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

Superchannel—Inside and Beyond Superstring
mathematics. The implication of the division of 1 into parts that approaches but does not
reach the zero becomes clear where we replace the wordings in Seife’s book with the language
of physics as propounded by Democritus. There we have:
“When you add up the distance that Achilles runs, you start with an atom, then break
to get half part, break to get one-quarter parts, …, and so on, with the terms getting
smaller and smaller, getting closer and closer to zero; each part is like a step along
the journey where the destination is zero (p.43)
This, in the Greek understanding, is the infinite void, that is, emptiness. The atoms cannot
move without emptiness. In this emptiness, this infinite vacuum, zero and infinity are wrapped
together. According to (Seife), this was a shocking discovery. Atomic theory was in a
quandary. Aristotle came to the rescue with a convenient fix that has persisted as a deep
problem in mathematical and philosophical logic to the present day. The atomists need infinite
vacuum for the atoms to move in. There is no zero that represents emptiness in their mathematics.
Under such a situation, no progress could be made. Aristotle’s solution is to ignore
the possibility of infinite vacuum and turn the universe into discrete nutshells. According
to Aristotle, there is no void but beautiful local spheres that surround the earth. In this way,
space is replaced by atoms which Aristotle sees as the habitat of the earth. The earth is surrounded
by local spheres (atoms) which are solidly bounded.
Aristotle who distinguishes between actual and potential infinity does not need the infinite,
nor the need to use it and so the potential infinity of dividing the line doesn’t exist
either. So the infinity of space and line are banished forever more until we can no longer afford
to ignore it if we are truly to understand the evolutionary nature of nature and human
nature. The issue is this. When space is excluded from matter, the points at the endpoints of
the line remain. What the Greeks banned in their mathematics and which forms the foundations
of the philosophy of Western world is the infinite vacuum of space which is replaced by
Aristotle with discrete atoms. Nonetheless, domineering as it was, Aristotle’s system was
destroyed by the reality of void and infinity, that is, zero and infinity. The matter is put succinctly
thus:
“Afterall, there were only two logical possibilities for the nature of the void, and both
implied that the infinity exists. First, there could be an infinite amount of void – thus
infinity exists. Second, there could be a finite amount of void, but void is simply the
lack of matter, there must be an infinite amount of matter to make sure that there is
only a finite amount of void – thus infinity exists. In both cases, the existence of the
void implies the existence of the infinite” (Seife, 47)
Notwithstanding the existence of void (zero, emptiness, space) and its infinity or that of matter,
the counting numbers are based on the outlook of Aristotle in which the atoms are standalone
and stand-apart entities in relation to the so-called void, that is, the space between and
among them.
To show that these counting numbers are the same as Aristotelian atoms, let us examine
the conditions which the Greeks, through Democritus give for the atoms. These are
(Cooke):
I
II
III
All matter is composed of atoms, which are bits of matter too small to be seen.
These atoms CANNOT be further split into smaller portions.
There is a void, which is empty space between atoms.
Atoms are completely solid
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Journal of Transfigural Mathematics Vol.1 No.1.2008