Part 1 | Part 2
Part 2: An Ancient Greek Computer
 An ancient astronomical calculator, built around the
end of the second century BC, was unexpectedly sophisticated, a
study in this week's Nature suggests. Mike G. Edmunds and
colleagues used imaging and high-resolution X-ray tomography to
study fragments of the Antikythera Mechanism, a bronze mechanical
analog computer thought to calculate astronomical positions. The
Greek device contains a complicated arrangement of at least 30
precision, hand-cut bronze gears housed inside a wooden case
covered in inscriptions. But the device is fragmented, so its
specific functions have remained controversial. The team were able
to reconstruct the gear function and double the number of
deciphered inscriptions on the computer's casing. The device, they
say, is technically more complex than any known device for at
least a millennium afterwards. The text is astronomical with many
numbers that could be related to planetary motions, and the gears
are a mechanical representation of a second century theory that
explained the irregularities of the Moon's motion across the sky
caused by its elliptical orbit. CONTACT Mike G. Edmunds (Cardiff
University, UK).
Read more here and
here
Source:
http://www.antikythera-mechanism.gr/
The recent discovery
....updated below is the latest discovery.....
12/27/06..... concerning this device. The Earth-Moon relationship
only uses 8 or 9 gears to show the relationship between Earth and
lunar orbits. After studying some of the other gear rotation
angles I chanced upon this very crucial discovery concerning the
planet Venus. The tropical year for Venus is 224.70069 Earth days
for one orbit.(Wikipedia) If you rotate this circumference 360
degrees along the Earth orbit number 365.246742 days
...Venus/Earth.... and multiply by the Sun Gear(64) you get the
value for m used in the article below:
Venus orbit / Earth orbit * Sun gear / ( 10^3 ) =
.0393700787 = m
224.6842679 / 365.246742 * 64 / ( 10 ^ 3 ) = .0393700787 = m
......the Venus orbit is m's source ??!!
Results 1 - 100 of about 1,170,000 for inches in one
meter. (0.17 seconds)
one meter = 39.3700787 inches
John Wilkins invents the meter
I'm continuing to read An Essay Towards a Real
Character and a Philosophical Language, the Right Reverend John
Wilkins' 1668 book that attempted to lay out a rational
universal language.
In skimming over it, I noticed that Wilkins'
language contained words for units of measure: "line", "inch",
"foot", "standard", "pearch", "furlong", "mile", "league", and
"degree". I thought oh, this was another example of a foolish
Englishman mistaking his own provincial notions for universals.
Wilkins' language has words for Judaism, Christianity, Islam;
everything else is under the category of paganism and false
gods, and I thought that the introduction of words for inches
and feet was another case like that one. But when I read the
details, I realized that Wilkins had been smarter than that.
Wilkins recognizes that what is needed is a truly
universal measurement standard. He discusses a number of ways of
doing this and rejects them. One of these is the idea of basing
the standard on the circumference of the earth, but he thinks
this is too difficult and inconvenient to be practical.
But he settles on a method that he says was
suggested by Christopher Wren, which is to base the length
standard on the time standard (as is done today) and let the
standard length be the length of a pendulum with a known period.
Pendulums are extremely reliable time standards, and their
period depends only their length and on the local effect of
gravity. Gravity varies only a very little bit over the surface
of the earth. So it was a reasonable thing to try.
Wilkins directed that a pendulum be set up with the
heaviest, densest possible spherical bob at the end of lightest,
most flexible possible cord, and the the length of the cord be
adjusted until the period of the pendulum was as close to one
second as possible. So far so good. But here is where I am
stumped. Wilkins did not simply take the standard length as the
length from the fulcrum to the center of the bob. Instead:
...which being done, there are given these two
Lengths, viz. of the String, and of the Radius of the Ball, to
which a third Proportional must be found out; which must be as
the length of the String from the point of Suspension to the
Centre of the Ball is to the Radius of the Ball, so must the
said Radius be to this third which being so found, let two
fifths of this third Proportional be set off from the Centre
downwards, and that will give the Measure desired.
Wilkins is saying, effectively: let d be the
distance from the point of suspension to the center of the bob,
and r be the radius of the bob, and let x by such that d/r =
r/x. Then d+(0.4)x is the standard unit of measurement.
