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Krag
6 Posts |
 Posted - 08 Oct 2012 : 10:02:38
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Well, today's the big day. Expect some harsh questions tomorrow Dr. Keller if nothing happens. :)
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Jim
1751 Posts |
Posted - 08 Oct 2012 : 16:05:54
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| The story Dr Joe is relating is based on models he follows very well. The predictions flowing from the story also are based on models. Don't blame the story teller for using only models for research. |
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Joe Keller
USA
930 Posts |
Posted - 09 Oct 2012 : 18:47:35
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Thanks for your comments, Krag and Jim, both of you.
Absolutely nothing happened on Oct 8 as far as I know! But I'm not letting down my guard completely.
It might be, that the "Oct 8" readings of the crop circles were mere accidents, but I still think it likelier that many or most of the crop circles were designed to signify that date. If so, then most likely, the circlemakers simply failed to get the date right. Maybe they knew it was only a guess, and decided to err on the side of a date that was too early rather than a date that was too late. Those who prepare for a date that is too early, still will have most of their preparations available if the true date of catastrophe is a few days or weeks later.
I had managed to send a three-page executive summary of my reasons for alarm about Oct. 8, to about half of my Harvard classmates who had put writeups in our 35th reunion book; about 300 got the summaries. The only response was from one astronomy major whom I knew well. He took me seriously and discussed it with some people he knew, but wasn't quite sure what to make of it all.
I had built a crude shelter in a corner of the hayfield on the other side of my driveway: it's more than a mere trench but not by much - it's less elaborate than the typical old-fashioned farmstead tornado shelter; it most closely resembles an old-fashioned root cellar. My landlord, who also owns the hayfield, gave me an ultimatum to obliterate my shelter or else he'd evict me. So far I'm stalling him. I called the U. S. Dept. of Homeland Security today, and the receptionist agreed to email me the phone number of the highest ranking Homeland Security official that she could. I plan to call him and ask him to arrange an executive order allowing tenants to build "tornado shelters" despite the landlord's objection. By analogy: if an intruder attacked the tenant with a knife, wouldn't the tenant have a right to shoot a bullethole into the wall if necessary to defend himself? A tornado shelter, or the equivalent, also is a form of self-defense.
I think that the inventors of the Mayan calendar chose Dec. 21, not because it was their best estimate of the date of catastrophe, but because the choice of a solstice or equinox would command respect from everyone, by proving their competence as astronomers. We only can infer from the Mayan calendar, that the inventors of that calendar thought the catastrophe would be closer to this winter's solstice than to either of the equinoxes. Otherwise they would have made it end at an equinox. It's 90 days from Sept. 22 to Dec. 21; Dec. 21 minus 45 days = Nov. 6. So maybe something will happen after Nov. 6.
Anyway, that nothing happened Oct. 8, certainly decreases the chance that anything will happen. But I'd say there still is a significant chance that something will happen. |
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shando
Canada
90 Posts |
Posted - 10 Oct 2012 : 09:16:51
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Regardless of the outcome, I have enjoyed your derivations Dr. Joe. At least you are trying to make sense of these mysterious appearances. Bravo & thank you.
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Krag
6 Posts |
Posted - 10 Oct 2012 : 12:46:01
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Thanks for the update. Good luck on your stormshelter fight!
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Joe Keller
USA
930 Posts |
Posted - 11 Oct 2012 : 13:17:47
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Thanks for your support!
There are at least two indications from crop formations, that the true date is tomorrow, Oct 12.
