To appreciate what is involved here, numbers must be defined with respect to the complex plane.A complex number is one which contains both a real and an imaginary part.

So in defining numbers in the complex plane, the horizontal (x-axis) represents the real part and the vertical (y-axis) represents the imaginary part respectively.

When we generate higher order roots of unity, we invariably generate imaginary as well as real results. For example when we obtain the four roots we obtain 1, - 1, +

iand -i(whereiis imaginary representing the square root of - 1). So in plotting these roots we need to use both the real and imaginary axis.When we plot the roots in this manner, they lie as 4 equidistant points on the circle of unit radius.

Likewise if we were to obtain the 100 roots of unity, they would again lie as 100 equidistant points on the same circle of unit radius.

The very notion of a mathematical dimension relates to direction (so I often use the terms interchangeably).

So what is one-dimensional has just one direction.

This is encapsulated in terms of linear understanding, which views the qualitative dimension of time as having just one direction of movement i.e. in a positive (forward) manner.

The understanding associated with the higher mystical stages is literally of higher dimensions.

H1 (the subtle realm) involves bi-directional understanding of a horizontal kind (relating to interior and exterior polarities). This directly corresponds with the holistic mathematical interpretation of two-dimensions, where the direction of movement for all relationships is both positive and negative.

In other words by appreciating the arbitrary nature of these polar reference frames, the asymmetrical direction of any relationship defined with respect to one reference frame, can be given a - relatively - opposite direction (with respect to the other frame).

The truly remarkable fact - which apparently is not recognised - is that the correct dynamic structure of space-time is provided by the mathematical interpretation of dimensions.

The reason why this is not commonly appreciated is because of the nature of (conventional) scientific understanding, which is linear (i.e. one-dimensional).

Therefore science is unable to accommodate the holistic interpretation of higher order dimensional understanding.

As mentioned in the previous note, when real numbers representing (qualitative) dimensions are indirectly expressed in quantitative terms, they become imaginary.

This is not just an abstract mathematical notion, but intimately relates to the very structure of reality.

So the physical dimensions of reality have indirect expressions as quantitative objects.

Indeed this is amply illustrated in sub-atomic physics where "empty" space continually gives way to the creation of short-lived virtual (i.e. imaginary) objects (as indirect expressions of their underlying dimensions).