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WORLD TRENDS AND ASTROLOGY IN THE LIGHT OF HETEROGENEOUS RESONANCE
S. Smelyakov
(December 22, 2002)
LIENHYPERTEXTE "mailto:pluto@velton.kharkov.ua" pluto@velton.kharkov.ua
The Numbers Rule the World
Pythagoras
Extending the conventional concepts of synchronism and resonance onto heterogeneous processes describing both natural and social phenomena by virtue of considering of both harmonic correlation of periods and non-harmonic correlation of periods and moments of time on the basis of Auric Time/Period Scale presenting the series of the Golden section number =1.618033& powers reveals a system of correlations between the planetary periods, Solar activity cycles, and basic periods in Nature and society that, in its turn, provides us with a new instrument for description of the global trends with the use of various Space phenomena including Solar activity, Eta Carinae events, comets, Mayan Calendar and some other, which, in common, define the current epoch to be a point of bifurcation of this civilization.
1. Wide-sense Astrology
During the preceding centuries, if not millennia, retaining of relative immutability of social relations and production abilities has led to a definite conservation of astrological concepts, within the bounds of which the modern astrology continuous to develop. At the same time, the revolutionary changes that take place in Nature and society over the last century and, especially, the decades due to an explosive informatization of society, growth of power potential, scientific knowledge and technological abilities are unpreceded in the history of this civilization and accompanied by significant intensification of energy emitting processes on the Earth and within the Solar System, or Solarsphere, itself [1].
Example 1. The amount of energy issued by humanity approaches the Earths energy excretion; melioration and water storage ponds have drastically changed the climate in definite regions. Moreover, the world wide effects are seen in acceleration of the Earths magnetic pole shift, in increased frequency and magnitude of significant catastrophic climatic events, etc. [1].
But if the qualitatively new trends have originated both on the Earth and within the Solar System, they must have their sources and possible new consequences. That is why revealing of the cause-and-effect relations which define the existing and new world trends from the point of view of synchronism of heterogeneous phenomena (including physical and archeological ones) may provide us with a powerful research instrument. From physical and mathematical viewpoints, this approach cannot be considered incorrect as far as it is based on the established synchronism between the events in Space and on the Earth, and though the absence of physical explanation for it makes a gap in our knowledge, it does not prohibit us from using such synchronism for predictive or other relevant purposes. The more so, the given below examples emphasize the efficiency and applicability of this approach.
With respect to time and place of birth of a human being, the conventional astrology takes account of static and kinematic parameters of definite space objects in Geocentric coordinate system that are related to the place of birth. Note, that from a physical point of view, this approach might be called astrology in a narrow sense, as it does not deal with mass or energy. After then, a psychological description and/or prediction for the given birthdata are obtained for that human being with the use of empirical rules that define a correlation between the values of these parameters or symbolic qualities being attributed to the planets and their configurations, and possible reflection of these numerals and symbols in traits and events.
Example 2. The inconsistency of the statement that astrology has no physical background is illustrated by a number of physical facts. For instance, in a series of experiments being conducted in 50-ies by Prof. G. Piccardi and his colleagues [2, 3] the rate of definite chemical reactions was continuously measured for ten years at different latitudes. On the basis of 250 thousand experiments it has been definitely shown that this rate depends on the level of Solar activity, continuously increases with latitude by 2.5 times as the laboratory position is changed from South to North Pole, and presents the yearly minimum around the Spring equinox when the Earth moves in the direction of the Galactic Center.
Application of these rules, as of laws in science, is based on the principle of analogy which, in its general astrological form, is given by the Hermetic axiom as above, so below; as below, so above. At this, if other object than a human being is considered (e.g. a state, or a company) this principle allows us to use the same rules, but in a natural conceptual adaptation to the essence of this new type of object.
Besides, this approach possesses the basic properties of a scientific theory: it includes axioms (viz. basic assumptions), which set up correspondence between the astronomical and psychological and/or eventual concepts, rules of drawing the conclusions, which use formal logic and calculus for obtaining conclusions from axioms, and allows us to verify the conclusions with taking account of the nature of the considered objects. It is obvious however, that due to their irreproducible nature these conclusions, as in medicine or economy dealing with different reaction of the objects being the same just in average, might be true (and, thus, verified) with a definite probability only. Nevertheless, in the sense of mathematical statistics, this verifiability is relevant to physical reproducibility of experiment for the case when the initial conditions could not be reproduced exactly, or the experiment itself cannot be repeated.
At the same time, as far as astrology rests upon the concepts of synchronism and resonance, but for static and kinematic factors, no obstacles exist that prevent us from considering the concept of resonance relative to its essence exchange of energy. For this, the third, dynamic, factor of influence is proposed to be taken into routine consideration, the more so the electromagnetic waves, high-energy particles and other energy-carrying media may exert explicit influence.
For the most powerful and, therefore, important dynamic factor we must take the Solar activity (SA), both the current SA level and the 11-year SA cycle, the influence of which on Nature, human beings and social processes (including wars, revolutions, etc.) is well known [2, 4, 5]. However, though the influence of the SA surges (first of all, in a form of sunspots) is known from the ancient times, it is rarely used in forecasting and analyzed, primarily, a posteriori due to a lack of reliable forecasting techniques for the SA level.
As well, a significant, although sporadic, influence over the Earth exert the comets that come from beyond the Plutos orbit. Thus, the miraculous synchronism [6 - 8] between the comet Hale-Bopps (HB) Time Focuses, the SA surges and significant events in Nature and society could not be explained until the recent years except by esoterically; but now it is known from Prof. J. McCanneys work [9] that a comet coming from the outer part of the Solar System possesses a huge electric charge, and alignment of such comet with two or more Space objects (especially with the Sun) results in discharge of the Solar capacitor with subsequent coercion onto the concerned Heavenly bodies.
