Nature's
Numbers
Ian Stewart 1995
Numerology is the easiest-and consequently the most
dangerous-method for finding patterns. It is easy because
anybody can do it and dangerous for the same reason. The
difficulty lies in distinguishing significant numerical
patterns from accidental ones. Here's a case in point.
Kepler was fasci-nated with patterns in nature, and he
devoted much of his life to looking for them in the
behaviour of the planets. He devised a simple and tidy
theory for the existence of precsely six planets (in his
time only Mercury, Venus, Earth, Mars, Jupiter, and Saturn
were known). He also discov-ered a very strange pattern
relating the orbital period of a
/
planet- the time it takes to
go once around the Sun-to its distance from the Sun. Recall
that the square of a number is what you get when you
multiply it by itself: for example, the square of 4 is 4 x 4
= 16. Similarly, the cube is what you get when you multiply
it by itself twice: for example, the cube of 4 is 4 x 4 x 4
= 64. Kepler found that if you take the cube of the distance
of any planet from the Sun and divide it by the square of
its orbital period, you always get the same number. It was
not an especially elegant number, but it was the same for
all six planets.
Which of these numerological observations is the more
significant? The verdict of posterity is that it is the
second one, the complicated and rather arbitrary calculation
with squares and cubes. This numerical pattern was one of
the key steps towards Isaac Newton's theory of gravity,
which has explained all sorts of puzzles about the motion of
stars and planets. In contrast, Kepler's neat, tidy theory
for the number of planets has been buried without trace. For
a start it must have been wrong, because we now know of
nine
planets, not six.
There could be even more, farther out from the Sun, and
small enough to be undetectable But more important, we no
longer expect to find a neat, tidy theory for the number of
planets. We think that the Solar System con-densed from a
cloud of gas surrounding the Sun, and the number of planets
presumably depended on the amount of matter in the gas
cloud, how it was distributed, and how fast and in what
directions it was moving. An equally plausible gas cloud
could have given us eight planets, or eleven; the number is
accidental, depending on the initial conditions of the gas
cloud, rather than universal, reflecting a general law of
nature" /
Zed Aliz said. In that
case, would Albert have thought of other, than a number nine
tram
The scribe, meanwhile noted
that, in the main text.
"nine
planets" occupies
the nineteenth line down of
page 103
Page 6 /
" The big problem with
numerological pattern-seeking is that it generates millions
of accidentals for each universal. Nor is it always obvious
which is which. For example, there are three stars, roughly
equally spaced and in a straight line, in the belt of the
constellation Orion. Is that a clue to a signifi-cant law of
nature?
Here's a similar question.
Io, Europa, and Ganymede are three of Jupiter's larger
satellites. They orbit the planet in , respectively, 1.77,
3.55, and 7.16 days. Each of these numbers is almost exactly
twice the previous one. Is that a significant pattern? Three
stars in a row, in terms of orbital period. Which pattern if
either, is an important clue..."
"
In addition to numerical patterns there are geometric
ones
"
"
Until recently the main shapes that appealed to
mathe-maticians were very simple ones: triangles, squares,
pen-
/
Page
7
/
tagons, hexagons,
circles, ellipses, spirals, cubes, spheres, cones, and so
on. All of these shapes can be found in nature, although
some are far more common, or more evident, than others. The
rainbow, for example, is a collection of circles, one for
each colour. We don't normally see the entire circle just an
arc; but rainbows seen from the air can be complete circles.
You also see circles in the ripples on a pond, in the human
eye, and on butterflies' wings.
Talking of ripples, the flow of fluids provides an
inex-haustible supply of nature's patterns. There are waves
of many different kinds-surging toward a beach in parallel
ranks, spreding in a V-shape behind a moving boat, radiating
outward from an underwater earthquake
"
"
There are swirling
spiral whirlpools and tiny vortices. And there is the
appar-ently structureless, random frothing of turbulent
flow, one of the great enigmas of mathematics and physics.
There are similar patterns in the atmosphere, too, the most
dramatic being the vast spiral of a
hurricane
"
"
There
are also wave patterns on land. The most strikingly
mathematical landscapes on Earth are to be found in the
great ergs, or sand oceans, of the Arabian and
Sahara deserts. Even when the wind blows steadily in a fixed
direction, sand dunes form. The simplest pattern is that of
transverse dunes, which-just like ocean waves-line up in
parallel straight rows at right angles to the prevailing
wind direction. Some-times the rows themselves become wavy.
in which case they are called barchanoid ridges; sometimes
they break up into
/
Page
8 /
innumerable shield-shaped
barchan dunes. If the sand is slightly moist, and there is a
little vegetation to bind it together, then you may find
parabolic dunes-shaped like a U, with the rounded end
pointing in the direction of the wind. These sometimes occur
in clusters, and they resemble the teeth of a rake. If the
wind direction is variable, other forms become possible. For
example, clusters of sand shaped dunes can form, each having
several irregular arms radiating from a central peak. They
arrange themselves in a random pattern of spots.
