Beelzebub's Buried Dog

The Mathematical Problem of the "Precession-Time Paradox"

There is no doubt anymore - outside the solar system, Einstein's complicated Theory of a non-linear gravitation does prevail considerably over Newton's linear. Can the so-called THEORY OF EVERYTHING be unraveled at last?

Experts at the International Astronomical Union, the NASA's Jet Propulsion Laboratory, the US Naval Observatory, the Max-Planck-Institute for Astrophysics, the Royal Astronomical Society, the National Research Council of Canada and other renowned institutes, as well as famous physicists like Dr. Stephen Hawking are not able to solve the problem, since they do not comprehend the fundamental physical and mathematical principles of the civil-calendar.

"The last time we had a real expert on these matters was with Fr. Clavius,* about 400 years ago."

Christopher J. Corbally, Vatican Observatory Research Group

*(Christophorus Clavius - the distinguished mathematician, who participated in the calendar reform of 1582)

In scientific textbooks it is generally claimed, that our Earth acts like a gyroscope. Viewed as a physical exception, Earth is suppose to precess opposite to its direction of rotation. The period of its complete precession cycle is said to take about 25 800 years. During this time period, it is claimed Earth supposedly goes through one retrograde rotation relative to the inertial system of the fixed stars. An additional time interval of one year of about 365 days must occur simultaneously. But since this time interval cannot be substantiated by actual time measurement, hence the theory of the Earth's precession does not have a proven scientific foundation.

A simple mathematical example shall explain the physical aspect of this precessional motion:

A...................B............................................................C

A gyroscope at point B on the line A-C makes n rotations with respect to the central point A in one complete period of revolution around A.

Logically, the gyroscope must make n + 1 rotations with respect to the distant point C.

Assuming the gyroscope makes 365.24219878 rotations per revolution around A, and within a certain time period it makes 25800 revolutions, the total amount of rotations with respect to A must equal:

n × R = 365.24219878 × 25 800 = 9 423 248.73

Assuming further that the gyroscope precesses and describes a complete retrograding precession cycle in 25800 periods of revolution, how many rotations does the gyroscope make in that time period with respect to A?

a) 365.24219878 rotations × 25 800 minus one rotation, equals 9 423 247.73 rotations

b) 365.24219878 rotations × 25 800 minus one revolution, equals 9 422 883.49 rotations

"Why one revolution?"

In order to understand this mathematical problem, we must analyze the time-discrepancy caused by this precession:

Please, refer again to the above diagram. Imagine the Earth standing still at point "B" in its orbital plane on the line "A-C" between the sun "A" and the fixed star "C". We will assume that the Earth has already completed its 25 800 revolutions of 365.24219878 rotations each, without precession.

Now we will make up mathematically for the one retrograding or precession motion of the Earth at point "B" in its orbital plane - first with a vertical and then with a 23½° inclined Earth's axis:

1) In the vertical position of the axis, the sun is always directly over the equator during the one retrograding motion of the Earth. This results in a change from a day to a night.

This time interval corresponds to one rotation relative to the sun or the stars in a period of 25 800 years, which is equivalent to about 3.34 s per year* or about 9.12 ms per day.

*equivalent to the regression of the fixed stars by yearly 50.26" on average

2) In the 23½° inclined position of the axis, the result is completely different. Not only does the change from a day to a night occur, but since the sun is now directly over the ecliptic of the Earth, also four seasons have to appear successively during this same retrograding motion.

That time interval corresponds to one revolution of the Earth around the sun, implying more than 365 solar days in a period of 25 800 years, which is equivalent to about 1223 s per year or about 3.34 s per day!

Is this time-discrepancy a physical fact or an illusion?

First of all we must understand what this enormous time-discrepancy really means, as the additional time interval of one year is only seemingly 'created'. How else can one explain a retrograding rotation of the Earth with an inclined axis, which has four seasons appear at the same time? Ultimately, this phenomenon would imply that the vernal equinox has to retrograde around the sun by not only 50.26" per year, but per day!

At some point in history the theory was put forward - maybe out of ignorance or even intentionally – that a precession of the Earth is the cause for the steady regression of the fixed stars, a phenomenon already observed since ancient times. It was realized, that due to such a precession a gradual shift of the seasons has to occur. In order to mathematically justify this theory, a sidereal year was 'invented'. Its time interval is suppose to be about 20 minutes longer than the precisely defined tropical year of 31 556 925.9747 seconds - the fundamental physical time interval for the definition of the SI second, an internationally accepted Standard of Physical Measurement.

Paradoxically, this so-called sidereal year of 365.256361 mean solar days, said to be the truest measure for Earth's period of revolution around the sun with respect to the fixed stars, has no physical relevance or practical application in astronomy and specifically in astrometry!

