Transfinite Complex Stages

These greatly complement the finite structures.

Again there is a remarkable mathematical explanation involved here.

The finite complex solutions (of the eight roots of unity), give rise - as we have seen to four complex solutions where real and imaginary coordinates are equal. The diagonal lines connecting the centre of the circle to these four points, in each case gives rise to a right angled triangle where they can actually be represented as zero. Using the Pythagorean theorem, the square on the hypotenuse (the diagonal line), is equal to the squares on the two other sides (the segments of the real and imaginary axes respectively). Because these line segments are equal in length, the diagonal line (in two dimensional terms) in each case is zero.

In mathematical terms, these diagonal or null lines indeed represent rays of physical light. Phenomenal experience is conventionally posited in conscious one dimensional terms. These lines - being inherently two dimensional - relate to matters own holistic base, i.e. the fundamental ground or potential from which phenomena emerge.

In complementary psychological terms, these diagonal or null lines represent rays of spiritual light. These lines here relate to the holistic basis of phenomenal experience which is inherently intuitive.

Indeed these diagonal rays relate - both in mathematical and psychological terms to what is properly transfinite.

So we now have the emergence of transfinite complex numbers in quantitative and qualitative terms. (The complex aspect comes from the relationship of this light with finite reality now understand in complex terms).

Just as earlier we could define imaginary numbers - in dynamic terms - as representing what is simultaneously both positive and negative, we now can give a fascinating dynamic interpretation of transfinite numbers as simultaneously both real and imaginary.

In psychological terms the positive real pole represents transcendent experience of the world (in relation to self). This is the transfinite intuitive basis of thinking.

The negative real pole represents transcendent experience of the self (in relation to the world). This is the transfinite intuitive basis of judgement.

The positive imaginary pole represents immanent experience of the world (in relation to self). This is the transfinite intuitive basis of perception.

The negative imaginary pole represents immanent experience of the self (in relation to the world). This is the transfinite intuitive basis of feeling.