Chapter
6
Page
81
" Nature's symmetries can
be found on every scale, from the structure of subatomic
particles to that of the entire universe. Many chemical
molecules are symmetric. The methane molecule is a
tetrahedron - a triangular-sided pyramid - with one carbon
atom at its center and four hydrogen atoms at its corners
Benzene has the sixfold symmetry of a regular hexagon. The
fashionable molecule buckminsterfullerene is a truncated
icosa-hedral cage of sixty carbon atoms. (An icosahedron is
a regular solid with twenty triangular faces;
"truncated" means that the
corners are cut off.) Its symmetry lends it a remarkable
stability, which has opened up new possibilities for organic
chemistry.
On a
slightly larger scale than molecules, we find symmetries in
cellular structure; at the heart of cellular replication
lies a tiny piece of mechanical engineering. Deep within
each
/ Page 82
/
"living cell, there is a
rather shapeless structure known as the centrosome, which
sprouts long thin microtubules, basic components of the
cell's internal "skeleton", like a diminu-tive sea urchin.
Centrsomes were first discovered in 1887 and play an
important role in organizing cell division. How-ever in one
respect the structure of the centresome is aston-ishingly
symmetric. Inside it has two structures, known as
centrioles, positioned at right angles to each other. Each
cen-triole is cylindrical, made from
twenty-seven
microtubules fused together along their lengths in
threes,
and arranged with perfect
ninefold
symmetry. The microtubules themselves also have an
astonishingley regular symmetric form. They are hol-low
tubes, made from a perfect regular checkerboard pattern of
units that contain two distinct proteins, alpha- and
beta-tubulin. One day, perhaps, we will understand
why nature chose these symmetric forms. But it is
amazing to see sym-metric structures at the core of a living
cell. "
Page
Finally if not sooner, Zed
Aliz Zed, said this, to the beloved, if motley
grew.
Brothers and Sisters of
the
THAT.
The he as in she that is
you, has an average, or otherwise life span, by which to
determine the truth of your reality, an apparent moment of
perceptive acuity. Glass measured sand, betwixt and between
zero and around the turn of a century. Regardless of where
you are, at this moment in the magical machinations of
adventure land, you are on your own, and for now, the
misconception of independent existence, leaves that illusion
yet to be worked out. First we have thee mountain to climb,
if for you the achievable miracle happily happens, the
realisation of oneness when it comes will, as it must, be
shared out equally.
However
at this moment of an average everyday day to day life, for
you, who juggle the spheres of your distractions, the time
has responsibly arrived for a stirring, for lo and behold a
sphere has fallen. When that happens the world stops, and
the question arises what am I doing. And who is the am I,
doing it.
You,
who are you ? the supposed you, spinning around in the midst
of an anywhere somewhere, at
18.5
miles per second. And, relative to some, upside down at
that.
Have
you ever known an un-perceptive state? Namuh,.in the A to Z
of your journey of change, have you ever known that?
Ignoring pre-conceptions of mortality.
Appreciate,
that your comprehending life force is the only vibration of
existence you have ever known.
Think of the miracle of
apparent change of which you are an integral part, the
wonder of it all, the pain of it all.
Truly waken to that dash of
iced water in a blind minds I
Consider reality, that
within the wholesome nature of its oneness, it appears, as a
different reality to each respondent, living, peculiar
particularity of its every participating perspective. All of
whom, magically experience that as from the centre of the
universe. Even the very hair of your head is known.
Intensify your visionary
faculty, think, the amazing wonder of imaginative evolution,
rubbed up against the living irritation of matter, and
integral to it, think a living reactive creative
metamorphosis of a totality.
Ask
of the Y, why is experience facilitated via certain senses ?
It is because THAT which spawned this evolving,
comprehending intelligent birth, in apparent independence
from its creative womb. Heeded well the delicate nature of
its young re-cycled progeny, for although learning from
these elementary possessions. They define apparent
boundaries, circumscribing the parametered prison,
of limited awareness. At this moment of our 'look
abroad through natures range natures mighty law is change'
we should understand this, the clock of our own making ticks
a tock on. Within the living scintillating monstrous wonder
of it all. If that conceived offspring is to survive. some
forced growth, towards the light of real comprehension is
required, a demonstration indicated, thoughts, an inkling of
positive growth on the cards.
