Requiem for Relativity

<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, ...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. ...<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Thanks for the post! You've given not only a springboard for discussion, but also a wake-up call.

I don't know exactly what will happen. Maybe all of a sudden one day, 90% of Earth's surface is baked by meteor swarms, or solar flares, or something that we haven't had at all since 6000 or 12000 years ago, then the survivors go back to the Bronze Age again. On the other hand, maybe there will be a warning, like cataclysmic brightening of Barbarossa, or solar behavior unprecedented in our history, or comets big enough to detect a few hours or days before impact, or preliminary jolts before "the big one".

My prediction? Known and/or unknown physical forces slay almost all humans on almost all of the world's surface. This will happen on some or all of the days within three months either side of Dec. 21, 2012. Patches will be accidentally spared with only moderate destruction (i.e. &lt; 50% death rate). I wish I knew more about where these patches will be, but scraps of historical and archaeological evidence suggest that large rivers and midsize lakes offer some kind of protection. Maybe it's as simple as getting in the water when a fireball comes, yet not such a big body of water that it makes a tsunami.

Shortly before the U. S. Civil War, U. S. newspapers ran articles denouncing "Crazy Sherman" because Sherman publicly predicted high casualties. It turned out that Sherman's prediction was way low, but his was the only prediction that even got it in the ballpark (source: Ken Burns' TV series, "The Civil War").

There's some evidence that undergroud shelters won't work: the Pyramid Texts say "the people of the mountains were exterminated", yet these are the people with readiest access to cliffs and caves. Our ancestors might have known that megalithic structures somehow sufficed where natural caves or digging in, didn't. These megalithic shelters might have been on hilltops (maybe even, mountaintops, e.g. Mt. Ararat or the Andes) to avoid some kind of toxic miasma mistranslated as a "flood".

It would have been nice if I had been able to persuade some of the government astronomers to lift a finger (two astronomers employed by the government, one at Harvard and one at the U. of Iowa, actually did lift a finger many times to help me, in practical ways)(Dr. Van Flandern's help, was at his own expense, long after he had ceased to be a government astronomer), but I think most were too corrupted by the tax money. They have bought into the poisonous attitude that it is more about turf than truth.

The "climate change" ethics scandal, though only marginally related to my topic (I don't know whether 2012 will bring warming, cooling, or neither; I'm betting on cooling, though CO2 reduction might be important anyway), might weaken the ability of the academic establishment to stonewall. If their stonewall cracks a day sooner - on Dec. 19, 2012 instead of Dec. 20, 2012 - it could make a big difference. The Wall Street Journal hasn't printed the short letter I mailed them the day after Thanksgiving, in which I point out that the science guild is unreliable, that anyone with a World Almanac and a checkbook calculator can prove for himself in five minutes that the Mayan calendar embodies profound astronomical and mathematical knowledge (e.g., the Long Count is an exact multiple of Uranus' orbital period), and that mainstream scientists had better get on the case.

I and several government (state and "private", i.e. semi-state, university) astronomers spoke at the North Central Region (NCRAL) amateur astronomers' conference in May 2009. I attended most of their talks but I'm pretty sure none of them attended mine. I also spent the previous two days hiking many miles around several nearby college campuses trying to recruit diverse faculty members, to attend my talk, but I'm pretty sure none of them attended either.

Maybe it's like this every time: 6340 yrs ago, 12680 yrs ago, etc. Maybe our ancestors (anyway, more or less our ancestors) left the Giza pyramids, Mayan calendar and other clues so that "next time it can be different".

It's said that only one, small, plain statue of Khufu is known. Khufu wasn't an egomaniac: he didn't even bother to have anyone make his statue. If he was buried in the pyramid at all, it was only because it was dear to him as his life's work. What is Khufu's pose in that statue? It's like the movie, "The Ten Commandments": "So let it be written, so let it be done!" and he's smiling.

Hi Joe, about eighty thousand years ago, the human race was almost wiped out. Favourite culprit being the super volcano Toba. If anything happened about six thousand years ago, it was a massive cultural leap forward.

I remember once a lecturer reading a fragment of a love poem y Sappho, you could have heard a pin drop in the room. Everyone felt that they had touched the mind of a woman from a bygone age. yet we are all painfully aware of of modern idiocies of interpreting the mind set, world view of an Alexander for instance. He did it for the chicks and fast cars school of thought. We can see him in red braces and a striped made to measure shirt.

