SPIRA SOLARIS:
Form and
PhyllotaxisAssigned
to the main heading SPIRA
SOLARIS this January 2007 essay owes its
origins to a number of events and issues, but the subtitle
itself (Form and Phyllotaxis) arises from the neglected Solar
System researches of American
mathematician Benjamin Peirce (1809-1880). His investigations and
conclusions resurfaced in September 2006 after the elevation
of the asteroid Ceres and simultaneous demotion of the planet
Pluto to the status of "Dwarf Planets." Essentially,with
Pluto
thus demoted Neptune once more becomes the outermost planet, as Peirce
stipulated on
theoretical grounds over 150 years
ago. First
published in 1850
and later recorded by his friend Louis Agassiz (1807-1873) in the
latter's
famousEssay on
Classification (1857:131)
Peirce theorised that "there
can be
no
planet exterior to Neptune, but there may be one interior to Mercury."Revisiting
my
own attempts to come to terms with the fundamental
structure of the Solar System in the first three sections of Spira Solaris
Archytas-Mirabilis
similarities between the
two approaches now
suggested
that while I had
unknowingly followed Peirce by omitting Pluto and adding an
inter-Mercurial object, I had missed the point completely when it
came to the significance of Neptune. Not so Benjamin Peirce.
Nevertheless, although Agassiz
provided additional details in his Essay
on Classificationconcerning
the latter's
Solar
System research including "the
ratios of the laws
of phyllotaxis"
in this same astronomical context, Peirce's major conclusion was cast
aside despite its potential significance. Although not stated in
these precise terms, it was
nothing less than the perception that
The
Solar System is
Pheidian in Form1and
Phyllotactic2
in Nature
Just how
right (or wrong)was Benjamin Peirce
concerning
the phyllotactic aspect of the Solar
System? He was certainly
one of the leading scholars of his day, and there is little doubt that
he
was also an influential scientist in his own right, as
the
following
excerpts from his Scientific
Biblography
attest:
PEIRCE, BENJAMIN (b.
Salem,
Mass., 1809; d. Cambridge, Mass., 1880), mathematics, astronomy. Graduated from
Harvard (1829;
M.A.,1833), where he was a tutor (1831-33) and professor (1832-80). In
mathematics, he amended N.
Bowditch's translation of Laplace's Mécanique
céleste
(1829-39);
proved (1832) that there is no odd
perfect number with fewer than four prime factors; published popular
elementary textbooks; discussed possible systems of multiple algebras
in Linear
Associative Algebra ... and
set forth, in A
System of Analytic
Mechanics (1855), the
principles and methods of that science as
a branch of mathematical theory, developed from the idea of the
"potential." In astronomy, he studied comets; worked on revision of
planetary theory and was the first to compute the perturbing influence
of other planets on Neptune; and worked on the mathematics of the rings
of Saturn, deducing that they were fluid. From 1852 he worked with the
U.S. Coast Survey on longitude determination, ... became head of the
survey (1867-74) (and) superintended measurement of the arc of the
thirty-ninth parallel in order to join the Atlantic and Pacific systems
of triangulation. Influential in founding the Smithsonian Institution
and the National Academy of Sciences. (Concise
Dictionary of
Scientific Bibliography,
Charles Scribner, New York
1981:540)
For my
own part, I intend to show
in this title
essay that Benjamin Peirce's phyllotactic approach to the structure of
the Solar system was indeed correct, all
ramifications and consequences notwithstanding.In
short, the
long-delayed
legacy of Benjamin Peirce
and the policieslaid
out in his
closing remarks to the
members
of the American
Association for the Advancement of Science concerning the
founding of the Smithsonian
Institution, and not least of all, the honest, unhindered pursuit of
knowledge:
"Let us profit by the example of Smithson,
and, instructed by the wisdom of this
high-minded son of England, learn to confide in our own rulers. Let us
be aroused to an
earnest and harmonious effort to accomplish the plan proposed by our
President at
Albany, for the building up of an "institution for science,
supplementary to existing
institutions, to guide public action in reference to scientific
matters." With the details of the
plan and the arguments in its favor you are familiar. You know how
useful it would be as
a protection from the wasteful expenditure upon abortive attempts to
reverse the laws of
nature. You know how much it is required to sustain the purity and
independence of
science, even within its own proper domain. You know that in no age or
country was there
ever a more urgent call for a scientific society, in which scientific
influence should
predominate, where it should not be smothered by excess of patronage,
and whence it
should not be liable to banishment through any spirit or form of
ostracism. If American
genius is not fettered by the chains of necessity, and helplessly
exposed to the assaults
of envious mediocrity, but is generously nourished in the bosom of
liberty, it will joyfully
expand its free wings, and soar with the eagle to the conquest of the
skies."