If the Earth is included in this process, in the Geocentric system this corresponds to conjunction or opposition of the comet and Sun (besides, we may suggest the square may also have a sound physical background as the electric and magnetic field strength vectors are perpendicular). But namely these aspects between the Sun, HB and Moon, and first of all Sun/HB conjunctions, were independently of Prof. J. McCanneys theory used [10] in astrological considerations when obtaining the comet HBs Time Focuses of influence!
Therefore, by taking account of that influence the SA, comets and other Space objects may exert over the Earths life side by side with the static and kinematic factors, when regarding astrology as science or knowledge that reflects the Space influence over the Earths phenomena, it makes no sense to exclude astrology from considering in a wide sense as well as the replenishment of the conventional approach (viz. astrology in a narrow sense) with the dynamic factors of influence on the ground of concepts of synchronism and resonance.
2. The Concepts of Synchronism and Resonance
For the sake of clarity of the further considerations, define the basic concepts of synchronism and resonance and consider how these phenomena may be described numerically. At this, special attention must be paid to error analysis; the actuality of this requirement corresponds fully to that how frequently it is ignored by those authors who use rough data and approximate methods for obtaining the results which, after then, are taken as exact dates and places in preparing the conclusions. As far as understanding of the below given numerical concepts does not require special skills in mathematics, the author hopes the reader might even make use of them.
Let A, B be some recurrent events that take place at definite moments of time. In a strict sense, these events are synchronous if they occur at the same moments of time. But this general definition is too rigid and, therefore, useless for describing the concept of simultaneous appearing of events for the dominant part of phenomena, because the parameters of the considered physical and social phenomena always show definite instability, their values are frequently defined statistically or by rough data. Besides, the events themselves require some time for development.
Example 3. Even the Earth spin parameters, though they are relatively stable, are subject to variations: nutation in longitude and obliquity may reach a dozen of seconds of arc, while difference between the Ephemeris and Universal time makes about 1 minute for the last century. Ignoring of these corrections may lead to significant errors when progressions or astrocartography maps are analyzed. Of course, much more significant error yields calculation of periods for social and natural phenomena, including detection of the main period and harmonics of the SA cycles.
As a result, none of the actual processes could be synchronous in the sense of mathematical equality, whereas the idea that stands beyond this concept and its ultimate, or dynamic, manifestation the resonance, presents the essence of actual interactions that take place in Nature and society; at this, definite discrepancy between the time parameters of such processes does not reject the possibility of interaction, but rather define its magnitude. Meanwhile, the considered processes do not, in common, satisfy those conditions that are required for application of extensive mathematical techniques provided for studying of random processes, nor the results these techniques may provide us with are appropriate for the subject. This is so, because (i) it makes a special problem how to estimate the probabilistic parameters for the considered events with a limited prehistory, (ii) a relatively large uncertainty in values of the source data results in obtaining of relatively wide confidence intervals for the solutions to have practical sense, (iii) application of those techniques requires use of special software and high skill in mathematics without providing a user with constructive tools for analysis of diverse problems.
That is why, with the due regard of the essence of the problem it makes sense to take advantage of the obvious and practicable numerical approach being based on the error analysis. For this, we firstly define the required concepts qualitatively and, then, show how they may be treated quantitatively, for establishing a synchronism or resonance between the physical, social and other types of processes with the use of threshold values being defined with respect to the time parameter errors pertaining to these processes. At this, we assume that an event is specified by its culmination point being defined with respect to its essence.
It is obvious, that, in general, we cannot obtain a result to be more exact than the accuracy of the source data allows us. To this end, the effectiveness of the error analysis consists in relative simplicity of setting the correspondence between the accuracy of the source data and the result. This allows us to explicitly adjust the decision making (e.g. relative to establishing of synchronism) to the accuracy of the source data and, further on, to use the result supplied with its error estimate (being as narrow as possible with respect to the source data) for subsequent use (e.g. in forecasting). Besides, effectiveness of this numerical analysis, in contrast to implicit ones, is stipulated by the possibility to easily estimate the conditional and unconditional probabilities for concurrent events by a direct consideration of the number of coincidences of events and their absolute time discrepancies, which provides a direct probabilistic (i) confirmation of presence of synchronism and (ii) estimate of synchronism for the purpose of forecasting.
Let some process a be defined by appearing of a recurrent event A that occurs at the specified time moments ti ,(i=1,2,), which form the sequence
ta = {, ti, ti+1, } i=1,2, . (1)
This event may specify definite value of some quantity (e.g. maximum, minimum, etc.) or some qualitative state (e.g. passing of the vernal point, culmination of social process, etc.). Call this determined process the periodic, if the difference Ta = ti+1 ti (to be called the period) remains its value for any i ; progressive, if the difference Ti+1= ti+1 ti for the subsequent cycle equals to Ti , Ti = ti ti-1 , and is constant; and irregular, if the initial sequence of moments
t* ={ t1, t2 , & , tk } . (2)
repeats with some period ta :
t1 , t2 , & , tk , t1 + ta , t2 + ta , , tk + ta , t1 + 2 ta , t2 + 2ta , , tk + 2ta , t1 + 3ta , .
Note 1. The sequence (1) presents arithmetic (geometric) progression if process is periodic (progressive). Irregular process presents the composition of k periodic processes, each with the period ta .
Example 4. The rotation of the Earth around the Sun presents a periodic process, whereas the Golden Section separation epochs of the Mayan Calendar present a progressive time scale [11]. The Time Focuses of the comet HB, that are specified by its alignments with Sun and Earth [10], present an irregular process as they are effective until now [7, 8] at the same dates corresponding to the Suns position at the first alignments.