Huh? Why 0.4? Why does r come into it? Why not just
use d? Huh?
These guys weren't stupid, and there must be
something going on here that I don't understand. Can any of the
physics experts out there help me figure out what is going on
here?
Anyway, the main point of this note is to point out
an extraordinary coincidence. Wilkins says that if you follow
his instructions above, the standard unit of measurement "will
prove to be . . . 39 Inches and a quarter". In other words,
almost exactly one meter.
I bet someone out there is thinking that this
explains the oddity of the 0.4 and the other stuff I don't
understand: Wilkins was adjusting his definition to make his
standard unit come out to exactly one meter, just as we do
today. (The modern meter is defined as the distance traveled by
light in 1/299,792,458 of a second. Why 299,792,458? Because
that's how long it happens to take light to travel one meter.)
But no, that isn't it. Remember, Wilkins is writing this in
1668. The meter wasn't invented for another 110 years.
Having defined the meter, which he called the
"Standard", Wilkins then went on to define smaller and larger
units, each differing from the standard by a factor that was a
power of 10. So when Wilkins puts words for "inch" and "foot"
into his universal language, he isn't putting in words for the
common inch and foot, but rather the units that are respectively
1/100 and 1/10 the size of the Standard. His "inch" is actually
a centimeter, and his "mile" is a kilometer, to within a
fraction of a percent.
Wilkins also defined units of volume and weight
measure. A cubic Standard was called a "bushel", and he had a
"quart" (1/100 bushel, approximately 10 liters) and a "pint"
(approximately one liter). For weight he defined the "hundred"
as the weight of a bushel of distilled rainwater; this almost
precisely the same as the original definition of the gram. A
"pound" is then 1/100 hundred, or about ten kilograms. I don't
understand why Wilkins' names are all off by a factor of ten;
you'd think he would have wanted to make the quart be a
millibushel, which would have been very close to a common quart,
and the pound be the weight of a cubic foot of water (about a
kilogram) instead of ten cubic feet of water (ten kilograms).
But I've read this section over several times, and I'm pretty
sure I didn't misunderstand.
Wilkins also based a decimal currency on his units
of volume: a "talent" of gold or silver was a cubic standard.
Talents were then divided by tens into hundreds, pounds, angels,
shillings, pennies, and farthings. A silver penny was therefore
10-5 cubic Standard of silver. Once again, his scale seems off.
A cubic Standard of silver weighs about 10.4 metric tonnes.
Wilkins' silver penny is about is nearly ten cubic centimeters
of metal, weighing 104 grams (about 3.5 troy ounces), and his
farthing is 10.4 grams. A gold penny is about 191 grams, or more
than six ounces of gold. For all its flaws, however, this is the
earliest proposal I am aware of for a fully decimal system of
weights and measures, predating the metric system, as I said, by
about 110 years.
Source:
http://blog.plover.com/physics/meter.html
More about calculator
....at the last website is the
complete schematic
breakdown of the device , shown in five gear colors , blue ,
yellow-sun gear , green , orange , purple and dark green. Thirty
gear numbers are shown , each having one of the above colors. The
key number constant used in all thirty gears is the modern metric to english conversion constant ...( 39.3700787 inches = 1 meter )...
rewritten to this form :
39.3700787 / ( 10 ^ 3 ) = m = 1/25.4
....all thirty gears are linked and can be turned all
at once by the rotation of any one gear in the system . I chose the
blue(50) gear as a starting point and turned this gear exactly
one-revolution or 360 degrees. The gematric formula for this angle
is the sacred number 72 , times one half the metric standard 254 (
254/2 = 127 ):
72 * 127 * m = 360 degrees
....this angle is transferred to the second blue(50)
gear because of its being self similar to the first blue(50) gear.
This angle is also transferred to the blue(32) gear because of a
shared axle. The next step is the blue(32) gear's link to gear ,
blue(127) .
This link is the famous sacred Alautun time cycle number
...2304...from Aztec and Mayan culture. Here is a link with the
explanation of the number:
http://www.mayadiscovery.com/ing/history/tiempo/tiempo2ing.swf
....this is very important to the explanation of the
Antikythera device because both the 1152 and 2304 units are Mayan
calendar constants measured in DAYS !! the same as the Antikythera
mechanism !!
