Measuring
The Great Mother
By
Bent Lorentzen
Published by PanGaia Magazine,
©2003
Remember those boring math classes where the teacher droned on
and on about geometry and math in a way that made guaranteed we'd forget
everything we'd learned as soon as we passed the final exam? Little did we
realize that, under the jargon was hidden a treasure trove of ancient wisdom.
Geometry means "measuring
the Earth." It derives from two ancient Greek words. Geo refers to the
Greek Goddess Earth, better known as Gaea. The other half of the word has as
its root the word meter, which is related to "measure." However, an
even older root to the word is "mother." Geometry, in its most
straightforward meaning, is simply a respectful and spiritual desire to
understand the relationship between humans, our world (and by extension, the
Universe) and the Great Mother.
Rianne Eisler, in her book The
Chalice and the Blade, alludes to an ancient conflict when men in antiquity
wanted to rule by inventing "laws" so that the simple law of the
Great Mother would be forgotten. The simplest law of the Great Mother was:
"Enjoy Earth, but do not hurt her."
Unfortunately, whether you work
with the number line (basic math), or multidimensional geometry, algebra and
trigonometry (the basis for calculus), it can become all too easy to forget
the heart of it all. Today, the most complicated types of conventional
geometry are used to calculate how a missile fired from a battleship in the
Persian Gulf can destroy targets in the very region where geometry
originated: the Mesopotamia Valley, known today as Iraq. Sad, isn't it?
According to Eisler, a thousand
years before the Greeks began to describe their Great Mother in terms of
distance and space in order to build temples, roads, and tunnels, the
Mesopotamians had already learned most of this artistry. These ancients
looked to nature for answers to their everyday work in harvesting fields of
wheat, and believed that there was no difference between the Great
Goddess, people, and the other life on earth. They believed that they were
searching for how Earth could provide a better life without hurting the Earth
Herself. One of the first recorded Mesopotamian ideas about the relationship
between nature and mathematics eventually became called the Pythagorean Rule.
It's a way of measuring two sides of a right triangle to calculate the length
of the triangle's last line (the hypotenuse), hence enabling a more
productive use of land.
Pythagoras, a Greek born in what
is now Turkey who studied the arts and sciences of the known world didn't
actually discover this rule by going out and measuring abstract stuff. Among
other things, he was a musician who enjoyed understanding how varying the
length of strings on musical instruments and different diameters of bells
produced different tones. As a philosopher, Pythagoras was deeply devoted to
the Great Mother. Later on, some of his students took his ideas to come up
with a system of better “working” with Mother Earth. And some time later,
when mathematics was invented through this philosophy, a Greek mathematician
named Euclid wrote the first geometry book recorded: Euclidean geometry.
In my opinion, there is no
difference, between a love and respect of Great Goddess and any sort of math.
Science and The Goddess
So how do we arrive at a more
perfect understanding of the relationship between science (and its language:
math) and the Great Goddess? Scientists say that fifteen billion years ago, a
tiny dot smaller than an atom exploded into what we call the universe. Within
nanoseconds, that creative explosion generated a primary fundamental
force, which then diverged into the four fundamental forces most physicists
ascertain created the stuff that makes up our current universe: including the
stars, planets, and, of course, all life as we know it.
Around ninety years ago, a
biologist by the name of D’Arcy Wentworth Thompson wrote On Growth and Form,
a book that shook the world for a while, but then was quickly forgotten. He suggested
that every single form in the universe, from the tiniest bacteria to the
biggest galaxy, obeys a simple rule that gives all these things their shapes
and functions. He thought it had to be something so simple most scientists
would never understand it.
One of his demonstrations was to
draw a dinosaur on a piece of geometry grid paper and then, with some simple
bit of math, those vertical and horizontal lines would curve a little, and
the dinosaur he had drawn would curve with it, and tada! you’d suddenly see
a perfect horse. Do the same thing to a gorilla, and tada! you’d get a human
being. He also showed that some of the oldest living things in the ocean,
like a jellyfish or hydra, look just like what happens to the surface of a
pond when a drop of water hits it. This can be seen today with highspeed
macrophotography.
To put a further twist on things,
a decade ago David Lindley wrote The End of Physics. He has helped build some of the most
expensive labs in the world (cyclotron particle accelerators) and is known as
one of physics’ most respected scientists. In 1994, he wrote, “Perfect
objective knowledge of the world cannot be had because there is no
objective world.” Okay, a bunch of complicated words; now, what did
Lindley mean? He simply said that when someone studies the world, it is
impossible to be completely “objective” since no one cannot separate
themselves from the world. (It’s impossible to be an “impartial observer” of
a system of which you are a part.)