The periodic processes a, b are called synchronous, if their periods satisfy the equation
Ta = k Tb , ke"1. (3)
This synchronism is harmonical, if k is natural or simple ratio (1/2, 2/3, etc.), and Auric (as adjective to Golden Section) if k = m , where =1.618033& is the Golden Section number and m is natural.
Note 2.Both of these types of synchronism are actual for the current consideration as they correlate algebraically the planetary periods, the average 11-year SA cycle duration, and Solar rotation period [21].
Respectively, the progressive processes a, b are synchronous, if their time sequences (1) coincide.
Example 5. A progressive Time Scale of the Mayan Calendar is close, or synchronous, to progressive process defined by the maxima in geophysical and some other phenomena over the 13 millennia [11].
Apart from more or less determined ones, the stochastic processes exist where the events may occur at random in a sense we do not know exactly when they would take place. For such a process, call it cyclic, if time intervals between the events are close to their average value, and sporadic, if these intervals show significant disperse.
Example 6. The development of the 11-year SA cycle presents a cyclic process with an average cycle duration of T0 = 11.07 years. Though an actual duration may take 7 to 17 years, it rarely differs from this average by more than 1 3 years. Although pandemics, surges of social disturbances and other phenomena show a trend to appear around the 11-year SA maxima [2, 4], they may occur at other moments; for this reason, they are rather to be considered as sporadic events.
The average period T0 plays the key part in the Solar-planetary synchronism [11]. Though it is accepted in astronomy, that the short-termed (up to 2 years) sunspot level predictions could only be efficient, considering of the Regular model [12] of SA maxima distribution, which is obtained on the basis of sunspot activity telescopic observations covering the period of 400 years, allows us to approach this problem in a different way. This model shows, that within the source data accuracy, the average period T0 determines the equally-spaced time intervals between the following model epochs (viz. years) of 11-year SA maxima
INCORPORER Equation.3
whereas the deviation INCORPORER Equation.3 between the actual INCORPORER Equation.3 and model INCORPORER Equation.3 epochs presents strikingly exact and symmetrical double-sided Relay distribution for the given astronomical data.
From statistical point of view, this model yields significantly less variance than a conventional one presuming successive development of SA cycles, and forecasts the epochs of SA maxima for hundreds of years with more accuracy than the epoch of the forthcoming maximum INCORPORER Equation.3 could be predicted by the common rule INCORPORER Equation.3, where INCORPORER Equation.3 is the year of the last actual SA maximum. What is more, 2/3 of the epochs of actual maxima (viz. 24 of 36 SA maxima over the XVII XX centuries) form pairs, or clusters INCORPORER Equation.3, which could be considered random, or accidental, just with the exceedingly small probability of order of 10-11, whereas the difference in years INCORPORER Equation.3 for each cluster equals INCORPORER Equation.3 where INCORPORER Equation.3 are taken in definite combinations. In other words, the SA maxima epochs show the trend to develop within the Relay-distributed vicinities of the model epochs INCORPORER Equation.3, while the same deviations INCORPORER Equation.3 (of actual from these model epochs) repeat in an integer number of INCORPORER Equation.3.
The processes a, c are called partly synchronous (p-synchronous, for short) with respect to event C, if each event A with a definite possibility is accompanied by the event C .
Note 3. If a and b are synchronous, they are generally p-synchronous; e.g. if k=3 in (3) then either the event A, or some event A being specified by a definite time shift of A, takes place with each third event B.
Note 4. This relation is asymmetric as it does not exclude that the event C may take place without the event A . However, this concept is useful in predicting the moments of appearing of cyclic or sporadic events by appearing of the determined (periodic, cyclic or irregular) ones, though it does not come the possible situations just to this case.
The pair-wise p-synchronous processes a, c and b, c come to resonance at moment t with respect to event C, if both events A, B take place at t.
Note 5. If a and b are synchronous periodic or progressive processes that come to resonance at some moment ti , they also come to resonance at the moments
ti Ta , ti 2Ta , ti 3Ta , ; (4)
ti + T , ti + T + 2 T , & , ( T = ti - ti-1 ), (4 )
ti - T , ti - T - -1 T , & ;
where + (-) is taken for the subsequent (preceding) moments. The same holds true for irregular processes, except that (4) must be corrected with respect to (2).
If one or both of them present cyclic processes, the relation (4) shows when they may (in average) come to resonance. More exact forecasting of the moments of resonance for cyclic and stochastic processes requires to know the distribution of (1); e.g. for the 11-year SA cycle maxima, this distribution is given in [12].
Consider now, how the defined concepts can be used with taking account of the error analysis.
As far as the most part of the considered process parameters may show definite time drift, could be measured with a limited accuracy only, and even be distributed with a definite degree of uncertainty reflecting their time-distributed nature, the accuracy with which a synchronism might be established must correspond to the accuracy of the source data. As far as periods of phenomena present the basic interest for this paper, are invariant to the origin of time coordinate and remain their ratios and relative accuracy with a change of time unity, when estimating the proximity of such quantities X and Y it is natural to use the following analogue of relative error
xy = | x - y | / min{ | x | , | y | }, (5)
where x, y are the values of X, Y or their estimations (viz. approximations) being used in calculations, and |x| denotes the absolute value of x.
Together with considering of relative error being appropriate for periods, in analysis of proximity of absolute time moments we must take account of the origin of the time coordinate, as the denominator of (5) depends on this origin, whereas the numerator does not. Hence, for this case we may either use the absolute error
xy = | x - y | , (5 )
if it is known, or use in denominator of (5) the values of periods relevant to these moments and consider for the threshold the absolute error * .
Use of (5), (5 ) allows us to consider the quantities X, Y equal to within the accuracy of xy , xy
X ( Y ( xy ) , or X ( Y ( xy ) , (6)
and to take them equal in the system of considered processes
X ( Y, (6 )
if the error xy (or xy ) does not exceed the threshold value * (* ) being accepted for this system.