20 calabtun = 1 kinchiltin = a cycle of 11520000000
days
20 kinchiltin = 1 alautun = a cycle of 23040000000 days
...so I would say that 1152 ( kinchiltin ) is a thing
of Mayan origin as is the 2304 (alautun ) number.
blue(127) = 2304 * m = 32 / 127 * 360 = 90.70866132
degrees
blue(24) = 2304 * m = 32 / 127 * 360 = 90.70866132 degrees
...that is when you turn the starter blue(50) gear 360
degrees, the blue(127) gear will turn 90.70866132 degrees. The
blue(24) gear shares an axle with the blue(127) gear and thus shares
the rotation of the blue(127) gear. Blue(24) gear then transfers
this rotation to the blue(48) gear . This angle of rotation is the
gematric number known as the Egyptian foot number ..1152...:
http://www.celticnz.co.nz/Clandonwebsitefiles/Clandon2a.htm
blue(38) = 1152 * m = 32/127*24/48*360 = 45.35433066
degrees
blue(48) = 1152 * m = 32/127*24/48*360 = 45.35433066 degrees
...blue(38) shares an axle with blue(48) and thus
transfers this angle of rotation to the so-called Sun gear...
yellow(64)..The number 19 appears here not as years of the Metonic
cycle but as DAYS!! on the edge of gear wheels:
Sun gear = 36 * 19 * m = 32/127*24/48*38/64*360 =
26.92913383 degrees
....all of the green gears share the same angle of
rotation as the Sun gear. The orange gears appear when the second
gear with 38 cogs appears as orange(38). It has the same angle of
rotation as the blue(38) gear:
orange(38) = 1152 * m = 32/127*24/48*360 = 45.3543306
degrees
orange(53) = 1152 * m = 32/127*24/48*360 = 45.3543306 degrees
...orange(53) shares an axle with orange(38) and thus
transfers this angle of rotation to orange(96)
orange(96) = 25 + m = 53*12 * m =
32/127*24/48*53/96*360 = 25.0393700787 degrees
...orange(15) and orange(27) gears share axles with
orange(96) and thus transfers angular rotation to the large gear
purple(223):
purple(223) = 53*12*27*m/223 = 36*m+360/223 =
32/127*24/48*53/96*27/223*360 degrees
..purple(53) edges with purple(223) thus picking up an
angular rotation of:
purple(53) = 54 * 6 * m = 32/127*24/48*27/96*360 =
12.7559055 degrees
purple(30) = 54 * 6 * m = 32/127*24/48*27/96*360 = 12.7559055
degrees
...purple(30) shares an axle with purple(53) and thus
the same rotation. Purple(30) edges with purple(54) resulting in an
angle turn of 7.086614166 degrees for purple(54):
purple(54) = 180 * m = 7.086614166 degrees
...three other gears share this angle of rotation and
thus the same axle, purple(20) , dk green(53) , dk green(15). dk
green(15) transfers the angle to gear dk green(60) and gear dk
green(12) which shares an axle with dk green(60):
dk green(60) = 180 / 4 * m =
32/127*24/48*15/96*15/60*360 = 1.771653542 degrees
dk green(12) = 180 / 4 * m = 32/127*24/48*15/96*15/60*360 =
1.771653542 degrees
...dk green(12) transfers the angle of rotation to the
last gear in the chain, dk green(60)
dk green(60) = 9 * m =
32/127*24/48*15/96*15/60*12/60*360 = .354330708 degrees
...showing the angles of rotation in spreadsheet form:
cl = clockwise, c
cl counterclockwise
GEAR GEMATRIA GEAR RATIO ROTATION ANGLE
blue(50) 72 * 127 * m 1 360 ccl
blue(50) 72 * 127 * m 1 360 cl
blue(32) 72 * 127 * m 1 360 cl
blue(127) 2304 * m 32/127*360 90.70866132 ccl
blue(24) 2304 * m 32/127*360 90.70855132 ccl