First, it recently was reported on Linda Howe's earthfiles.com, that sometime in the first week of September, a typical crop formation (large, complex, well laid out, stems bent aboveground) was found near the Hopewell mounds in Ohio. Howe displays excellent aerial photos, one of which is almost perfectly overhead. The Hopewell site is somewhat analogous to Stonehenge: possibly built to honor crop circles of long ago. The formation has 43 circles, but 7 of these are conspicuously hollow, not filled in. If the formation were made Sep. 2, then Sep. 2 + (43-7) = Oct. 8. The 7 hollow circles might signify extra days to give a range Oct. 8 - 15, as if the circlemakers do not know the date exactly. The very last meaningful crop formation of this season in England, which I discuss in an earlier post, also suggests this range, because according to my interpretation, it showcases a timeline between Oct. 8 and Oct. 15 (which I recognized as the new moon).
Second, from cropcircleconnector.com, I learn of a crop formation at Cheesefoot Head (1), near Winchester, Hampshire, reported Aug. 9. Despite the many distracting interpretations offered, this is the most obvious illustration of the number 64 that it is possible to make. The "fancy work" of the formation merely serves the purpose of the fancy work on printed money: redundancy and authentication. Aug. 9 + 64 = Oct. 12. This formation hardly could have gone undiscovered even one day, because it is near a paved highway and also a very populated area (county fair?) as appears on aerial photos. |
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Jim
1751 Posts |
Posted - 13 Oct 2012 : 14:50:18
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| Dr Joe, I still think the problem is within the model. Why not research the model and find out why so many false conclusions are generated? You can keep moving stuff around and get new dates I guess and why not? Everyone does it. |
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Joe Keller
USA
930 Posts |
Posted - 16 Oct 2012 : 15:44:21
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Oct. 3, Oct. 8, Oct. 18 and Dec. 21: alternative "first days of winter"
quote:
Originally posted by Jim
...Why not research the model and find out why so many false conclusions are generated? ...
Thanks for the post Jim; it inspired me to try harder to do this. A famous fragmentary inscription of Seti I, discussed in mainstream archaeology journals, ominously mentions "the first day of winter" as "the beginning of eternity" of "Year One". What is "the first day of winter"?
First alternative for "first day of winter". Our tradition is, that the first day of winter is the winter solstice, which is Dec. 21 this year, the end date of the approximately 5125 yr Mayan calendar cycle.
Second alternative. The longstanding ancient Egyptian calendar had a 365-day year (no leap year) divided into twelve 30-day months plus 5 extra days at the end. These twelve months were divided into three, not four, seasons: summer, winter and spring. My own research (building on the work of Prof. Eduard Meyer) suggests that originally, the ancient Egyptian year began at the summer solstice. So, our "first day of winter" this year, if we were ancient Egyptians shipwrecked on Gilligan's Island without our records, and starting fresh, would be June 20 + 120 days = Oct 18.
Third alternative. Suppose instead that we were ancient Egyptians and had not lost our records, and were not starting fresh. We likely would know that our calendar had begun 6339 years ago (my best estimate discussed on this messageboard for several years now, building on the work of Prof. Meyer) and that the seasons had been redefined several times in addition to several other irregularities in the calendar over the centuries. Therefore we might define the "first day of winter" as a whole number of 365-day years, after the winter solstice of 6339 years ago:
As in previous posts, I'll adopt Clemence's 1946 version of Newcomb's cumulative precession, together with (see last term) Van Flandern's correction:
50.23819"*T + 0.0001108"*T^2 + 0.00000000017"*T^3 + 0.0136"*T
which gives a precession of 87.323deg from 4327BC to 2013AD.
