Considering a point cannot be halved, as the division of a point still results in the point, what we observe is a form of multiplication.

Take for another example the biological cell. When it splits to reproduce, does it divide itself or multiply itself? Or both? Either way we see a process of individuation.

Furthermore, a point divided through the mirroring of divisive 2, in which -1 dimensional line “halves” the point 2 times, results in the point as three. Where the standard act of division results in a fraction of the original, what we observe here is an approximation of 1 point through multiplicity. This approximation observes these parts in themselves as extension of a point as points.

In these respects the divisive value merely acts as a set of-1d lines connecting multiple points.

It is in this understanding of point division that the algebraic expression of standard division “x/y” is equivalent to “(1+y)*x = z” in which “y” equals the number of divisive -1d lines, “x” equals the number of sets connected by these lines and “z” equals the total number of points.

In these respects a point divided is actually a point multiplied as the point itself remains as a point. Multiplication and division are identical duals relative to the point as "1".

Agree/Disagree Why?