Requiem for Relativity

What is Barbarossa's period?

My estimates of the catastrophic "Barbarossa period" seem consistent:

1. Barbarossa's sidereal orbital period from the sky surveys (6340.07 tropical yr) has a "sigma" error of > 1 yr and < 9 yr. Fitting an orbit to the sky survey positions, I found the radial speed only to the nearest 1 part in 1000, because it seemed that smaller differences surely were insignificant. This implies a sigma, for the radial speed, of > 1/4000, and a sigma for the total kinetic energy and hence (by the virial theorem) total energy and major axis, of > 1/10,000. By Kepler's 1.5 power law, the sigma for the period thus is > 1/7000.
The sigma error in estimating the centroids of the light patterns on the sky survey scans, seems to be < 1 arcsec, and the observed path about five deg, so the error in initial and final angular speeds is < sqrt(2)*1arcsec/2.5deg = 1/6400. With about a 1/40 increase in radius during the 1/20 radian travel (between the centers of the first and second segments), the angular speed decreases 1/20, so the sigma of this decrease is < sqrt(2)/6400*20 = 1/225, hence the sigma of the radial speed is < 1/450, and by the previous paragraph, the sigma of the orbital period is < 9yr.

2. Brauer's lake varves, together with the Mayan calendar, imply 12683/2 = 6341.5 yr, but Brauer's earlier articles contend with uncertainties of several years, so it seems likely that, somehow or other, such uncertainties still exist.

3. My reconstructed Sothic/Arcturian Egyptian calendar gives 6340.503 tropical yr before the winter solstice 2012AD (it must begin on a summer solstice, and Earth's orbital eccentricity has a small effect). A year corresponds to a quarter-day error in heliacal rising, which is reported only to the nearest day, so 6339.503 and 6341.503 tropical yr also are likely.

4. The "Legendre 2 Resonance" estimated from the first 25,000 pairs of Legendre polynomials, is 0.809023. From the first 5000 pairs it's 0.809047. From the first 1000 pairs it's 0.809168 (all these are by direct computations without interpolation, using an Intel Pentium CPU). This shows an accurate 1/n tail. Adding the tail to the 25,000 pair computation, gives x = 0.809017 = cos(36) = 0.809016994. Multiplication of sec(36) by my best Mayan Long Count general solar system resonance (5124.58yr) gives 6334.47 tropical yr. However, I don't know whether the polynomials should be weighted equally, as I did, or not.

5. Resonance with the proto-Jupiter implies 6339.501 tropical yr. The main uncertainty here, is the configuration of the proto-Jupiter's mass ring. The chief alternative, equal masses at 120 deg intervals, gives only 4/5 as much centripetal force as the approximation I used. So the uncertainty in orbital period is roughly 1/5 * 1/2 * 1/1000 * 1/4 = 1/6 yr.

6. Resonance with half (never whole) orbital periods of the seven largest planets, defined as minimum sum of squared deviations from odd half-periods, gives 6339.522 tropical yr. The resonance with Mercury is so sensitive to tiny changes in the Barbarossa period, that it would dominate everything else, so, I omitted it. Pluto's long-term average orbital period seems uncertain due to its eccentricity and interaction with Neptune and other planets.
I took the usual (e.g., 2007 World Almanac) sidereal orbital periods of Jupiter (11.862 Julian yr), Saturn (29.458 yr), Uranus (84.01 yr) and Neptune (164.79 yr). I calculated yesterday that the oldest observation of Jupiter recorded by Ptolemy (occultation, 3rd cent. BC) and Ptolemy's own opposition observation of Jupiter (2nd century AD) both are consistent, vis-a-vis modern ephemerides, with orbital period 11.862 yr (I found 11.8624 and 11.8619 yr, resp.)(data from Olaf Pedersen's book on Ptolemy).
I used Wikipedia's sidereal orbital periods for Venus (224.70069 day) and Mars (686.971 d). I used 365.25636 d for Earth's sidereal period. For this calculation, the inner planets need greater accuracy than does Jupiter, so it seems unlikely that Ptolemy's observations would help much.
Mars, Jupiter, Uranus and Neptune had nearly n+0.5 cycle (range: n+0.43 to n+0.54). The sum of squared deviations from the nearest odd half-cycle, was 0.2247 at 6339.264 Julian yr, 0.1711 at 6339.364 Jul yr, and 0.1957 at 6339.464 Jul yr. Quadratic interpolation gave the minimum at 6339.383 Julian yr = 6339.522 trop yr.

