Requiem for Relativity

July 28 crop circle (Jubilee Copse, near Hannington, Wiltshire) confirms Oct. 8 +/- 7 date

This crop circle contains a 12x12 grid; the crop in 65 of the squares in unflattened, and 79 are flattened. This indicates 144/2 = 72 +/- 7 days. July 28 + 72 days, is October 8.


July 22 crop circle (Aldbourne, Oxfordshire) confirms Oct. 8 date

This is a square inscribed in a circle, but altered so one side of the square is short. If each side of the square should have been 365.25/4 days, then as I measure the slanted aerial photo on the screen, the short side is 77.26d. July 22 + 77d = October 7. The three dots draw attention to the "moving" end of the short side: they signify past, present, and, the biggest, fanciest dot, the future.

Correcting for Earth's eccentric orbit using the trapezoidal rule for integration, a more exact time for the short quadrant, which if complete would have ended about Oct. 7 + (91.31 - 77.26), is

77.26d * (1 + 2/60 * (cos(16+14) - sin(16))/2) = 78.02d

which gives July 22 + 78d = October 8.


June 12 (reported) crop circle (Silbury Hill, near Avebury, Wiltshire) confirms Oct. 8 date

This small formation was discovered June 12, but may well have been formed a day or two earlier. It shows a "sun" with five Earth / full moon alignments in a regular pentagon. There is a "3rd quarter" moon (geocentric) at 11h GMT on June 11, and another at 08h GMT on Oct. 8. This suggests that these circlemakers had some familiarity with our calendar and clocks. Be that as it may, the interval for formation of the crop circle, June 11 (?), to Oct. 8, thus covers five "3rd quarter" moons exactly.

Werewolves of London again?

Even before I made this second post about crop circles, a Boston banker who reads this messageboard, emailed me that he thought it might be a signal to co-conspirators in a rigged stock market crash. The circles I discuss here, not only indicate Oct. 8, they refer to the number of days in a week, dates of the month and hours of the day; if extraterrestrials knew about those details of our language, they wouldn't need to be cryptic.

This conspiracy would have to be London-based with inside men in the RAF. October is the month most associated with big stock market drops, and Monday (e.g. Oct. is the day of the week most associated with them. The crop circles might be made at night by aircraft emitting microwave beams.

Jubilee Copse July 28 crop circle confirms October 8 date

This 12x12 checkerboard crop circle has 12 words of 12 "bits" of information each. We know which are the rows and which the columns, and which end begins the word, because the first "bit" of each word is a broader rectangle. These broader rectangles are found along one side of the checkerboard, the righthand side as the circle usually is shown on the computer monitor.

Each row is thus read from right to left, and is a twelve-digit binary representation of a real number between 0 and 1. The rounding error cannot exceed 1 part in 2^13 = 8192. This corresponds to 1.07 hour if the unit is a year, or 0.044deg if the unit is a circle.

The seventh row (number) is the easiest to interpret. This number, multiplied by the 365.24219 days of the current tropical year, gives 291.498 days. The latest winter solstice was Dec. 22, 2011, at 05:30 GMT. Adding that many days, gives Oct. 8, 2012, 17:27 GMT.

Seven and eleven are the largest prime numbers < 12. This might be a hint that the 11th row (number) is akin to the 7th, and indeed they are nearly equal. However, the 11th number does not seem to correspond to the great circle arc swept by the sun between 05:30 GMT Dec. 22, 2011 and Oct. 8, 2012. Instead, it seems to correspond to the distance traveled by the sun in space (relative to the Earth) as a fraction of the distance covered in one sidereal year.

My first-order approximate calculation gives an end date Oct. 8, 2012, 15:48 GMT. Because the rounding error from these 12-digit binary numbers can correspond to more than an hour, this and the previous date are consistent with each other, up to rounding. In my approximation, I found the arc from the JPL ephemeris apparent RA & Declination, which refer to the equinox and ecliptic of date, then subtracted the precession. I then approximated the Earth-sun radius variation, with perihelion at 11deg longitude, as proportional to the negative cosine of (longitude minus 11deg), and integrated the tangential motion, neglecting the radial motion.

My second-order calculation uses eccentricity 0.016723 (from data in the 1987 CRC Handbook of Chemistry & Physics) and a perihelion at sun longitude 13.56+270 = 283.56, which is the mean of the apparent geocentric sun longitudes, at the perihelion times given to the nearest hour by the USNO for 2011 & 2012. I retained all terms of second order in the eccentricity, and found that the 11th number corresponds to the fraction of distance traveled to 16:41 GMT Oct. 8, less than half as far from the other value, as the first-order calculation was.