According to the JPL ephemeris, the J2000 heliocentric ecliptic longitude of the Earth-Luna barycenter will be 89.8133 & 102.8474 at the Dec 2012 solstice & Jan 2013 perihelion, resp.; the eccentricity determined from the peri- and aphelia that year, is 0.016685, implying that Earth lags about 0.438 days at the solstice, due to noncircularity of Earth's orbit. Because the JPL ephemeris doesn't go back earlier than 3000BC, I had to make reasonable extrapolations from the JPL values, to find Earth's eccentricity for 4327BC as 0.018986 and perihelion 83.2293. For a solstice then at 89.813+87.323 = 177.136, Earth would be ahead in its orbit about 2.202 d. The time for a circularized orbit between the 4327BC and 2012AD solstices is 76.47 d modulo 365 d. So the 365 day count date from the 4327BC winter solstice, would be
Dec 21.467 - (76.47 + 2.202 + 0.438) = Oct 3.36
Fourth alternative. Let's apply day lengthening to the third alternative. The Oct 3 date becomes 17:23 GMT Oct 8 (my best estimate from crop formations) with a day *shortening* (!) of 6.3 ms/cyr. This is not impossible, in view of the USNO chart showing a fairly steady change in day length of -2ms (yes, minus!) from 1973 to 2011AD (see http://tycho.usno.navy.mil/leapsec.html ).
*** Thus perhaps the crop formations have been encoding, simply the date and time this year that is a whole number of 365-day Egyptian years, after the winter solstice of 6339 years ago.
*********
The crop formations also seem to be referring to the Oct 18 date (i.e. 120 days after the summer solstice; what I call the "second alternative" above). Oct 18-10 = Oct 8. At least one recent crop formation, which I discuss above, on this thread, refers to Oct 12. Another, made Oct 14, which I have not yet discussed, seems to encode simply the number one, and hence refers to Oct 15. Oct 12-8 = 4; Oct 15-12 = 3. So the formations might be referring to Oct 8+4+3+2+1 = Oct 18. |
Edited by - Joe Keller on 24 Oct 2012 13:41:59 |
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Jim
1751 Posts |
Posted - 21 Oct 2012 : 20:20:34
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| Dr Joe, You got the best model in the world at JPL for generating orbital details. I am hoping you will look at the basic idea at JPL about the barycenter. It seems to me in the real world the barycenter moves in a much different way than the generator indicates it does. The generator has the barycenter orbiting the sun in strict accordance with Kepler. But, in the real world that would mean the moon pushes the Earth toward the sun at full moon and away from the sun at new moon. Makes no sense-right? Anyway, this is just a few meters or so and it averages out to zero over the whole orbit of the moon from nm to nm or whatever. But, for very fine detail like you do it makes a mess of it. |
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Joe Keller
USA
930 Posts |
Posted - 10 Nov 2012 : 18:28:52
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Circlemakers offering statistical information?
The normal distribution occurs in physics as, for example, the Gaussian wave packet and as complementary gaussian Heisenberg uncertainty curves. It's likely that the circlemakers are able only to give such a normal distribution for the expected time of the catastrophic event.
Following the "CRC Handbook of Tables for Probability & Statistics", 2nd ed., p. 125, the "standardized random [normal] variable" is
1/sqrt(2*pi) * exp(-x^2/2)
The circlemakers likely would prefer this variable for the same reasons that human mathematicians do, and would presume that humans prefer it.
Interpolating linearly in the above tables, I find that the half-maximum occurs at x = 1.1776. Another salient abscissa is 0.7832; this is the abscissa at which x = F(x), i.e. the area under the curve to the left of x, equals the area of a rectangle orthogonal the coordinate axes, whose corners include the origin and (x,1).
The ratio of these two abscissae is 1.1776/0.7832 = 1.5036. Of all the crop formations, the most unequivocal and compelling presentation of a number, is the "64" chessboard formation of Aug. 9 in Hampshire, which I discuss in a previous post; 64/1.5036 = 42.565. The Ohio formation, variously reported as early or mid September, has 43 circles, 7*6 = 42 around a small central one, suggesting 42 and a fraction. These two formations together, 64, and 43 (or 42 and a fraction), suggest the ratio 1.5, and hint that 64 days is the half-maximum of the normal curve for the predicted time of catastrophe.
