Paradoxes Resolved, Origins Illuminated
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T O P I C    R E V I E W
Samizdat Posted - 05 Dec 2005 : 16:29:49
Has any of you read, or have you preliminary thoughts on the new book by Michael Strauss, "Requiem for Relativity: the Collapse of Special Relativity?"
20   L A T E S T    R E P L I E S    (Newest First)
Joe Keller Posted - 07 Oct 2015 : 20:48:54
Alternative reading of Giza-Saqqara-Mars date

Above I mentioned that within the accuracy to which the Unas-Djoser distance at Saqqara seems to have been determined, Earth's diameter at Saqqara is the geometric mean of the Unas-Djoser distance and the major axis of Mars. This relation would be exact if the Unas-Djoser distance were 356.36m; my determination of the distance, is 365.2m. Though Wikipedia gives the coordinates of Unas to the nearest 0.1", which is roughly to the nearest 3m, Wikipedia gives the coordinates of Userkaf and Teti only to the nearest 1", which is the nearest 30m and it is not obvious that Unas is in better condition than these two other pyramids. Indeed the average of the four corners of Unas estimated by me on the Google map, differs from the Wikipedia coordinates by 0.3" latitude and 1.1" longitude.

I also mentioned that although there is no pyramid ("Pyramid X") at Giza corresponding to Unas, I could determine the distance X-Menkaure from the hypothetical gnomonic projection map, tangent at the autumnal equinox of date, (Regulus, Mars, Jupiter) --> (Menkaure, Khafre, Khufu) at Oct 3.478, the time giving the correct length ratio for Giza's actual interpyramid distances. This predicted X-Menkaure distance is 478.06m. I could have used Oct 3.556, the time from the gnomonic projection, tangent at Spica, (Venus, Regulus, Mars, Jupiter) --> (Unas, Djoser, Userkaf, Teti); this time is the mean of the two times giving correct length ratios UnasDjoser/DjoserUserkaf and UnasDjoser/DjoserTeti, and it gives a predicted X-Menkaure distance of 472.075m. About midway between these is the value 475.15m which is exactly 4/3 * 356.36; that is, it would correspond to 3/4 of the major axis of Mars.

Since the pyramids of Egypt seem to be informing us of two quantities, 1.0 and 0.75 times "2a", the major axis of Mars, let's look at the JPL Horizons ephemeris and learn when the distance between Mars and Earth will assume the values a and 3/4*a. Mars is 1.0*a from Earth at 02:42 GMT Jan 17 2016; Mars is 0.75*a from Earth at 11:32 GMT Feb 23 2016. Mars' elongation from the Sun is 79.0982 and 98.9006deg, resp.; the difference is 19.8024. (These distances are at the nearest minute, so the last digit is not significant.)

Recall that above I found that for the hypothetical Pyramid X at Giza, the slope X-Menkaure, for the gnomonic projection map of Oct 3.478, would be 58.1609 (the slope Menkaure-Khufu measured N of modern true E) + 26.6773 (the hypothetical break angle at Oct 3.478) = 84.8382; the slope Unas-Djoser is 64.9119 (range consistent with Wikipedia coordinate rounding intervals, 64.3220-64.9698) and the difference is 19.9263.

This suggests a time corresponding to the elongation of Mars corresponding to the northerly direction. That elongation would be 98.9006 - 84.8382 + 90 = 104.0624 which is obtained at 02:10 GMT Mar 03 2016.
Joe Keller Posted - 05 Oct 2015 : 20:45:58
Giza and Saqqara: using orbital parameters of Mars to warn of Oct 6.85 GMT?

The time, Oct 3.50 GMT, indicated by my above analysis of Saqqara and Giza, didn't seem to be associated with much on Earth except a hurricane. It might be, that the visually striking arrangement of Venus, Regulus, Mars and Jupiter, was exploited as a warning: the time indicated was that of the special arrangement of heavenly bodies, even though the best estimate of the time of disaster was not exactly that time, but rather a few days later when no especially striking arrangement is to be seen. That is, a time was chosen near the estimated disaster time, when a visually striking configuration of heavenly bodies was to be seen. Indeed the relative minimum standard deviation of the distances between those four bodies, that is, the minimum, of their standard deviation divided by their mean, occurred Oct 3.71.

