TRANSITION FROM POINT TO RADIAL LEVEL

INTRODUCTIONThe culmination of the point level represents a void or experience which is completely formless. This absence of finite manifest phenomena represents a pure experience of what is spiritually transfinite. Indeed it is simply pure intuition without conscious reductionism.

In mystical traditions, this is referred to as the contemplation of transcendence. One has now reached a state of development where one intuitively experiences the whole of reality (without distraction of partial phenomena). This can fruitfully be referred to as the wave aspect of spiritual light.

The transfinite is also recognised in mathematics but in a very confused fashion. This is hardly surprising. The infinite or transfinite notion relates directly to what is intuitive (and only indirectly to what is rational). At best - as with the methods of Cantor - transfinite quantities can only be approached therefore in an indirect fashion. Without corresponding intuitive insight, understanding of the results obtained is doomed to misinterpretation.

We have seen earlier - at the transition from linear to circular level - that every number has a negative as well as a positive aspect (both quantitatively and qualitatively).

We saw later - at the transition from circular to point level - that every number has an

imaginary as well as a real aspect (again both quantitatively and qualitatively)..

We now see - at this transition from point to radial level - that every number has a transfinite as well as a finite aspect.

What this simply means is that the understanding of numbers always involves implicit as well as explicit recognition. Explicit recognition relates to rational conscious understanding. Implicit recognition relates to intuitive unconscious understanding. Just as natural light is necessary to see an object in physical terms, intuition or spiritual light is equally necessary to see an object in psychological terms.

Thus 2, for example, as a phenomenal perception represents the finite aspect of that number.

The transfinite aspect of the same number relates to the intuition or mental light (i.e. insight) necessary to see - in understanding - this finite phenomenon in the first place. In the dynamics of experience, finite and transfinte aspects are inextricably linked. Thus when the two are abstracted, paradox inevitably follows.

The transition from point to radial level initially involves experience of the void and the transcendent pole of spirituality. This represents the culmination of the real transcendental structures of the point level (i.e. superstructures) and leads to the real aspect of the transfinite paradigm.

However the void gradually gives way to a plenum-void. There is now also the culmination of the imaginary transcendental structures of the point level (i.e. substructures) and leads to a complementary imaginary aspect of the transfinite paradigm.

This is referred to in the mystical literature as the contemplation of immanence. This can be looked on as the particle aspect of spiritual light.

Just as contemplation of transcendence enables one to look at the universal whole (to which each part is related), the contemplation of immanence enables one to look at the unique parts (to which the whole is related).

Transcendence provides - in direct terms - the spiritual underpinning of dimensional experience (to which phenomena are related); immanence provides in complementary terms - the spiritual underpinning of phenomena (within such dimensions).

Of course in full mystical experience these two poles directly coincide. However some separation is inevitable even into the radial level.

In mathematical terms, the real transfinite aspect of number relates directly to the dimensional aspect of number. In other words the general number concept (to which a particular number relates) has an (intuitive) transfinite as well as (rational) finite significance.

The imaginary transfinite aspect of number relates directly to the quantitative aspect of number (within a given dimension). Each particular number again has an (intuitive) transfinite as well as (rational) finite significance.