To this end, for the error * it is natural to take a relative error presenting an average accuracy of the least exact but actual source quantity within the considered system of processes. As far as the planetary periods and SA cycle and Suns rotation parameters present the basic parameters in this system, those of 11-year SA cycle, as the least exact, allows us to estimate [11, 12] the value of * by 0.01, or 1%.
The events on the Globe may be simultaneous, but be recorded by adjacent dates due to difference in time zones. Besides, some numerical estimates of definite continuous phenomena (e.g. on estimating the sunspot number, ssn) are averaged and assigned to the date corresponding to a definite time zone. Therefore, when dealing with such events as ssn cycles, we are provided with a natural absolute error of 1 day which might be taken for a threshold value * when checking the coincidence of events. In this case use of relative error (5) in (6), (6 ) may be substituted by absolute errors xy , * .
The process types may now be quantitatively defined as follows.
Let over the observation period the event A take place at moments t1 , t2 , & , tN ; then,
- if they are supposed to be equally spaced with a period a , consider the error (1) being defined by the maximal error (5) between the intervals ( ti+1 - ti) , ( i = 1, 2, & , N-1), and the known constant a or its estimate the average period value Ta = ( tN - t1 ) / ( N 1 ) and call this process periodic, if
(1) ( * ; (7 )
- if the sequence of time intervals ti = ( ti+1 - ti) , ( i=1, 2, & , N-1 ), is supposed to coincide with the predetermined time intervals 1, 2, & , N-1, consider the error (2) being defined by the maximal error (5) between the pairs ti , i and call this process progressive, if
(2) ( * ; (8 )
- if they are supposed to be distributed at the specified time moments 1, 2, & , N, , ( i = 1, 2, & , N ), consider the deviation a being defined by the maximal deviation i = | ti i | between the pairs ti , i and call this process irregular, if
a ( * , (9)
or, if a presents the minimal time interval (i+1 - i), (i=1, 2, & , N-1), if
(3) = a / a ( * ; (9 )
- if the process is supposed to be cyclic, consider, as in the latter case, the maximal absolute deviation a , but for the equally spaced moments i , ( i = 1, 2, & , N ), and the standard deviation , 2 = =[( 1)2 + ( 2 )2 + & + ( N )2 ] / (N-1), for the discrepancies i = | ti i |; after then, with respect to the rule of three sigma call the process cyclic, if
a ( = 3 . (10)
Note 6. If in the last case a ( * , the process a becomes a periodic one; in general, the difference between these two typesconsists in a larger degree of randomness of the last process. The criterion (10) might be eased or strengthen, but in the given form it naturally correlates the disperse of values ti around i , which is defined by , in a sense that the maximal deviation a is admissibly large and any value ti does not leave either of the adjacent intervals (i-1 , i), (i , i+1).
Otherwise, the process is considered to be sporadic.
Example 7. Rotation of the Earth presents a periodic process, since Earth Year<< *. The 11-year SA cycle is a cyclic process, as the maximal absolute deviation of ti from i is 5.36 (years) [12], = 1.88 and, therefore, (10) is true: 5.36 < 3 1.88 = 5.64. Process of coming of visible comets is a sporadic one, as the time interval may vary from 1 to dozens of years and, hence, comets exceed 1, whereas the Time Focuses of the comet HB present an irregular process with HB equal to 1 (5) day(s) for the SA surges (for natural and social phenomena), as they manifest themselves at the same dates since 1997 [7, 8].
Note 7. The defined types of synchronism specify just the basic models and in the least degree pretend to cover all possible types of correlations. Thus, though coming of the comets presents a sporadic process, those ones that have arrived since 1996 show the coincidence of their cardinal points with the comet HBs Time Focuses; e.g. the comet Hyakutake (1996) and Ikeya-Zhang (2002) cross the comet HBs trajectory at a close vicinity of Algol almost at the same dates of April 11, 1996 and April 7, 2002, that is at the comet HBs Focal belt of April 7-11 being specified by the comet HB s alignment with New Moon and Algol.
The processes a, b are synchronous, if correspondence (3) of their periods (or average period for a cyclic process) or time sequences (1), with respect to their types, is accurate (6) to within * (*, respectively).
The processes a, c are partly synchronous with respect to event C, if each moment of time ta of appearing of event A is accompanied by the event C at the moment tc with a definite probability P(C/A)>0, and these moments and the error ac (in the sense of (9) ) satisfy the equation
ta ( tc (ac), ac ( * , (11)
or
ta ( tc ( ac ) , ac ( * , (11 )
if ac is defined in the sense of (9).
Notes. 8. A probability p may take a value within the segment of 0 to 1; the more the value of probability p, the more chances for the event being described by it to occur. In the above definition the conditional probability P(C/A) reflects a priori degree of possibility for the event C to appear if the event A has taken place.
9. In many cases the last definition allows us to expand a sporadic process (e.g. the harmonics of the SA cycles) over a system of cyclic, periodic, progressive and irregular ones.
10. Mathematically, if the processes a,c and b,c are pair wise synchronous in a sense of exact equality, then a and b are also synchronous. However, disperse of the source data may result in a situation where the equation (6) does not hold true for a and b, because ab> * . Such exceptional situation cannot be excluded within any interval approach, and the respective boundary singularity might only be resolved with taking account of some additional (physical, etc.) considerations; e.g. by increasing the * for this particular case.
11. If k in (3) is large enough or is presented by ratio of large numbers, the synchronism between the events is instable both physically and numerically, since it neither assumes effective interaction, nor provides sufficient absolute error for defining a unique absolute value of period T , as small enough absolute variations of Tb , within the scope of * , result in k-fold variation of kTb .
