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  

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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-  

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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  

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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  

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"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  

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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

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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