At the beginning of the 1950's, when accurate clocks and methods of sidereal time measurement were available to precisely determine the tropical year, it became evident that a precession of the Earth cannot exist, as it was believed. Instead of accepting this truth, it was decided - for whatever reason - to obscure this knowledge by introducing the new and complicated reference-system of the vernal equinox*.

* ".... a base position from which the mean time can be calculated was established. This base position is the vernal equinox, an imaginary point in the sky that is, nevertheless, calculated with great accuracy by astronomers. Practically, the location of the vernal equinox is found by reference to the position of the fixed stars." Funk & Wagnall’s New Encyclopedia

The natural and dependable system of the 'sidereal-time-clock' became obsolete. New star catalogues and elaborates tables including formulas to pre-calculate the positions of stars were now available, which made the actual measurement of sidereal time unnecessary. It could not have been made any easier, especially for hobby-astronomers. Since there were no skeptics there was no suspicion that something was not right about the theory of the precession of the Earth.

If precession is considered to be a physical fact, then one should also be able to measure and substantiate the additional physical time interval of more than 1223 seconds per year.

Any time-delay in a planet's rotation period with respect to the inertial system of the fixed stars due to a precessional motion of the planet’s axis, can never have any influence on the planet’s actual revolution period around its sun.

Completely contradictory to this statement is therefore the assertion about the time period of the so-called true sidereal year, which only appears to exist in the supposition that a precession of the Earth exists. But this would mean that the time interval for each consecutive revolution period of the Earth around the sun with respect to the position of the fixed stars should be about 20 minutes longer than the tropical year (the absolute physical measurement standard for time).

This is in reality not the case.

Does one seriously believe, that because of precession the Earth can 'loose' an entire year after 25 800 revolutions around the sun, only to have 25 799 tropical years completed?

In order to visualize this absurdity, the sun and the stars will have to rise and set one additional time in about every 71 years throughout this whole precession cycle. And this extraordinary cosmic phenomenon has to occur without being noticed, despite precise methods of time-measurement. But then again, how is it possible to measure something that does not exist?

"The following measurements are proof, and they are factual, that the average figure for the regression of the fixed stars is about 50.26" annually, and it has nothing to do with a precession of the Earth, but is due to the effect caused by our entire solar system orbiting a 'central sun'." (K-H. Homann)

Practical Observation and Measurement of Sidereal Time with respect to Sirius:

My meridian tansitition time measurement with respect to Sirius (using the UTC atomic-time radio signal from WWV Fort Collins/Colorado), which I conducted over a period of 5 consecutive years, resulted in the following mean sidereal rotation time for the Earth.

Obviously, as indicated by the adjective mean all variations in time caused by periodic or any other fluctuations of the Earth's axis, as well as the assumed precession of the axis, must be included in the 5-year observation period. Technically speaking this is still the easiest and best available method to measure and determine a mean sidereal day.

First meridian transition time of Sirius on 20.04.1994 at 20:16:48.5 hours

Last meridian transition time of Sirius on 19.04.1999 at 20:21:34.5 hours

The total time span between those two measurements is exactly 157 680 286 seconds.

(5 × 365 mean solar days of 86400 s plus the time-difference of 286 seconds on the last day)

In this same time interval exactly 5 × 366 sidereal days (meridian transitions) were completed. As a result, the mean sidereal day with respect to Sirius is:

157 680 286 s ÷ 1830 = 86164.09071 seconds.

Note: The mean sidereal day is officially published with 86164.091 s mean solar time, while the mathematically calculated mean sidereal day is exactly 86164.0905382 seconds. Therefore, my precise measurement of 86164.09071 s with respect to Sirius is within the acceptable range of accuracy.

A maximum error in observation of ± 0.5 seconds between the two (first and last) meridian transition of Sirius during the period of 5 years would have the following results:

minimum: 157 680 285.5 s ÷ 1830 meridian transitions = 86164.09044 s

maximum: 157 680 286.5 s ÷ 1830 meridian transitions = 86164.09098 s

Due to the apparent precession, the measurable mean sidereal day should be about 86164.09966 seconds, since logically the actual mean rotation time of the Earth by 86164.0905382 seconds can only be measured with a delay in time relative to the inertial position of the fixed stars. In other words, if precession were indeed to occur, absolutely no fixed star can ever have a mean meridian transition time of 86164.0905382 seconds.

This physical fact would imply that my measurement with respect to Sirius contains an error of observation by about 16.7 seconds (5 × 3.34 s per year), not to mention the +1223 s with each sidereal year!

Note: Many 'experts' have suggested to me to "correct" or "compensate" my observation for precession by either adding or even deleting about 9.12 ms daily!