Last night I discovered also that the azimuthal orientation of the line of pyramids, both at Saqqara and Giza, refers to the "true anomaly" of Mars. Suppose that the EW line on the ground at these sites, corresponds to the position of Mars in its orbit, when Mars is at a distance from the Sun, equal to Mars' semimajor axis. In a perfect Keplerian orbit, this would be the same as when Mars lies at a semiminor axis, in contradistinction to the usual definition of zero true anomaly at the semimajor axis corresponding to perihelion. The true anomaly at a semiminor axis is arcos(-e) = 95.35995deg where e is the eccentricity. Reasonably since Egypt is in the northern hemisphere, Mars moves counterclockwise on the Giza and Saqqara maps.

Using my maximum-likelihood position estimate, the slope of the line Unas-Djoser at Saqqara is 64.9112 N of E; the extremes possible within the rounding intervals of the Wikipedia coordinates are 64.3220-64.9698. Adding the maximum-likelihood slope to the true anomaly of the minor axis, and converting to mean anomaly using the well-known formulas, I can find not only the time past the semiminor axis, but also the times past the perihelion and before the aphelion, assuming a perfect Keplerian orbit. Really, the distance from the Sun may equal a*(1 +/- e) a few days before and again after the extreme radius is achieved. So, I will use the time of extreme radius, which is very near the midpoint of the two a*(1+e) times, for example. For the semiminor axis time, I use the time when r=a.

This results in three time estimates:

from semiminor axis May 22 2015, I get Oct 6.820
from perihelion Dec 12 2014, I get Oct 6.814
from aphelion Nov 20 2015, I get Oct 6.926

These figures are slightly different because the orbit of Mars is not perfectly Keplerian (perturbations by Jupiter and Earth, for example).

Suppose there was a marker at Giza, south of Menkaure, which represented Venus. From the computer program I've already written, I can calculate where that marker should be. So, I have a slope and a distance X-Menkaure at Giza which corresponds to Unas-Djoser at Saqqara. Amazingly, this slope corresponds to true anomaly 180.1981 (all these slopes are using modern N, though use of Petrie's N, 0.0944deg to the west of modern N, would make little difference).

As a final hint that these slopes refer to Mars, I find that the distance Unas-Djoser, and the semimajor axis of Mars, have as their geometric mean, the radius of Earth at Saqqara. The error of this is well within the ~0.3% uncertainty of the Unas-Djoser distance. At Giza, the scale, using the calculated position of the "lost pyramid", X, is exactly 4/3 as great, which would imply some distance 3/4 as great as the semimajor axis of Mars.
Joe Keller Posted - 29 Sep 2015 : 12:15:28

Abandoning my earlier interpretation of Giza, I tried to interpret Giza as I had Saqqara. A few days ago I succeeded.

The three large pyramids at Giza are a gnomonic projection map whose tangent point is the present autumnal equinox:

Menkaure = Regulus
Khafre = Mars
Khufu = Jupiter

The four large completed pyramids at Saqqara are a gnomonic projection map whose tangent point is the present position of Spica:

Unas = Venus
Djoser = Regulus
Userkaf = Mars
Teti = Jupiter

In my previous posts I explain how I estimated the positions of the centers of the Saqqara pyramids first by averaging maps found in books, then later and more accurately by forming a maximum-likelihood estimate based on coordinates given by Wikipedia combined with my own taking of Google map coordinates. The first method indicated about Oct 3.35 +/- 0.05, and the latter method Oct 3.556 +/- 39 minutes (the spread indicates the times that the broken line's two length ratios, AB/BC and AB/BD, lettering the pyramids south to north, each satisfy the predicted value). Later I used more precise ecliptic coordinates, and refined this to 3.550 +/- 40 mins. The two angles involved (ABC and ABD) differed from predicted by 0.9 and 0.5 deg, consistent with the accuracy of my Saqqara position determinations.