Bearing that in mind, let's try and think like an ancient celt for instance. "There was a time of great troubles and tribulations. Those that went and made offerings to the sacred lakes; doorways to the other world; survived and those that didn't perished." Any standing water meant a great deal to people who had never seen a mirror, and who obviously knew that water had powerful magic. The point is, that we now simply cannot comprehend their world view. The same goes for baleful Sirius. It seems to change colour all the time.

On this board most people would have to say, that some change in the core of a planet, would e instantaneously transmitted to the core of the sun. How that information might effect things would be open to debate. But things are going to take time in the region of tens of kilometres per second. So, stuff must be already happening. Low mass stuff at first, changes in the magnetosphere of the sun springs to mind. That's why I thought of the tsunami on the sun, pretty major event that. Now if such changes have been noted, then the powers that be have decided not to tell anyone. To tell the truth, I wouldn't say anything either. If our time is up, why worry people?

<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 />...If anything happened about six thousand years ago, it was a massive cultural leap forward. ...

...If our time is up, why worry people?

<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

It hasn't yet become canonical academic dogma, but recent articles in mainstream archaeology journals say that there was a drastic reduction in human cranial diversity in N. America and probably in Europe too, roughly 6000 yr ago (I cited the most important article - a lengthy, careful analysis of the N. American crania - in one of my posts earlier this year). The date is uncertain because of the small number of N. American skulls and the uncertainty in dating them. It was really a drastic reduction: prior to roughly 6000 yr ago, the cranial diversity in N. America alone, was much greater than in the entire world today.

The old theory, pretty much German National Socialist anthropology c. 1937, was, that some genetic mutation(s) occurred among Europeans c. 6000 yr ago, which allowed the mutant group, which happened to speak proto-Indo-European, to outproduce or outfight their neighbors, kill them off and/or seize or buy the neighbors' women (so that after many generations, only the neighbors' mitochondrial DNA was left, as modern English have mainly Danish nuclear DNA and British mitochondrial DNA), spread proto-Indo-European language all over Europe and west Asia, and greatly upgrade civilization. Alfred Rosenberg (even today, his text sits in the open stacks of most big university libraries) cited the obvious similarity of some common ancient Egyptian words to Indo-European, and the obvious European appearance of many Old Kingdom aristocrats, as evidence that even ancient Egypt was part of this evolutionary explosion. Sumer and very early China (six-foot red-haired folks in Mongolia) can be worked into the theory somewhat. (Even such mainstream sources as the American Heritage Dictionary, say that the Indo-European languages mysteriously exploded from a common root c. 6500 yr ago.) The new cranial data from N. America, contradict the foregoing National Socialist theory of recent human evolution. It's no longer necessary to rebut the quasi-National Socialist anthropologists with shaky nurture-over-nature arguments (Franz Boas et al) or by throwing them in prison (outlawing "racism").

It's unlikely that in N. America, too, and at the same time, hugely advantageous sporadic mutation(s) drastically reduced the human diversity on the continent. It's likelier that there was a worldwide cataclysm, with a survivor effect on linguistic and cranial diversity on both continents. If something randomly wiped out, say, England and Germany and Russia, then almost all northern Europeans would have French culture, language and physiognomy. About 6500 yrs ago, I think, this did happen, and the survivors happened mainly to be Indo-European in Europe, and Athabascan (e.g. Navaho, Apache) in western N. America. High civilization suddenly appeared almost everywhere simultaneously c. 5000 yr ago, not because of a brain mutation in Nordics or Semites or somebody, but because people everywhere had to rebuild for a thousand years after being almost wiped out. About the only things left of the "antediluvian" civilization, are some megaliths. The antediluvians, judging by the megaliths, by the hints left about astronomy, Barbarossa's orbit, etc., and by the lack of artifacts on the scale of, say, Hoover Dam or the battleship Missouri, seem to have been about as advanced as 16th century Europe.

There was no drastic climate change 6000 yr ago. Central N. America became only moderately drier, transitioning to the same forest types it has today.

The reason to worry people, is, as I said, so "this time it can be different". The more I "worry" people, the likelier that powerful instruments will be brought to bear, research will be done, and survival techniques improvised. None of these cyclic cataclysms exterminated mankind. As on the advertisement for last month's hit movie, "2012", the question is: who will survive?

