Connect the Dots
Connect the main peripheral points of the image (Athena, a Stone-Age engraving from La Marche, France) by straight lines.
This boundary is the
'Frame' - the simplest whole category of data to inspect for hints of planned layout in the image.
We can look at this data both as geometric, (points set on a plane), or numerical (a set of numbers).
Beginner's luck
In 1985, at
the end of
computer Stone-Age, I was one of the 'primitives'. I had begun to explore the image still using the classic ruler and compasses. Soon, working with life-size
copies of the image showed me that I was far too heavy-handed for the finesse of the original artist. I had to step into the modern world, and get a
sheaf of 2:1 blow-ups from the nearby printers to better match my skills to the engraving.
It just so happens that at 2x life-size, the
engraving's units of length equal the metric system! Our
readout in millimeters matches the designer's intended values.
a Semantic Game - Important Quotes
The distances between points of the Frame in
millimeters give a set of thirteen whole
numbers, enough to show off advanced knowledge
of properties of numbers, Pi, Phi, Equinoctial
Precession (mathematics and astronomy), as well as ability to
produce brilliant logical puzzles..
Some of the quotations found within the Frame are very impressive:
Pi
= 3.1415926535897932384626433832 Twenty-eight decimals
Phi
=
1.6180339887..
Ten decimals
Equinoctial
Precession
- rates match today's
state-of-art measurements
Among the lesser lights of the Frame, the following approximation of Pi appears five times!
355 / 113 = 3.141592..
I propose that the
Frame is the best solution for the above stated purposes among similar
sets of numbers.
Earth specific
At
the same time, other planets with intelligent life in this
Universe have most likely other precessional specifics. This would make
the precessional aspects of the Frame irrelevant to them. Obviously, if
precession were still to be included, the Frame would have to be
somehow modified.
Could the obviously non random Frame be the result of blind chance?
That
depends on how many unique Frames of thirteen
whole
numbers there are in the range from 16 to 175, with
total length of somewhere between 1,100 and 1,350. Each
number can appear more than once, and the order matters, as well.
There are octillions of such sets (X,000,000,000,000,000,000,000,000,000, twenty-seven zeroes).
Therefore, if the Frame is intelligent, it is not by accident.
But, how does one know that the Frame cannot be surpassed?
My
above proposition cannot be proven or disproven by listing and
analyzing all the combinations for relevance to the
purpose. It is easy to write a program, which could do it,
but, just to list all the sets, a top super computer of AD 2012 going through twenty
quadrillion FLOPS per second would take thousands of years!
No,
the Frame cannot be eclipsed, because its authors had the first go at
it, and predictably, took away the best choices, beginning with
the number 113, and so on. To
drive home the point, if the Frame is not sheer genius, let
anyone make it better! To my best knowledge, any change will
incurr massive losses
of functionality..
The
Frame, the outside of the image, is a fitting introduction to its complex interior.
It helps to make the case that the
Stone-Age site of La Marche
had been tampered with heavily,
or even staged in its entirety, fourteen millenia ago.
Game Rules
The Frame scrambles into about 4,000 unique combinations of
segments, but breaks up into only 156 unique
pieces
(individual segments, and groups of contiguous segments), in addition, to something called 'the Strong
Connection'
between points B and G, which connects segments
across
the Frame, as if they were direct neighbours ( as if B and G were
connected through subspace ).
The search for intelligence is focused on sets of contiguous segments (game pieces). Like text, or speach flows, so does the Frame, generally clockwise. Sequences
of neighbouring segments make sense in the context with other game pieces, or within themselves. The rule is
that the game piece(s)
for the next move must be either a part of the presently used game piece, or
immediately adjacent to it.
Individual
segment values in sequences are seen as connected by any of
the manipulation signs (+, - , /, x), as long as it makes good sense. Composite numbers may be converted into factors, and millimeter values are also seen in whole centimeters.
