*Earlier this year a conversation between Slavek Kwi, Dallas Simpson and I begun after I published my work ‘Circadian rhythm disorders’ where a text accompanies the sound piece. After this exchange, which focused on the different relation that a sound piece and its text could have for each artist, we realised that writing can have a very individual and personal meaning for everyone. For example, when an artist is working on a certain piece, all that things that occur around him during that period of time might have an influence on this piece whether consciously and unconsciously.*

*As a result of this conversation Dallas sent me a series of text that he wrote about different ontological questions that he has made during this artistic process.*

*This is the first chapter and we would like to make emphasis that this is not a scientific text and doesn’t pretend to be one, but instead these are reflections made by an artists towards subjects that in some way connect with his artistic creation and research processes.*

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**Some considerations of paradox**

**By Dallas Simpson**

Interesting analysis on your webpage “Investigating the Obvious”. I think we need to go much deeper to tackle the “problem”.

We may consider paradox in its absolute form to represent an indicator of dimensional boundary phenomena. Linguistically the situation arises when a reality is expressed across two or more non-local referential frameworks. The paradox arises because their is one common attribiute expressed in BOTH non-local realms, yet viewed from within each non-local realm the expression of the complex reality is different. This can easily be seen in the following statement: “Ink is blue, sea is blue, therefore sea is ink”.

The cause of the logical contradiction is obvious: the attribute blueness, although common to both “sea and “ink” is only a trivial attribute and does not of itself define either the complex quality of “seaness”, or the complex quality of “inkness”.

But we have to observe this statement in a particular way to understand deeper dimensional information contained within it. I shall now invert our observation:

Viewed dimensionally as realms of abstraction, sea is non-local to ink. Blue expressed in the realm of sea expresses a distinction of “blue sea”, blue expressed in the realm of ink expresses a distinction of “blue ink” from the dimensional principle of potentialities, “the nature of the expression of a potentiality is dependent upon the quality of the dimensional realm in which it is expressed”.

So: any colour expressed as a distinction in the realm of “sea” gives rise to an expression of that colour of sea, and similar for “ink”.

Notice, in this trivial example how we confer dimensionality with ACTIVE boundary properties: sea is non-local to ink. They are dimensionally partitioned. The existence of this dimensional partitioning is the property of the dimensionality which “allows” the expression of distinctions of reality in each realm – or not!

This gives rise to the dimensional principle of expressed and unexpressed potentialities:

The expression of potentiality in a realm of quality is conditional. We can see this clearly in set theory- only potentialities of the same type (quality) as the set can be expressed as distinctions within that set. If they are not compatible they are excluded, they “do not belong to that set”.

Normally we view the operation of sets from the point of view of us assigning realities, as an ongoing continuum of process unfolding in time, to the set.

This viewpoint is particularly powerful if we are writing the set allocation down on a piece of paper! This is the “spacetime continuum” viewpoint. But underlying what we are doing with our pencil and paper is the process of abstraction in our mind which provides the milieu (dimensional structure) for us to make that allocation and it is my proposal that active dimensional process are underlying our selections. These process can be understood as being derived from the primary properties of dimensionality itself.

In mathematics the expression of COMPLEX NUMBERS in the Argand Wessel Gauss complex plane, but not in the pure number plane is a powerful example of this “dimensional exclusion” process relating to the fundamental properties of dimensionality determining the conditional expression of potentiality. The complex number has to be expressed in two parts (real/imaginary) because there are both real and imaginary potentialities- “non-local phases” – contained within its total reality.

In a sense there is a direct analogy with the wave / particle duality. If the complex number is observed within the realm of real number, we can only see the real number component. If viewed from within the realm of imaginary number we only see the imaginary number component.

The trick with the Argand complex plane is to produce a realm of complex dimensionality – a dimensional realm attributised with the qualities of both real and imaginary number on orthogonal spatial axes (this is a spatial model).

Only this complex realm of quality “allows” the full expression of the bi-phasic complex number.

Observing the photon expressed within the realm of spacetime, allows the expression of a “particle”, observing the photon expressed within the realm of quantum, allows the expression of a wave. The conditions of our experiment determine which realm we are observing the photon in. The “paradox” of the “wave particle duality” arises as a direct consequence of the properties of dimensional partitioning of the total reality of the photon across non-local realms (quantum / spacetime) and applying the principle of potentialities.

“The quality of a dimensional realm determines the nature of the potentiality expressed within it” – Dimension Theory. We may also say that Paradox itself is an indictor of the presence of complex realities parallel expressed across two or more non-local realms.

Paradox is an indicator of dimensional partitioning.

There is much I could write on this area.

Dallas Simpson.