It can be concluded, that the annual regression of the fixed stars by 50.26" on average allows for only two explanations:

- a precession of the Earth's axis

- a revolution of our entire solar system around a central sun

Since it was proven that a precession of the Earth cannot exist as claimed, Earth's mean sidereal rotation time of 86164.0905382 s can only coincide with one true "axis-star", which is orbited by our solar system.

"And because our Earth has this decisive mean sidereal rotation time with respect to Sirius, the Dog Star, there can no longer be any doubt about the central position of Sirius relative to our solar system. The mathematical proof, the observations and measurements, as well as a complete understanding of the fundamental physical and mathematical principles of the civil-calendar will bring the theory of gravitation - at least concerning the gravitation outside of our solar system - into a completely new light. Has Einstein's theory of a non-linear gravitation been greatly underestimated, and is this not the basis to finally unravel the so-called 'theory of everything'?"

Time Deviation and Adjustment of the Civil Calendar to the Tropical and Sidereal Year

The assumption that Earth's polar axis precesses opposite to its direction of rotation, whereby the Earth, after completing a retrograding precessional cycle around the sun, looses one year of about 365 mean solar days with respect to the apparently true sidereal year of 365.256361 mean solar days, although paradoxically one additional tropical year must occur due to precession, does also completely contradict the precise mathematical time-keeping of our civil calendar.

It is an undisputed fact, that our civil calendar is mathematically synchronized to the actual revolution period of 31 556 925.9747 seconds. This physical time interval for the Earth to complete its orbit around the sun with respect to the inertial system defined by the position of the fixed stars is still the absolute criterion for time.

Please, refer once more to the previous simple diagram.

The absolute center of the Earth "B" has completed one full 360° revolution around the sun "A" after exactly 31,556,925.9747 seconds or one tropical year.

Assuming for the moment, that the Earth's rotational axis does not precess, an observer on the Earth's surface, for example, would measure with the aid of a meridian-transition instrument exactly 365.24219878 rotations of the Earth with respect to the sun "A" and exactly 366.24219878 rotations with respect to the inertial point of reference or fixed star "C", since:

365.24219878 × 86400 s = 31 556 925.9747 s = 366.24219878 × 86164.0905382 s

According to the generally accepted claim that it takes the Earth about 25 800 years to make one retrograde precession cycle, the following celestial-mechanical process would have to occur after a period of 6450 years:

The fixed star "C" will appear to our observer approximately 21 600 seconds later in his meridian-transition instrument, since he will notice a time-delay of about 9.12 milliseconds per day* or about 3.34 seconds per year with respect to the fixed star "C". Of course, the same is true with respect to the sun "A".

*(Note: 86400 s ÷ 25800 revolutions equals about 3.34 s per revolution or 9.12 ms per rotation)

Interestingly, our observer will also notice another phenomenon taking place during this quarter period of precession, because the 23½° inclined Earth's axis has changed its direction in space with respect to the sun or the fixed stars. In other words, the sun "moved up" by 23½° along the ecliptic during those 6450 years, while for example the fixed star "C" appears 23½° lower in our observer's meridian instrument.

If we were to choose a specific point in time when the Earth "B" crosses the imaginary line "A-C", say January 1 at 00:00 h, then after 6450 revolutions of the Earth "B" exactly 6450 × 31 556 925.9747 s have elapsed with respect to the sun "A". However, due to the assumed precessional motion of the Earth's axis, our observer still has to consider the time delay of 21 600 s.

Since the Gregorian Calendar has a defined length of 365.2425 days, it is only about 26.03 seconds longer (365.2425 × 86400 s = 31 556 952 s) than the tropical year of 31 556 925.9747 seconds. Therefore, after 6450 revolutions of the Earth a time difference of 167 893.5 s or 46.64 hours must occur and our calendar must then indicate December 30, instead of January 1. Due to the assumed precession the 21 600 s have to be deducted now from the 167 893.5 seconds; 46.64 h minus 6 h = 40.64 h

Consequently, the total time difference that our calendar needs to be corrected for is almost 2 days.

Please, see the diagram "Time Deviation and Adjustment of the Civil Calendar to the Tropical-Sidereal Year"

As indicated earlier, the change in direction of the 23½° inclined Earth's axis in space due to precession does create a unique problem:

It was said, that after exactly 6450 revolutions of the Earth, while crossing the imaginary line "A-C" at point "B" on January 1 at 00:00 h, our civil calendar will indicate December 30. However, in those 6450 years the position of the sun relative to the Earth's equator has also changed at point "B", and instead of winter on the Northern Hemisphere it is spring. Based on further calculations, this paradoxical shift in time appears to create an additional difference in time of 91.31 days (¼ year) in 6450 years or about 20 minutes per year:

91.31 days × 86400 s/day ÷ 6450 years = about 1223 s/year

Here we have those mysterious 20 minutes of time-manipulation, resulting from each revolution of the Earth around the sun; i.e. a time difference of about 1223 s between the tropical-sidereal year of 365.24219878 mean solar days and the apparently true sidereal year of 365.256361 mean solar days.

