Requiem for Relativity

July 19, 2009 Liddington Castle, Badbury, crop circle encodes 2012 Venus transit

This crop circle signifies two transits of Venus with a transit of Mercury in between. There were/will be transits of Venus June 2004 & June 2012, and a transit of Mercury Nov. 2006. As at Stonehenge & Old Sarum this month, the groups of three solid disks, represent Mercury, Venus, & Earth. The lines from Venus & Earth, to the concentric disks at each end of the configuration, imply that the concentric disks, are transits of Venus as seen from Earth.

August 18, 2008, Hampshire, and Nov. 15, 2007, Wiltshire,
crop circles encode Nov. 13, 2012 total eclipse

Let's first consider the Aug. 18, 2008, crop circle. The distal half of the circumference of the righthand circle, is hollowed (in a stylized way); this represents the half of Luna's orbit farthest from the Sun, and implies that Luna's line of nodes is perpendicular to Earth's orbital radius, so that the hollowed part of Luna's orbit is the part which is below (or above) the ecliptic. The same stylized hollowing, occurs in both connections between the right- and lefthand circles. Each of these connections, together with its two dots, represents a pair of successive (total or partial) solar eclipses, occurring about half a year apart at opposite ends of Luna's line of nodes. This often happens, and happens consecutively; there is little unique about the two pairs Nov. 25, 2011 & May 20, 2012; and May 20, 2012 & Nov. 13, 2012.

The uniqueness is given by the one remaining feature, as shown on Andreas Mueller's diagram ( www.cropcirclescience.org ). This is the slightly off-midline dot at left. With a protractor, I measure this dot as 9.3deg above the midline, but correcting for the flattening, on my screen, judging by the large nearby circle (which is 49x56mm on my screen), I find 10.6deg. The first eclipse of the above-mentioned trio, Nov. 25, 2011, is unusual: it occurs (maximum eclipse) with Luna relatively far from the ecliptic, at ecliptic latitude -1.0575 (ascending node) according to the JPL ephemeris. Using the average inclination, 5.14deg, of Luna's orbit, this implies Luna is 11.8deg clockwise of the line of nodes (at maximum eclipse). This is the same as 11.8*27.32/29.53 = 10.9 "degrees" of the synodic month cycle, where I've used the ratio of the sidereal to the synodic month.

The above-mentioned 2007 crop circle is a simpler, more cryptic version of that in 2008. Here, the smaller disk, on the left, represents Earth; the inner circle around it, Luna's orbit; the inner connecting line, the line of nodes at eclipse season; the two small disks, a pair of eclipses half a year apart. The date of the 2007 crop circle, is exactly 365 days * 5, prior to the Nov. 13, 2012 eclipse.

Two more crop circles, and a Venus transit at Saturn

Months ago, I posted here, my analysis of the famous July 15, 2008 crop circle near Avebury, England, that showed the positions of the planets on or near Dec. 21, 2012. For review, my best effort found that using the longitudes I measured on the most often seen internet photo (with correction for oblique view, but making no assumptions about the orientation of the crop circle), the minimum total variance of these measured longitudes (more precisely, of their differences from Earth's), vs. ephemeris ecliptic longitudes, occurs at 02h UT, Dec. 22, 2012.

There is another crop circle, which shows a large disk representing the Sun, and three smaller disks in line with it; the farthest disk has a ring probably signifying Luna. However, there is no alignment like this (which, if perfect, would be a simultaneous transit of Mercury & Venus) of the three inner planets, within decades of 2012. Yet there is something which, in "projective geometry" or "complex analysis", is analogous to a straight line: namely, a circle.

Because of the positions of Mercury's & Venus' ascending nodes, Mercury's conjunction with Venus in Dec. 2012, brings Mercury especially near the circle in space defined by Earth, the Sun, and Venus. Mercury is closest (in the sense of a local minimum of the distance) to this (ever-changing) circle, at about 03h UT, Dec. 24, 2012.