The last formation of this year, on cropcircleconnector.com, was in Wiltshire on Oct. 14. Its layout suggests that Oct. 14 is 3 "standard deviations" or similar measures, before the peak of the probability distribution, i.e. the maximum likelihood. If it refers to the 42 day interval, then Oct. 14 + 3*42 = Feb. 17, 2013, is the date of maximum likelihood. The half-maximum likelihood is reached Feb. 17 - 64 = Dec. 15, 2012. Three "half-maximum likelihood half-width" intervals before this February peak, would be Feb. 17 - 3*64 = Aug. 9, the date of the "chessboard". Also, Oct. 14 - 42 = Sep. 2, is a plausible date for the Ohio formation.
The much emphasized Oct. 8 date, is the date on which the number of days before the maximum likelihood, equals the reciprocal of the cumulative probability. Oct. 8 is 132 days before Feb. 17, i.e. 132/64 * 1.1776 = 2.4288 standard deviation units before it; the cumulative probability left of this point is 1/132.025, according to the "tail-end z-table", online at
users.ece.gatech.edu/~hughes/ece4000/Ztable.pdf.
For any number of days, N > 2, before the maximum, there will be a value of the standard deviation, which makes the cumulative probability on that day equal to 1/N, but if, as here, the half maximum must be exactly an integer, the equation becomes Diophantine with only a few approximate solutions such as Oct. 8.
Comment and summary. The circlemakers aren't trying to confuse us. They don't know the date of the catastrophe, but do know the normal probability distribution for it: the peak likelihood is Feb. 17, 2013, and the standard deviation is 64/1.1776 = 54.35 days (about two sidereal, or better, draconic, months). The half-width, half-maximum of the curve, has been indicated by the "chessboard" in Hampshire, to be what we are to assume is exactly 64 days; the chessboard formation appeared Aug. 9, 64*3 days before Feb. 17. There is another simple measure of the spread of a normal distribution, which is almost exactly 1/1.5 times the half-width half-maximum; this "x = F(x)" spread would be about 42.6 days, and indeed is indicated by the Oct. 14 formation in Wiltshire, which indicates three units of 42 days, to either side of Feb. 17. The September formation in Ohio indicates 42 plus a fraction and may well have appeared 42 days before the Oct. 14 Wiltshire formation.
Oct. 8 comes exceptionally close to satisfying a Diophantine equation: the area under the tail to the left of Oct. 8, i.e. -132.0 days, given that the half-width, half-maximum is 64.0 days, is almost exactly 1/132.0. No one, especially a preprogrammed computer that has traveled for thousands of years to get here, could do much better than this, to tell us the mean date and the width of a normal distribution, without knowing our language. Also, as I mention in previous posts, redundancy and a slight puzzle-like quality are defenses against interference and disinformation.
The mathematics is all from high school or from introductory college courses. The circlemakers are making it about as simple as it can be made. Don't be misled by fanciful religious or hyperspecialized mathematical explanations.
