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.
Garrison Gibson: books and blog 