Similarly, James Gleik, in Chaos:
Making of a New Science, suggests that all disciplines that explore our
selves, our world and our universe, from esoteric spirituality to arcane
physics, use a type of geometry that borders on the magical: fractal
geometry. One of the features to fractal geometry is “a sensitive dependence
on initial conditions.” Or: what exists in the observable macrocosm of the
“system” (us, the world, the Universe) is a reflection of what exists in the
unseeable microcosm, ad infinitum.
The EverExpanding Fractal
Universe
In his earlier years in Austria,
Einstein liked to daydream, which in later life evolved to what he called
“thought experiments.”
Here’s my own thought experiment
that touches on fractal geometry. Let’s say you’re interested in learning the
circumference of a pond. A map describes it as being 100 feet around. Just to
make sure the map is right, you measure the real distance along the pond’s
edge. Surprise! You find it is more like 200 feet because the pond’s edge has
all sorts of little curves and small bays that the pond’s mapmaker thought
unimportant. But you don’t stop there.
Okay, now imagine a special bird
that eats only little pond insects at the very edge where water touches land.
That bird might have to walk five hundred feet to go around the 100foot
round pond because along the pond’s edge, the bird has to walk around rocks
and tiny curves of land no one considered in the gross estimation of the
pond’s circumference.
Now, let’s further imagine a
special kind of insect that can only live exactly where the pond water
touches land. If that insect had to walk around the 100foot round pond, it
would get very tired because it might have wound up walking several miles.
Why? Because for that insect, the pondedge included walking around pebbles
and bits of sand that also make up the shore.
Let’s now postulate a bacterium
that can only live at the place where water meets land. That tiny bug would
wind up walking (they don’t really walk) thousands of miles because for the
bug, the shore also includes the little cracks in each grain of sand where
water meets land.
Let’s now dream of a special kind
of creature that is so small it could fit inside an atom and will never die,
but must always live along the shore of the pond. It is an immortal creature
and has lived since the beginning of time and will only die when the last
star in the heavens has twinkled out. If that tiny creature were to try and
walk around the 100foot round pond, it would never finish the trip! Why?
Because for this tiny creature, the pond’s shore also includes all the tiny
little spaces between molecules, between atoms and inside atoms. No matter
how fast this tiny creature is, it would never make it around the pond.
Mindblowing, isn’t it?
And, although we don’t know that
such a creature exists, it could. Remember the creative force of
lovemaking, from embryonic evolution to a full human, is all part of the same
“system” within fractal geometry.
Geometry and the Brain
Let’s take a look at the part of
you body that helps you have an imagination: your brain. When a baby is born,
his or her brain has millions and millions of nerve cells, and each nerve
cell is connected (synapse) to many other nerve cells at the ends of several
strands (dendrites). Each one talks to the others through a tiny change
in electricity and biochemical messengers (neurotransmitters); the more times certain nerve tips talk to each other, the
stronger those connections become. This creates memory or habits, which is
part of learning. When nerves don’t talk together, they curl away from each
other until gone.
When a baby needs something, she
or he will babble, cry, smile, and even throw a tantrum. The parents’
response can affect which connections thrive and which fade — fostering love
and imagination, or loneliness and rigidity. If the connections don’t develop
properly, whole clusters of nerve cells that act together (neuronal grouping)
to form feelings, habits and memories through special nerve cell bridges
between these groups (reentrant looping) can lead to dysfunctions. Also
the two sides of the brain may not talk to each other very well.
Hence, we’re right back to the
roots of math: an almost magical relationship between humanity and the Great
Goddess. As students of the ancient art of geometry, we have an obligation to
insist that our teachers not forget the old wisdom behind it all. Geometry,
and its complicated allies, trigonometry, algebra and calculus, but most
intriguing of all, fractal geometry, can and do reveal incredible secrets of
the universe.
Further Reading
Rianne Eisler, The Chalice and
the Blade, HarperSanFrancisco, New York, New York, 1988.
Michael E. Gilpin, Group
Selection in PredatoryPrey Communities, Princeton University Press,
Princeton, New Jersey, 1975.
James Gleick, Chaos: Making a New
Science, Viking Press, New York, New York, 1987.
Stephen W. Hawking, A Brief
History of Time, From The Big Bang to Black Holes, Bantam Books, Toronto,
Canada, 1988.
David Lindley, The End of
Physics: The Myth of a Unified Theory, BasicBooks, a Division of Harper
Collins Publishers, New York, New York, 1994.
Rupert Sheldrake, The Presence of
the Past, William Collin, Cornwall, England, 1988.
D’Arcy Wentworth Thompsen, On
Growth And Form, University Press, Cambridge, England, 1914, 1957. s
— Bent Lorentzen is a writer
living in Denmark. His current projects include translating Danish books
into English . His epic fairytale novel Dragon Moon is available at the
Twilight Times Books Website: http://twilighttimesbooks.com/DragonsMoon_ch1.html
