Requiem for Relativity

Reworking Playfair's "Remarks on the Astronomy of the Brahmins" (part 3)

As Playfair noted, the "equation of the Sun", i.e. the maximum difference between the Sun's apparent and mean longitudes, is a well-defined quantity that can be accurately determined with primitive tools, so it is a good way to date the Hindu astronomical tables. In part 1, I used two modern estimates of trends in Earth's eccentricity, to get 4800BC and 4900BC as the date of the tables.

The best modern estimate I can find, that is in a form usable by me, is in Laskar, Astronomy & Astrophysics 157:59-70 (1986), Tables 2 & 3, pp. 61-62. Laskar gives two different fourth degree polynomials, whose coefficients differ only slightly. The coefficients shrink steadily so those of t^4 are about 1/30 as big as those of t; his t is in units of 10,000 yr, so at 6000 yr, the t^4 term is only 1/150 as big as the t term. I also improved my calculation slightly, by using precise numerical integration, for the apparent-mean Sun inequality, instead of third order approximation.

Using the average of the two coefficients offered by Laskar, I get 4929BC as the date corresponding to the Hindu "equation of the Sun", 2deg10'32". Using the two formulas separately, I get 5083BC & 4796BC (mean 4940BC). So, the four authoritative formulas I've used for Earth's eccentricity thousands of years ago, all indicate that the Hindu "equation of the Sun" discussed by Playfair, was current sometime between 4800BC and 5100BC.

The analogous equations of Mars, Jupiter, and Saturn, which I gleaned either from Playfair or directly from Bailly's book (to which I have access on microfilm), are subject to various interpretations, because they involve three bodies. My various calculations, mostly using Laskar's formulas, indicate that these Hindu values are either no older than ~2000BC, or are inaccurate.

The Hindus said that Luna's orbit is inclined 4deg30' to the ecliptic (Playfair, sec. 15). Very modern authority, Simon et al, Astronomy & Astrophysics 282:663+ (1994) says (3.4.a.2) that Luna's mean inclination changes linearly, so slowly that the difference between the modern and Hindu value (using ecliptic of date for each) is 2 billion years! However, Simon gives 5.1566898deg for 2000.0AD. Brown, Monthly Notices of the Royal Astronomical Society 74:552+ (1914), pp. 552 & 561, on the other hand, gives 5.128164 +/- 0.000008deg, based on data from 1847-1901. Linear extrapolation based on the midrange of Brown's data, implies 900BC; but this is only a guess.

Playfair (sec. 40) says the Hindus gave the regression of Jupiter's aphelion as 15deg in 200,000 yr. Modern authorities say that Jupiter's aphelion progresses, and much faster. Jupiter's node also progresses, but at a rate roughly 100x the above figure. If the node is meant, rather than aphelion, and progression is meant, rather than regression, and years were mistranscribed as centuries, I find that the value, 2700"/century, is correct for 9000BC +/- 1000. This is according to the third degree polynomial in Clemence, Astronomical Journal 52:89+ (1946), p. 92. Clemence segregates some terms into a sinusoid of frequency equal to the "great inequality" of Jupiter and Saturn (disparity from exact 5:2 resonance). This phase of this sinusoid is unknown for such a distant epoch, but would affect the result +/- 1000 yr. Also, the range is outside that for which cubic polynomials generally are accurate for these phenomena.

Sense & Synchronicity: Mt. Meru Comes to Microsoft

Let's recall: Mt. Meru, in Hindu legend, is said to be 84,000 yojanas high (the yojana is the ancient Hindu counterpart of a mile, equal to several of our miles, apparently varying over the centuries). (Some less accurate sources round this to 80,000 or even to 100,000.) Mt. Meru also is said to be the home of the Gods, analogous to Mt. Olympus (recall that U. S. Air Force reservist Sid Padrick, said that friendly humanlike beings told him they lived on a somewhat distant unobserved planet in our solar system, even hinting at Barbarossa's longitude by mentioning that it was in conjunction). Furthermore, according to Wikipedia, it was said that the entire known solar system (Sun plus planets) revolves around Mt. Meru as a unit.