Concluding remarks from "The
Address of
Professor Benjamin Peirce, President of the American
Association for
the Year 1853, on retiring from the duties of President"
THE
EXPONENTIAL PLANETARY FRAMEWORK: METHODOLOGY AND DATA
Bode's Flaw
Bode's "Law" - more correctly the Titius-Bode relationship - was an
ad hoc scheme for approximating mean planetary distances that was
originated by Johann Titius in 1866 and popularized by Johann Bode in
1871. The " law " later failed in the cases of the outermost
planets Neptune and Pluto, but it was flawed from the outset with
respect to distances of both MERCURY and EARTH, as Titius was perhaps
aware.
II
The Alternative Describes an alternative approach to the structure
of the Solar System
that employs logarithmic data, orbital velocity, synodic motion, and
mean
planetary periods in contrast to ad hoc methodology and the
use
of mean heliocentric distances alone. [ Previous version:
http://www.spirasolaris.ca/sbb4b.html
]
III
The Exponential
Order The constant of linearity for the resulting planetary
framework is the
ubiquitous constant Phi known since antiquity. Major
departures
from the theoretical norm are the ASTEROID BELT, NEPTUNE, and EARTH in
a resonant synodic position between VENUS and MARS. [ Previous version:
http://www.spirasolaris.ca/sbb4c.html
]
IVd2
Spira Solaris and
The Middle Ages Ostensively the translation of Aristotle's De
Caelo from medieval latin to French, Nicole Oresme's Le Livre
du
ciel et du monde [ ca.1375 CE] was more than a translation and a
commentary.
The numerous references in this work to the insights of the Arab
scholar
Ibn Rushd [Averroes,1128-1198 CE] lead back to Plato's Republic,
Archimedes, Pythagoras, and the Golden Section in
early
Alchemical contexts.
IVc
Spira Solaris, the
Fourth Planet and Fifth Element PROCLUS [ Commentary on the
Timaeus of Plato ]: "For through analogy the universe is
completely
rendered one, this having the power of making things that are divided
to be one, of congregating things that are multiplied, and connecting
things that are dissipated.
Hence theologists surveying the cause of these things in the Gods,
enclose
Venus with Mars, and surround them with Vulcanian bonds; the difference
which is in the world being connected through harmony and friendship.
All
this complication and connection likewise has Vulcan for its cause, who
through demiurgic bonds connects sameness with difference, harmony with
discord, and communion with contrariety."
V
Spira Solaris.The
Chaldean Oracles. Proclus, and Johannes Kepler Examines the
role played by the Chaldean Oracles in influencing the
Neoplatonist Proclus [410 - 485 CE] and the connection between the
latter, The Harmonies of the
World, and the Harmonic Law "conceived on the eighth day of the
third
month in the year 1618" by Johannes Kepler [1571-1630 CE].
VI
Spira Solaris and
the Universal Ouroboros Explores the historical antecedents
and the relationship between the Equiangular Period Spiral, the
Ouroboros, Alchemy, and the
Sun.
VII
Spira Solaris and
the
Three Parts of the Wisdom of the World The spiral
configuration
is found on rock art in regions as distant as Nicaragua, Italy,
Indonesia,
and the United States. It is also found on the Plains of Nazca in Peru,
on
Malta, in France, in Britain, and especially in Ireland, where a
complex
triple spiral is illuminated on the winter solstice inside the
Neolithic
Site at Newgrange. What is the significance of this complex motif, what
message
was it intended to convey, and where does the inquiry lead?
Did
the Greenland Vikings simply fade away, or was there more to their
story and more to the Viking Sagas in addition? It would seem that
there was far more. In fact sufficient evidence exists to suggest that
the last Vikings triumphed over the Northwest Passage and that the
legendary lands of the Viking Sagas
- Helluland, Markland and Vinland - are located on the West Coast
of North America, not the East. Helluland extending from
Etolin
Island in Alaska south past the Bella Coola region of British Columbia;
the Queen Charlotte Islands more than meeting the basic requirements
for Markland
with British
Columbia's Cowichan Valley at Duncan in the south-east corner of
Vancouver Island providing the
most logical technical fit for Vinland itself. But this is only part
of the story . . .