Why are no good maps of the crop circles available? Online, it's rare to see anyone attempt to measure angles, and because they don't show their work, even those are hardly reliable. Only one researcher, a German, routinely puts a "North" arrow on his diagrams. Aerial views of crop circles never are from high altitude, never indicate the height or direction of the view, nor the time of day nor which way is north: so, angles never can be found exactly. Yet crop circle investigators occasionally remark on the presence of Royal Air Force craft over the circles on the morning they appear. So, the government has precise, professional-quality maps of these crop circles but never shares those maps with the public. |
Edited by - Joe Keller on 11 Nov 2012 15:29:15 |
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Joe Keller
USA
930 Posts |
Posted - 12 Nov 2012 : 12:47:05
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Why the half-width half-maximum uncertainty of doomsday is 64 days
The time of an event involving one electron, has Heisenberg standard deviation uncertainty dt = 1 / omega = hbar / (m * c^2) where m is the electron mass, and the famous relations of Heisenberg, Planck, and Einstein have been used. If Earth participates in an event, as if it were completely decomposed into electrons or positrons, M/m of them, the time uncertainty would be dT = sqrt(M/m) * dt where M is Earth's mass. A neutron can decompose into an electron and a proton, so although baryons are composed of quarks, maybe ultimately quarks can behave as if they decompose into electron masses. Using the 1987 CRC Handbook "consistent values" M = 5.9763*10^27 gram, m = 0.9109534/10^27 gram, hbar = 1.0545887/10^27 erg-sec, c = 2.99792458*10^10 cm/sec, I find
dT = 38.1856 days
Let's further speculate that not only actual leptons (electrons & positrons) but also an equal number of equivalent subspace "holes" participate. Also, let's assume that the associated mass-energy of the electric fields of the (maximally compressed) leptons and holes, does not participate. This introduces correction factors
sqrt(2) * (1 + 1/137.036) = 1.4245336 --> T = 54.3967 days
The half-width half-maximum is T * 1.1776 = 64.058 days, almost exactly equal to the whole number given by the Aug. 9 crop formation in Hampshire. |
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Joe Keller
USA
930 Posts |
Posted - 13 Nov 2012 : 20:59:25
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Famous 1990 crop formation trio, indicates Dec 15 - Feb 17 - Apr 22 Full Width Half Maximum
The earliest crop formations shown in Lucy Pringle's gallery, at
lucypringle.co.uk
are the three in 1990. These are the famous "Zeppelin" rock music album cover formation of July 11 in Wiltshire, another less famous and slightly simpler formation also July 11 in Wiltshire, and another formation, simpler than either of the others, July 13 in Hampshire.
In comparing these, it's best to turn Pringle's photo of the "Zeppelin" formation, upside down. The top three disks of that formation now signify Mercury, Venus & Earth; Earth has the three-pronged fork for third planet, and is connected to a "bull's eye" with a line plus two extra bars for emphasis. The other formation of that day, is the same but omits Mercury, Venus and the three-pronged fork; also Earth is below the bull's eye instead of above it as in the Zeppelin formation.
In the bottom parts of both July 11 formations, Venus is denoted by a two-pronged fork. The big bull's eye with either a three-pronged fork or a three-pronged comb, and a small stump opposite that, is Earth again. The stump is the Sun's geocentric ecliptic longitude, and the fork is Earth's heliocentric ecliptic longitude. The two-pronged fork on the connected Venus disk, gives the heliocentric ecliptic longitude of Venus, relative to Earth's, in about Dec. 2012 (Zeppelin formation) or Apr 2013 (other July 11 formation).
The "other" July 11 formation, has a small disk at the bottom, connected by a line to the Earth disk; the junction with this line signifies the longitude of Lunar apogee. In the Zeppelin formation, a line through the small disk and an even smaller one nearby, serves this purpose.
The July 13 formation has four bars, not two. This means that the two July 11 formations signify the half-maxima. When I overcome the difficulty of finding angles exactly from these photos taken from unknown distance, azimuth, altitude, and aim point, then I'll be able to test this theory, and give exact dates. |
Edited by - Joe Keller on 14 Nov 2012 15:45:25 |
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Joe Keller
USA
930 Posts |
Posted - 14 Nov 2012 : 16:04:30
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Why Algieba was chosen
In previous posts I show that the latitude of Teotihuacan is such that Algieba would have precisely reached the zenith there, at its opposition in early 2013, if the small pole shift deduced by Petrie from the Giza layout, had not occurred. According to Sky Catalog 2000.0 and the NASA Lambda coordinate utility, the J2000 ecliptic longitude of Algieba (neglecting aberration) at 2013.0AD is 149.6161. According to the JPL ephemeris, the Sun reaches this longitude plus 180 deg, i.e. opposition to Algieba, slightly before 03h GMT Feb. 18, measuring the Sun's longitude using *the ecliptic of date*. Correction to J2000 coordinates, changes this time to a little after 07h GMT Feb. 18. So, the opposition of Algieba occurs only a day after the maximum catastrophe probability, according to my interpretation of the crop circles. |
Edited by - Joe Keller on 14 Nov 2012 16:11:00 |
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Joe Keller
USA
930 Posts |
Posted - 17 Nov 2012 : 17:02:57
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quote:
Originally posted by Joe Keller
Famous 1990 crop formation trio, indicates Dec 15 - Feb 17 - Apr 22 Full Width Half Maximum ...