The
Frame offers at least ten major games
- 360 degrees of order symbolizing Pi
- Quoting Pi
to twenty-eight decimals
- 360 degrees of order quoting Phi
to ten decimals
- The Strong
Connection (all combinations function)
Repeating Pi approximations to six
decimals
- Frame ordered by segment size (Zodiac, Osiris numbers)
- Frame ordered by unique segment size (Zodiac, Osiris numbers)
- Equinoctial
Precession value quotes on three levels of accuracy
- Cyclical fractions and the 'Wheel of 113' (the cycle
as a pie-chart of moduli)
The Frame also involves (beautiful) geometry:
- The Hex-machine (a grand design of three generations
of 6-pointed stars
- Two 5-pointed stars, same origin
There are other plays, which score a point on their own.
Let the Games begin
The Frame serves as the
doorway into the picture, but there must be something to draw us in, some
attention-getter, as good as a sign above a door handle.
Obvious & Simple Order: The
Section of Regular Proportions
The five segments spanning points between H to
M exhibit regular mutual proportions. The relative
distance
intervals are: 27-54-108-81-27, or 1-2-4-3-1. Such perfect proportions look deliberate, and open the door to further study.
The Frame lends itself to transformation into a
pie-chart.
Pi
as 3.14 - a direct readout
The first two segments could symbolize Pi, because in whole centimeters, 27 & 139 millimeters read out as 3 & 14.
And then we read out 16 as the number of millimeters in the segment on the right.
3 14 16
Pi rounded to four decimals
All three segments in whole centimeters give 3 14 2, Pi rounded in the fourth digit.
The Sweet 16
The 16 is of interest in part because
it gives the first two digits of Phi, the acclaimed Golden
Ratio, while having next door neighbors, which add up to 314, the first three digits of
Pi
139 + 175 = 314
16 18 Phi's first four digits
Use the same 'trick', and round the 175 millimeters to 18 centimeters. The two-segment section then reads 16 18,
the first four digits of Phi. Before this observation counts in full impact, however, I have to
remeasure the 175 segment, to make sure it is at least a
hair over 175 mms.
14 + 18 = 16 x 2 The average of
16's neighbors in whole centimeters would then be 16, the same digits.
16 x 2, or 162 gives Phi rounded to three
digits. By itself, this
would be just a curiosity, but the use
of factors of composite numbers to communicate a desired value is
very heavy in this sector of the Frame.
16 18 Phi's first four digits
The same three segments, all in whole centimeters, read:
If this three-segment section seems to posit the
subjects of Pi, Phi, and Composite Numbers, the rest of the Frame complements it perfectly!
The Frame without the three segments 139-16-175 (the Top Three in the pie-chart)
The Frame without the three segments 139-16-175 leaves a ten-segment section, which forms a regular pattern!
Clockwise, two sections of 340 (680)
precede twice 108 (216).
What
is the ratio between the groups?
Pi (3.14.....)
!!!
The entire section:
680/216
= 3.14...
The first three
digits are those of Pi.
Pi (3.14.....)
!!!
and within the section, the same ratio:
340/108
= 3.14...
A Composite Number:
The second 340 section (clockwise) comes right after the segment of
80. The total is 420, which as a composite number is also 3 x 140,
or 314 .
360 degrees of order
In the diagram below, the Frame without the pie-chart's Top Three, abuts on 139 on the left, and 175 on the right, which add up to 314.
Embedded
in 314 is 16 or, 314
&
16 We've
been here before, but now the three top segments serve to conclude
the Pi equations found in the remainder of the Frame. The
Frame is shown to make sense with regards to Pi on the whole,
as well as in parts! This by itself ought to be enough to convince
us that the Frame had been so planned. But the
wheel keeps turning..
Game:
Composite Numbers - the segment pair 175 & 113
two great plays:
To the right of 16, the segment duo 175 & 113 makes two great plays out of the same playbook, once Phi, once Pi:
175 +
113 = 288 = 16 x 18 Seen without the multiplication sign:
1618,
the
first four digits of Phi!
Although 288 breaks down into various multiples of
whole numbers, the 16 before 288 seems to indicate that if
we
look at 288 as a composite number, it should be in this
manner, with 16 leading.
Pi !!! Seen
as a composite number, 175 can represent 35 x 5. In digits
only, it is 355. Next to the 113 segment, it makes possible the following:
355
/ 113
=
3.141592..
Pi to six decimal places!!!
This is only one of five instances of this approximation here.