My "Barbarossa period", though originally discovered by me as Barbarossa's sidereal orbital period, 6340 +/- 7 yr, calculated from four sky survey appearances, I more precisely define as 6339.5 tropical yr, from the summer solstice 4328BC (start of Egyptian calendar according to Arcturian date of Amenhotep I) to the winter solstice 2012AD (end of Mayan Long Count). In my Oct. 18 post, I noted that the Barbarossa period equals 84,000+ sidereal months. For a precise calculation, I use the tropical year instead of the sidereal (because the calendars define the period in tropical years, not sidereal, and there is evidence that Egyptian and Hindu astronomers eschewed the true sidereal year, preferring phenomena such as heliacal rising, or the right ascension of one bright star); adjust the tropical year to its mid-interval length according to Newcomb's linear formula for precession (in, inter alia, the 1965 Astronomical Almanac); for consistency, use the tropical month instead of the sidereal; and adjust the tropical month to mid-interval length according to the linear formula in Wikipedia. The Barbarossa period is:

84,748.2 tropical months (the secular trends only barely affect the last decimal place)

So, "The solar system revolves around Planet X - Barbarossa in 84,748 tropical months, and there is advanced life on Barbarossa" has been remembered as, "The solar system revolves around Mt. Meru which is 84,000 yojanas high, and Mt. Meru is the home of the Gods."

There is yet another way that the parameters of Barbarossa have been remembered as "84,000". Barbarossa's latus rectum is 84,147.3 times Luna's semimajor axis (the secular trend in Luna's semimajor axis isn't quite big enough to change the last digit). The latus rectum, is arguably the most important measure of the size of Barbarossa's orbit: it is the numerator of the formula giving radius as a function of the true anomaly, theta; and at the critical phase, in Dec. 21, 2012AD, Barbarossa is at theta = 91.022deg, only a degree past the latus rectum, and at distance 85,073.8 Lunar semimajor axes.

So, "Catastrophe occurred when Barbarossa was near, its latus rectum which is 84,147 times Luna's semimajor axis" also became "Mt. Meru which is 84,000 yojanas high".

None of the foregoing involves synchronicity; it only involves the garbling of information over millenia, and perhaps the intentional encoding of information in myths which were likelier to be remembered. On the other hand, synchronicity, as I understand it, is a significant coincidence that not only is unexplained, but cannot be explained by, or to, the limited minds of human beings. Here is a fictitious example:

"I counted the flowers on my houseplants, then got my mail, and there was a bill for the same number of dollars; this happened every day for a year."

If it happened one day, it could be chance, but to happen every day, were this fictitious example to be true, would indicate some kind of organizing process (or organizing being) in the world, far beyond human understanding.

Near Microsoft headquarters in Redmond, Washington, is a boulder. A large building was constructed near this boulder this summer; according to my research, the zoning permit was granted April 8, 2010, and construction began quickly the same day. I and some others have photos of the building after its exterior was completed, and of a sign in front of it; these photos were taken Oct. 11.

The sign says:

"PROPOSED LAND USE ACTION
Project No: L090463/L090464
Title: Redmond Medical Office Bldg.
Description: 84,715 sq.ft. medical office
bldg. & emergency care clinic
Applicant: ***** Co.; contact: D**** D****
Contact: D**** L****
City of Redmond
(425) 556-2471
WWW.REDMOND.GOV/LANDUSEAPPS "

This superficially appears to be a routine bureaucratic notice, but there is synchronicity:

The summer solstice, 2010AD, is 84,714.7 tropical months after the summer solstice, 4328BC. As above, this figure is corrected (to midrange value) for the (barely significant) linear secular trends in the tropical year and month. It also is corrected for the (1.8 day) effect of eccentricity, on the time of the solstice at the different positions on Earth's orbit; I considered the change in perihelion and eccentricity too.

From numerical analysis, I thought the 1-sigma error in my calculated orbital parameters for Barbarossa, was 1/1000. However, the calendar data suggest it is only 1/10,000, and various resonances between the planets and protoplanets (discussed in my earlier posts) suggest 1/20,000, i.e. +/- 4 Lunar semimajor axes. Be this as it may, my orbit for Barbarossa gives a Sun-Barbarossa distance of 84,715 Lunar semimajor axes, at the summer solstice, 2009 AD (2009AD, not 2010AD).

The "Project No." also involves synchronicity. In an earlier post, I showed that the original height of the pyramid of Khafre, relative to the base of the pyramid of Khufu, is to the Lunar proxigee (closest approach of Luna to Earth, including perturbations away from the Keplerian ellipse), as one day is, to the period of Barbarossa. Wood's 1986 value of the proxigee is 356,375km. Vyse gives 1011 cm as the height of Khafre's base above Khufu's. This implies a height for Khafre, above its own base, of

-1011cm + 356,375km / (6339.5*365.24258) (4328BC trop yr) * (1-1.5ms/d/cent*63.4cent)(4328BC day) = 5661.5 inches,

well within Petrie's 5664 +/- 13 inch estimate. (Using the height above Khufu's base, and using the proxigee, allowed the smallest height for Khafre.) Maybe some ancients preferred to measure in Lunar proxigees rather than Lunar semimajor axes. Barbarossa's Latus Rectum, in proxigees, is

L = 90,528

only 7/10,000 more than the "L090463" or "L090464" figures in the bureaucratic notice.