12. If the processes a and b are synchronous, they are also p-synchronous with the probability P(B/A)=P(A/B)=1.
However, even large enough value of P(C/A) does not disclose the might of p-synchronism to a full scope: if the most part of events C takes place within the close vicinities of the events A, we may conclude that the synchronism is much more pronounced. For describing the latter situation numerically, consider the probability of randomness of synchronism QAC between all events C and A, as the synchronism does not consider how frequently the event C takes place without the event A. For this, consider the total number NC , NA of events C, A, respectively, over the interval of observation T, and the number of times NCA the events A, C coincide within the accuracy *.
Let N = min( NA , NC ) and ti , (i=1,2,& ,N), be time intervals between the most close pairs (Ai, Ci) of events A, C. As we estimate the randomness of synchronism, assume the events A, C be not correlated and C to be uniformly distributed in time. Then, the conditional probability P(C/A) is estimated as
P(C/A)=NCA / NA . (12)
By considering the width of intervals ti with respect to interval of observation T, together with the number N with respect to NC, we obtain [13] an estimate for QAC with the use of combinatorics and basic concepts of the theory of probability. The below calculations illustrate that the results are overwhelming.
The Time Focuses of the comet Hale-Bopp [10] were specified in Spring 1997 by the moments of comets alignment with the Sun, Earth and Moon. A posteriori, it was discovered, that the local SA maxima took place in close vicinities of these Focuses. The first period of observation (July 1997 April 1998) includes 9 Focuses and 16 local SA surges being measured in ssn (sunspot number) [14]. As far as in accordance with the above consideration the time and date for the Focuses are specified for the GMT, the coincidence of the Focus and local ssn maximum dates is accepted within the threshold absolute error * = 1 day (Note, that even 5 day orb corresponding to a natural disperse of natural and social phenomena might be taken; the more so, the HB s Time Focuses are defined by the Sun/HB conjunctions: in this case a conventional 5 orb of Ecliptic for the Sun corresponds to 5 days).
As far as the differences between the Focuses and local SA maxima, in days, are as follows [13] 0, 0, 4, 2, 1, 1, 0, 2, 0, the estimation for the conditional probability P(SA maximum/ Focus) of appearing of local ssn maximum at the comet HBs Focus for an exact coincidence being defined by the discrepancy of * = 1 day makes
P1 day orb ( SA maximum/ Focus ) = 6/9 ( 0.67,
whereas this value for the Sun = 5 days orb is as follows
P5 day orb ( SA maximum/ Focus ) = 9/9 = 1.
At this, the probability of randomness of synchronism Qssn/HB between the 9 HB s Focuses and 16 local ssn maxima is estimated [13] by the value Qssn/HB = 10-12. For comparison, this value is about several dozen times lesser than the ratio of a poppy-seed and the Earth radii; or 1000 times lesser than a chance for a citizen of this Globe to win the only prize being raffled among 10 billion people.
In other words, the local ssn maxima and comet HBs Time Focuses are synchronous with a probability PSA/HB = 1 10 -12 = 0.999 999 999 999; from a physical viewpoint, this means the determined correlation.
Moreover, this synchronism continues until now. Thus, in 2000 there were two more events that might be considered as such that were organized by the Providence for energizing [14] these Factors of Influence and Focuses [10]: a Solar Storm, the largest and most destructive since 1991 on July 14, 2000 (viz. exactly at the Focus T6) that was accompanied by an explosion of the comet Linear (about July 22) the first comet to be seen in three years (viz. after the comet HB!). Further on, the largest SA splashes in 2001 took place in the vicinity of the Focuses T5 and T7. Besides, on April 2, 3 (viz. within an orb of the Focus TB), the Sun produced two X-class flares, one of which had the largest X-ray magnitude seen to date in Cycle 23 and, to some estimations, was the largest in 25 years; the subsequent diverse SA manifestations (X-ray emissions, sunspots, coronary mass ejection) had resulted in massive bombardment of the Earth in the following two weeks, which coincided with the distributed HB Time Focus TB (April 7 11). This coincidence that takes place for the fifth year might be considered random, but just with a fantastically small probability of approximately 10-50 [8].
From materialistic point of view an event with such vanishing probability can be considered as impossible, though from Theosophical point of view this may denote the only thing, that the Sun being the Brain and the Heart of the Solar System [15] has turned its intent look to the Earth by aimingly participating in the Earthy processes [7,8] on the phase of rise of its activity within the 11-year cycle through directing complementary energy inflow [1, 8, 9 et al] in conjunct with the HB's Focuses.
Example 8. Besides, two more historical examples are worth to be mentioned. In 1991, on the second crest (after that of 1989) of the 11-year maximum, the sunspot level has raised by 4 times in 11 days and on August 21 it reached an extremely high value of 300 units (a yearly maximum); note, that namely in those days, August 19 21, the coup d'etat in the USSR took place that had mortally wounded it, and in the subsequent days its Republics had started to proclaim independence. In 2001, on the second crest (after that of 2000) of the 11-year maximum, the sunspot level had raised by 2.5 times in 11 days and on September 9 it reached an extremely high value of 291 units (nearly a yearly maximum), and two weeks later even the level of 320 units, whereas September showed the maximal average of the year.
Independently of these astrological and numerical considerations, a physical theory has been put forward [9] that explains comets influence by electrical interaction between the Sun, comet and Earth, that is caused by an extremely high electric charge of the comet within the Solarsphere capacitor. This theory and a great size of the comet Hale-Bopp approaching the size of Moon [9] explain those large effects this interaction has exerted to the Earth and Sun. At the same time, as far as this interaction manifests itself at the Focuses until now, we may assume that the supposed channels [13] not only provided the electrical interaction [9] in 1997-1998 (when the comet HB was at perihelion), but had left ionized channels in the Space that continued to support interaction, after the comet flew away, when the Earth recurrently passed the same Ecliptical points of alignment.
