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The Auric Time Scale & the Mayan Factor
by Sergey Smelyakov and Yuri Karpenko

Ed. N.: "The Auric Time Scale and the Mayan Factor (Demography, Seismicity and History of Great Revelations in the Light of the Solar-Planetary Synchronism)" has been published in 1999 in Kharkov (Constanta Publishers). Professor Sergey V. Smelyakov (Ukraine) is ISAR’s international vice-president and member of the Golden Fund of Cyclic Science of Russia and NIS. Yuri Karpenko, M.E., is member of the Astrological Research Society "Hamburg School" and member of Astrovita. Only the introduction and the first chapter are newly published here in HTML format. The complete text is available in RTF and DOC formats via ZIP compressed file.


The world is one and indivisible. But what can present its unity in number, or specify the community (or synchronism) between such fundamental features of this Universe as periods of planetary revolutions and 11-year Solar activity cycle, trends in demography and the Mayan Calendar, the epochs of coming of Great Teachers of humanity, not speaking about geological, economical and other cycles in Nature and society?

As it turns out, the historical structure of all these phenomena is synchronized by the Golden section number F = 1.618 033 9… (or by Fibonacci series, as its integer presentation) and the average period T0 = 11.07 (years) of 11-year Solar activity cycles.

This synchronism is described with the use of rather simple object – the Auric series, viz. a geometrical progression F = {...F-2, F-1, F0 = 1, F1, F2 ...} being infinite to both ends, the unit F0 = 1 of which corresponds to the Earthy year, or to T0. For this series, the terms Fk, 2.Fkcorrespond to most known basic periods in Nature and society (from biology to geology, including economical cycles), and in this sense the series F defines the Scale of the basic phenomena periods. From the other hand, it specifies an exponential structuring of time in a form of sequence of intervals with duration decreasing in the Golden section, and in this sense the series F specifies the Scale of evolutional time.

In elaboration of previously established synchronism of periods (viz. Scale of basic periods in Nature and society), the forcible arguments are obtained to consider the Auric Time Scale as specifying the structure of global processes in dynamic, or "absolute" time, as well.

This miraculous historical synchronism being quite exactly specified both by the Auric structure of the Mayan Calendar and 2000-year trend in population of China, and by prominent historical events and geophysical cataclysms has allowed to put forward some forecasts for the forthcoming decade and a half, as well as to correct the date of expiring of the Mayan Calendar being associated with prominent changes in all spheres of life.


Revealing of cyclic processes in Nature and society, as well as determining of their periods and initial points for spiritual, scientific and applied purposes are attracting attention of a man since the ancient times. At this, such basic properties of Time as periodicity and succession-of-events were always close, but not equivalent.

These days, we may only imagine we can qualify with confidence the entire system of the ancient knowledge, including count of time, as the most things were enciphered, and unveiling even some of them makes us astonished. Thus, as the cuneiform tablets show, the Ancient Babylonians were watching the phases of Venus, which became possible for modern astronomy only after invention of telescope in the XVIIth century. Not less admiration is provoked by the Mayan Calendar the Auric structure of which is studied below; though it has almost nothing in common with Solar and Lunar cycles which make the basis of the most calendars, the Ancient Maya knew the duration of the average Solar year with several digits after the decimal point, their concept of counting the days is now accepted in astronomy (Julian days), and their Calendar for Venus was accurate to within two hours per 500 years! That is why we may suggest this calendar to hide some more secrets of Time.

Revealing of cyclic processes in Nature and society is commonly carried out by detecting the basic period T of the phenomenon, which is preferably considered to be immutable, though sometimes harmonics are considered, viz. the periods kT and T/n where k and n are integers or rational numbers. Once these basic periods specifying the phenomena of various nature have been detected, we may state a problem of studying of synchronism between them. For this, the concept of Solar-planetary synchronism (SPS) was introduced.

In the narrow sense, the SPS is understood as a mathematical description (or system) that correlates the periods of the Solar system planetary revolutions, Solar rotation and average period of 11-year Solar activity cycle. It was found that this system behaves itself algebraically as if its structure consists of, at least, two components: harmonic (or linear) and exponential (or nonlinear) ones. At this, the first of them specifies time in a conventional uniform scale where the Earthy (e.g. tropical) year is taken for the unit, with respective derived units from seconds to centuries and millennium; the second, or the Auric Time/period Scale (ATS), presents the infinite discrete set of periods F = {...F-2, F-1, F0 = 1, F1, F2 ...}, viz. the geometrical progression with the ratio being equal to the Golden section number F = 1.618 033 9…; its unit, F0 = 1, might be set up to any physical period (tropical year, average 11-year Solar activity cycle period, etc.) belonging to the system. This selection of time unit specifies the absolute value of periods relative to the chosen unit-period, though it does not influence the synchronism.