The Giza result is even more precise, as would be expected from the 10 cm accuracy (confirmed by Cole) of Petrie's survey. The length ratio AB/BC (only one ratio because there are only three points at Giza) satisfies the predicted value at Oct 3.478, only 104 minutes before the Saqqara time. Furthermore the one break angle BAC differs only 13 arcminutes from predicted. Though this is twenty times the error of Petrie's survey (400 meters * 1/200 radian = 2 meters = 20 * 10cm) and also ten times the typical 1 arcminute error which Petrie found in the Giza construction (even in its present damaged form) the agreement, of the time, with Saqqara is remarkable. A 1.1 arcminute error in the determination of the ecliptic latitude of Mars, wholly suffices to explain the error in the Giza break angle.

I determined the positions of the tangent points for both the Giza and Saqqara maps, that is, the points on the ground corresponding to the autumnal equinox and to Spica, resp. Google maps show nothing remarkable there, but the point for Giza is heavily urbanized (highway and large buildings) and that for Saqqara intensively farmed.

It would have been difficult for ancient people to determine modern sidereal times, due to difficulty estimating the rate of Earth's rotational slowing; indeed modern estimates of the long-term rotational slowing over thousands of years, based on ancient astronomical records, vary 10-30%. Instead the ancients might have encoded in their maps, the modern angle, known as zenith distance, of Spica from the zenith at Saqqara when Spica is on the meridian, that is, the difference between the modern declination of Spica and the latitude of Saqqara. Indeed this is found in the Saqqara map. The slope of the Unas-Teti line is, according to my maximum-likelihood estimate, 48.7801deg N of E. The precision with which I can determine such angles at Saqqara is tenths of a degree, so it is impossible to differentiate on this basis between the slightly different alternatives for ancient North or ancient latitude. The best fit happens to result from assuming the modern latitude of Saqqara but the ancient North indicated by Giza. We find 29.8713 (modern latitude of Djoser) + 11.2412 (modern declination of Spica) = 90 - (48.7801 (measured slope Unas-Teti) - 0.0944 (correction for ancient Giza North) ) = 0.78 arcminute.

So one might guess that the slope at Giza, Menkaure-Khufu, would indicate analogously the zenith distance of the autumnal equinox when Spica is on the meridian, but this is not the case. We find that when the zenith distance of the autumnal equinox equals the complement of the slope Menkaure-Khufu, corrected for the ancient Giza North, i.e. 90 - (52.2293 - 0.0944) = 90 - 52.1349, assuming the modern latitude of Khafre, the sidereal angle (i.e. right ascension of the meridian) is 204.3095, which corresponds to Oct 3.448. Adopting instead 30.0 deg for Khufu, or using modern N, affect the result by less than a minute of time. Though this sidereal angle recurs daily, it is suspiciously near to the Giza alignment time 3.478 - only 43min earlier.

Recalling also that the individual pyramid orientations at Saqqara --> Oct 3.535 (see earlier post) albeit with an exp(-1/2) interval (standard deviation equivalent) Oct 2.142-4.858, we can average our four time estimates, 3.535, 3.448, 3.478, 3.550, with equal weight to find

2015 AD Oct 3.503 = 12:04 GMT +/- 35min SEM
Joe Keller Posted - 14 Sep 2015 : 18:50:32
Pyramid orientations, cont.

My previous post about pyramid orientations contains some approximations: that a grossly non-normal distribution is normal, that grossly dependent events are independent. So, here is a rigorous analysis I have made that provides even greater corroboration of the gnomonic projection map:

First we have the slopes of the pyramids relative to NSEW; we could call these the expected slopes, phi(i), measured as N of E. Then, for a given time t, we have the celestial coordinates of date, of Venus, Regulus, Mars and Jupiter. By the following linear equations, these imply the "observed" slopes phi(i)' :

Decl(Regulus) - Decl(Venus) = 1/2 * (phi(1)'-phi(2)')
Decl(Regulus) - Decl(Mars) = 1/2 * (phi(3)'-phi(2)')
Decl(Regulus) - Decl(Jupiter) = -phi(2)'
RA(Regulus) - RA(Jupiter) = -phi(4)'

The primed phi(i) will not exactly equal the unprimed. Approximating the probability density of the unprimed, as normal (for example, if Petrie's ancient north is used, the distribution of phi(1) is normal with mean -0.785 and standard deviation sigma = 0.260 ) gives an overall probability density, for a given t, that is the product of the probability densities of each phi(i)', which in turn are equal to 1/sqrt(2*pi) * exp( -1/2 * (phi(i)-phi(i)')^2 / sigma(i)^2 ).