Contrary to my guess in the above Nov. 13, 2012, message, the two July 11, 1990 crop formations indicate the fall 2012 and spring 2013 equinoxes. I drew the cardinal points of the ellipses (circles distorted by the angle of the photo) by eye, and made a lowest order correction for the oblique view, by stretching the ellipses into circles mathematically by a "homothetic transformation". For example, if the major axis is at theta = 10 deg, a point on the ellipse is at theta = 30 deg, and the axis ratio of the ellipse is 0.8:1, the true angle is estimated as 10 + arctan (tan(30-10)*1/0.8) = 34.5deg. Because the axis ratios were never extreme, the corrections were never more than a few degrees. Because the individual crop circle disks are much smaller than the altitude from which the photos were taken (that is, almost all the error is from oblique view, not the finite distance) this correction should remove almost all the error.
For the "Earth" disks, I drew a line through the base of the "flag" and the base of the "stump" on the opposite side of the ellipse. For the Venus disks, I drew the line through the base of the flag and the center of the ellipse. For Luna, I drew a line through the two small circles near the Earth disk; the smaller of the two small circles seems to have been cut off of Pringle's photo (or maybe there was none).
The JPL ephemeris gives these longitudes:
fall equinox 2012, Sep 22 14:49 GMT
Earth (heliocentric J2000) 359.82
Venus (heliocentric J2000) 68.18
Luna (geocentric, equinox of date) 267.36
spring equinox 2013, Mar 20 11:02 GMT
Earth (heliocentric J2000) 179.81
Venus (heliocentric J2000) 354.88
Luna (geocentric, equinox of date) 97.97
For comparison, the crop formations indicate positions relative to Earth, equivalent to
fall equinox 2012
Venus (heliocentric J2000) 65.9
Luna (geocentric, equinox of date) 274.3
spring equinox 2012
Venus (heliocentric J2000) 358.1
Luna (geocentric, equinox of date) unknown; part of formation missing in photo
Thus the Luna position is off by only 7 deg (half a day's motion) and the two Venus positions off by only 2 or 3 deg (3 to 5 days' motion). What is being bracketed, is not the Feb. 17 date, but rather the winter solstice, bracketed by the two equinoxes depicted by the July 11, 1990 formations. |
Edited by - Joe Keller on 17 Nov 2012 17:14:31 |
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Joe Keller
USA
930 Posts |
Posted - 19 Nov 2012 : 18:25:22
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Related prime numbers: a circlemakers' trademark
The July 11, 1990 date for the two crop formations indicating the 2012 autumnal & 2013 vernal equinoxes, might have been chosen because of the following special relation which serves as a trademark of their authenticity:
x^2 / y - y^2 / x = approximate integer, where x & y are prime
July 11, 1990, is 8108 days before the 2012 autumnal equinox (Sep 22) and 8287 days before the 2013 vernal equinox (Mar 20). 8287 is prime and 8108 is almost prime: 8108 = 4 * 2027, and 2027 is prime. Using the prime number 2027 instead of the nonprime 8108, we find
8287^2 / 2027 - 2027^2 / 8287 = 33,384.00295 |
Edited by - Joe Keller on 19 Nov 2012 18:29:52 |
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Joe Keller
USA
930 Posts |
Posted - 10 Dec 2012 : 16:11:31
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Here's my rewritten post about the Australian crop circle discovered Nov 23, 2012
This rewrite is extensive, and because it was delayed, I had deleted the original version, something I rarely do. Also, this is my rewrite of the version I lost in an internet connection glitch, which caused me briefly to have to post a summary.