Also on Dec. 21, 2012, is a transit of Venus visible from the center of Saturn (transits of Venus are about three times commoner at a point on Saturn than at a point on Earth, but it's still remarkable that Venus transits should occur in the same year for both Saturn and Earth). According to the JPL (Jet Propulsion Laboratory, or Jack Parsons Laboratory?) ephemeris' retarded positions as seen from the Sun, the centers of Saturn and Venus align with the edge of the Sun, at 11h35m UT Dec. 21, 2012. Using the mean orbital radii, the light times from the Sun to Venus & Saturn, are 6m & 79m, resp. Therefore at 11h29m, Venus was actually at its "retarded" position, and Saturn was actually 73m of travel, ahead of alignment. Venus' period is 1/50 of Saturn's, so approx. 73/50 = 1.5m later, at 11h30.5m, Venus' and Saturn's centers would align with the edge of the Sun (not apparently as seen from Saturn, but geometrically). The trailing edge of Saturn would align with the leading edge of Venus, and the edge of the Sun, at 11h25.5m, only 14m after Earth's winter solstice.

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New message May 26, 2010 (I'm placing it here because I get a "file full" message when I try to post it as an ordinary new message).

Evidence that the May 22, 2010 crop circle near Wilton, Wiltshire (England) codes for last new moon before winter solstice, 2012

This crop circle is a pie with twelve equal slices, naturally, the twelve synodic months = 29.53*12 = 354 1/3 days making about one year. Some suppose that crop circles like this are designed to tell us something any freshman calculus student learns, like Euler's formula or the first ten digits of pi. Would humans spend thousands or millions of dollars, to monumentalize freshman calculus for a few days in a crop circle? Would a nonhuman risk who-knows-what expense, danger, interplanetary combat or other horror, to deliver such a redundant message? We already know, that anyone or anything that can produce such an impressive crop circle, surely must include on their team, individuals who have learned freshman calculus and the like. They don't need to recite freshman calculus, to convince us that they are intelligent.

The circles bring news. The message is something we don't know, or that isn't yet widely known or believed. The circles are, literally, propaganda. They are just cryptic enough, to avoid mass hysteria, and to command the respect given to that which one must work to understand. Or maybe the circlemakers don't want to bother with, or can't intercept or interpret, our language, and figure that if we can't "get it", then "tough luck".

Andreas Mueller has, according to his website, a Diploma in Graphic-Design from the famous Academy for Fine Arts and Design in Saarbruecken, Germany. Surely someone with such rigorous training would orient his diagram of this crop circle, to exact geographic North (for some reason, I never see a "North" arrow on any photo or diagram of a crop circle!). What seems to be the most complete reproduction of Mueller's full diagram available on the internet, shows (like Mueller's usually shown "preliminary" diagram), after correction for its elliptical shape on my browser, that segment A1A2, which I believe represents the last of the twelve New Moons in 2012 (B1B2 represents the first New Moon in 2012) ends, moving clockwise, 10.0 +/- 0.5 deg clockwise of North. The bars in each sector seem to encode, inter alia, information about the ecliptic latitude of the New Moon relative that of Venus and the Sun. Therefore the New Moon likely is at the center of the sector, that is, 10-30/2 = 5deg counterclockwise, i.e. before, North, which implies that North is Dec. 13+5 = 18, 2012. On the other hand, Marie Asmer's diagram, also published on the internet, places the end of this sector at nearly the exact top, which implies that North is Dec. 13+15 = 28.

Somewhat as others have done, let's transcribe each sector as a sequence of 8 digits, base 4, with: nothing = 0, a halfbar in the counterclockise part = 1, a halfbar in the clockwise part = 2, and a full bar = 3. Starting with Mueller's B1B2 and moving clockwise to end at A1A2, and also starting at the outside of each sector, the base 4 numerical equivalents of the sectors are:

a) 22212102 (Asmer reads first digit 0, but Keller, Mueller say 2)
b) 02212112
c) 12212132
d) 32230102
e) 02203112
f) 12212132 (Keller reads last digit 3, but Mueller, Asmer say 2)
g) 12230122
h) 12001122
i) 32331122
j) 02023102
k) 30100312
l) 23313032

The matrix is highly nonrandom:

1. c=f
2. h & i are equal in their last 4 digits
3. the last digit is always 2
4. for a through g, the 3rd digit is always 2
5. the 2nd & 3rd digits are equal except for h, i, j, k
6. for the 1st & 5th digits, a string of 7 is shifted by one
7. the 2nd & 6th digits always add to 3

Only for two months, Nov. & Dec. 2012, do the 2nd & 6th digits not equal 2 & 1, resp. These two months are indeed special. November's New Moon is very near the ecliptic and ascending: there is a total solar eclipse. December's New Moon, still ascending in ecliptic latitude, is the only one of the twelve, which is farther North in ecliptic latitude, than Venus at the same time (the Dec. New Moon is just 0.9deg farther North, in ecliptic latitude, than Venus).

