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

Superchannel—Inside and Beyond Superstring
other source can it be if not God ?
[Adam Drozdek: Beyond Infinity. Augustine and Cantor]
From what we have above, numbers and geometrical objects don’t need to justify their e-
xistence and if we can know eternal numbers then we don’t even need to ask about their
source because their source is God.
Augustine says the eternal and divine numbers are in God and that the numbers of mathematics
are a reflection of and not the real divine numbers.
If we have to relate this to reality, Augustine would say these divine and eternal numbers
which are in God and may still come to us contain divine reality, are inside where the
human reality that includes mathematical, physical and other realities has its seat. However,
Drozdek’s argument that God has to exceed infinity, somehow throws a spanner in the
works. He says:
“God necessarily has to exceed infinity; since infinity can be real, it is conceivable for
it to be part of the physical world. For example, the world can be envisioned as a
sphere, but this sphere would be limited and it would always be possible to conceive a
larger sphere - even an infinite number of such spheres. Hence, God exceeds any such
imaginable sphere, and since it is the very essence of God that nothing limits him
(divina essentia incircunscripta), then - according to the famous saying - God is an
infinite sphere with center everywhere and circumference nowhere.”
This cannot hold because it is the very nature of infinity to transcend what can be counted as
material physicality within the confines of discrete boundaries. Infinity is unreachable except
through zero which brings forth other infinities – inner infinities – inside the zero itself. The
problem of physics with infinity has to do with the fact that infinity transcends what can
physically be defined. It is beyond the limits of, whilst including a sphere inside spheres and
whirls inside whirls. That’s why Georg Cantor calls God the absolute infinity, which, according
to him is unreachable.
From David Valdman in his Mathematics and Reality we have the following on mathematical
reality:
The concept of graphing a function is a perfect example of this—high-school education
gone horribly wrong. What does it mean to say y = f (x)? This is a mapping of x as it
ranges over the real line, onto the real line (R→ R). You plug numbers in, and get
numbers out. It is the literal taking of a line, a one-dimensional space—a cut rubber
band, if you will—and morphing it appropriately. For instance, let's “do” y = x2.
Taking your cut rubber band, fold it in half (since negative numbers become positive),
and stretch its end. A more complicated example: y = sin(x) can similarly be described
as coiling a taut string around your hand and elbow. Notice that I'm asking you to do
something. A function is a verb: a performance on a space. However, when someone
asks you what is y = x2, you might say it is a parabola: a thing. Where is the parabola
in this description? The parabola only exists when we consider the function y = x2 as a
collection of points (x, x2). A parabola is a noun: it is the "trace" or the "range" of
points (x, x2) that are the result of the action of mapping x → (x, x2) over some do
main”.
The parabola made of points is one of the realities of mathematics. But this reality only
exists on the condition that its foundations are valid. In other words, the reality of anything
cannot be discussed in isolation from the conditions under which it arises. This matter has
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Journal of Transfigural Mathematics Vol.1 No.1.2008