Curachmen "For nearly an
hour
the men stood waiting to launch the curach. It was blowing fresh from
the south-west, with hard squalls of wind and rain; and the breakers
came charging in, rank after rank, in unending succession. From time to
time the men would retreat before the biggest sea, afterwards shoving
their curach well out into the water again. It looked as if the
long-awaited deibhil, or
lull, would never come..." [ G. J. Marcus. The
Conquest of the North Atlantic, Oxford University Press,
New York 1981:3-4.] (PDF: 26 kb; also in HTML)
A MACKENZIE SOUND CARVING
MacKenzie Sound
"The rock carving in this photograph was found at a remote place on the
north end of Vancouver Island about 50 miles from Alert Bay by Stephen
Lablosky of 12320 Old Yale Road, Surrey. The figures are about 8 inches
high and 1/4" deep on the face of a large granite boulder. What
interests both he and I about this carving is that it can't be Indian,
nor is it feasible that a logger would have the skill to do such work.
Because of the religious symbolism and because of the skill necessary
to carve in granite, we tend to believe that early Hudson's Bay
explorers left it ... but for what reason?" [ C. Lillard, "Notes
and Queries,"The
Raincoast Chronicles FIRST FIVE, Numbers 2 and 4,
Edited by Howard White, 1976, 1994:91,193
]. (Single-page PDF:
167 kb; also in HTML)
FOR
THE RECORD: WI TE MANEWHA
For the Record
"A
spendid cast of the deeply carved face of Wi te Manewha was taken by
Lindauer and Sir Walter Buller. His moko was perfect, the lines cut
exceptionally deeply, even to the eyelids. It was said that the
tattooing was done twice to make deeper markings. The cast was made
during the lifetime of the chief. It
is of considerable ethnological value because it is the only known
instance of an old-time Maori permitting such a thing, since the head
was considered sacred."[ An extract from MAORI
PAINTINGS: Pictures from the Partridge Collection of Paintings by
Gottfried
Lindauer. Edited by J. C. Graham, A. H & A.W. Reed,
Wellington, 1956]. (HTML; also in PDF: 440 kb)
COAST
SALISH / SQUAMISH WELCOME FIGURE
Should you wander down an increasingly urban
pathway along the western
bank of
British
Columbia’s Capilano River – the natural boundary separating North
and West
Vancouver – you may come across a small inscription on a rock
by the wayside. Carved with care, it is clearly modern, inscription and
text alike. It says sadly and simply:
Strength
in your weeping,
Tears that
come seeping,
Down the old
canyons,
Back to the
sea.
From The
River by Jean Gowland
Passing under a bridge the path continues along the pavement of a road
that leads around a large Mall, where (now separated from the river by
a wire and split-board fence) the path curves south again into a small
wooded
area. Finally, one eventually reaches the rivermouth and
following the shoreline to the
west, a small bay bounded by a pair of rocky outcroppings. Augmented
and
strengthened, these too are modern, and often visited for they extend
outwards from the beach area of West Vancouver’s Ambleside
Park. At the
end of the largest outcropping, however, there is another recent
inscription, this time on a bronze bi-lingual plaque. But here the text
is accompanied by something else, namely a large wooden figure looking
out over the Inlet towards the southwest with both arms outstretched.
This is the Coast Salish “Welcome
Figure” erected by the Squamish First
Nation to commemorate the first “Gathering of Ocean Canoes” in
the summer of 2001. For this is their land; this is their will,
and this is their generous welcome.