What
is this living everything,? Within the limitations of
description it is the eternal THAT, a totally just, karmic,
and harmonically perfect creative process, It
comprises everything, and in thee Eht Namuh, by and large
would be experienced as an abstraction, unless matter
manifest.
It is the one, the mother
and father of completeness, and seen through a glass
starkly, sparkly.
Human
existence, survives a fractional distortion
of the true reality.
To be perfectly honest John,
without beating about the bush, we as a common or garden
entity, reside for the moment, in slumber deep, lost in -
Rip, Oblivion, Van Winkle time. Self absorbed, within the
spiral of our conjured growth. The question that has to be
asked, will the physical home of our common parentage burn
down afore we waken, because dear friends, it is already
burning. The quite essential moment of the quintessential
moment is at hand, and the tip of the tongue words that
spring to mind are, not a moment too soon .
Oh
Namuh, in the now of your forever, a sea swelling, see
change of comprehension, has to be effected by the three
score and ten year olds There are dimensions to
slip, and recognition to be made, of the existence of other
realities of mentalities. It is time to strike, did I say
spark, that rock, that the water of spirit flow within
ourselves, endlessly, intuitively, and with every
comprehending empathy. Embracing union with every
manifestation of THAT inhabiting our reality. To
finally understand that creative intelligence, is not only
within and without, but in between. It is a
totality, a supremely intelligent creative living perfection
of that everything.
Is
it not, that in the now of our change we are entered into a
state of critical mass, said Zed Aliz not laughing, but
lamenting neither. Karmic response being Karmic
response.
Oh
Namuh, hypnotised, magnetised being, embrace the constancy
of knowing, required by THAT creative intelligent living
consciousness on which you so rightly depend. Give
recognition to its amazing magic, unbelievably, ingeniously
expressive, executing the turns and twists of its star magic
life. See with all I's every manifestation and
wondrous demonstration of THAT supreme, living,
consciously inventive metamorphosis. THAT, which within our
blindness, is available to us only within our so limited,
hog-thigh'd perceptive range. Beings curbed by the
imaginative potential of mind as expressed in thee and me.
Drowning in the present of our energised playground. Our
thinking having been miraculously transformed from blessed
worm, to thee n' me Eht Namuh, living minds inside the
amorphous plasticity of existence, understood as our
finality.
THAT same reality which
says, in deeds a plenty to them as in wakefullness
understands, I am
THAT.
We see reality obliquely,
refracted and opaque, the enlightened constancy of living
creative purpose being well nigh lost to our sensibilities,
lose in the pleasure-dome, or otherwise, of our own making.
Wandering lonely as a crowd, passing through a living dream.
Somnambulistic, imaginatively stunted, seeking for meaning
around the back of the mirror, instead of doing an
Alice.
No matter the escape into
space, still art thou Oh Namuh as far away from the truth as
ever.
Time to do an Alice, said
Alizzed, and quick as you like along with a number of
companions, who for now shall remain nameless, hopped, as
White Rabbitz do, through the mirror of their future
past
Prize open, open the
prize
Apply with painstaking care,
the unveiling of the living reality.
Do you understand what is
being said here dear friends, fellow sufferers, the reality
you are pleased to call your own, intelligently lives, that
is it, no theories, everything lives.
THAT, three letter word
exists in everything, is everything.
Your task, prove it.
The
physical imaginative manifestation of the
meandering straight line of this journey requires that you
the reader supply the necessary drama, from Labyrinth,
to Magic Mountain , and all the in-between images
of the
Great Divide.
Mathematics and the
Imagination
Edward Kasner and James
Newman
1940
Page
221
"
9.
For instance, the riddle of the Epimenides concerning the
Cretan who says that all Cretans are liars
"
The Bull of Minos
Leonard
Cottrell
THE QUEST
CONTINUES
Page
90
"
Out in the dark blue sea there lies a land called Crete
a
rich and lovely land washed by the waves on every
side, densely peopled and boasting
ninety
cities
.
One
of the
ninety
towns is a great city called Knossos,
and
there, for nine
years , King
Minos ruled and en-
joyed the friendship of almighty
Zeus."
Frontispiece
quote
"Furthermore, after he (Theseus) was arrived in
Creta,
he slew there the Minotaur
(as the most part of ancient
authors do write) by the
means and help of Ariadne; who
being fallen in fancy with
him, did give him a clue of thread,
by the help whereof she
taught him, how he might easily
wind out the turnings and
cranks of the Labyrinth."
Plutarch (North's
translation) "
Page 111
'Theseus
and the Minotaur.'
"as
related by Appollodorus.