In the broad sense, the SPS denotes coincidence of the periods specified by the Auric Time Scales Fk and 2.Fk with the known basic periods of most fundamental cycles in Nature and society, within the range of minutes to hundreds of million years. By having not a hint for explaining this, we, however, may see [6] that ATS closely correlates practically all fundamental periods of phenomena in Nature and society namely through the Golden section, and not harmonically.

But the concept of Time includes not only periods, chronology or succession of events make the essence of it. So, if the powers of the Golden section, viz. the series F, define, in aggregate (or simultaneously), the fundamental periods in Nature and society which flow in parallel, we may suggest, that the Scale F defines, when its values are considered in succession, the phases of evolution, or historical cycles, the duration of which decreases with factor F.

Should the first hypothesis have obtained the forcible arguments being briefly discussed below, testing of the second hypothesis relevant to the evolutional time specified by the ATS makes the essence of this work. This way, the situation might be likened to transfer to sun-clock or GMT from a stopwatch or tuning fork, which measure periods. For this, let us try "to adjust the clock" to the "standard time signals".

As it requires to specify some time reference point, consider well-dated historical events and trends within the structure of Auric cycles specified by the Mayan Calendar which is unique in world due to its accuracy in count of days; besides, its starting point is defined quite definitely and far in the past, while its date of expiring in 2012 AD, is actual for our days. For the same purpose consider also the population of China, since the demographic data for this country covers the period of 2000 years, in addition to some cosmogeneous factors being considered below.

In order to avoid confusion, the dates and duration of time periods are specified in conventional Gregorian calendar and tropical years (a) and days (d). For short, the values in Tables and some intermediate results are rounded; they are calculated in compliance with the precision of the presented source data.

Finally, the main new results of this work are presented in Para. 12 and in Conclusions. Paras. 1-7 explain, in brief, the required methodology being earlier [6] discussed in details, whereas Paras. 8-11 are devoted to verification of stability of the demographic model.

1. Source Data

Revealing of the laws that describe the time dependencies for the cosmogeneous objects still continues to present an unsolved problem the actuality of which is defined not only by theoretical interest. Its significance for application arises, in particular, from the established synchronism [3,4,6] between the periods of planetary revolutions, Solar rotation, and 11-year Solar activity (SA) cycle from the one hand, and cyclicity of a number of biological, geological, social, and other processes with duration of seconds to hundreds of million years (and, might be, in a much more wide interval), from the other hand.

However, without obtaining of general mathematical model, that describes the planetary (viz. in a narrow sense) synchronism, there exists no possibility for studying such synchronism in a broad sense, which, in a system, correlates the periods of phenomena of both Cosmogeneous and Earthy nature. For this, a mathematical model of the Solar-Planetary Synchronism (SPS) has been developed [6], which is based on the discovered algebraic structure of periods of the basic Solar System objects. The internal structure of this model is specified by the Auric Time/period Scale (ATS) that presents both the essence of the established SPS, and general model which allows to correlate, through the principle of Unison/Resonance being described below, the SPS periods with the known fundamental periods of cyclic phenomena in Nature and society.

In elaboration of studying of periods, in this work the concept of Auric Time Scale presenting a mathematical model of the SPS is applied to analyzing the phenomena in "historical" time with the aim to verify the hypothesis that the global processes in Nature and society are developing in exponential, or evolutional time being also specified by the ATS rather, than in linear, or harmonic time being described by conventional unvaried periods.

As far as the booklet [6] is published in small circulation, the basic concepts being required for describing new material are given in paras. 1 to 7.

It is known [3,4 et al.], that growth of Solar activity exerts significant influence not only upon atmosphere and biological objects (first of all, onto nervous system and, then, onto cardio-vascular system), but over biosystems and society as a whole. Thus, as it was shown by A. Chijevsky [3] in 1924, maxima in distribution of extremal social events (revolutions, riots, wars, etc.) are closely correlated with the 11-year SA cycle maxima. Due to high degree of integration of the world society, this influence is so important today, that those social and economic forecasts, which describe the state and development of complicated systems [5] might hardly be regarded efficient unless this factor is taken into consideration.