GEORGE
WOODCOCK : PEOPLES OF THE COAST
A Witnessing "Yet it was in one way the most dramatic dance
of the whole night, for the drummers came down out of the bleachers to
join those on the floor and make an avenue of sound through which the
old dancer progressed, with hundreds of voices shouting out her song,
and her attendants scattering handfuls of coins among the drummers and
the singers. It was obviously a farewell, for we felt no doubt that
this was the old woman's last dance, and that she and everyone
else knew it. But it was also the kind of assertion of continuity, for
here was a person who had been a child in the last flourishing of the
old native culture, and by supporting her in her dance the rest of the
people were not only proclaiming their continuity with the past but
also celebrating the revival of the old ways." [A
Witnessing: The concluding chapter of George Woodcock's PEOPLES
OF THE COAST : The Indians
of the Pacific Northwest, Hurtig Publishers, Edmonton,
1977:209-214.] (HTML; also in
PDF: 56kb)
QUANTUM
ENTANGLEMENT : THE STARFISH TELEGRAPH
Quantum Entanglement:
"I hoisted the anchor and arrived at Barney's to find him collapsed
and hemorrhaging. I took him in my boat to the nearest settlement,
leaving the two starfish in a bucket of sea water in the shack. Barney
later died in the Prince Rupert hospital.When I got back to
Kettle Inlet, the starfish were dead. The water should have been
changed every twenty-four hours or oftener.The years have
passed and I've never related this story for fear that I might become a
candidate for the funny house. Quite recently I read an article similar
in regard to plants which gave me the courage to contribute my story at
this time." (C.H. Doane [ "The Starfish
Telegraph,"The
Raincoast Chronicles SIX/TEN, Number 10.
Edited by
Howard White, 1976, 1994:237 ]. Single-page PDF:
29 kb; also in HTML)
THE
TIMES AND TIDES OF JOHN DAVIS THE NAVIGATOR (1550-1605)
The Times and Tides
of John
Davis: Selections
from The Voyages and Works of John
Davis the Navigator (1880). [ PDF: One page Index (as below) ]
The
original 1880 publication of The
Voyages
and Works of John Davis the Navigator, more often than not
restricted
to
Special Collections and Rare Book Departments, etc., is currently
available on the Internet as a large, graphics-based GoogleDigital PDF file.
Because of its sheer size, however, the various topics
in this 515-page volume may still tend to overwhelm the
casual
reader, especially in this particular format. For this reason, selected
segments from the above are provided here in smaller, searchable PDF
files that retain the original
antiquated English texts, typesetting and
pagination. The choice of material, however, does
not center on the voyages of
John Davis per se, but on his
use of the
heliocentric concept and the impact of this understanding on the
development of
Elizabethan navigation in general. Thus, in addition to The Worlde’s
Hydrographical Discription (1595) and Seaman’s
Secrets (1594,1607) by John
Davis himself the
selection includes the “Note
on the New Map” of A. D.
1600 by Charles Henry Coote and an extensive Bibliographical
List of Works on Navigation during the Reign of Elizabeth
prepared by Albert Hastings Markham. Lastly, an additional supplement: Introduction,
Symbols and Abbreviations, and a Short Bibliography to Copernicus and
Kepler (1952) by Charles Glenn Wallis has also been included to
provide a necessary background for
the
opposing geocentric and heliocentric planetary theories of the
time. [
Sources: John Davis, Albert.Hastings Markham and
Charles
Henry Coote in The
Voyages and Works of John Davis, the Navigator,
The Hakluyt
Society, No. LIX, London, 1880.
Charles Glenn Wallis in Great Books
of the
Western
World 16, Editor-in-Chief Robert Maynard Hutchison, William
Benton, Chicago 1952:481–495. ]
RELATED MATERIAL: The World Encompassed by
Sir Francis Drake "Collected out of the Notes of Master Francis Fletcher, Preacher in this
employment, compared with divers others notes that went in the same
VOYAGE. Printed at London
for Nicholas Bourne, dwelling
at the
south entrance of the Royal Exchange, 1652." (PDF: 856 kb)
CHARLES
LILLARD : INTRODUCTION TO WARRIORS OF THE NORTH PACIFIC
" Now that there is no longer a western frontier, we are slowly
recognizing the American "melting pot" and the Canadian "mosaic" for
what they are, stewpan and collage. Also, we are learning our ancestors
rode roughshod over the land with little consideration for the future.
They took the land, built their towns and villages, and then, knowing
they had civilized a new world, died. What we are no longer sure of is
our own place in this new world of theirs. The question asked by
Margaret Atwood in Survival belongs
to all of us: "what do you do for a past if you are white, relatively
new to a continent, and rootless?" Personally, I doubt anyone
will answer Atwood's question satisfactorily. The wording is too
exquisitely subjective, every answer leads to a new question. A maze
this large and confusing suggests we no longer believe in the Noble
Pioneer, this creature has gone the way of the Noble Democrat and the
Noble Savage–older myths created by earlier North American historians.