blue(48) 1152 * m 32/127*24/48*360 45.35433066 cl
blue(38) 1152 * m 32/127*24/48*360 45.35433066 cl
sun gear(64) 36 * 19 * m 32/127*24/48*38/64*360
26.92913383 cl
green(32) 36 * 19 * m 32/127*24/48*38/64*360
26.92913383 cl
green(32) 36 * 19 * m 32/127*24/48*38/64*360 26.92913383 ccl
green(50) 36 * 19 * m 32/127*24/48*38/64*360 26.92913383 ccl
green(50) 36 * 19 * m 32/127*24/48*38/64*360 26.92913383 cl
orange(38) 1152 * m 32/127*24/48*360 45.35433066 ccl
orange(53) 1152 * m 32/127*24/48*360 45.35433066 ccl
orange(96) 53*12 * m = 25+m 32/127*24/48*53/96*360 25.0393700787 cl
orange(15) 53*12 * m = 25+m 32/127*24/48*53/96*360 25.0393700787 cl
orange(27) 53*12 * m = 25+m 32/127*24/48*53/96*360 25.0393700787 cl
purple(223) 53*12*27*m/223
32/127*24/48*53/96*27/223*360 3.031672609 ccl
purple(53) 54 * 6 * m 32/127*24/48*27/96*360 12.7559055 cl
purple(30) 54 * 6 * m 32/127*24/48*27/96*360 12.7559055 cl
purple(54) 180 * m 32/127*24/48*27/96*30/54*360 7.086614166 ccl
purple(20) 180 * m 32/127*24/48*27/96*30/54*360 7.086614166 ccl
purple(60) 60 * m 32/127*24/48*27/96*30/54*20/60*360 2.362204722 cl
purple(15) 60 * m 32/127*24/48*27/96*30/54*20/60*360 2.362204722 cl
purple(60) 15 * m 32/127*24/48*27/96*30/54*20/60*15/60*360 .59055118
ccl
dk green(53) 180 * m 32/127*24/48*27/96*30/54*360
7.086614166 ccl
dk green(15) 180 * m 32/127*24/48*27/96*30/54*360 7.086614166 ccl
dk green(60) 180/4 * m 32/127*24/48*15/96*15/60*360 1.771653542 cl
dk green(12) 180/4 * m 32/127*24/48*15/96*15/60*360 1.771653542 cl
dk green(60) 9 * m 32/127*24/48*15/96*15/60*12/60*36 .354330708 ccl
...how does this data relate to the earth-moon
interaction? One can observe that the last gear in the chain of 360
degree rotation , blue(32)...if one makes this gear analogous to the
moon lunar cycle...29.530588 days in one orbit around earth , then
blue (32) and the lunar cycle share an axle that rotates 360
degrees. Transferring this 360 degree rotation of the lunar cycle to
the earth cycle around the sun...365.246743 days in one tropical
year , on this earth cycle axle , place the 5 sets of 47 (235)
markings of the exterior dials of the device on the earth axis of
rotation and multiply by the metric m :
29.530588 / 365.2467463 * 5 * 47 *m * 36 = 26.92913386
degrees = 19 * 36 * m = sun gear(64)
29.530588 / 365.2467463 * 235 / 254 = 26.92913386 degrees = 19 * 36
* m = sun gear(64)
...this is exactly the angle turned by the sun gear
when the blue(50) gear is rotated once!! Checking the number
constants I wanted to see if the number 37 is any where in the
angles of rotation or in the gear numbers. Strangely it sits at the
heart of the Earth/Moon link. When the lunar cycle 29.530588 days is
rotated once (360 degrees) on the Earth cycle .365.246743 days... an
angle of rotation is generated on the Earth cycle rim:
29.530588 / 365.246743 * 360 = degrees of rotation of
Earth orbit disc = 29.10638332
....37 derives this angle through the 47 markings on
the outside dials of the device:
(( 37 ^ 2 ) - 1 ) / 47 = 29.10638332 degrees
...which means the 37 form can generate the sun gear
angle for all of the green gears:
(( 37 ^ 2 ) - 1 ) / 47 * 235 / 254 = 26.92913386
degrees = 36 * 19 * m
Copyright © J.Iuliano
Presented with permission.
Related Links
|