Example 9. The analysis of correlation between the 21 most destructive (relative to number of victims) earthquakes on Record in the world [16] and the separation epochs of the Auric partition of the Mayan Calendar specified by 7 dates over the period of 1142 years undoubtedly testifies [11] that they are synchronous, since the probability of randomness of this synchronism, QQuakes/MC is not greater than 10-10 10-14 , or 10-12 in average, what is close to Qssn/HB=10-12.
Therefore, if the probability P(C/A) (or QAC) is estimated and it is significantly large (small)) for a determined (viz. periodic, progressive, cyclic or irregular) process a and process c, this gives us the ground to conclude that these processes are p-synchronous, or simply synchronous. At this, in the required cases the probabilistic criteria for testing such hypotheses may be used though there exist no need in them for such vanishing probability as, e.g. Qssn/HB=10-12.
The pair-wise p-synchronous processes a, c and b, c come to resonance with respect to c at the moment t, if both events A and B take place at t with respect to (6).
Note 13. If the processes a and b are p-synchronous, they repeatedly come to resonance; if synchronous, the moments of resonance are defined by k of (3) except for a case of boundary singularity that must be considered separately.
The probability of appearing of the event C at resonance is defined as follows
Pab(C) = 1 - [1 - P(C/A)] [1 - P(C/B)] = P(C/A) + P(C/B) [1 - P(C/A)].
As far as the value in square brackets is greater or equal to zero, we obtain
Pab(C) ( P(C/A), Pab(C) ( P(C/B),
which means that there are more chances for the event C to appear at resonance than at a separate synchronism. For instance, if P(C/B) = P(C/A) = , then Pab(C) = + (1- ) = 0.75.
If resonance of three events A, B, D takes place relative to C, and P(C/B) = P(C/A) = P(C/D) = , then
Pabd(C) = 1 - [1 - P(C/A)] [1 - P(C/B)] [1 - P(C/B)] = 0.875.
Hence, a resonance of two events increases the probability of appearing of event C by 50%, and of three events by 75%. In general, the more non-synchronous events take place at resonance with respect to event C, the less the time&space uncertainty and greater the probability for the event C to occur. This rise in probability of appearing of an event accompanying some determined events makes the mathematical background for an astrological rule of three acknowledgements: if some event C with a relatively high probability may synchronously occur with either of three determined events, this event C would almost undoubtedly take place had these three events occurred at the same moment.
The presented approach does not pretend to provide explanation of the causes of interaction of heterogeneous processes, though sometimes it does provide the probabilistic evidences to a theory as in the case of the comet HBs Focuses and McCanneys physical explanation. Thus, from the one side, the known synchronism may be used for the purpose of forecasting without knowing of the physical cause and effect relations; one the contrary, the discovered correlation between some processes might be used for revealing of synchronism between three or more processes, which, at first sight, have nothing in common.
3. The Global Resonance at Present
Resonance, in a common sense, is understood as a simultaneous action of several factors of influence, which are similar in their action or applied to a definite element. In physics, the resonance is understood as increase in amplitude of mechanical, electrical or other quantity, or exciting oscillation of one object when the exciting frequency of another object approaches some natural frequency of the former one. Besides, in oscillating system the phases must coincide for the resonance to take place.
The phenomenon of resonance is the basis of functioning of some systems and quite undesirable hinder for others. A resonance occurring in an oscillatory circuit being tuned to coincidence of frequency with the radio signal forms the basis for radio communications, whereas a resonance in an engine may cause its destruction.
On the contrary, a unison being commonly understood as a desirable (or non-destructive) resonance, is the necessary thing in music, singing, etc.
Besides, we see that actually the same resonances make the basis for psychological and predictive astrology: in both cases the natal chart is used as a reference point, whereas in the former case these are studied the aspects presenting a phase resonance, and in the latter case the transiting or progressive conjunctions, oppositions and other aspects are searched which define the resonant harmonics/periods in time.
The phenomenon of unison and its ultimate form resonance, relates directly to the discussed question, as the dynamic factor may cause both transfer of a desired influence and irreversible or destructive changes. Thus, the astronomical observations present the following examples of resonance between the Space objects the periods of which make small rational ratios (period is the inverse value of frequency).
Example 10. Orbital spreading of asteroids is not uniform: distribution of asteroids in sidereal periods shows a number of minima (Kirkwoods windows) corresponding to simple ratios (1/2, 1/3, 2/5, 3/7, etc.) as asteroid and Jupiter periods; these period ratios lead to strong disturbances and loss in motion stability. In other words, out of the asteroid revolution periods those are knocked out which coincide with Jovial harmonics.
The same situation takes place with the slots in the Saturnians rings.
This concept is also grounded theoretically by Kolmogorov, Arnold and Moser who proved that instability catastrophes in planetary systems can be prevented by planetary periods of revolution that form highly irrational quotients, whereas commensurable ratios-quotients formed by simple integers like 1 to 1, 1 to 2, 2 to 3 and so on can induce resonance catastrophes by amplifications of disturbances.
This theoretical conclusion explains why the exact harmonical synchronism or resonance is so seldom in natural phenomena and testifies to validity of the proposed interval approach when searching correlations between the Space and Earth phenomena.
However, if quite exact synchronism does take place, it ought to attract our attention due to its high potential effectiveness; the more so if it correlates the dynamic interaction of the basic objects. To this end, as far as the average 11-year SA cycle duration T0 (See Example 6) specifies the basic unity of the Auric Time Scale for the Solar System [11], last, but not least example must be presented, which shows that our Solar Systems heart is beating in resonance with the Galaxy.