I again used the most orthogonal of the images posted on cropcircleconnector.com, a Rosco Williams aerial photo, but this time just for variety I printed it out from weekio.com. My raw measurements, along a line through the flower center and petal tips along the long axis of the vescia piscis, are
top edge top outer circle 14.7 mm
top edge top inner circle 20.1
top edge bottom circle 37.2
flower center 50.0
bottom edge top circle 62.7
bottom edge bottom inner circle 75.2
bottom edge bottom outer circle 88.2
Denoting the raw measurement by x and the corrected measurement by y, I found "a" in the formula
y = -1/a * (exp(-a*x) - 1)
such that the diameters of the two outer circles become equal. The corrected measurements are
14.43, 19.60, 35.51, 46.97, 57.99, 68.49, 79.07
With this correction, the overlap is only 0.70 mm greater than for a perfect vesica piscis (i.e. pair of equal circles through each other's centers). This is within my ruler error and/or the higher-degree error of the correction formula, so I'll assume a perfect vesica piscis, which would have overlap area equal to 0.2430 of the total figure area. The area outside full-width half-maximum of a normal distribution, i.e. farther than 64 days from Feb. 17 according to the theory of my recent previous posts, is 0.2390, giving an error of only (0.2430-0.2390)/0.2390 = 1.7%. Furthermore the flower's six interpetal areas each are divided in two by fine lines, suggesting 2^6 = 64.
The areas between the outer & inner circles, using the corrected diameters, are 0.1388 & 0.2652 for the upper & lower circles, resp. This agrees with the area under the normal curve before Dec 21 (winter solstice) 58 days before Feb 17, which for a normal curve of half-width half-max 64 d, is 0.1429, and the area after Mar 20 (spring equinox) 31 days after Feb 17, 0.2842. The errors are (0.1388-0.1429)/0.1429 = -2.9% and (0.2652-0.2842)/0.2842 = -6.7%, resp.
Summarizing: the Australian crop formation discovered Nov 23, 2012 (said to have been made an estimated week or more earlier) uses an arcuate design, to signify a normal distribution with mean 31 days before the 2013 spring equinox and 58 days after the 2012 winter solstice. The half-width half-maximum is indicated by the flower, to be 64 days.
Addendum Dec 14: For greater accuracy, I averaged my measurements on my old printout from cropcircleconnector.com and my new printout from weekio.com (they are the same Rosco Williams photo and though the sizes are slightly different, that hardly affects the important results):
top edge top outer circle 15.8 mm
top edge top inner circle 21.1
top edge bottom circle 37.8
flower center 50.0
bottom edge top circle 62.35
bottom edge bottom inner circle 74.65
bottom edge bottom outer circle 87.3
Assuming that the formation really is exactly a vesica piscis, I have two conditions on the corrected measurements: that the outer circles have equal diameters, and that the overlap be half that diameter. This allowed me to specify a higher degree correction formula,
y = x + A*x^2 + B*x^3
where A = -0.0043856 & B = +0.000022134, and the corrected measurements now are
14.792, 19.355, 32.729, 41.803, 50.666, 59.418, 68.603
The areas between the outer & inner circles, using these new corrected diameters, are 0.1480 & 0.2775 for the upper & lower circles, resp. This agrees even better with the area under the normal curve before Dec 21 (winter solstice) 58 days before Feb 17, which for a normal curve of half-width half-max 64 d, is 0.1429, and the area after Mar 20 (spring equinox) 31 days after Feb 17, 0.2842. The errors are (0.1480-0.1429)/0.1429 = +3.6% and (0.2775-0.2842)/0.2842 = -2.4%, resp. |
Edited by - Joe Keller on 14 Dec 2012 13:16:39 |
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Joe Keller
USA
930 Posts |
Posted - 16 Dec 2012 : 19:31:51
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Asteroids 511 Davida, 39 Laetitia, 947 Monterosa, 1717 Arlon: indicate date Jan 4, 2013 with full-range half-max Nov 22, 2012 - Feb 23, 2013
In posts years ago, I noted that these four asteroids have rotation periods clustering near the shortest value known. These periods are remarkable not only because they are short, but because they are so nearly equal. These four comprise the entire cluster: the other short periods known, differ much more.