The Asteroid Resonance

I speak of a 6339.5 year, cataclysmic Barbarossa period. I and many others speak of a 5125 year Mayan Long Count period. Exceptionally many solar system resonances (i.e., common multiples) occur for both these periods.

There is a "third period" for which exceptionally many solar system resonances occur. This is: the Mayan Long Count, times two, divided by the golden ratio; i.e. 5124.58 Julian yr / cos(36), where I use as the "essential" Mayan Long Count, the best harmonic resonance with the main solar system periods, according to their modern values. This third period is 6334.329 Julian yr.

There is a significant tendency for asteroid orbital periods to resonate with this "third period", that is, for their orbital periods to divide it. Those asteroids which have attracted the most attention (for reasons other than bizarre orbits) should have the most accurately known long-term average periods. Also, massive asteroids should have less chaotic orbits (perturbing most of their interactors through many cycles, before they themselves are perturbed); and very slowly rotating asteroids should be most immune to unknown forces involving rotation.

So, I chose the eight asteroids on Wikipedia's list of the most massive:

1 Ceres
2 Pallas
3 Juno
4 Vesta
10 Hygiea
15 Eunomia
511 Davida
704 Interamnia

To gain statistical sensitivity, I augmented these, with ten presumably very massive asteroids from Wikipedia's list of those largest in dimension (but cautiously, only those on that list, for which all three body axes are given):

7 Iris
16 Psyche
19 Fortuna
29 Amphitrite
45 Eugenia
52 Europa (note allowed conflict with name of Jupiter's moon)
65 Cybele
87 Sylvia
88 Thisbe
107 Camilla

Lastly I added five from Wikipedia's list of slow rotators:

253 Mathilde
288 Glauke
1220 Crocus
3691 Bede
9969 Braille

Wikipedia's list of slow rotators, had three more "asteroids", named only by a more modern system, but two of these had orbital periods that I couldn't find quickly searching the Web, and the other of the three had an orbit resembling that of Halley's comet. So, I didn't use these three.

My statistic, "f", was the sum of the natural logarithms of the fractions of an orbit, by which the "third period", 6334.329 yr, failed to contain a whole number of periods of the asteroid. Thus the most significant result, is that for which the product obtained by multiplying all the leftover fractional periods (e.g., 0.201 period too much, 0.102 period too little, etc.), is the smallest. The distribution of "f" is nearly normal, because "f" is the sum of many (23) terms, each of which has, the same distribution which differs not too extremely from a normal one. Elementary calculus gives the mean and variance of the distribution for one term, and from that, the mean and variance of f are found by very elementary statistics.

According to this, the tendency for these 23 asteroids' periods to divide wholly into 6334.329 Julian yr, is significant at sigma = 2.2, i.e. p = 1.4%. Also, nine of the 23 quotients lie within 0.0845 period of a whole number; the binomial significance of that is p = 0.94%.

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(update Dec. 17, 2009)

In my above set of 18 very massive asteroids, another significant feature, is that the asteroids whose rotation periods are less than, but most nearly equal to, half that of the giant planets, also show the best orbital resonance with the 6334.329 yr period.

The harmonic average sidereal rotation period of Jupiter+Saturn+Neptune, weighted by mass, = 2*5.1185h (data from 2007 World Almanac); same, including Uranus, = 2*5.1874h. So, the theoretical breakpoint is either 5.12h, 5.19h, or a compromise.

Seven fastest rotators in my set of 18 very massive or very large asteroids:

29 Amphitrite: 5.39h, fractional excess orbital period 0.706
4 Vesta: 5.34h, fractional excess period 0.926
87 Sylvia: 5.18h, fractional excess period 0.414
511 Davida: 5.13h, fractional excess period 0.003
107 Camilla: 4.84h, fractional excess 0.012
16 Psyche: 4.20h, fractional excess 0.044
65 Cybele: 4.04h, fractional excess 0.521

I gleaned three more, massive asteroids from Wikipedia's list of asteroids of large dimension, by accepting members of that list which have only one or two dimensions given (624 Hektor was excluded because it is a Trojan asteroid with period equal to Jupiter's):

48 Doris
13 Egeria
94 Aurora

An article on the USNO website, by Dr. James L. Hilton, lists some of the most massive asteroids. Here I learned of four more, massive asteroids (all at least 1/400 the mass of Ceres):

11 Parthenope
20 Massalia
121 Hermione
216 Kleopatra

None of these seven, have orbital periods close to resonance with 6334.329 yr, but the shortest rotation period among them, is 5.385h. So, none would be expected to show such resonance, according to my hypothesis.