Summary: If the center of each sector represents a New Moon in 2012 (i.e. in the year preceding the winter solstice, 2012) then the diagrammatic "top" of the cropcircle corresponds to Dec. 23 +/- 5, 2012. Also, the 2nd, and, redundantly, the 6th, digits of the code, signify that the Nov. & Dec. New Moons are special. Indeed, these are the New Moons that (Nov.) eclipse the Sun at the ascending node, or (Dec.), still ascending, nearly match the latitude of Venus.

More on Crop Circles

A few are known hoaxes, or even open publicity stunts with no hoax component. Some are true extraterrestrial communications, warning us of the date, Dec. 2012; these use astronomical hints, because apparently they are one-way communications from some kind of "space brothers" who know nothing of our language. Many crop circles are, I think, government-issue disinformation intended to dilute and deflect the effect of the true circles; this includes most of the "geometric" and "mathematical" crop circles, as well as the shallow mathematical explanations for some of the true extraterrestrial crop circles.

The famous "pi" circle really has nothing to do with the digits of pi base 10. It shows conjunctions of Mercury near the ecliptic, alternating superior and inferior conjunctions, between the transit of Mercury in 2006, and the last conjunction of Mercury in late 2012. There are several hints in the circle, that this is what is shown. I'm recovering from H1N1 influenza, but hope in a few days to post the quantitative explanation I have.

The "pi" crop circle: June 1, 2008 near Banbury Castle, Oxfordshire

This crop circle is not intended to represent "pi" in decimal form. This crop circle depicts selected conjunctions of Mercury between the Nov. 2006 transit, and the last Mercury conjunction in 2012. It is an astronomical clock, whose hands point to late 2012.

The three disks at the top, of the usual internet photo of this crop circle, represent Earth, Venus, & Mercury. The lefthand side of the Earth disk is, relative to the center of the central Sun disk, no more than about a degree away from geographic North, assuming that the straight double tracks were made NS according to the Global Positioning System now on many farm tractors (and also according to the schematic of the circle, that I found online). I determined angles by measuring with a protractor, on a printout of an online photo, then correcting for perspective: both slant (flattening of circles) and nearness (varying scale, i.e. converging lines).

The arc from the lefthand side of Earth, to the notch at 6:00, is, as I measure, within about a half degree of 180deg. This arc, I think, signifies Mercury gaining 180deg on Earth, i.e. a time interval between conjunctions. It is a clue that the crop circle is about conjunctions of Mercury. Another arc, from the short line segment at Mercury, to the outermost notch (the notch near 7:00) also is within about a half degree, of 180deg.

By switching the beginnings, there arise two more arcs; these are the ones that are explicitly drawn. From the lefthand side of Earth, to the 7:00 notch, is 146deg; Mercury gains this much vs. Venus, in 58.6d on average, about the same time, 57.9d, as needed for Mercury to gain 180deg vs. Earth. The longer arc, from the short line segment at Mercury, to the 6:00 notch, measures 213deg. I don't fully know why that angle is important, but on average, Mercury gains this much on Venus, in 85.5 days. The six conjunctions of Mercury, which the inner notches of the crop circle seem to depict, are separated by five time intervals. Four of these time intervals, are multiples (4.08, 2.05, 6.05, 8.92) of this mysterious 85.5 day period.