Summarizing: the only time interval consistent with all my estimates and their uncertainties, is 6339.503 tropical year, corresponding to an Egyptian Year One at 4328BC.

In the previous post, I mention correlations of the "Legendre 2 Resonance", in our solar system. More such correlations are:

1. The mass ratio Venus / (Earth + Luna) = 0.8050950.

2. Using Luna's average eccentricity of 0.0549, the angular momentum ratio (Earth rotation)::(Earth-Luna orbit) is 1::4.877 (Earth's dimensionless polar moment of inertia = 0.3307, per YV Barkin, 2009; vs. 0.4 for a homogeneous sphere). If the ratio were 1: instead, then the number of Earth rotations per sidereal month would (to first order, that is, until the ratio began to deviate appreciably from 1:) remain constant as rotational and orbital angular momentum exchange. That the ratio is near 1::5 instead of 1: suggests that somehow other quantities are involved.

From a 1977 review of Robert Gentry's work on radio-halos (today I find this review, of uncertain authorship, posted on Dr. Gentry's own website):

"Gentry believes the evidence points to one or more great
'singularities' that have affected Earth in the past, representing
physical processes which we do not now observe. ...Further (as we will explore in a subsequent review), Gentry concludes that the most recent singularity may have occurred only several thousand years ago."

Apparently Gentry doesn't have a Ph.D., but is primary author of many items about radio-halos, that appeared in Science, Nature and other leading journals in the 1970s. Today I scanned most of these that are on Gentry's website. I found no calculations of the age or epoch of anything, only lengthy discussions of laboratory measurements and possible chemical processes of radio-halos. Gentry's later writings often mention 6000 yrs, but I find no evidence that this figure comes from any radio-decay calculation, rather than Ussher's chronology of the books of Moses. Afterwards I searched RV Gentry in Web of Science (Science Citation Index), found almost all of the 35 articles that seemed relevant (i.e., about actual radio-halo studies, not cosmology or creationism)(especially his major articles, which mostly were in Science or Nature), on the shelves in the Iowa State Univ. libraries, skimmed them, and found no actual date computation more recent than a lead/uranium date of 250,000yr for coalified wood (Science 194(4262):315+, 1976).

Nonetheless, it appears from the above that at least one reviewer, sanctioned by Gentry himself, concluded that Gentry's work suggests, not any creation event, recent or otherwise, but rather, an unknown cyclical atomic phenomenon of period several thousand years. This supports my theory, of Barbarossa events every 6340yr.

Glacier Peak and Mt. Avachinsky

These two especially active "Ring of Fire" volcanos, in Washington state USA and in Kamchatka Russia, resp., erupted frequently c. 6300-5900 yr "BP" (i.e., yr ago), with a few hundred years uncertainty of C14 calibration.

These volcanos might be "canaries in the coal mine". Let's watch them (more than Yellowstone, the rare, though huge, eruptor featured in the recent movie "2012").

(Avachinsky is smaller than, and not the same as, Ichinskaya.)

More About the "Legendre 2 Resonance" (generally, "Jacobi 2 Resonance")

This is a fundamental mathematical relationship that I have discovered. Choose a real number x between 0 and 1, and a large whole number n. Evaluate the first n Legendre polynomials, at x (this is fast, using the "recurrence relation"). Take the logarithm of the absolute values of these evaluations, and multiply that logarithm, by 2*pi/log(2). The result is, a set of n negative real numbers.

The periodicity of this set, can be found by convolution with cosine and sine. That is, add the cosines of the numbers (all the cosines will be 1, if all the Legendre polynomials have values of the form +/- 1/2^k) to get a sum "S1", add the sines to get a sum "S2", and consider f = S1^2 + S2^2. The absolute maximum of f is at x=1, because there all the Legendre polynomials are 1, and all the logs are 0. However, there is, in the limit as n approaches infinity, an important relative maximum at x = cos(36 degrees) (or at least very close to cos(36) ). As detailed in my recent post, I used an Intel Pentium CPU (in a Hewlett-Packard desktop computer) to find "f" for n=1000 (i. e., the first 1000 pairs of Legendre polynomials), n=5000 and n=25,000; then used the accurate 1/n tail to estimate that the local maximum occurs for x = 0.809017 = cos(36) = (1 + sqrt(5))/4 = "golden ratio"/2.