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(update Dec. 20, 2009)

From the online IRAS asteroid catalog at VizieR, I got a list of all asteroids of estimated average diameter &gt; 150km. Of these, 22 already are among the 25 most massive and/or largest asteroids considered above. Three more, I exclude because they are Trojans (5.0 &lt; a &lt; 5.4). Of the 72 new large asteroids remaining on the list, Wikipedia gives the rotation period and a sufficiently precise orbital period (i.e., to 0.1 day or better) for only 15. Changes in the layout (authorship or vintage) of the Wikipedia articles as I went down the list, correlated with blocks of asteroid articles consistently giving or not giving the rotation period, or giving this or that precision for the orbital period. This suggests that many more of these asteroids might have adequate data elsewhere.

Anyway, I used the 15 additional asteroids with adequate data on Wikipedia:

6 Hebe
22 Kalliope
31 Euphrosyne
39 Laetitia
49 Pales
85 Io (note allowed conflict with name of Jupiter's moon)
96 Aegle
130 Elektra
238 Hypatia
241 Germania
259 Aletheia
283 Emma
324 Bamberga
423 Diotima
444 Gyptis

The shortest rotation periods are 4.148h (22 Kalliope), 4.775h (423 Diotima), and 5.138h (39 Laetitia; this is the same rotation period as 511 Davida, q.v. above). The other 12 rotation periods all are &gt; 5.52h. Laetitia's orbital period is second-closest (remainder, 0.931) to a whole divisor of 6334.329 Julian yr.

The closest (remainder, 0.936) is 49 Pales, whose rotation period is said to be 10.42 +/- 0.02h, but probably really is 5.21 +/- 0.01h. Pales is the only asteroid (of the 26, among the 72, for which any rotation period is given) whose rotation period is given with error bars. Only three of the 26 rotation periods, fail to be stated to the nearest 0.01 or 0.001h. Apparently the reason for Pales' low precision, is reliance on the rather difficult determination in the rather old study of Schober et al, Astron Astrophys Suppl 36:1-8, 1979. Schober gives the period of 92 Undina, another of his three studied asteroids, to 0.02h accuracy also; though of 88 Thisbe, to 0.0006h accuracy.

Schober's lightcurve shows that 49 Pales' true rotation period likely is 10.42/2 = 5.21h. Pales has a deep secondary minimum, noted by Schober. In contrast to 88 Thisbe, 49 Pales' secondary is much less deep than its primary. However, like 88 Thisbe, 49 Pales' secondary, according to Schober's plot (p. 4, upper left especially) occurs exactly 180deg from its primary. A much weaker secondary at 180deg, can be due only to reflectance difference or to axis wobble. Yet "...reflectance for most [asteroids]...is close to constant over the whole surface." (Zwitter et al, A&A 462:795-799, 2007, p. 797) and if reflectance varies considerably, the peak reflectance will be at some random phase which will destroy the 180deg phase of the secondary minimum. So, the "secondary" minimum really is a weaker recurrence of the primary minimum, affected by wobble.

Another of these asteroids, 168 Sibylla, has a rotation period disputed by a factor of 2. Wikipedia cites the Lowell Observatory's Asteroid Orbital Elements Database for its rotation period of 23.82h. Pilcher et al, Minor Planet Bulletin, 2008, give Sibylla's rotation period as 47.009 +/- 0.003h = 2*(23.5045 +/- 0.0015h).

Asteroids 241 Germania, 259 Aletheia, and 324 Bamberga have rotation periods 15.51h=3*5.17h, "15h"*(5.00+/-0.17h), and 29.43h=6*4.905h, resp. Though their rotation periods are whole multiples of ~ 5h, none of their orbital periods is very close to a whole divisor of 6334.329.