Now consider that we do not know what was used for North at Saqqara. Arguably it could have been Petrie's Giza north; arguably it could have been practically the same as modern north (this is the current mainstream opinion among geophysicists) or arguably it could have been something else. For a given t, we can calculate the overall probability density, for any Saqqara "North" measured as theta W of modern N, simply by replacing phi(i) with phi(i)-theta. This is a normal type of distribution in theta, and easily can be summed (i.e. integrated) over all theta (only theta within a few degrees of zero will give an appreciable integrand).

The time maximizing such a sum, i.e. the likeliest t in view of the relative orientations of the pyramids with unknown north, is, amazingly, Oct 3.535, only 0.021d = 30min different from my best gnomonic projection map value of 3.556 found above. However the "error", as determined by the 0.6065 ordinate value analogous to that found at one sigma for a normal curve, is rather large: Oct 2.142 to Oct 4.858.

For this optimum t, the mean theta (theta is normally distributed) is 0.377deg E of N, with standard deviation 0.177deg. Possibly the pole oscillated between longitude lines bisected by the longitude line of Giza/Saqqara. If the pole lay on one of these asymptotes and then another, the deviation in the direction of "North" would be, for small deviations from modern N, proportional to the alteration of the 30th parallel. That is, the deviation at Saqqara could be 5'40" (the deviation at Giza) * (30-29.87127)(for Djoser) / (30-29.97611) (for Khafre) = 0.509deg. This is within one sigma of the North direction inferred from the orientations of the Saqqara pyramids and celestial coordinates of the bodies.

For t = 3.535 and theta = 0, i.e. modern north, the observed (i.e. astronomically implied) orientations are more positive (more counterclockwise) than the expected (i.e. actual pyramid bases and their nearby walls). These deviations are, for i ranging from 1 to 4: +1.07, +1.61, +1.24, and +0.26 sigma, surely suspicious because although they are believably moderate, they are all positive. For theta = -0.377, i.e. the maximum likelihood theta for the overall maximum likelihood t = 3.535, the deviations are -0.38, +0.26, +0.71, and -0.30, a good fit for all.

There is indeed evidence at Saqqara that North was ~0.5deg E of modern north. G. Magli includes in his Saqqara map, some pyramids and other structures that I think are sometimes called "South Saqqara". Here, lies the large, well preserved and sharp "Mastaba El Faraun". On the satellite Google map, I measured at two levels, accented by shadow, on the west edge. One slope was 0.58 and the higher level 0.52deg E of N!
Joe Keller Posted - 10 Sep 2015 : 14:41:03
Pyramid orientations confirm Oct 3 date

To review, let's recall that at first, I used average positions, on four printed Saqqara maps, traced onto graph paper. I had found three maps in books at the Iowa State Univ. library, but one, Lehner's, was unusable because it was on two pages and aligning the pages was too difficult. In hindsight, I think I could have used the topographical level curves to align Lehner's. I did use Lauer's which was on two pages also but was bound in such a way that the two pages could flatten as one continuous. Another map was from an Oxford Atlas. A friend loaned me another book with a map, and I printed out a map that was online. Using equitably averaged positions (I first rendered the maps to be of the same scale and orientation, by linear transformation of coordinates) I found that the four large completed pyramids at Saqqara (Unas, Djoser, Userkaf and Teti) are a gnomonic projection sky map, centered at Spica, of Venus, Regulus, Mars and Jupiter at Oct 3.35, 2015AD, plus or minus about an hour.