If one convolutes with the zeroth and first Bessel functions, J0 and J1, instead of with cosine and sine, that relative maximum occurs at the same abscissa, x = cos(36). That is, find the values of all the Legendre polynomials, take the logs of their absolute values, multiply by 2*pi/log(2), and find the values of J0 and J1, instead of cosine and sine, for this set.

For n=400 (that is, the first 400 pairs of Legendre polynomials) I found (using an IBM 486 computer, programming with BASIC in double precision) this relative maximum at 0.80939, for n=800 at 0.80921, for n=1600 at 0.809113, and for n=3200 at 0.809063. (For all these, the last digit is by rough interpolation "by eye".) The successive differences are 0.000180, 0.000097, and 0.000050. This shows a fairly accurate 1/n tail, so the abscissa for n = infinity can be estimated by the geometric series, as 0.809013. This hardly differs from cos(36) = 0.809017. (I evaluated the Bessel functions using their symmetry or antisymmetry to get a positive abscissa, then used Hankel's semiconvergent series to fifth degree, per Jahnke & Emde, for abscissas > 16; and 27 terms of the power series, for abscissas < 16. Experiment showed that the cutoffs 16 and 27 were plenty big to make the error negligible.)

In the limit of large n, the Legendre polynomials' recurrence relation gives the sequence defined by P(n+1) = r*P(n) - P(n-1), where r = 2*x. Thus I find that when r equals the golden ratio, this sequence tends especially to lie near powers of 0.5, if it starts as the Legendre recurrence relation.

The Legendre and the Chebyshev polynomials are special families within a two-parameter collection of families of orthogonal polynomials called Jacobi polynomials. For all families of Jacobi polynomials, the recurrence relation, in the limit of large n, approaches the simple relation, P(n+1) = 2*x*P(n) - P(n-1). The zeroth and first Chebyshev polynomials are the same as the zeroth and first Legendre polynomials (1 and x, resp.). Though the Chebyshev polynomials have this simple recurrence relation from the beginning, and the Legendre polynomials only approach it in the limit of large n, one might expect the Chebyshev polynomials likewise to have a resonance peak (i.e., relative maximum of "f") at cos(36). Surprisingly, the Chebyshev polynomials have a resonance trough (relative minimum of "f"), not peak, at cos(36).

(With the IBM 486 CPU and double precision, I find that for n=800 pairs of Chebyshev polynomials, the trough is at 0.8090076; for n=1600, 0.80901217; and for n=3200, 0.80901458, where all the last digits are rough interpolations "by eye". The successive differences are 0.00000457 and 0.00000241, showing a fairly accurate 1/n tail, though here instead of a peak at decreasing abscissas, there is a trough at increasing abscissas. The geometric series estimate for n = infinity, is 0.80901458 + 0.00000241 = 0.80901699 = cos(36).)

Approximately, the Mayan Long Count (an approximation to a 5124.58yr resonance of solar system periods), times 4/(golden ratio), equals twice the Barbarossa period. The Long Count contains approximate whole numbers of periods of Jupiter, Saturn, Uranus and Neptune, and of Luna's apsidal advance. For some reason, so likewise does the Long Count * 4 / (golden ratio).

Thus the Barbarossa period contains approximate whole or half-whole numbers of these periods. The five year difference between the actual Barbarossa period, est. 6339.364 Julian yr, and the 5124.58 yr resonance basis of the Mayan Long Count * 2/(golden ratio) = 6334.33, causes the actual Barbarossa period to lack the Lunar apsidal and Saturn resonances, but to gain a Mars (half) resonance.

"I do not take kindly to the argument that because certain working hypotheses may not possess eternal validity or may possibly be erroneous, they must be withheld from the public."

- C. G. Jung, "Symbols of Transformation", quoted in "Psychological Reflections" (Princeton, 1970), p. 183.

Hi Joe, I think that's okay if you happen to be a Carl Jung, or a Einstein, Gell Mann, etc. I think it's counterproductive here. People are just going to wait until 2012, they're not going to allocate telescope time to it, for fear of looking like idiots if nothing happens in that year. If something horrendous does happen, then nobody is going to be that bothered about a possible brown dwarf, we'll all be far too busy burying the dead to worry about observational astronomy. Something of a Cassandra situation for you, and that has to be frustrating but people are just going to wait and see.

What did you make of the recent huge tsunami on the sun? So unusual that they thought it was a computer glitch.