If this is so, is it not possible that the history we have learned from
our text books, this history we call ours, may be ambiguous? [ Charles
Lillard: Introduction toWARRIORS OF THE NORTH PACIIFIC: Missionary
Accounts of the Northwest Coast, the Skeena and Stikine Rivers and the
Klondike, 1829–1900, Edited and Annotated by Charles Lillard,
Sono Nis Press, Victoria, B.C. 1984:10. PDF: 124 Kb;
also in HTML
]
Times Series Analysis.
The advent of modern computers permits the investigation of planetary
motion
on an unprecedented scale. It is now feasible to treat single events
sequentially and apply detailed time-series analyses to the results;
also in PDF.
TIME
SERIES GRAPHICS
Time Series Graphics
Examples of chaotic and resonant planetary relationships in the Solar
System and
a possible link with Solar Activity.
THE
TYRANT'S NUMBER
The
Tyrant and the Bride
The Number of the Tyrant is 9. What is the Number of the Bride?
Plato's Republic is an enduring and much admired work, but the problems
presented here have still confuted hundreds, if not thousands of
inquiring minds since Plato's time [427-347 BC]. So be forewarned, this
is not a simple
matter; nor is it a matter of simple arithmetic, either. Clues abound
everywhere, but watch for phantoms and misdirections nevertheless.
(HTML; also in PDF:
212 kb)
PYTHAGOREAN
FRAGMENTS
Pythagorean Fragments
Selections from the Doxographers, Fragments of Philolaus, Fragments
of
Archytas, Metaphysical and Political Fragments. (HTML; also in PDF: 204 kb)
"Time
is the moving image of Eternity,
Plato remarked among the Stars.
Eternity is the sudden wholeness of Time,
Apollo answers amid the Flowers."
The first
and concluding chapters from The
Origins of Alchemy in Graeco-Roman Egypt by Jack Lindsay,
Ebenezer Baylis and Son, Trinity Press, London 1970 ( PDF: 230 kb).
THE
STAR OF BETHLEHEM AND BABYLON
The
Star of Bethlehem and Babylon From a technical viewpoint the
detection of the faint but
unquestionably visible planet URANUS by Babylonian astronomers in 9 BC
provides one of
the more logical mechanistic explanations for the phenomenon. A
non-denominational discourse for open minds.
BABYLONIAN
MATHEMATICS AND
SEXAGESIMAL NOTATION
Babylonian Mathematics
and Sexagesimal Notation Base-60 has its advantages, e.g., the Maya
relationship of 81 synodic months = 2392 days results in a decimal
value of 29.5308..days for the mean synodic month. In Base-60 it is
exactly 29;31,51,6,40 days
(the modern estimate is 29;31,50,7,30 days).
BABYLONIAN
PLANETARY THEORY AND THE HELIOCENTRIC CONCEPT
Babylonian
Planetary Theory Babylonian Planetary and Luni-Solar Parameters,
Babylonian
Methodology and the Heliocentric Concept. Babylonian mean values for
all four types
of month are: 29;31,50,8,20 days (Mean Synodic month), 27;33,16,20 days
(Anomalistic month), 27;19,18 days (Mean Sidereal month) and
27;12,43,56 days (Draconic
month).
A year of 365.256469days (essentially the heliocentric motion of Earth)
is readily obtained from the Babylonian mean sidereal and mean synodic
months. The unexplained
trapezoid in two Babylonian astronomical cuneiform texts for
Jupiter from the Seleucid Era (310 B.C.-75 A.D.) Partial
analysis by Otto Neugebauer (Astronomical
Cuneiform Texts, 1955:405,430-31; single-page PDF, 34 kb)
PROJECTILES,
PARABOLAS AND
GALILEO'S FOURTH LAW OF PLANETARY MOTION
Velocity
Expansions of
the
Laws of Planetary Motion [HTML]
or PDF
(475 kb).
[ABSTRACT ( Journal of the Royal
Astronomical Society of Canada, Vol. 83, No. 3, pp. 207-218,
June 1989 ) ]
"Kepler's Third Law of planetary motion: T2
= R3 (T = period in years, R =
mean distance
in astronomical
units) may be extended to include the inverse of the mean speed Vi (in
units
of the inverse of the Earth's mean orbital speed) such that: R = Vi2
and T2 = R3
= Vi6.
The first relation
- found in Galileo's last major work, the Dialogues Concerning Two
New
Sciences (1638) - may also be restated and expanded to include
relative
speed Vr (in units of Earth's mean orbital speed k) and absolute speed
Va
= kVr... This paper explains the context of Galileo's velocity
expansions
of
the laws of planetary motion and applies these relationships to the
parameters
of the Solar System. A related "percussive origins" theory of planetary
formation is also discussed." May 20, 2011 Update: With
slight modification the latter percussive theory might also be applied
to the origins of recently discovered "rogue
planets" thought at present to be roaming the universe in
surprising large numbers.