Then I used a maximum-likelihood synthesis of Wikipedia coordinates and Google satellite map coordinates (average of four pyramid corners). This gave a somewhat tighter fit, at Oct 3.556 plus or minus about half an hour. Not only were the length ratios of the pyramid-polygon more consistent, but the angles matched the sky map more closely too.

Now I'm finding that the orientations of the pyramids confirm the above in an entirely different way. On the Google satellite map, I measured the orientation of each pyramid three times. I always used either a long straight intact portion of the pyramid base, or a long straight intact portion of a nearby wall. I always used at least one line from the pyramid base and at least one line from a nearby wall that was not part of the pyramid base. I assumed all pyramid bases and wall structures were rectangular. The result is:

Unas -0.785 +/- 0.260

Djoser -4.270 +/- 0.280

Userkaf -2.473 +/- 0.718

Teti +10.593 +/- 0.663

These are in degrees, with (+) indicating N of E. The errors are standard error of the mean. The printed maps show these slopes but often inaccurately, varying several degrees. I have adjusted my slopes to refer to geographic North at the time of Giza's construction, according to Petrie: 5'40" W of modern N. These four Saqqara pyramids were built some before and some after Giza's, but all during the Old Kingdom.

My theory is that the slope of Teti indicates the difference in Right Ascension (in the celestial coordinate system of date) between Jupiter and Regulus. The slope of Djoser indicates the difference in Declination between Jupiter and Regulus. The difference in slope between Djoser and Unas, indicates twice the difference in Declination between Regulus and Venus. The difference in slope between Djoser and Userkaf, indicates twice the difference in Declination between Regulus and Mars.

Note the linguistic similarity: Venus = Unas or Unis, uSERkaf = Mars or Ares ?

Using elementary statistical methods of combining standard deviations, I found that the best match of all four parameters (RA Regulus - RA Jupiter, Decl Regulus - Decl Jupiter, Decl Regulus - Decl Venus, Decl Regulus - Decl Mars) occurs at

Oct 3.87 +/- 0.73
shando Posted - 31 Aug 2015 : 09:31:54
Originally posted by Larry Burford

[shando] "Lin...didn't do it..."

How do you know?

Someone using his account is one theory we are considering.


Someone with that name appeared on the FB page. Said he was not a member (or forgot he subscribed) and disavowed any knowledge of the postings.
Joe Keller Posted - 28 Aug 2015 : 12:51:54
Best fitting time from Saqqara: Oct 3.556 (13:21 GMT) 2015

My previous post details how the four large finished Saqqara pyramids (Unas, Djoser, Userkaf, Teti) are a gnomonic projection map of the celestial bodies Venus, Regulus, Mars, and Jupiter, respectively. The center of the gnomonic projection is at the star Spica. Present positions of the stars are used, and fit better.

I was reluctant to use online latitude and longitude coordinates for the pyramids, because I have seen grossly erroneous online coordinates for the Giza pyramids. I have never seen erroneous coordinates on Wikipedia, however (though surely there might be some due to the huge number of places entered there). So, trying the Wikipedia coordinates yesterday reached the top of my list of things to do.

The Wikipedia coordinates for Djoser are to the nearest 0.01 arcsec, for Unas 0.1", and for Userkaf and Teti, 1". Because 1" is not precise enough to tell me anything new, I determined "maximum likelihood coordinates" by the following reasoning: I assumed that the Wikipedia coordinates are correct within their range of possible rounding error. That is, x", for example, signifies a uniform "a priori probability" of the true value being between x-0.5 and x+0.5. Likewise x.y" would signify x.y-0.05 to x.y+0.05, and x.yz" would signify x.yz-0.005 to x.yz+0.005. Then I considered my alternative latitude and longitude coordinates, obtained by averaging my estimates at the four corners of a pyramid, on the satellite Google map. Because these Google map coordinates are exact, they afford an exact "maximum likelihood estimate". If the Google coordinates lie within the rounding interval of the Wikipedia coordinates, I use the Google coordinates. If the Google coordinates lie outside the rounding interval, I use whichever end of the rounding interval is nearest. I applied this method to all four pyramids.

