On the subjects of
circles and geometric shapes as they pertain to infinity and general
constructions, one might want to include zero-dimension points, one
dimension strings and membranes (branes) of two or more dimensions as
well. Instead of a finite number of sub-atomic particle-waves there
could be an infinite selection potentially that could be brought into
actuality from God’s infinite set of all sets including itself.
Sure that is for
finite human consideration absurd, yet it might be the case even so.
I wrote a post on
circles and infinity in 2011 and reprint it below. Running into it
again I thought it should be updated to mention branes and an
infinite field of fields that can be turned off or on in any portion
to actualize a design of God. If an infinite dimension brane of all
branes existed reductions to space-time being within itself that are
consistent with consistent rules and particle-wave may occur in any
way shape or form that was calculated and set to form in time
(calculation is a human paradigm rather than divine though).
On Quantum Infinite
Circles
June 30, 2011 05:51
PM EDT
Infinity was the
topic of a book by John D. Barrow published in
2005. He wrote of
the theologian Nicholas of Cusa’s work on the
infinite circle (in
radius) amongst other topics and the way Nicholas
described any given
section of a circle infinite in radius as being
indistinguishable
from an infinite line segment (straight).
As the infinite
circle expands to infinity in size (such an infinite circle
ought to be
incapable of comparison to other infinite shaped objects
(like Euclidean
solids) theoretically, for it would then need to be of a
given finite size)
any local area seems nearly without curvature.
I wanted to remark
about a more simple and evident aspect of the
infinite circle.
Earlier Barrow pointed out Aristotle’s work on potential
and actual
infinities-especially in mathematical series of numbers.
The difference
between a potential and an actual infinite circle is
more of a paradox
than the largest number known to which one may
add one more forever
(N+1).
A circle of any size
must be complete in order to exist. I believe I
must be referring to
a 2 dimensional circle for perhaps no other may
exist (The circular
characteristic of a hula hoop is meaningful in just
two dimensions of a
three dimensional object).
At any rate the
infinite circle to actually exist would then no longer
be infinite in size,
but finite. An infinite circle could exist only in
potential, yet a
potential circle cannot exist, or does not exist except
perhaps as a
continually increasing circle expanding like an infinite
universe regarded as
a spherical construction of an infinite number of
simultaneously
expanding, contiguous circles. A hyper-inflating
universe expanding
with space-time might be exemplary.
An infinite circle
could never exist as a finite actual circle or even as
an increasing in
size circle expanding forever from a singularity of
infinitely small
size without being compared with co-existent
additional infinite
circles of a larger temporal size making the primary
infinite expanding
circle a smaller infinity at any given point in the
process. Comparison
of infinities seems bound to happen if they are
actualized within a
temporal progression. A forever-increasing-in-size
infinite circle
would be finite at any given point in time.
Perhaps Bertrand
Russell would have regarded the infinite circle as
a categorical
problem. It is an abstract thought and perhaps without
meaning akin to a
square circle. One might need extra dimensions to
make the appearance
of corners from a continuous finite slope (a
circle) comparable
to a gravitational force in one time dimension.
The transition from
thought constructions to real world possibilities
for existence would
seem to require consideration of how an infinite
circle might be
constructed given the quantum packets or material
available in the
Universe. It seems unlikely that an infinite circle could
ever be made to
exist, yet string theorists conjecture that universe
sized strings left
over from the start of the Universe might exist and
be observed one day
(I don’t know much about that topic). Perhaps
they inflated
unbroken expanding with space-time from less than a
Planck length in
size to the size of the Universe today.
The nature of
infinity philosophically considered does appear to
support conjecture
about the Universe even in light of contemporary
cosmology and
concepts of God. One may get the notion that God
would need to
surpass Gödel’s incompleteness theorem criterion.
That is God would
need to contain all infinities as part of His nature.
Containing
temporality is a similarly challenging problem; how can an
infinite temporality
be contained and foreknown by a greater than
temporality God?
Barrow quotes Augustine on the matter of infinities.
These classic
theological and philosophical issues re-examined with
the tools of a
mathematical astrophysicist are interesting reading.