Alchemy is a
subject of which we have all heard of, and which is yet a mystery. In
some ways
it belongs to the world of mystery stories from the past. We
remember perhaps the shade and wonderful light of Rembrandt's etching
of the Alchemist, or the stories we read in Chaucer or Ben Jonson. Was
the alchemist a philosopher, deep in a mysterious study
where he discovered the secrets of transmutation? Was he just a
charlatan involved in a particularly
fantastic kind of mumbo-jumbo? Was he simply a forerunner of the
scientists of today? Or had he an occult knowledge which we cannot hope
to acquire in
our materialistic environment?[
Introduction to The Arts of the Alchemists, C.A.
Burland, 1986-1; for more on the scope and complexity of this subject
see: Timeline of
Alchemical Books and Various Alchemical
Texts from the extensive collection of material available at the The Alchemy Web Site
]
THE MADNESS OF MANKIND
Chapter 19 "
You may have heard me called an atheist, but that's not quite true.
Atheism
is unprovable, so uninteresting... My field of interest is the
psychopathology known as Religion .... Lucretius hit it on the nail
when he said that
religion was the by-product of fear - a reaction to a mysterious and
often
hostile universe. For much of human prehistory, it may have been a
necessary
evil - but why was it so much more evil than necessary - and why did it
survive when it was no longer necessary? "[ condensed from Chapter 19:
"The
Madness of Mankind,"3001: The Final Odyssey by Sir Arthur C.
Clarke,
1997:136-142;
PDF: 27 kb ].
OCTOBER THE FIRST
IS TOO LATE
Grave e Mesto "
The time for departure came. We all agreed that delay would be bad. I
took one last look around. There was the electronic box, the thing I
had come to think of as a piano ... I had a strong urge to play on it
for one last time. I told the others, saying I would prefer to be
alone, that I would follow in a few minutes. Melea answered: ' Don't be
too long.
There isn't much time.' I began to play. I realized that only in music
could I find the answer I was seeking to the questions of the previous
evening.
Argument I could follow, it weighed with me, yet I could decide nothing
from it. I did not know exactly what the music was, it was an
improvisation
not so much on a musical theme as on the agony of the destiny of man. I
continued to play on and on, aware at last that I had made my
commitment. I was
playing the Schubert Andantino when Melea returned." [ The end of Chapter 14, October
the First is Too Late by Sir Fred Hoyle, 1968:158-172; PDF: 57 kb ]
JACQUETTA
HAWKES: SUN
OF INTELLECT
Man and the Sun
" In following the solar cycle of this book, I have honoured those who
worshipped the Sun God in his many forms. Yet I have also honoured
those
scientists whose probing minds have dispelled the simple divinity of
the
star. The members of the Holy Office were right to be fearful of the
ideas of Copernicus to see that they would lead to the destruction of
many of
the old religious forms. They were wrong as well as ridiculous trying
to turn back the tide of science, of man's efforts to comprehend the
physical universe, for that pursuit is a part of what is divine in
humanity. We
have to honour both the King of Heaven and Prometheus. The present
peril and
despair of humanity show that we cannot live without religious meaning
although we may do without religious institutions. (The time may come
when even
those few who still follow them turn against priests who in
gem-encrusted
copes and mitres, serve Him who taught poverty and humility, who betray
Him who taught love of one enemy by raising no murmur against a
holocaust
of hate.) If we cannot find god in the world, we lose Him in ourselves
and
become contemptible in our own eyes. We become mere statistics. For
this is
the greatest evil coming from the unbalanced Apollonian mind. Science
has
won power over the universe of matter by breaking down and down, by
numbering and measuring. So at last everything that cannot be broken
down,
numbered and measured must be deemed not to exist. Science is uniting
man with
the sun in a totality of energy and matter. That is communion at the
lowest
level of being. But we have always been right to seek it also at the
highest." [ Quotation
from the
concluding chapter of Man and the Sun
by Jacquetta Hawkes,
1962:239-241. Also in PDF ]
"For
over forty years Alexander Thorn, Emeritus Professor of Engineering
Science and Emeritus Fellow of
Brasenose College, Oxford, has surveyed and planned stone circles and
other prehistoric settings of standing
stones in Great Britain and Brittany. He was assisted by his son, Dr.