The Asteroid Resonance - Part 2

In the previous post, I show that my sample of 25 of the most massive (according either to gravitational observations, or to their large dimensions) asteroids, exhibits a breakpoint at somewhere between 5.13h and 5.18h sidereal rotation period. Asteroids just below, but not exceeding, this rotation period, are in orbital resonance with the 6334.329 Julian yr resonance. (This resonance is the empirical 5124.58 yr resonance, on which the Mayan Long Count apparently was based, times sec(36); cos(36) is half the "golden ratio" and also the abscissa of major resonances and antiresonances of Jacobi polynomial families, with powers of 2).

The three asteroids (Davida, Camilla, Psyche) in best orbital resonance, happen to have consecutive rotation periods among the 25. The chance of this is p = (25-2) / (25*24*23/6) = 1.0 %.

Others have said that Earth's rotation period originally was near 5h. For now, let's pretend that Earth's axis is perpendicular to the ecliptic. If angular momentum were transferred from Luna's orbit back to Earth's rotation, Luna's orbit would become synchronous (assuming a circular orbit then) at 4.86h; then R/r = 2.29, i.e. Luna is slightly inside the Roche limit (for a fluid body; this would be outside the Roche limit for some plausible rigid moons).

If the angular momentum return, from Luna to Earth, stopped when Luna reached the fluid-body Roche limit R/r = 2.88 (using the traditional value 2.44 for the equal-density case, and correcting for densities) then Earth's sidereal rotation period would be 4.98h. If early Luna had density only 1 gram/ml (Earth::Luna density ratio = 5.5), then the fluid-body Roche limit would be R/r = 4.31, and Earth's rotation period there, 5.24h. So, a moderately less dense early Luna, originating at the fluid-body Roche limit, could imply an original Earth rotation period between 5.13h and 5.18h, i.e. the critical period suggested by the asteroid data.

Really, Earth's axis is tilted 23.44deg to the ecliptic; consideration of the vector components of the infinitesimal rotation, implies an Earth rotation period of 5.05h, not 4.98h, when Luna was at the fluid-body Roche limit. At this accuracy, assumption of other suggested values of the fluid-body Roche limit (2.423 generally is thought most accurate) hardly matters, nor does assumption of an average tilt of 24deg instead of 23.44, nor does averaging the cosines of the total Earth-Luna inclination 23.44 +/- 5.1deg, nor does modification of the Roche limit by inclusion of the Sun's tidal force.

Early Luna must have been less dense; suppose it were basalt rubble which eventually compressed to solid basalt today. The density ratio of "solid" to "broken" basalt is ( www.simetric.co.uk ) 3.011/1.954 = 1.155^3. So, the Roche limit would have been 16% greater, the angular momentum retained by Luna 8% greater, and that of Earth ~ 1.6% less. That is, Earth's rotation period would have been 5.05*(1.016) = 5.13h. If early Luna were a broken basalt rubble at the fluid-body Roche limit, Earth's rotation period would have been exactly the critical rotation period (rotation period of 511 Davida; also, half the mass-weighted harmonic mean rotation period of Jupiter, Saturn & Neptune) at which asteroids show orbital resonance with my "third period", 6334.329 yr. (This "third period" has a deep mathematical relationship to the Mayan Long Count, and also approximates the Barbarossa period; see earlier posts.)

Baalbek

Wikipedia's Baalbek article has a simple groundplan of the Baalbek temple site. Called "Nordisk familjebok.png", this map is oriented with East at the bottom and North to the right.

In the upper left corner, is a dotted line presumably corresponding to the oldest part of the structure. This line is oriented, according to my protractor measurements from the screen and from the printout, 15 +/- 1 deg north of east.

At the winter solstice in 2012, Barbarossa's heliocentric ecliptic latitude will be -11.803. At the last Barbarossa event, approx. 6340 yr before 2012AD, Earth's axis was tilted almost exactly toward Barbarossa's ecliptic longitude, with obliquity (polynomial formula, 1990 Astronomical Almanac) 24.134 deg. This implies that Barbarossa's declination then was +12.331.

My quick estimate, is that an object with this declination, viewed from 34.007N (the latitude of the Baalbek temple) would rise 15.1 deg N of E. So, the Baalbek temple seems also to incorporate, in its oldest known strata, the "unexplained azimuth" (i.e., azimuth toward the rising of Barbarossa c. 4328BC as seen from a given temple's latitude) recently noted by Shaltout et al in Egyptian temples (see my earlier posts on that subject).