The result was the best agreement between the pyramid positions, and the gnomonic projection sky map, yet achieved. Numbering the pyramids and the corresponding celestial bodies, 1234, we consider the length ratios 23 to 12, and 24 to 12. We also consider the break angles 123 and 124. The break angle 123 is just under 1.0 deg discrepant between the pyramid positions and sky map, and the break angle 124 is just over 0.5 deg discrepant, at the compromise time Oct 3.3556. This compromise time was chosen as halfway between the two times, about an hour apart, when the length ratios of pyramid and sky maps are equal. Better agreement hardly can be expected, at the accuracy of pyramid positions that is available.

Giulio Magli stated in his 2009-2010 article, "Geometry...Saqqara", on, that the Saqqara plateau is flat enough that the error in Google map coordinates due to the effect of altitude with the oblique angle of the satellite views, was negligible for his purposes (presumably his statement excludes the coordinates of the pyramid peaks, which are grossly affected by the obliquity). Though Lauer's map of Saqqara is a contour map, it is difficult to tell, from the abbreviated published version of Lauer's map that I have, what the relative altitudes of the pyramid bases are.

Today I hope to find time to explore the possibility that the three main pyramids at Abusir are a map of the three brightest stars of the constellation Lyra, under the same gnomonic projection.

The relative positions of Venus, Regulus, Mars and Jupiter on the morning of Oct 3 in North America, are shown in a diagram in the recently published October issue of Sky & Telescope.
Larry Burford Posted - 27 Aug 2015 : 12:37:19
[shando] "Lin...didn't do it..."

How do you know?

Someone using his account is one theory we are considering.

Larry Burford Posted - 27 Aug 2015 : 08:26:26
Actually he is a member. Since 2013.
shando Posted - 26 Aug 2015 : 14:25:47
Lin is male and he didn't do it - someone using his name did. He is not even a member on this site.

see Deep Reality Physics at this link on facebook:

Joe Keller Posted - 26 Aug 2015 : 01:57:40
Originally posted by Larry Burford

Don't assume it's really fixed yet. Working - to some extent. Fixed - stand by.

Lin Cornelison is a candidate for our hacker. ALL of Lin's messages are spam.

(Let me know if you spot an exception.)


OK - all those I've looked at, look like spam. Thanks for your time, skill and effort.

I think someone might be taking my work on archaeological "warning dates" seriously. I had communicated with quite a few of my Harvard classmates about the Sept 17 and Sept 19 dates especially. Then guess what! George Noory says on "Coast to Coast AM" during his recent first-hour interview with economist Catherine Fitts, that someone has announced that obscure Jewish lore suggests that there will be some kind of disaster Sept 19 this year. Maybe someone found Jewish lore to match my dates, or someone just assumed the part about it being Jewish lore. After all, Jewish lore is to a large extent the same thing as Middle Eastern lore, and this seems to be primarily an ancient Middle Eastern phenomenon.
Larry Burford Posted - 25 Aug 2015 : 18:55:50
Don't assume it's really fixed yet. Working - to some extent. Fixed - stand by.

Lin Cornelison is a candidate for our hacker. ALL of Lin's messages are spam.

(Let me know if you spot an exception.)

Joe Keller Posted - 22 Aug 2015 : 17:12:22

I see the hacking damage is still substantial but the messageboard of Dr. Van Flandern's website is now usable. I've analyzed the Saqqara site in Egypt. It's my most convincing yet. I just finished the work yesterday.

The time Saqqara indicates, is 5AM CDT Oct 3, 2015.

The Saqqara pyramids mark points which are a gnomonic projection map of Venus, Regulus, Mars and Jupiter when the three planets are near, but not at, their triple conjunction this fall. The center point of the gnomonic projection (tangent point of the plane to the sphere) is Spica. Wikipedia states that the gnomonic projection is the oldest known map projection of the sphere, and was credited by the Greeks to Thales.