Archibald Stevenson Thorn not only in the
surveying but also in the preparation of many of the subsequently
published papers. His standards of planning
have been far higher than those of the average archaeologist and
certainly superior to most of the 19th
century
antiquarians whose plans of circles were often inaccurate and slipshod.
It has been the misfortune of those
interested in megalithic rings that often only such inexact plans have
been available. For a good plan three criteria apply. The survey itself
must have been precisely done, using adequate
equipment, measuring to several points around each stone at ground
level; an accurate scale must be provided
on the drawn plan; and True North must be shown, preferably towards the
top of the page. Alexander Thom's
plans fulfil all these conditions and they must be regarded as the
finest and largest collection of stone circle plans
ever assembled by an individual.Yet many of them have never been
published. Others have been so reduced that their value has been
diminished. Consequently, all his plans of British circles have been
gathered together here, nearly always one to
a page with an accompanying text opposite giving information about the
site. The only omissions, at Thom's
request, are the Callanish rings, recently surveyed by the Geography
Department of Glasgow University, and
Stenness of which a plan has been published in the Proceedings of the Society of
Antiquaries of Scotland 107,
1978.
The resulting collection of plans should be invaluable to anyone
wishing to study stone circles.
During his researches Professor Thorn concluded that the prehistoric
builders of these rings used an almost
universal unit of measurement, the Megalithic Yard of 2.72 ft or 0.83
metres; sometimes laid out non-circular
rings in flattened circles, ellipses, egg-shapes and compound figures
whose construction was based on the
understanding and use of right-angled triangles with integral sides;
and had an empirical knowledge of
astronomical phenomena. The plans usually include the geometry Thorn
has deduced for the sites, and the
accompanying notes contain Thom's conclusions about the lengths of the
diameters and sometimes the
astronomy, if any, for each ring.These
ideas remain contentious but this book is not concerned with the
controversy. None of it detracts from
the excellence of the plans, over 200 of them, which will be
indispensable for anyone researching the British
stone circles." [
Aubrey Burl, introduction to Megalithic
Rings: Plans and Data for 229 monuments, by A.
& A.S. Thom, collated, with archaeological notes by Aubrey Burl, BAR International Series 81,
Oxford, 1980.
].
Alexander Thom's statistical methodology (including Broadbent's
Criterion),
background materials, analyses and far-reaching
conclusions were published in Megalithic Sites in
Britain
(1967, 1971).
Details
from the latter work are provided below for
those who might wish to judge this complex matter for themselves: PART
1: Introduction,
Statistical, Mathematical and Astronomical Backgrounds, Megalithic
Yard, Conclusions.
(PDF,
6.4 Mb; smaller
Web-View PDF: 2.27
Mb).
PART
3: The
Calendar, Indications of
Lunar Declinations. (PDF, 3.7 Mb; smalller
Web-View PDF: 1.15 Mb)
PART
4: The
Outer Hebrides, A Variety of
Sites. (PDF, 5.6 Mb;
Smalller Web-View PDF: 1.94
Mb) APPENDIX: A Remarkable 4000 Year-Old Egyptian
Ship with hinged, portable A-frame mast and other sophisticated
features.
Single page Graphic
with text (PDF);
also in HTML.
SCHOLIUM:
NEWTON'S MATHEMATICAL PRINCIPALS OF NATURAL PHILOSOPHY
Scholium:
Newton's
closing paragraph " And now we might add something concerning a
certain most subtle spirit which pervades and lies hid in
all gross bodies; by the force and action of which spirit the particles
of bodies attract one
another at near distances, and cohere, if contiguous; and electric
bodies operate to greater distances, as well repelling as attracting
the
neighboring corpuscles; and light is emitted, reflected, refracted,
inflected, and heats bodies; and all sensation is excited, and the
members of animal
bodies move at the command of the will, namely, by the vibrations of
this spirit, mutually propagated along the solid filaments of the
nerves, from the
outward organs of sense to the brain, and from the brain into the
muscles. But these are things that cannot be explained in few words,
nor are we
furnished with that sufficiency of experiments which is required to an
accurate determination and demonstration of the laws by which this
electric and elastic spirit
operates." (also in PDF)
Why did
Sir Isaac Newton end his opus
magnum in this way?
A simple statement of faith? Or was it something more encompassing?