Years ago, I noted that these asteroids align (i.e. roughly equal heliocentric ecliptic longitudes modulo 180deg) in about Dec 2012. Just today I found time to return to this topic.
I got their heliocentric J2000 ecliptic longitudes (I rounded these to the nearest 0.01deg) from the online JPL ephemeris, for the dates Dec 1, Dec 31, Jan 30, and Mar 1. These data allowed very accurate third degree Newton's forward-difference interpolation. Davida's longitude is near 360 at these times; the other longitudes are near 180. So, I added 180 to Davida's so that I could consider agreement modulo 180, i.e., collinearity with each other and with the Sun.
The minimum standard deviation of the set of four longitudes, is 3.408deg, at Jan 4.4 GMT, 2013. The standard deviation is sqrt(2) times this (i.e. the variance is twice the minimum) at Nov 22, 2012 and at Feb 23, 2013. The mean longitude (mod 180) of the four, at the time of minimum variance of their longitudes, is 177.62deg. |
Edited by - Joe Keller on 16 Dec 2012 20:48:12 |
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Joe Keller
USA
930 Posts |
Posted - 17 Dec 2012 : 18:39:38
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Davida, Laetitia, Monterosa, Arlon: resonance at 6339.49 Julian yr
This resonance has nothing to do with any Jupiter resonance. It is a resonance that has appeared only during the last few years. Also, it involves large prime numbers, unlike the asteroid-Jupiter resonances.
The JPL Horizons online ephemeris, current today, Dec 18, 2012, gives periods for these asteroids with the osculating elements in the headers of their ephemerides; the Wikipedia articles on them also give periods. The two sets of periods differ considerably, so let's use the periods of latest epoch. For 511 Davida, 39 Laetitia, and 1717 Arlon, these would be from the Wikipedia articles, which cite JPL data as the source for all three, and give epochs Aug 27 2011, Dec 31 2006, and May 18 2008, resp. For 947 Monterosa, the current JPL header gives a more recent epoch, Sep 30 2012, than the Wikipedia article. Using the periods of most recent epoch, all supposedly from JPL data, we have:
Davida 5.63009883 yr
Laetitia 1682.713 d = 4.607017 yr
Arlon 1188.041866925004 d = approx. 3.252681361 yr
Monterosa 4.5609 yr
I find that exactly 1126 (prime factorization 2*563) Davida periods
= 6339.49128 Julian yr
= 1949.004707 (1949 is prime) Arlon periods
= 1376.051 (prime factors: 1376 = 2^5 * 43) Laetitia periods
= 1389.96 (prime factors: 1390 = 2 * 5 * 139) Monterosa periods
where only significant or almost-significant digits have been carried. Using the JPL periods of older epoch (1998 for Davida, 1988 for Laetitia, 2005 for Arlon & Monterosa) there is no such resonance. This suggests that only in the last few years have these asteroids converged to a period resonance. |
Edited by - Joe Keller on 18 Dec 2012 16:01:42 |
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Jim
1751 Posts |
Posted - 18 Dec 2012 : 21:54:17
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| Dr Joe, It is good to see you are back at the JPL site. You can fix these problems here that's for sure if you keep focused on the stuff being generated(or maybe I'm delusional). |
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Jim
1751 Posts |
Posted - 18 Dec 2012 : 21:56:41
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| Dr Joe, It is good to see you are back at the JPL site. You can fix these problems here that's for sure if you keep focused on the stuff being generated(or maybe I'm delusional). |
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Requiem for Relativity