Hi Joe, how does this relate to the Metonic month? There is that famous bronze age "witch's hat" that shows the 19 year cycle of the moon.

(Edited) It was thought for a long time that the various henges of Europe were about the sun but now it's thought they were about the moon. These people were on the cusp of changing from hunter gatherers to farmers. The nineteen year event was to show the people that the moon was still the "boss" as it were.

Another quick thought about this, is on the famous shepherd speech in Oedipus Rex, about Arcturus. To the modern ear, he just seems to e twittering on about nothing but to the Greek audience?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Stoat</i>
<br />Hi Joe, how does this relate to the Metonic month?

...speech in Oedipus Rex, about Arcturus.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Hi Bob! Thanks!

Playfair says that the ancient Hindus mention the Metonic cycle, but do not mention the supposedly more useful Saros cycle. Playfair also says (sec. 12) that the Hindus mention that the Lunar perigee (apse) revolved in 3232 days = 8.8487 Julian yr; 3232 d. also is the modern value given in Lang, Astrophysical Data (1992), though the most modern and exact sources give a period of 8.8504 Julian yr = 3232.61 days. Ptolemy equated 3277 synodic months to 3512 anomalistic months; this is equivalent to saying that the apse revolves in 8.8487 Julian yr, so Ptolemy was in exact agreement with the ancient Hindus, on the period of Luna's perigee advance.

Sophocles' mention of Arcturus as a commonly used calendar marker, supports the idea that the Egyptians and Hindus used it in various ways to mark dates.

Sense & Synchronicity (Part 2)

The Lunar proxigee (absolute closest approach) is less, than the Keplerian perigee with mean elements. Practically all the difference, 5974 km, is due to the Sun. The primary effect, is due to the angle between perigee and the Sun, i.e., the phase of perigee. The secondary effect, is due to the season of the year, because of Earth's eccentricity.

Neglecting the effect of Earth's eccentricity, that is, minimizing the perigee with respect to Lunar phase, but averaging it over season of the year, should give a perigee minus proxigee difference, (1 - Earth ecc.)^3 times as big, i.e. only 5679.8 km, thus 356,669.3 km for the proxigee.

If the Egyptians used this proxigee in planning the height of Khafre's pyramid (so Khafre's height above Khufu's base would be to Luna's "proxigee", as one day is to the Barbarossa period) then the calculation of Part 1 becomes

-1011cm + 356,669.3km / (6339.5*365.24258) (4328BC trop yr) * (1-1.5ms/d/cent*63.4cent)(4328BC day) = 5666.5 inches, now 2.5 in. more than, instead of 2.5 in less than, Petrie's 5664 +/- 13 (ch. 8, end of sec. 67, in Birdsall's online edition of Petrie's book). In units of this yearly averaged proxigee, Barbarossa's latus rectum is

L = 90453

six times closer, to the 90463.5 indicated by synchronicity (see Part 1), implying an error of only 1/9000 in my calculated latus rectum for Barbarossa.

Hi Joe a little update on that Hawking radiation problem, I used the wrong value for the Planck mass, not that anyone is too sure of what it is!

We have, Power = hbar * c^6 / 15360 * pi * G^2 * M^2 for the e.m. side of things

We have, Power = hbar* c^-2 / 15360 * pi * G^2 * M^2 for the gravity side of things

c = 2.99792458E 8
G = 6.67428E-11
hbar = 1.05457148E-34
M = 4.3413642 (which is the Planck mass micro lack hole)

Putting some numbers in 1.1173369E-51 / 15360 * pi * G^2 * M^2 = 2.8980456E-19

That's about 1.72135 times the charge on the electron. Why? I do think I've made some sort of basic mistake here. I really think this should be exactly 1.6021764187E-19

The trouble is, that it has to mean altering that denominator and it is constructed from the sacred cow of 8 * pi * G
I think the denominator is going to be 0.5 hbar and the numerator is going to have 2 * 1/137 in it. Though having said that, it's bad enough saying that something, gravity, can go faster than light, without questioning the derivation of the Planck mass.