The 12th number, seems to correspond to the change in Luna's right ascension, between Luna's crossing the ecliptic Oct. 4, and "the event", Oct. 8. This number is a fraction of 180deg, not 360deg; this halves the rounding error. The difference between ascending and descending nodes is arbitrary; one or the other always will lie within 180deg. Because of the thirteen times greater angular speed of Luna vs. the sun, and the halving of the unit interval, this number could give the time of "the event" to within two minutes, instead of an hour. The time given by this twelfth number is Oct. 8, 2012, 17:23, differing only four minutes from the time implied by the seventh number. Maybe this is luck; or maybe even the circlemakers don't know the time to within minutes, but decided to make the twelfth time close to the seventh, rounding error and all, to impress us with their skill and with the importance of the message.

The numerology of the June 12 Silbury Hill crop circle (see previous post) suggests that the circlemakers know about the hours of our day and the days of our month. On the other hand, the numerological relation could have been mere luck, or Dr. Jung's "synchronicity" (an organizing principle perhaps above the circlemakers). Logically, the June 12 crop circle message stands, even without the numerological extras.

Today, August 2, I find that the 8th of the base-2 numbers in the crop formation, again assuming that the unit is 360degrees, equals the difference in right ascension (apparent; equinox of date, per JPL Horizons) between Luna's center and Mars, at 16:51 GMT on Oct. 8.

Assuming they signify fractions of a 180deg arc, the 1st & 2nd numbers differ by 1741". The geocentric angular diameter of Luna at its apogee Oct. 5, is 1769". Also, the mean of the 1st & 2nd numbers, is the reciprocal of 2.71888, close to the base of natural logarithms, 2.71828... .

At 2012.8AD, according to the 1990 Astronomical Almanac, p. B18, Earth's mean obliquity is 23.43763deg. According to Simon et al, Astronomy & Astrophysics 1994, Luna's orbital inclination then, to the ecliptic of date, is 5.15668deg. So Luna's maximum declination would be 28.5943deg. The 3rd number, assuming it is a fraction of a 360deg arc, is 28.652deg.

Another Jubilee Copse binary number decoded

For the angle between Mars and Venus on Oct. 8, the light-time correction happens to be small, only 4". The 5th binary number in the Jubilee Copse crop formation, if it represents a fraction of 180deg, would represent 84.7265deg. The JPL ephemeris gives this as the difference in ecliptic longitude (apparent, using ecliptic of date) between Mars and Venus, at 19:42 GMT, Oct. 8.

More natural, would be to project Mars' position onto the great circle tangent to Venus' sky path (tangent at, say, 17:23 GMT) rather than Earth's ecliptic. The 5th number (times 180deg) equals this difference in "longitude", at 18:22 GMT.

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The August 2 crop formation at Chalk Pit, near Wootton Rivers, Wiltshire, is an Archimedes spiral of approx. six turns. This crop formation would have been made at almost exactly the time of the full moon, 03:27 GMT. Two full moons in the future, would have been Sept. 30.

The arclength of an Archimedes spiral is given exactly by an elementary integral (CRC tables #156). The ratio of the length of six turns, to the length of one turn, is 33.5441. What if the mean synodic month, 29.5306 d, were replaced by this number of days? We would have Aug. 2 + 2*33.5441 = Oct. 8.

August 1 crop circle (Avebury Stone Circle, Wiltshire) gives Oct. 12 date; July 31 (Windmill Hill, Wiltshire) gives Oct. 8; July 29 (Andechs Abbey, Bavaria) gives Oct. 9 (8?)

This formation shows 13 disks trailing Jupiter, 7 trailing Venus and 6 trailing some other planet. By interpolating in the JPL ephemeris (which gives positions apparent at the Sun) I found that this crop circle indicates, by one method of analysis, the time T = 19:04 GMT, Oct. 12, 2012.

A planet's "synodic period" is defined as the time for recurrence of the same Earth-Sun-Planet angle. I approximate this angle by its projection onto Earth's ecliptic of date. Thirteen synodic Jupiter periods after the above specific time T, Jupiter's longitude, corrected to a fixed equinox, has changed the same amount, as has Venus' longitude after seven synodic Venus periods. That is, Earth's longitude is the same after 13 synodic Jupiter periods as after 7 synodic Venus periods.

The angle by which both the Jupiter's and Venus' and Earth's longitudes change, is 70.939deg. This is close to the 69deg angle given by Jocelyn Cazes on her diagram, which is posted on the website

cropcircleconnector.com

Addendum #1, Aug. 7: If I choose T = Nov. 17, approximately, then the change in Earth's longitude after six synodic Mars cycles, equals that after seven synodic Venus cycles, except for sign. So, the smallest planet depicted in the crop formation, might represent Mars. Venus was placed between Mars and Jupiter, to hint that it is the planet involved in both comparisons.

