A thought experiment: imagine an infinitesimally small dimensionless point. Now double this nothingness an infinite number of times and what do you get? Just more nothingness or perhaps an infinitesimally small ‘something’ on the cusp of measurement? This is stage one, as represented by Book 1 of this Work – “Forbidden Fruit” – a dimensionless point possessing the attributes of existence.
Now take this infinitesimally small yet immaterial something and start doubling. From one point to two points, to four, exponentially incrementing the number of points towards a line of infinitesimally short length. This would represent stage two, as represented by Book 2 of this Work, the emergence of conditions equating to the possibility of the first of the three spatial dimensions. A point conceived as delineating and expanding into a line or vector of no length.
Books 3 & 4 expand on this theme, the vector of no length incrementing until it becomes a plane of no width, the plane incremented until it materializes as an infinitely small embryonic space or solid. Book 5 completes the experiment with the materialization of this imagined dimensionless point in three-dimensional space on the cusp of elevation into the fourth, time reduced to the duration of a timeless instant. A timeless moment where the dimensionless point has acquired a potential for existence in space and time.
Yet, and this is the conundrum, the very thought of this dimensionless virtual particle may appear infinitely more substantial than the actuality being conceptualised. We can endow our imagined point with the mathematical notions of colour, spin and charm – and view our feats of logic like magicians or gods, as our conceived something manifests out of nothingness once we start to look for it, as it always does – but these universal laws are the mother not the daughter of reason.
To provide a framework for visualizing this process of dimensional iteration I’ve been forced to adopt certain conventions. These derive from and are perhaps intrinsic to the obvious restriction of needing to convey this within the confines of a flat two-dimensional surface. A constraint further compounded by the impossibility of portraying a length of no thickness let alone a point of zero dimensions. So humour me if you will as I try to explain how I attempt to circumvent this problem.
Imagine a line, divide it in two, divide it again into four and then think of this as your x axis, Repeat again for the y axis and you should now how a grid that divides a square into sixteen equal portions as follows:
If the two axes are scaled from 0 to 4 it is then possible to identify 25 points of intersection with values ranging from 00 to 44, where the first and second digits correspond to positions along the x and y axes respectively.
These are strictly speaking non-dimensional but in the spirit of this work let us assume they possess the attributes of existance in three-dimensional space – my first convention.
So, to navigate around this work, let’s consider each of these co-ordinates as being represented by a drawing or, to use the venacular of this work, let’s call them verses. In following this metaphor a sequence of five verses along one axis would be a chapter and the grid as a whole a book:
…. and since the work as a whole concerns the emergence of a dimensionless point in three-dimensions, let’s reveal the work in full, all 125 verses – 5 per chapter, 5 chapters per book, 5 books in all – through a value range of 000 to 444, each defined according to its position with respect to x, y and z axes. An unimaginable location finally endowed with the attributes of spatial presence, the map if not the territory.