(The above relation had eluded me until December 21, 2011, a long time!)
Game: Quoting Pi to twenty-eight decimals
Opening Moves
We already know these opening moves. The
millimeter values 27 and 139 round to centimeters as
3 and 14. This
is symbolization of Pi by a two segment sequence. but
once we acknowledge, we cannot ignore the 16, which
is next to it : 3-14-16..
Pi rounded to four decimals.
Still using 16, subtract it from its right-side neighbor: - 16 + 175 gives 159. Replace 16 with 159.
We get: 3
14 159 - the first 6
digits of Pi.
The same result with just three of the four segments:
314
(175+139)
159
(175-16)
Pi (3.14159..)
!!!
Pi
= 3.1415926..
Pi to seven decimal places
3 14
159
(175-16)
260
(113+147)
314
(175+139)
159
(175-16)
260
(113+147)
The
two segments to the right of 175 add
up to 260
millimeters, or 26
centimeters.
Last, 175 by itself: Pi
= 3.1415926535..
To
get up to ten decimals, 535 would be it.
175
= 5 x 35 (535) Pi = 3.1415926535..
To recap, 175 so far worked with everything in the neighbourhood, in yielding thematic references (Pi and Phi) :
175 + 139 = 314
175 + 113 = 288 =
16 x 18 (1618, Phi in four digits)
175 - 113 = 62
0.62 is Phi-minor rounded to two decimals
175 - 16 = 159
follows the sequence after 3.14
175
= 35 x 5 (355) / 113 = Pi = 3.141592..
175
= 5 x 35 (535) follows the sequence after 3.14 159 26
In addition, 175&146
also counts as a legitimate pair, because the segments are in the best possible symmetry on
the Frame, what with gaps of 452 and 453
millimeters between them. This pair plays an important role later in this
chapter, On the other hand 175 / 108 = 1.620..,
Phi rounded to two
decimals, does not count for lack of a direct connection.
The number 175 is very busy!
The
section of six segments reading out all those key values is
shown in color in the pie-chart above. It covers just over
half the circuit (617 units).
Next, clockwise to this section is
80mms, or 8 cms.
Pi
=
3.14159265358..
Pi
= 3.14159265358979..
To
get up to fourteen decimals, 979 would be it.
After 8(0), the next nine segments
average seventy-nine
units each !
113 + 146 + 27 + 54 + 108 + 81 + 27 +139 + 16 = 711 = 9 x 79
Those are the three digits we
are looking for.
Time to note that in reading
the Pi-value out to fifteen digits, we have
covered more
than the
entire Frame, once again.
15
At this point, I had to go back to the web to look up some more Pi
decimals
:) To extend the Pi sequence by three more digits, we need a 323.
Is it not amazing that 711 factors as 9x79,
and 3x237,
and nothing else? We see here six digits of Pi in a row, 979 323, but unfortunately, the
seventh digit (7) is off by one. Luckily, there is a pure way
to get the digits (323). For that, and the rest of the Pi quotation there is
The Strong Connection
We've stopped on the segment of 16, at
the point B, where we've been before. This is where the Strong
Connection cuts acrosss
the Frame to G. Note, how in the image below, the B-G line travels through the
origin point of the purple square, actually the Square, one of two all-important elements in the geometry of the image. ( more on
the
Strong Connection)
The line itself also serves as the main axis of a certain key hexagon. Anyhow, the 16
& 175 on one side become directly connected to 113, and
146 on the other side, the latter two being part of the sequence 80, 113, 146 (total 339).
This sequence, named Tri-balance, is of great importance, and it is also part of the Strong connection.
Is it a coincidence that in
the pie-chart 16
balances perfectly over the 339
section?
The symmetry between the two is
the best possible (the intervening spaces are 435 on the right, and
436 on the left).
Likewise, the symmetry between 175 & 146 is the best possible (the intervening spaces are 453 on the right, and
452 on the left)
From here on, progress comes exclusively from the Strong Connection as (16 & 80 + 113 + 146), from relations between its segments, or from segments directly next to it.
339
- 16 = 323 !!!
Pi
=
3.14159265358979323....
!!!