Massive stars are key astronomical objects. They mark the end of their stellar lives as supernovae whose peak luminosity can equal the entire radiant output of a galaxy of a trillion stars. The extreme members of this class might produce hypernovae, cataclysms hundreds of times more energetic still. The Milky Way contains at least one possible member of this putative class of hypernova progenitors, the massive, luminous, and relatively nearby star Eta Carinae [21] (Eta Car, or Foramen). Eta Cars properties do really impress [20]: its radiative power is 50000000 times of the Solars power, its radius makes the distance Earth from the Sun. Flashes of supernova are quite actual for this study, since all of them, that have been registered in our Galaxy over the last millennia, are synchronous with the Auric epochs of the Mayan Calendar [11].
150 years ago, Eta Car underwent a giant outburst; it released as much energy as a supernova. The star survived the event, though such massive objects are not, generally, the long-livers. The Eta Cars behaviour during the 90s has been unprecedented in its modern photometric record. A more pronounced brightening occurred in 1998; this new phenomenon, more extreme than any brightness change seen in Eta Car during the past 50 years. In 2003.5 (viz. around July 1, 2003) Eta Car is expected to undergo an X-ray eclipse, which is believed to occur every 5.52 years and is thought to be correlated with the 5.52 fading of high excitation lines [22]. This gives us the following
Example 11. Near the comet Hale-Bopps Time Focus of July 4, 2003, the periodic process of Eta Cars basic events and the irregular process being specified by the comet Hale Bopps Time Foci [7] come to resonance with respect to natural and social events which they may cause with respect to their factors of influence (For more details on Eta Cars influence, see the next issue).
The death of Eta Car is likely to be one of the most explosive events ever experienced in the Galaxy, though astrophysics cannot exactly determine neither the current evolutionary state of this star, nor the length of time until eventual end as a supernova or hypernova. However, it is expected that: analysis of the 5.5 yr X-ray cyclic variation, timing of flares, and variations in column density may be the best means to fully determine the physical parameters of Eta Car, and so determine its evolutional state [21]. To this end, the proposed approach allows us to establish a fundamental synchronism between the Eta Cars and Solar activity cycles on the basis of the following data. The duration of the basic Eta Car cycles, being estimated by 2020 days [23], makes TEC = 2020/365.24 = 5.5306 tropical years. Twice this value, TE = 11.061 yr coincides with the average 11-year SA cycle duration INCORPORER Equation.3 within the relative accuracy of INCORPORER Equation.3. The reference point 2003.5 and this value TEC specify the Eta Carinae event distribution as a periodic process: INCORPORER Equation.3 INCORPORER Equation.3.
Example 12. (1) In terms of cycle duration being inverse to the frequency of the events, the average period T0 = 11.07 yr of the 11-year SA cycles presents the second harmonics of the basic Eta Carinae radiation event cycle period of TEC = 5.5306 yr with the accuracy of (0 = 0.08%.
(2) Within the existing two-centennial observation data, the 11-year SA cycles and Eta Carinae events present the synchronous processes, cyclic and periodic ones, where the model peaks tk* of the SA Regular Model (See Example 6) present the Most prominent Eta Carinae events [20] with not less accuracy than the peaks i* being defined by the accepted Eta Carinae event distribution.
Note 14. Example 12 and relative stability of the Regular model of the 11-year SA cycles allows us to assume, that Eta Carinae presents a Master-Clock for the 11-year Solar Activity Cycles; namely, that:
(i) the synchronism between the 11-year SA and Eta Carinae event cycles is not random;
(ii) the huge emissive power of Eta Carinae assumes it to be a master generator for the Sun;
(iii) if so, before the Eta Carinaes giant eruption in 1827 the periods T0, TEC were equal.
So far, the conventional concept of resonance implies use of harmonic ratios of periods. To this end, the conventional astrological aspects present sound harmonics of the basic period (basically, the tropical year): opposition relates to 1/2, trine to 1/3, etc. (though the Golden Section partitions were also proposed [17], they used in seldom cases). However, the discovery of the Auric Time Scale [11] being presented by the Golden Section number =1.618033& powers shows that it defines both the system of the basic periods in Nature (including the SA cycles, planetary periods) and society, and the spiral of evolutional time, at least for the preceding 13 millennia, that fits the Auric structure of the Mayan Calendar.
Due to its origin, this type of non-harmonical resonance might be called a mathematical one; however, as far as the Golden Section is exceedingly widespread in natural phenomena and arts as a fundamental element defining their structure relative to time and space [17], the Golden Section resonance should rather be considered as specifying the development by analogy, or implicit qualitative development that evolves in progressively shorten time intervals in contrast to conventional harmonical resonance which specifies explicit physical (or visible) impacts or changes that repeat in equal time intervals.
In complicated systems, the process of coming to the point of resonance in many cases may be described mathematically in terms of the catastrophe theory where a bifurcation point is considered as such point of a process (or system) trajectory, from where the development of the process goes via the one of several alternative ways which differ significantly one from another both qualitatively and quantitatively. At this, it is almost impossible to predict: transfer to what one of these new trajectories would take place as the transition could be caused by a small variation in system parameter on approaching this point. This concept quite definitely reflects possible change in the course of the world events at the crucial moment of history, which frequently arises accidentally or unexpectedly for contemporaries (See Example 8) but at the resonant terms being predicted by astrologers. That is why knowing of such non-experienced resonant moments, where the bifurcation points (for a man, or a state) may take place, might only be obtained through the use of the concepts of resonance and synchronism that correlate heterogeneous processes specifying both dynamic and conventional static and kinematic factors of influence.
Conclusion
Use of the suggested approach for studying of synchronism between the Space and Geophysical phenomena, as well as historical and archeological evidences has allowed us to reveal at least 5 factors of simultaneous global influence which, at present, come to resonance causing a series of natural and social effects.