Addendum #2, Aug. 7: The July 31, Windmill Hill, Wiltshire crop circle, shows five binary numbers of eight digits each, which I list from the inside to the outside of the spiral:

01010000 = 80
01000101 = 69
01000001 = 65
01000011 = 67
01000101 = 69

The first "0" of flattened crop, is to enhance the legibility of the second (first meaningful) digit, always a "1". The only number which appears twice, is 69 and

July 31 + 69 = Oct. 8

The full moon is Aug. 2, so 67 might be the count from then to Oct. 8, a backup in case the formation was not discovered the day it was made.

The following times of that month also are noteworthy:

max speed of Luna toward Earth: July 19, 17:27 GMT
max " away from " : Aug. 4, 16:00 GMT

If Luna's orbit were not perturbed by the sun, that is, if Luna's orbit were a perfect ellipse, these times would be for the latera recta, 90 deg from the perigee and apogee, as measured from Earth's center. The former time is 81 d (not 80 d) before Oct. 8; the latter time is 65 d before Oct. 8. The fastest speed of the Earth-Luna barycenter toward the sun, occurs Oct. 5, 23:39.

Addendum #3, Aug. 8: The Andechs Abbey, Bavaria crop formation is listed as discovered July 29, but always there is the possibility that it was formed slightly earlier, maybe before midnight July 28, or even before dawn July 28 and not noticed. July 28 + 72 = Oct. 8. This formation consists of 12 nested tetrahedrons. Some faces of the tetrahedrons are missing, to allow the nesting. This suggests that the meaning is in the number of edges (6) not the number of faces (4). The bold lines on the intact faces, also suggest attention to the edges. Twelve tetrahedrons times six edges per tetrahedron = 72.

Have you ever noticed that when two objects that have the property of mass approach each other the space between them shrinks? Could it really be that simple? Does space condense in the presence of mass?

I'd procrastinate, but I can't seem to find the time

August 13, 2005 crop circle, Woolstone Hill, near Uffington, Oxfordshire, indicates Oct. 7 or 8, 2012

I'll explain this one according to the train of thought, that the circlemakers seem to want us to have. The most emphasized number in this crop formation, is six (which can be seen either as flat, or as faces of stacked cubes).

The next most emphasized number, is sixteen (the number of small squares forming the large perimeter square). There is a subtle ambiguity, though: 16, or 15? Each of the small squares contains a spiral-like sequence of monotonically lengthening tiny rectangles. The longest tiny rectangle is on a side of the small square, which rotates 90 degrees from one square to the adjacent square, except for one step, where it does not rotate (the next rotation is 180 deg to compensate). So, there are 16 small squares, but these rotate only 15 times.

This ambiguity, "15 or 16?", parallels the ambiguity, "sidereal or synodic month?". For the length of the mean sidereal month, I use polynomial 3.4.a.1 of Simon et al, Astronomy & Astrophysics 282:663 (1994) p. 669; it gives 27.3216616 d during the entire interval Aug 2005 - Oct 2012. For the mean synodic month, I modify the mean sidereal month according to a sidereal year of 365.25636 d, getting 29.5305889 d. The ratio of synodic to sidereal month is

16/15 * 1.0133 = 16/15 * (1 + 1/75)

so the "15 or 16?" ambiguity hints that the circle deals with both sidereal and synodic months.

There is another kind of month often used by astronomers, especially ancient astronomers predicting eclipses: the draconic month, averaging 27.21222085 d during the interval. Also, there is the anomalistic month, averaging 27.5545498 d.

Since the 16 and the 6 in the crop formation are qualitatively different in design, we are supposed to multiply them as factors, rather than add them as we would objects of the same kind.

16*6 = 96 draconic months
= 2612.373 d
= Aug 13.0, 2005 + 2612.373 d
= Oct 7.373, 2012

Repeating the above calculation with sidereal months, gives

Oct 17.880

With anomalistic months, it gives

Nov 9.237

and repeating it with synodic months, but using 15 instead of 16, gives

Nov 21.753

What about the fine radial segments, called "feathers" by many who study this crop formation? Of the innermost group of feathers, I count blocks of 11, 11, 11, 10, 10, 10. Of the outermost group of feathers, I count 18, 18, 18, 19. Of the middle group of feathers, I count 11, 11, 11, 11.

The average value of blocks of the innermost group of feathers, is 10.5. For the time estimate based on the sidereal months, I have

Oct 17.880 - 10.5 = Oct 7.380

perfectly agreeing with the time based on the draconic month. The total number of feathers in the middle group is 44. Thus based on the synodic month, I have

Nov 21.753 - 44 = Oct 8.753

and finally for the anomalistic month, using half the total number of feathers in the inner group, 63/2 = 31.5, I have

Nov 9.237 - 31.5 = Oct 8.737

The four results agree almost perfectly in pairs:

Oct 8.737, 8.753, and 7.380, 7.373