The main pyramids at Saqqara are, south to north:

1. Sekhemkhet
2. Unas
3. Djoser
4. Userkaf
5. Teti
6. Merykare

The names and spellings vary but these seem to be the predominant names. Often the Merykare pyramid is called the "unexcavated" or "destroyed" pyramid. I found no very precise map of Saqqara. Instead I averaged the four usable maps that I could find in books (3) or online (1). I averaged them equitably by preliminarily transforming each map with a translation so that mean x = 0 and mean y = 0, a rotation so that sum x^2 was maximized, and a contraction so that mean (x^2 + y^2) = 1. Then I found that, making a gnomonic projection map of the celestial sphere, centered at Spica,

pyramid 2 = Venus
3 = Regulus
4 = Mars
5 = Jupiter

and that this is most exact at Oct 3.3 or 3.4 GMT, 2015. By this I mean that the length ratios and break angles of the broken interpyramid lines 234 and 235 equal those of the abovementioned gnomonic projection sky map. Between the pyramids, and the map, the break angles differ by about half a degree or a degree and a half, but this can be corrected with one or two sigma change in the pyramid positions, where sigma is the standard error (standard error of mean, i.e. standard deviation divided by sqrt(4) ) estimated from the scatter of the four maps. Simultaneous matching of the length ratios, if I use the overall mean standard error of all the pyramids, would require about three sigma change in pyramid 4, but pyramid 4 has about three times greater standard error than the other pyramids, so if I allow for this larger standard error, then it is really only about one sigma.

When I correct the longitude of Mars by decreasing it 0.24 deg, which has the same effect as the abovementioned three (really one) sigma change in the coordinates of pyramid 4, then the two length ratios, of sky map and pyramid, become equal simultaneously, at Oct 3.42 GMT = 10AM GMT Oct 3.

The fit is only about half as good if the 4500 year proper motions of Regulus (and Spica, though this has little effect) are omitted. That is, the rms error of the angles about doubles and the time difference between the two matches in length ratio also doubles.

Pyramids 1 and 6 seem to serve as checks on the positions of the others. To high ( ~ 1% ) accuracy,

a) pyramid 2 is the midpoint of pyramids 1 & 3
b) the segment 16 is parallel to the segment 25
c) the distance 56 is half the distance 12 (or 23)

Using (a) to correct the position of pyramid 2, replacing it with the average of 1, 2 & 3, improved the agreement with the map but only so slightly as to be hardly worthwhile. Likewise (b) and (c) already are so accurate that I would expect any correction of the pyramid positions intended to satisfy (b) or (c) exactly, also to be so slight as to be hardly worthwhile. However these relationships with the extra pyramids 1 & 6, could salvage a situation in which pyramids 2, 3 and/or 5 were annihilated or rebuilt in the wrong place. Maybe there was a 7th pyramid, now gone, that satisfied some simple relation serving as a check on the position of pyramid 4.

On Google Earth, pyramids 2 through 5 are obvious but 1 and 6 are difficult to see. I have recorded coordinates for pyramids 2 through 5 from Google Earth, estimating by eye the intersection of the diagonals of their bases. The parallax error from using their peaks would have been considerable. The result was about as good a fit as from my averaging the four maps above. The main difference is that with the Google Earth data, the length ratios match at Oct 3.4 and 3.5, i.e. 0.1 day later. The angle matches were about as good. Soon I will make a more accurate estimate by averaging the four corners of the pyramid bases.

The map in one of my books, has a north arrow that seems to be exactly horizontal on the page and a large photo also oriented orthogonally on that page. This allowed me to measure the azimuth of the line 123. I did this two ways. With a protractor I found, to about the nearest half degree, that the azimuth is 23.5 deg east of north. Measuring vertical distances and using the sine function, I found, also to about the nearest half degree I think, 23.0 deg. So the orientation of 123 seems to have been chosen to represent the obliquity of Earth, not when the pyramids were planned and built (it was almost 24.0 deg then) but rather, now. However, I later did the same, using the sine, for the best of my maps, that from Lauer's book, using the orthogonal border of the map, and found 23.85 deg to about the nearest quarter degree. This would be 23.95 degree using Petrie's presumed shift of 0.1 deg in geographic north as determined from Giza. So it seems likelier that they used Earth's obliquity as it was 4500 years ago. This also is supported by my Google Earth result (from the pyramids' diagonal intersections by eye): 24.7 deg (the effect of the correction to geocentric latitude was insignificant at this precision).

