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

Superchannel—Inside and Beyond Superstring
tional process. They are present in the core of a dynamic relational process that involves variations
continually diverging and converging co-creatively around a changing theme, not
divergences that have to be removed from the Darwinian competition to be number one, alone,
at best exalted and exhausted at standstill at the end of the struggle for eternal life that
has no life at all! Ideals are to be attained but once attained they transform into further ideals
such that what it being struggled for here has been attained but is yet to be attained.
It is like love. Or it is the heart of love, the truly evolutionary ideal. It is somewhere
there. But it is here. As soon as it is attained, it produces others of its kind which show that
what has been attained is the beginning of a journey without an end. Like walking on a continuous
line. Like infinity too.
Evolutionary Reality and the Transfigural Perspective
The place to begin with reality and existence is the question, what is number? The Greeks
grappled with this question for so long and when they reached continuity, they had to abandon
it even though its lack of solution produced other types of number apart from natural
numbers that we got from them such as reals, rationals and transcendentals all of which
complicated the problem rather than solving it. These creations were aimed at solving what
number really is, which is, as we show below, a plurality.
So, originally, what is number? John Mayberry has this to say:
As Klein points out, in Greek mathematics a number was defined to be a finite plurality
composed of units, so what the Greeks called a number (arithmos) is not at all like
what we call a number but more like what we call a set. It is having a finite size
(cardinality) which makes a plurality a “number” in this ancient sense. But what is it
for a plurality to have a finite size? That is the crucial question. The Greeks had a
clear answer: for them a definite quantity, whether continuous like a line segment, or
discrete – a “number” in their sense – must satisfy the axiom that the whole is greater
than the part. We obtain the modern, Cantorian notion of set from the ancient notion
of number by abandoning this axiom and acknowledging as finite, in the root and ori
ginal sense of “finite”– “limited”, “bounded”, “determinate”, “definite” – certain
pluralities (most notably, the plurality composed of all natural numbers, suitably defi
ned) which on the traditional view would have been deemed infinite.
[John Mayberry, The Foundations of Mathematics in the Theory of Sets,
(Cambridge University Press), p.x]
It is this definition of number as a finite plurality that gave the inspiration for the creation of
sets of set theory. Sets are numbers seen as not being alone but being contained in their past
if not in their future. While this plurality grapples with the demands of the Ancients on what
number is, it fails to accommodate the space both inhabits and is inhabited by numbers. It
only deals with the inhabitants as discrete entities. In other words, inside the set of numbers
or things, there are spaces between them. This, as we said, is not the fault of sets but that of
the Ancients who abstracted numbers out of their environmental context. It is this very space
which a thing needs for its breathing, indeed for its being alive and the same which makes
the world the breathing-point of transfigural mathematics. It is the very space which a thing
needs for its motion. It is this very space which is necessary for the flow of life, yes of love
itself. It is inclusion of space in things and things in space that makes all of Nature flow.
Where things flow, they are never alone because One flows in the Other and the Other
in One. And where this is the case, every number is a plurality that includes itself and the
others by including space which now includes it. This is the foundation that produced the
18
Journal of Transfigural Mathematics Vol.1 No.1.2008