"King Minos had
through conquest, become overlord of Athens and as a tribute
demanded each year twelve noble Athenian youths and maidens
whom he could sacrifice to the Minotaur. This was the
monstrous progeny of Mino's wife Pasiphae, a nymphomaniac
whom only a bull could satisfy . It was kept by Minos in a
labyrinth - designed by his chief craftsman Daedalus,
beneath his great palace at Knossos. So tortuous was this
maze, with its many twisting passages, blind alleys and
false turnings, that no man having once entered could ever
hope to find his way out again unaided. And within it lurked
the Minotaur, waiting to devour its victims. Every year,
according to the legend, twelve of the flower of Athenian
youth, men and maidens, met their death in this
way.
Then came the
year when the hero Theseus, son of
old
/
Page 112 /
Aegus, lord of Athens was
numbered among those to be sent to Crete
-
but, writes
Apollodorus:
"some
affirm
he offered himself voluntarily. And as the ship
had a black sail, Aegeus (the father) charged his son, if he
returned alive, to spread white sails on the ship. And when
he came to Crete, Ariadne, daughter of Minos, having fallen
in love with him,offered to help him if he would agree to
carry her away to
Athens and have her to wife.
Theseus having agreed on oath to do so, she besought
Daedulus to disclose the way out of the
Labyrinth."
"Daedulus the Smith,
another great figure of legend, was a combination of artist,
craftsman and engineer whom Minos employed as a kind of
Master of the Kings Works."
"
says Apollodorus: "
"
At his suggestion she gave Theseus a clue [
thread] when he
went in. Theseus fastened it
to the door, and, drawing it after
him, entered in. And after
having found the Minotaur in last
part of the Labyrinth, he
killed him by smiting him with his
fists; and, drawing the clue
after him made his way out again.
And by night he arrived with
Ariadne and the children [pre-
sumably by this the writer
means the rest of the twelve Athenian
men and girls destined for
sacrifice]at Naxos. There Dionysus
fell in love with Ariadne
and carried her off; and having brought
her to Lemnos he enjoyed
her, and begot Thoas, Staphylus,
Oenopion and
Peparthus.
" In
his grief on account of Ariadne [continues the
poet]
Theseus forgot to spread the
white sails on his ship when he stood
for port; and Aegeus (his
father) seeing from the Acropolis the ship with a black
sail, supposed that Theseus had perished; so he cast himself
down and died
"
"But that was not the end of
the story. King Minos, when he learned of the connivance of
Daedalus in his daughters escape, imprisoned the guilty
engineer, with his son Icarus, in the Labyrinth. Then
followed the invention of the first flying machine, 3000
years before Leonardo da Vinci
Daedalus
constructed wings for himself and his son, and
en-
joined his son when he took
flight, neither to fly high, lest the
/
Page 113 /
glue should melt in the
sun and the wings should drop off, nor
to fly near the sea, lest
the pinions should be detached by the
damp. But the infatuated
Icarus, disregarding his father's in-
structions, soared ever
higher till, the glue melting, he fell into
the sea called after him
Icarian and
perished,"
'Daedalus',
'made no such mistake.'
'He flew, on
unscathed to the court of King Cocalus, in Sicily. But says
Apollo-dorus:'
"Minos pursued Daedalus and in every country he searched he
carried a spiral shell and promised to give great reward to
him who should pass a thread through the shell, believing
that by that means he should discover Daedalus."
"Having
come to Camicus in Sicily [ writes Apollodorus] to
the court of Cocalus, with whom Daedalus was concealed, he
showed the spiral shell. Cocalus (Lord of Sicily) took it,
and promised to thread it, and gave it to Daedalus."
"Such a challenge was irresistable to
Daedalus."
"He knew well that his
new Lord, Cocalus, was as incapable of working out
math-matically the curves and convolutions of the shell as
was Ariadne's handsome but stupid lover in memorizing the
twists and turns of the Labyrinth. So, just as he had
provided Theseus with the clue of thread which even he could
not mis-understand , so he provided the King of Sicily with
a method of threading the shell which was brilliant in its
simplicity."
"Cocalus took it , and
promised to thread it
and Daedalus
fastened a thread to an ant,
and, having bored a hole in the spiral
shell, allowed the ant, to
pass through it . But when Minos found
the thread passed through
the shell, he percieved that Daedalus
was with Cocalus, and at
once demanded his surrender.
Cocalus promised to
surrender him, and made an entertainment for
Minos."
Page114
"And then follows one of
the most mysterious records in the chronicle:"
"but after his bath Minos
was undone by the daughters of Cocalus"
At this point ZedAlizZed
removed a stone from out the who of the understanding
scribe.
On the way to coming
here they went there.
The Emerald
Tablet
For this reason I am
called
HERMES
TRISMEGISTUS
because I hold three
parts of the wisdom of the whole world
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