JTfM Vol 1 No 1 2008 - ONLINE EDITION - Inclusionality Research

Superchannel—Inside and Beyond Superstring
tively definitive logic. We also need to recognise that this premise resides not only in the
foundations of numerical definition, but also in the related, unnatural dimensional constraints
of idealized geometrical figures.
Stilled Life – The Dimensional Collapse of
Euclidean and Superficially non-Euclidean Geometry
The definitive framing of Nature within an infinitely extended cubical box with a fixed centre
but no outside is characteristic of the idealistic geometry of Euclid, which collapses the
infinite dynamic possibilities of space throughout everywhere (i.e. as a non-local presence)
into just three structural dimensions. Through this geometry, space, time and matter/energy
are conveniently homogenized in a way that enables them to be packaged and quantified in
independent, uniformly linear units that can be added, subtracted, divided and multiplied as
whole entities and fractions according to the rules of elementary arithmetic.
The unrealistic and self-referential nature of this geometry is immediately obvious
from its representation of dimensionless points, widthless lines and depthless planes, all of
which signify the complete exclusion of space from matter. It abstractly imposes discontinuity
and cannot reproduce the dynamic continuity and radial dimensionality of natural fluid
flow from which it can only be derived by solidification. It models the crystalline arrays in a
block of ice, but not the fluidity of what can melt and vaporize from this block through the
inclusion of ‘latent heat’ (i.e. inclusion of ‘space’ as a vital presence, not a passive absence).
It is an artificially imposed inversion of natural order, which puts the cart before the horse
but nonetheless remains deeply embedded in the metaphorical ‘building block’ foundations
of objective logic, science and mathematics.
This way of thinking was reinforced by the success of Newtonian mechanics in describing
the world as a set of moving whole bodies separated by empty space. According to this
schema, all movement, or acceleration, deceleration or redirection of movement was measurable
in accordance with fixed time intervals and attributable to calculable external force.
Linearity was given precedence over non-linearity and gravity assumed to be a property of
mass alone. And yet, as Newton himself admitted in his preface to ‘Philosophiae Naturalis
Principia Mathematica’: ‘I wish we could derive the rest of the phaenomena of nature by the
same kind of reasoning from physical principles; for I am induced by many reasons to
suspect that they all may depend upon certain forces by which the particles of bodies, by some
causes hitherto unknown, are either mutually impelled towards each other, and cohere in
regular figures, or are repelled and recede from each other; which forces being unknown,
philosophers have hitherto attempted the search of nature in vain; but I hope the principles
laid down will afford some light either to this or some truer method of philosophy’. He also
commented that ‘it is not to be conceived that mere mechanical causes could give birth to so
many regular motions ... this most beautiful system of the sun, planets, and comets, could
only proceed from the counsel and dominion of an intelligent and powerful Being’.
Kepler, on the other hand, saw space itself as God, the great co-ordinating, harmonizing
geometric influence orchestrating the ‘Music of the Spheres’. As he said in his
‘Memoir’ (cited by Koestler and Butterfield, 1989): ‘Why waste words? Geometry existed
before the Creation, is co-eternal with the mind of God, is God himself (what exists in God
that is not God himself?); geometry provided God with a model for the Creation and was
implanted into man, together with God’s own likeness --- and not merely conveyed to his
mind through the eyes.’
In truth, having reduced Nature down into discontinuous rectilinear packages that neatly fit
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Journal of Transfigural Mathematics Vol.1 No.1.2008