written 12
May, 2018
published 24 May 2018
I was fortunate in my college
experience. I took calculus in high
school, so the three years of math, as part of my engineering degree, were
upper level subjects. I retain little of
the rigor of those subjects now, but still appreciate the concepts
presented. One of my favorite classes
was "n" dimensional geometry, a study of the relationships between
dimensions. The dynamic between two
specific dimensions is repeated between any other pair, without limit.
Edwin Abbott wrote
"Flatland" in 1884 to illuminate this kind of dimensional perspective. Flatland is a two-dimensional world,
inhabited by intelligent polygons and lines.
One of them, Square, dreams of going to a one-dimensional world of
intelligent points, where he unsuccessfully tries to describe his world to
them. When he awakens, he is visited by Sphere,
an intelligent being from a three-dimensional world. Square can only see Sphere as a circle of
varying sizes, as Sphere intersects Flatland.
At each level, the inhabitants doubt the reality of the higher
dimensional being, as do four-dimensional materialists of today.
I am particularly fascinated by the
relationship between two-dimensional waves on the ocean surface, where the
three-dimensional volumes of the ocean and atmosphere intersect. We experience the world as four-dimensional
space/time, so the relationship between two and three dimensions is within our
perspective. Each individual ocean wave
peak has a unique location, distinct from any other wave peak, yet all arising
from, and remaining part of, the same ocean.
This simultaneous individuality and unity is visually obvious and represents
a shift in dimensional perspective. It
helps us imagine dimensional perspective shifts into higher dimensions.
We are used to thinking of
dimensions in terms of integer numbers, but fractal geometry introduces
non-integer dimensionality. A straight line
is one-dimensional, but picture a very wiggly line, never crossing itself,
drawn on a piece of paper. If it wiggles
enough, it could almost cover the entire surface. This can be thought of as, say, a
1.8-dimensional object, more than a one-dimensional line, but less than a
two-dimensional plane. Similarly, a
convoluted ocean surface could be thought of as, say, 2.3-dimensional, more
than a flat plane, but less than a volume. In this way, complexity within a given
dimensionality begins to extend into the qualities of the next higher
dimension.
Some consider the brain as a
consciousness transceiver, able to send and receive conscious thought, rather
than containing them. If we assume, for
a moment, that consciousness is a quality of a higher dimension than material
matter, the complexity of the human brain pushing into this higher dimension
might explain how it can host self-awareness.
Patterns in higher dimensions show
up in the real world in many situations.
Complex non-linear systems with multiple feedback loops, like weather
systems, are described as chaotic, sensitive to initial conditions, and
difficult to predict. However, they are
quantifiable by stable patterns called strange attractors, existing in higher
dimensions.
British biologist Rupert Sheldrake
proposes that higher dimensional patterns, which he calls morphogenetic fields,
direct the growth of organisms as they shift from the few initially identical
cells immediately after fertilization, to an array of differentiated cells constituting
a mature, multi-celled organism.
At the galactic scale, we have known
for decades that black holes are areas of such intense gravitation that the
shape of space/time is distorted, and energy and matter disappear once they
cross an "event horizon". The
laws of physics break down in the singularity that is the center of a black
hole. Some speculate that space/time is
ripped, opening a hole through higher dimensions. Recent theoretical work suggests there may be
reciprocal white holes, where energy is entering our universe. The original Big Bang is considered one of
these events. Science fiction has long proposed
warp speed travel over galactic distances utilizing wormholes, and folding
space/time in a higher dimension.
In a closed system, energy dissipates
over time, for example, a cellphone battery running down. But if a system is not closed, new energy can
come into the system at any point, recharging the battery. A system closed at one level of dimensions is
open to higher levels. We don't really know if our world is closed or
open.
