Requiem for Relativity

Mathematician John Playfair dated Hindu astrology tables to 4300 BC

Koenraad Elst is a contemporary Flemish Belgian philologist. According to Elst's website, "[Elst's] research on the ideological development of Hindu revivalism earned him his Ph.D. in Leuven in 1998." One of Elst's main positions, is skepticism of the "Aryan Invasion Theory" of Indian history.

Elst's essay, "Aryan Invasion Debate", subpart "Astronomical data and the Aryan question", 2. Ancient Hindu astronomy, 2.1. Astronomical tables, first paragraph:

"One of the earliest estimates of the date of the Vedas was at once among the most scientific. In 1790, the Scottish mathematician John Playfair demonstrated that the starting-date of the astronomical observations recorded in the tables still in use among Hindu astrologers (of which three copies had reached Europe between 1687 and 1787) had to be 4300 BC. His proposal was dismissed as absurd by some, but it was not refuted by any scientist."

I never heard of the above, until today. Is it not remarkable that by reinterpreting "Sothic" dates, I had fixed the start of the Egyptian calendar at 4328 (or maybe 4329) BC?

From sec. 3.3:

"...it is encouraging to note that the astronomical evidence is entirely free of contradictions..."

Elst lists many other Indian astronomical dates; the oldest of these, ~4000 BC, were derived in various ways by various men, perhaps the earliest of whom were Hermann Jacobi, who correlated the constellations to ancient meteorological seasons (Elst, sec. 3.1), and B. G. Tilak, who interpreted a RgVeda allegory to place the equinoctial point in the constellation Orion. Tilak (Elst, sec. 4.2; or sec. 2.4.2 in another online source) relied on Rg-Veda 10:61:5-8; but strangely, Ralph T. H. Griffith's authoritative translation, "The Hymns of the RgVeda" (Motilal; Delhi, new revised edition 1973), relegates these verses to a Latin-only version on p. 653 of Appendix 1; verse 10:61:9 begins, "The fire, burning the people, does not approach quickly...".

For a shorter discussion similar to Elst's, see MN Dutt, transl., "Rg-Veda Samhita" (#22 in the Parimal Sanskrit Series; 1906, reprinted 1986) vol. 1, Introduction, pp. xvi-xviii.

"The next is the Orion-Period, 'which, roughly speaking, extended from 4000 to 5000 BC... . This is the most important period in the history of the Aryan Civilization. ...This was pre-eminently the period of Hymns.' "

- Dutt, p. xvii, quoting Prof. Tilak of Bombay

Reworking Playfair's "Remarks on the Astronomy of the Brahmins"

Playfair's lengthy remarks originally were published in 1790 in the Transactions of the Royal Society of Edinburgh, vol. 2 (the remarks are said to have been received in 1789). They also are available in an online "Google" book of Playfair's works, and as a chapter in Dharampal's book, "Indian Science & Technology in the 18th Century". Let's rework Playfair's remarks with the help of modern ephemerides.

In sec. 33, Playfair says that the Hindu astronomers gave the maximum "equation of the sun's center" (i.e. maximum difference between actual and mean solar longitude) as 2deg 10' 32". Assuming an observer at the Earth-Luna barycenter, and finding the angle to third order in the eccentricity, I find that it corresponds to e = 0.018985. From the eccentricity formula in the 1965 Astronomical Almanac (which counts centuries from 1900) I find that the date would be 4800 BC. Interpolating quadratically from the eccentricities given by Dziobek, "Mathematical Theories of Planetary Motions" (1892) in Table VI, p. 294, I find that the needed eccentricity occurs at 4900 BC, in good agreement with the 4800BC date implied by the 1965 Astronomical Almanac's eccentricity polynomial.

In sec. 17, the sun's "apogee" is said to be given as 77deg "from the beginning of the zodiac". In sec. 22, Aldebaran is said to be given as 53deg 20' "from the beginning of the zodiac". Suppose that the text has been corrupted: "apogee" should read "vernal equinox". Including proper motion, Aldebaran's longitude, in coords of the equinox & ecliptic of date, at 4800BC, was 335.931, implying that the so-called "apogee" (really, vernal eqinox at the epoch of the original almanac) was at longitude 335.931-53.333+77 = 359.60. It would coincide with the vernal equinox 0.40/360*26000 yr later, i.e. 4770BC.