One might well ask why the sky map was not centered nearer the objects in question, perhaps at Regulus, thereby practically eliminating distortion whatever the projection chosen. I can think of two reasons:

A. Choosing Spica as the center gives "five for the price of four", a fifth object correlated with the map, without placing another marker (the pyramids might be refurbishments or augmentations of the original markers).

B. Spica is, and for 5000 years has been, much closer to the autumnal equinox than Regulus. Spica is brighter than Regulus and has much smaller "proper motion". It might have been predicted that we would be using gnomonic projection astronomical maps centered at or near Spica.

C. It might have been planned to include Saturn and Antares in the map. If so, then Spica would have been an ideal compromise center. On Google Earth I have found coordinates for a suspicious mound in a cultivated area north of Saqqara, which might correspond to Saturn or Antares.

A more accurate and detailed map of the six main Saqqara pyramids, would allow me to estimate their centers more precisely. This may well produce an even more convincing correlation with the sky positions.

I don't have time to discuss it here, but there are several well-documented, "accepted by mainstream authorities" instances of Mayan and Vedic, at least, astronomical knowledge accurate enough to predict things such as solstices and planetary positions to one-day accuracy in 5000 years. If ancient scientists knew that a sudden natural disaster were to occur in this solar system on a certain day 5000 yrs hence, they would look for whatever happened to be the most striking planetary alignment on that day, for example the near triple conjunction, near Regulus, throughout October. Then they would construct a map of that, exact for the day in question. That is what they did, and that is their warning to us.
rderosa Posted - 04 Jul 2015 : 14:16:01
Originally posted by Joe Keller

Hello all,

Congratulations to Mr. Burford for getting the messageboard back online after this severe hack attack!

Joe, is it really back? Do you happen to know if this Lin Cornelison person is still active? I still see thousands of messages from her.

Joe Keller Posted - 03 Jul 2015 : 17:39:10
Hello all,

Congratulations to Mr. Burford for getting the messageboard back online after this severe hack attack! Still, my posts are gone after the one about Teotihuacan. So here is a summary from memory of the most important. After I realized that Teotihuacan signified the date Sept 08, 2016 (the three largest pyramids are a stereographic projection of Venus, Regulus and Spica from a pole at the autumnal equinox) I realized that Giza is a twin triangle:

Let the center of Khufu's pyramid be A, Khafre's be B, Menkaure's be C. Let the line AC intersect the perimeter of Khafre, at D and E. Then ABE and CBD are stereographic projections of Jupiter, Regulus and Arcturus at Sept 17 & 19, 2015, resp. This is perfect if Khafre's base is rotated about 3 deg clockwise and is about 1% smaller, and Jupiter is about 30" farther north. This 1% size increase makes the actual Khafre a sort of compromise which minimizes the inaccuracy caused by the 3 deg rotation. I think Khafre was oriented toward north, but the predecessor marker, some sort of square wall, had this subtler purpose for its orientation which had been forgotten by the builders of Khafre's pyramid. Pyramid GII-a, the satellite pyramid south of Khafre, is about 3 deg off center, supporting my theory.

At Cahokia are two "pentagrams" each with several symmetries. These involve the biggest and the most durable, mysterious mounds (e.g. #66 & #67 - see Moorehead's work from the 1920s). The pentagrams share one mound in common; and their central lines of symmetry are exactly 30 deg apart. One pentagram gives "right ascensions" (or acute angles related to those) and one gives "codeclinations" in a celestial coordinate system using the autumnal equinox as the pole. The three positions so given, are those of:

1. Venus' stationarity in RA in July 2015
2. " for early Sept 2015
3. Luna at 21h GMT Sept 16 2015.

n/a Posted - 16 Jun 2015 : 14:14:50
n/a Posted - 16 Jun 2015 : 14:14:50
n/a Posted - 16 Jun 2015 : 14:14:50
n/a Posted - 16 Jun 2015 : 14:14:50
n/a Posted - 16 Jun 2015 : 14:14:50

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