These factors are defined by coming of cardinal points of Tropical and Solar Zodiacs to coincidence at the boundary of the XXI century [18], forthcoming termination of the Mayan Calendar in 2012 which defines the Golden Section structure of the global trends [11], outer Space impacts and intensification of the Solar activity cycles [1, 13], rise in activity of Eta Carinae, the events of which are synchronous with the 11-year Solar activity regular maxima, and coming of a series of conjugate comets in 1996 2002 that have manifested their influence being synchronous with the SA surges [7, 8] whereas the most effective one of them the comet Hale-Bopp with the size of Moon by some estimations [9, 19] was seemingly not the main and the last (at present) representative of this series of the Space Heralds.
Therefore, the due regard of the scale of this resonance of global factors of influence at the current epoch of beginning of the XXI century gives ground for specifying it to present a point of bifurcation of this civilization, or, more precisely, of that one being known for us within the existing historical memory.
References
A.N. Dmitriev. Planetophysical State of the Earth and Life, 1998. LIENHYPERTEXTE "http://www.tmgnow.com" http://www.tmgnow.com
A.L. Tchijevsky. Space Pulse of Life. Misl: Moscow, 1995. - 768p. *
Piccardi G. Symposium international sur les relations entre phenomenes solaires et terrestres en chimie-physique et en biologie.P. 1-210. Presses Academiquelle Europeennes. Bruxelles, 1960.
A.L. Tchijevsky. Physical Factors of the Historical Process. Kaluga, 1924. *
Cycles in Nature and Society. Iss. 1 and 2. Proc. of the 3rd Int. Conf. on Cycles in Nature and Society. Stavropol University, 1995. - 358p. *
Smelyakov S. Research Project: The Focuses of the Comet Hale-Bopp the Magic Spectacles for Seeing the Mosaic of the Mundane Trends? 2001, LIENHYPERTEXTE "http://www.isarastrology.com" http://www.isarastrology.com
Smelyakov S. The Focuses of the Comet Hale-Bopp the Magic Spectacles for Seeing the mosaic of the Mundane Trends? 2001, LIENHYPERTEXTE "http://www.isarastrology.com" http://www.isarastrology.com
S. Smelyakov. An Astrological Background of the Acute World Trends. 2002 - LIENHYPERTEXTE "http://cura.free.fr/" Centre Universitaire de Recherche en Astrologie LIENHYPERTEXTE "http://cura.free.fr/xx/18smelya.html" http://cura.free.fr/xx/18smelya.html
J.M. McCanney. Planet X, Comets and Earth Changes LIENHYPERTEXTE "http://www.jmccanneyscience.com" http://www.jmccanneyscience.com
Smelyakov S. Whether the Comet Hale-Bopp is Opening the Gate to the Forthcoming Decade? Kharkov, 1997, - 28p. LIENHYPERTEXTE "http://www.isarastrology.com/" http://www.isarastrology.com/
Smelyakov S. and Karpenko Yu.. THE AURIC TIME SCALE AND THE MAYAN FACTOR LIENHYPERTEXTE "http://cura.free.fr/xx/20smely2.html" http://cura.free.fr/xx/20smely2.html or Gziped PostScript file:
LIENHYPERTEXTE "http://temporology.bio.msu.ru/EREPORTS/smelyakov_auric_time.gz.ps" http://temporology.bio.msu.ru/EREPORTS/smelyakov_auric_time.gz.ps
S.V. Smelyakov. Interval Approach for Super-long-term Forecasting of Sunspot Activity Maxima. - In: Numerical Methods and Error Bounds. Academic Verlag: Berlin, 1996. pp. 255 260.
Smelyakov S. The Heavenly Colleagues and their Earthly Pursuits, or Whether this is Uranus for Whom the Battlefield is prepared? Kharkov, 1998.-32p. *
Sunspot indices LIENHYPERTEXTE "http://sec.noaa.gov" http://sec.noaa.gov
H.P. Blavatsky. The Secret Doctrine. Vol. 1-4, Moscow, 1992.
National Earthquake Information Center. Most Destructive Known Earthquakes on Record in the World, 1999. LIENHYPERTEXTE "http://www.neic.cr.usgs.gov" http://www.neic.cr.usgs.gov
T. Landscheidt. The Cosmic Function of the Golden Section. Kosmos; Vol. XXIV, N.4, Vol. XXV, N.1.
Smelyakov S. The Solar Zodiac and the Age of Capricorn. TIA, Vol. XXIX, N.1, pp.41-45.
See also Issue 2 of this series.
M. Hazlewood. Blindsided. Planet X Passes in 2003. Earthchanges! (See also LIENHYPERTEXTE "http://planetx2003.com" http://planetx2003.com )
20. Eta Carinae Properties. LIENHYPERTEXTE "http://iagusp.usp.br/~damineli/etafacts.html" http://iagusp.usp.br/~damineli/etafacts.html
21. K. Ishibashi, M.F. Corcoran, K. Davidson et. al. Recurrent X-Ray Emission of Carinae and the Binary Hypothesis. The Astrophysical Journal, 524:938-987, 1999 October 20.
22. M.F. Corcoran. Eta Carinae: The 2003.5 Observing Campaign. 2002
LIENHYPERTEXTE "http://lheawww.gsfc.nasa.gov/users/corcoran/eta_car/2003.5/" http://lheawww.gsfc.nasa.gov/users/corcoran/eta_car/2003.5/
23. International Campaign To Monitor The 2003.5 Event In Eta Carinae. A. Damineli, Jos H. Groh e Fabiana Munhoz LIENHYPERTEXTE "http://www.usp.br/agenciausp/repgs/2002/pags/082.htm" http://www.usp.br/agenciausp/repgs/2002/pags/082.htm
NOTE: An asterisk denotes publications being available in Russian only.
The author expresses his deep gratitude to the Isars Board
for the interest to this series and financial support,
that made it possible to continue this project
PAGE 15
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