This yearly time difference can be calculated mathematically, but based on observation and according to physical laws it cannot exist in reality.

In closing, I pose two uneasy questions, which thus far the experts are unable to answer decisively:

1. Is the exactly defined time period of the tropical year of 31,556,925.9747s (which is mathematically based on a very precise mean sidereal day to which even the atomic time second has to be synchronized) derived from the about 9.12ms longer sidereal day, although such a sidereal day is not used in practice for any time-reference or astronomical calculations?

2. If a true sidereal reference point for the tropical year is a pre-calculated imaginary point or direction in space, then what other reference point or fixed star is used, in order to determine a sidereal year of 365.256361 Earth rotations and consequently a sidereal day, that must have an additional time-difference of more than 3.3 seconds per daily rotation of the Earth, since the yearly time-difference between a sidereal year and a tropical year is supposed to be 1,223.6 seconds more, with each consecutive 360° revolution of the Earth?

Karl-Heinz Homann RR1, Site 19, C2 Peers, Alberta - Canada T0E 1W0

e-mail: uhomann@telusplanet.net

Appendix "Beelzebub's Buried Dog"

*The Relativity of the Concept of Time*

"First of all, you must know that in calculating Time the ...beings of that planet (Earth) take the 'year' as the basic unit ...and they define the duration of their 'year' as the time it takes for their planet to make a certain movement in relation to another cosmic concentration - that is to say, the period during which their planet, in the process of 'falling' and 'catching up', describes ...a ... revolution around its sun." "But since ... you do not yet have any idea of the exceptional peculiarities of Time, you must first be told that genuine Objective Science defines this cosmic phenomenon thus:Time in itself does not exist, there is only the totality of the results issuing from all the cosmic phenomena present in a given place. Time in itself no being can understand by Reason or perceive by any outer or inner being-function. It is possible to evaluate Time only by comparing different cosmic phenomena occurring under the same conditions and in the same place where Time is being considered. It should be noted that in the Great Universe all phenomena, without exception, wherever they arise and are manifest, are simply successive, lawful 'fractions' of some whole phenomenon which has its prime arising on the '... Sun Absolute'.In consequence, all cosmic phenomena, wherever they proceed, have an 'objective' significance. Time alone has no objective significance, since it is not the result of the fractionating of any definite cosmic phenomenon. Issuing from nothing, but always blending with everything while remaining self-sufficiently independent, Time alone in the whole of the Universe can be named and extolled as the 'Ideally-Unique-Subjective-Phenomenon'. Thus, ...Time ...is unique in having no source on which its origin depends, and it alone, like 'divine Love' always flows independently and blends proportionately with all the phenomena present in all the arisings in any given place in our Great Universe." "...since Time has no source of its arising, and its presence cannot be precisely established, as can be done for all other phenomena in every cosmic sphere, Objective Science has, for its examination of Time, ...(a) standard unit.... Objective Science has established ....that all ...beings ...sense the ....action, by which they define Time, forty-nine times more slowly than it is sensed ....on the ... Sun Absolute. Consequently, the process of the flow of Time is forty-nine times quicker for the beings on ....planet Earth ....than ...on the Sun Absolute."

G.I. Gurdjieff (1872-1949) , "All and Everything - Beelzebub's Tales To His Grandson"

"If Gurdjieff had intended his meaning to be readily accessible to every reader, he would have written the book differently. He himself used to listen to chapters read aloud, and if he found that key passages were taken too easily - and therefore almost inevitably too superficially - he would rewrite them in order, as he put it, to "bury the dog deeper." When people corrected him and said that he surely meant "bury the bone deeper," he would turn on them and say it is not the 'bones' but the 'dog' that you have to find. The dog is Sirius, the dog star, which stands for the spirit of wisdom in the Zoroastrian tradition."

J.G. Bennett (1897-1974) , "Gurdjieff - Making a New World"

NOTE: The period of revolution for Sirius B around Sirius A is about 49 years.

"The starting point of creation is the star which revolves round Sirius and is actually named the "Digitaria star"; it is regarded by the Dogon as the smallest and heaviest of all the stars; it contains the germs of all things. Its movement on its own axis and around Sirius upholds all creation in space. We shall see that its orbit determines the calendar."

Marcel Griaule and Germain Dieterlen in African Worlds