(339+16 also plays a role)
After this, the Pi digits are 8 462 6433.. Of course, there is 8(0), another sought after digit, as part of
the section of 339.
Pi
= 3.141592653589793238....
!!!
The 339 section was used above to give 323 by having 16 deducted from it. Then a part of the Strong Connection, the Tri-balance (339) was used, 8(0).
Now, still using the Strong Connection, the three segments between 16 and 339, plus one segment clockwise from 339 total 462 (435 + 27).
Pi
= 3.141592653589793238462..!!!
Next digits are 6433 To get these digits, we use the 80 part of the Tri-balance (339) twice:
a) to subtract 16 from it
80 - 16 = 64
b) to subtract it from 113 on its left. The difference is 33
113 - 80 = 33
Pi
= 3.1415926535897932384626433
The end of this wonderful Pi sequence (832) goes back to its very beginning.
The Strong Connection begins with 16. What
is to the left of it? - The two-segment section with which it all began: 27 & 139 (3 & 14 in whole centimeters).
27 + 139 = 166 = 83 x 2 (832)
Factorisation works again.
Pi
= 3.1415926535897932384626433832
Pi given to twenty-nine significant digits! This sequence is a Stone-Age mark to beat!
I suspect, the quote finally hits
the wall here, because it is back to its very beginning.
(1-11-12: Since I broke my right elbow on X-mas Day, while skating, with extra time on
my (left) hand, I could do a bit of editing on this
chapter. The last three days saw me add ten digits to the sequence, with one arm tied up! :)
Around
the Frame in Phi
As to Phi, we are at Phi as 1618.. The last Frame part
we used was 113 in
175 + 113 = 288 = 16 x 18 = four digits of Phi in a row = 1618
In effect, it's five-in-a-row, because the next Significant Digit is a zero. Using 1,618 is equivalent to using :
Phi to five significant digits
113
& Phi
Does 113 have anything to do with Phi?
Phi
= 1.6180 339 887..
where we find 113 in
339
= 113 x 3 and
887 = 1000 - 113
Judging by the above, the answer is a conditional yes.
Moreover, two Frame distances are 113s.
The Frame
less twice 113 equals 1,000
units even.
1.618
034
Phi rounded to six decimals
First,
C to F is 340, and D to G is 340 again.
Obviously there is some emphasis on 340, here. Is it
because Phi rounded to six decimals is
1.618 034
?
g
Phi!
1.6180339..
There is no
way to express a zero all by itself (1.618
0 3), but, we could replace the 8
with 80. We see this value in the very next sequence of three
segments 80_113_146.
It is 80 being first in a short
sequence totalling 339, the Tri-balance.. This sequence works for multiple purposes.
h
Phi!
1.61 80 339 887.. (Phi in ten decimals)
What is left of the Frame after
we remove the Tri-balance (339) from it? Not 887?
Indeed, the Frame
(1226) divides into sections of 339 and 887.
Once more, the game does the entire
circuit of the Frame. That chalks up another point for it.
Visual
Confirmation!
There is an obvious inner
divide in the image - the line subtending
both the 339 and 887 sections. From H to E,
the image has a point on this line eight consecutive times out of nine
possible, and the miss is by only a little bit. The
subtended section of 339 is like a yellow parasol, on which B-G is the shaft :)
Follow
the Perfect Arrow
Look
at the shaft of the umbrella, it is a perfect arrow striking through the
bull's eye
- as the B and G points
connect across the image by a line through the red
crosshairs in the center of the image - the center of the Square, and the
engraving's
geometrical system. The shaft divides the 120 degree
angle FGH into two 60 degree angles - the arrow is symmetrical. It could be a component of a
hexagon (a regular geometrical figure).
The pivotal 0,0 point in the
center of the system creates an equilateral
triangle with the points E, F, and G, as shown below.
Nice result, the head rests on the triangle's basis, and
is about equidistant to
the other bases.
This
triangle
simply begs experimental completion into a hexagon centering in the 0,0
point, the center of the Square.
Result: the
hexagon's lines fit the image really well. This is clearly evident, just follow the lines.
Note: this hexagon is constructed from two other
hexagons! For this grometrical beauty see: The Frame - Game 9 - The
HexMachine |