The six inner notches are placed to emphasize their grouping and relationship with each other; they are not exactly where Earth is, at the time of the relevant conjunction of Mercury. None are far from Mercury's (ascending node = 48) line of nodes. So, all represent close conjunctions, i.e. conjunctions for which Mercury's ecliptic latitude is small. Between the transit of 2006, and the end of 2012, there are, according to the online JPL ephemeris, twelve Mercury conjunctions for which Mercury's geocentric ecliptic latitude, at the Greenwich midnight closest to the time of smallest Mercury-Earth-Sun angle, is less than or equal to 1.0deg in magnitude:

1. Nov. 9, 2006 0.12
2. May 3, 2007 0.67
3. Oct. 24, 2007 0.47
4. Apr. 16, 2008 0.40
5. Nov. 25, 2008 0.70
6. May 18, 2009 0.39
7. Nov. 6, 2009 0.47
8. Apr. 29, 2010 0.67
9. Oct. 17, 2010 0.09
10. June 13, 2011 0.50
11. May 27, 2012 0.08
12. Nov. 18, 2012 0.70

The number after the date, is the linear distance from Venus, to the Earth-Mercury line (precisely, using data for the Greenwich midnight closest to conjunction, it is the Earth-Venus distance in A.U., times the sine of the difference between the geocentric ecliptic longitudes of Mercury and Venus). Let's select the Mercury conjunctions which not only have Mercury's ecliptic latitude less than or equal to 1.0deg, but also have Venus less than 0.50 AU from the Earth-Mercury line:

1. Nov. 9, 2006 0.12
3. Oct. 24, 2007 0.47
4. Apr. 16, 2008 0.40
6. May 18, 2009 0.39
7. Nov. 6, 2009 0.47
9. Oct. 17, 2010 0.09
11. May 27, 2012 0.08

At #3, Venus is only three days away from the ecliptic, whereas at #7, Venus is 1.4deg from the ecliptic. If I keep #3 but discard #7, and exchange #11 for #12, I get:

1. Nov. 9, 2006 0.12
3. Oct. 24, 2007 0.47
4. Apr. 16, 2008 0.40
6. May 18, 2009 0.39
9. Oct. 17, 2010 0.09
12. Nov. 18, 2012 0.70

These are the conjunctions of Mercury shown schematically on the crop circle.

I carefully measured the position of the big dot near the last (i.e. innermost) conjunction (each of the six innermost steps in the spiraling line represents a conjunction). With correction for Earth's orbital eccentricity (Earth's variable orbital angular speed) the dot's position corresponds to Earth's, at Nov. 20, 2012 (or a similar date in other years).

2012 AD transit of Venus starts over Hawaii; 4328 BC summer solstice was inferior conjunction of Venus.

According to NASA's website, the "external ingress" at Honolulu, is 22:09:59 UT, and the "internal ingress" there is 22:27:38. (Due to parallax, the times vary several minutes, for the various locations on Earth.) What might be more important physically, is the "central ingress", i.e. the time when Venus' center crosses the Sun's limb. By interpolation, the time of "central ingress" would be, as seen from Honolulu, about 22:19 UT, June 6, with the Sun at altitude 88deg in Honolulu. Also by interpolation in the NASA table, the "central egress" seen from Honolulu, would be June 7, about 04:35:30 UT, with the Sun at altitude 7deg in Honolulu. The midpoint of the transit, as seen from Honolulu, would be June 7, 01:27 UT.

Hawaii's latitude is about the same as that of Olympus Mons on Mars, or the Great Red Spot on Jupiter. Hawaii is Earth's highest volcano, and Olympus Mons is Mars'. This 2012 transit of Venus, starts when Hawaii is near Earth's subsolar point.

The summer solstice in 2012 is June 20, 23:09 UT. The weight of my evidence is, that the original Giza-based Egyptian calendar, began at the summer solstice, 4328 BC. So, the time interval between the start of the Egyptian calendar, and the midpoint of the 2012 AD Venus transit as seen from Honolulu, is (2012+4328-1)*365.242187d - (13 + 22/24 - 18/1440)d = 6338.716 * 365.25636d = 10303.735 * 224.70069d, that is, 6338.716 Earth sidereal yr, or 10303.735 Venus sidereal yr. The solstice at 4328 BC occurs with Earth at about right angles to its perihelion, so Earth lags about 1/30 radian = 0.005 cycle, and the difference between Venus and Earth, at the summer solstice 4328 BC, really is only 0.735 - 0.716 - 0.005 = 0.014 cycle = 5deg. That is, the summer solstice of 4328 BC was, at least approximately, an inferior conjunction of Venus.