At this, it might be recalled that the Solar activity is understood as a complex of diverse phenomena which cover Sun’s regions of more than few thousand kilometers in diameter (sunspots, flare pads, prominences, etc.) and show pronounced time-dependent variations. Meanwhile, it must be noted also, that the prevailing statistics, both historical and numerical, is collected just for sunspots; in some circumstances they could be observed without a telescope, and this was testified to by the ancient chronicles, which associated emerging of sunspots with evil omen. Besides, as the increase in all manifestations of SA is closely correlated with the growth of sunspot number, the sunspot activity can be taken for the direct indicator of the Solar activity as a whole, not speaking of its esoteric significance [9].

Therefore, with respect to that influence the SA exerts over all spheres of Nature (including social events and individual human beings [1,3,4]), it becomes unreasonable to exclude from consideration those periods, which specify this activity. For this, in addition to planetary revolution periods of Mercury to Pluto, the average 11-year SA cycle period T0and Solar equator rotation period t are taken for system consideration. Note, that all these values are given below in the units of Earthy tropical year (a). At this, if T0 determines the duration of the basic cycle of Solar activity within which four basic phases of background influence are specified [3], the period t determines the periodicity of current SA influence specified by allocation of the actual sunspots, because they exert their influence mainly when passing the central Solar meridian.

As far as the polarity of sunspots and other factors is altered in the sequential 11-year cycles, and the SA influence increases sharply when the sunspots pass the central Sun’s meridian at invisible side as well, consider also the periods 2 T0 (heliomagnetic) and t = t / 2 being not less actual than the basic ones. Besides, for verifying the model, the revolution periods of comet Halley T©and ring of asteroids TA are considered.

As it is the question of principle that among all these periods the planetary ones are only known within the sufficient precision, for the purpose of this study it is required to define the accuracy of the remaining source data. Thus, it is suggested for t to take the value of the sidereal rotation period of the Solar equator (in days, d), t = 25.1 (d), and for the average sidereal asteroid ring revolution period TA to take the arithmetic mean of revolution periods of the most stable elements – all minor planets, or the greatest asteroids with diameters exceeding 100 km., which equals to TA = 4.21 ± 0.5 (a). For the period of comet Halley an average value T©=76 (a) is taken.

Relative to the value of period T0, which plays the key part in the Solar-planetary synchronism, the following must be said. At present, a conventional model of deterministic (viz. defined analytically) description of the SA time developing process is absent; moreover, even the average duration T0 of the 11-year SA cycle is estimated with an error of up to 3%, whereas the inter-maxima periods took the values from 7 to 17 years. Though it is generally accepted in astronomy that the short-termed (up to 2 years) sunspot level predictions could only be efficient, which cannot give a solution to the problem, considering of the Regular model [7] of SA maxima distribution, which is obtained on the basis of sunspot activity telescopic observations covering the period of 400 years, allows to approach this problem in a different way, as far as for the most social and economical applications [3,5] it is sufficient to know namely the years of maxima.

The adequacy of this super-long-term forecasting model had been grounded [7] by a number of direct and indirect acknowledgements, including the Chronicles covering 2200 years [6]. Thus, this Regular model shows that within the source data accuracy of ± 0.07 (a) the obtained average period of 11-year SA cycle makes

T0= 11.07 (a) (1)

and determines the equally-spaced time intervals between the following model epochs (viz. years) of 11-year SA maxima

T*k = 1605.27 ±T0.k, (k = 0, ± 1, ± 2, ...) (2)

by the data of 17 – 20 centuries, whereas the deviation dk= tk- t*k between the actual tk and model t*k epochs presents strikingly exact and symmetrical double-sided Relay distribution for the given source data. From statistical point of view, this model yields significantly less variance than a "conventional" one which presumes successive development of SA cycles, and allows to forecast the epochs of SA maxima for tens and hundreds (!) of years with more accuracy than the epoch of the forthcoming maximum tn-1 could be predicted by the common rule tn+1= tn + T0 where tn is the year of the last actual SA maximum.

And 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 {ti, tj}, which could be considered random, or accidental, just with the exceedingly small probability of the order of 10-11, whereas the difference in years for each cluster, Dij= | ti - tj |, is equal to integer times the period T0 within an error of 0.3%; these integer factors being kij - fold to T0 are as follows:

{ kij } = {2, 3, 6, 7, 14, 17, 18, 23, 29, 35}, (2')

where 3 and 17 are met twice. In other words, we see that the SA maxima epochs show the trend to develop within the Relay-distributed vicinities of the model epochs (2), but not in these epochs exactly, while the same deviations dk  (of actual from these model epochs) repeat in an integer number (2’) of T0 being defined by (1). Therefore, all these properties allow to accept the value (1) as not random and, thus, most accurate estimate for T0.

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Sergey Smelyakov and Yuri Karpenko: The Auric Time Scale
& the Mayan Factor
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