Besides this 4800BC date, which I find two ways above, there is another way, besides the several discovered by Playfair and Bailly, to get the Kali Yuga date (3102BC) from the almanac. Sec. 10 says that the sidereal year, given by the almanac, is abnormally long: 365d 6h 12' 36". (Correcting for the shorter days in 3000BC, the 36" becomes 09".) This exceeds the modern value of the sidereal year, 365.25636d, by 1/176,000, but is too short to be the anomalistic year, which by interpolating to 3200BC in Dziobek's table, I find to exceed the sidereal year by 1/121,000. This year seems really to be a special kind of "sidereal" year: the time between moments when the RA of the Sun, in the equinox and ecliptic of date, equals the RA of Arcturus. It is a kind of sidereal year relative to Arcturus. I discovered this by using the NASA lambda online utility, to find the RA, in coordinates of the equinox and ecliptic of date, of Arcturus at various ancient dates, corrected for proper motion. Then I used the JPL Horizons online ephemeris, to find the Sun's RA-to-RA time for those dates, then corrected for a year's change in Arcturus' RA, getting 3036BC, in good agreement with the 3102BC date determined for the Kali Yuga according to planetary conjunctions.

Reworking Playfair's "Remarks on the Astronomy of the Brahmins" (part 2)

In sec. 15, Playfair says, that the Hindu tables say that the Sun's apogee advances 1" in 9 yr, relative to the stars. In the last paragraph of my previous post, I mention that at 3000BC, the Arcturian year (a kind of sidereal year that does not depend on defining an ecliptic) advanced, relative to the true sidereal year, 2/3 as fast as the Sun's apogee. The Sun's apogee at ~3000BC, according to Dziobek, advanced 11"/yr (a value that changes little over the centuries). So, the anomalistic year (year to Sun's apogee or perigee) advanced (11/3) " / yr relative to the Arcturian year; maybe this was corrupted to 1/(3^2) " / yr. Alternatively, and more likely, maybe 11" / yr was corrupted to 11" /century = 1/9 " /yr.

In sec. 34, Playfair says that the Hindu tables give the obliquity of the ecliptic as exactly 24deg; this might involve rounding error. Anyway, I find from the polynomial formula in the 1992 Astronomical Almanac, p. B18, that the obliquity of the ecliptic at 3150 BC was exactly 24deg.

In Sec. 8, Playfair says the Hindus give the general precession as exactly 54"/yr. According to the 1965 Astronomical Almanac, p. 490, the general precession at ~3000BC was 50" - 1" = 49"/yr; but above, I found that the Arcturian year advanced, then, 7"/yr. So, 56"/yr would have been the general precession then, relative to the Arcturian year rather than the true sidereal year. Also, because at 3000BC the pole was tipped toward a longitude ~45deg from Arcturus' longitude, the maximum speed of advance, of the Arcturian year relative to the true sidereal year, would have been 10"/yr. The figure, 54" = 49" + (10/2)", is a midrange value useful for that half of the precession cycle when the Declination of Arcturus is most northerly.

Now the arc, 77deg (see sec. 17) between the mysterious "beginning of the zodiac", and the misnamed "apogee" (really, the vernal equinox at 4800BC) can be explained:

77deg / (54"/yr) = 5133yr = Mayan Long Count = 5125yr.

Hi Joe, I wonder if I can pick your brains on this hawking radiation problem. We've got
Power = (16pi G^2 M^2 / c^4) (pi^2k^4 / 60 hbar^3 c^2) (hbar c^3 / 8pi G M k)^4

That gives us Power = hbar c^6 / 15360 pi G^2 M^2

Well, the power is just how bright it is, and it's very bright as the mass fall to the Planck mass. Now I think the Planck mass is going to be closer to 3.07E-9 than as normally given. It doesn't matter too much though as at the moment I'm only after ball park figures.

Let's say that the speed of gravity is roughly c^3 Then we need to change the terms of the first bracketed expression, which is the surface area of the Schwartzchild radius for light. For gravity it will be a much smaller radius. So change that c^4 to c^12

That cancels out and we are just left with a c^2 in the denominator of the second bracketed term. So multiply hbar by the reciprocal of c^2 Now I reckon that that gives us the reciprocal of the speed of gravity squared. P = hbar * 1.112E-17 /15360 pi G^2 M^2 which gives us a rough answer of about 5E-19Js^1

I think I better add, that in the three bracketed equation for power, there's another term, epsilon which is taken as unity. I think that needs to be looked at. As does something called the trans planckian problem but I do like the power coming out somewhere near the basic charge value.

<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, I wonder ...Let's say that the speed of gravity is roughly c^3 ...<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Hi Bob,

For the "units" to be right, shouldn't it be "c" times some "dimensionless" constant or other (e.g., 137^3) ?

- Joe