From the written artefacts of the ancient Mayas, which have survived until these days, first of all the date structures (that means records of numerical data) have been reliably deciphered and unambiguously defined. We mean their numerical value-the amount of elements, which are the days of the Mayan dating (MD). These informations are concerning mainly the calendar data, providing us a set of calendar data and a set of date differences based upon that calendar data. The mutual combination of the Mayan calendar dates and their topology (i.e. their mutual space layout on the stone steles and codexes), have been leading the earlier researchers to the assumption that it is going mainly about the calendar-astronomical data.We are remarking that the ancient Mayas used only integers and performed the mathematical operations of addition and substraction. Those two mathematical operations with integer numbers are well documented by the rich archeological evidence, which is multiplying year by year.

The task we have set for us is to find a correlation coefficient to translate the dating between the Mayan and the Julian dating used in contemporary astronomy. As the following task we will show some mathematical methods we have used to complete our work. It has been very difficult for us to get the up-to-date archive materials, literature and snaps from recent archeological sites in the time of releasing this report – that means the XII. Congress UISPP 1991 in Bratislava – Slovakia. We have nevertheless got and analysed a sufficient amount of calendar dates, predominantly from the older researches. We have been coming out (like many researchers) of the presumption, that the vast majority of the dates represents records of periodical astronomical phenomena, such as the typical phases of the moon, equinox, solstice, and typical positions of visible planets. The dates at our disposal, transferred into the decadical form, allowed us to employ statistical methods to prove that this dates are in fact astronomical. What, then, is our procedure?

It is known, for example, that the period between full moons is 29.530 588 days. If some of the dates, we should examine, represent the dates of full moon, the above constant ought to be contained between such dates, with no remainder. The quotient must be at the same time expressed as an integer, or as a number whose fractional part is relatively very small. The quotient could be positive as same as negative. It will be negative when the remainder is after multiplying and substracting very close to the value of number one, but smaller than one.In that case, we are thinking about the mistake of size of the gap to number one in its absolute value, that means always with the mistake in the set of positive number closing to zero.

We must say that between some of these dates (which in fact express the number of days from the beginning of the Mayan calendar) are differences of many years, even centuries. It is then obvious, that much of the data was rather calculated independently of experience. Our statistical method is based upon the computer observation: we are trying to see how often, with what frequency, these dates fulfil our ”integer criterion” (i.e. those which contain a certain constant-e.g. the synodic month-in such a way that the number of times the constant is contained is expressed by an integer) would occur in a set of randomly selected numbers, and compare this percentage to the one we get from the original Mayan set.

 For the calculation itself we have developed the following algorithm: each member of a set of several hundred calendar dates was divided by a concrete astronomical period (for example for moon by the number 29.530588). Next, the fractional parts of this quotient were compared. If then there occurred a bigger set of numerically identical (or very similar) remainders in number, which was beyond what could be expected in terms of normal probability, we would have discovered what we were searching for. In such a case, it is very probable, that these original dates, whose fractional parts are numerically identical after having been divided by a concrete astronomical period, are representing concrete astronomical phenomenon-for example, the synodic moon.

These calculations were performed an a computer, on which we also modelled phenomena according to random distribution with the set conditions of random scatter. We are examining, for example, the probability of getting similar 34 cases (out of 400 randomly generated numbers multiplied by the constant 29.530 588-the synodic moon), when the difference between separate fractional parts was 0.05 as was the one from original Mayan set. If we were to receive 20 positive results out of one thousand model situations, the probability of our having identified actual moon data would be 50:1. Such moon data would refer to either full or new moon.

Using this algorithm, we succeeded in identifying the sets of dates which evidently describe astronomical data; equinoxes, solstices and characteristic moon phases. Moreover, with the moon dates we found not just one, but two groups of calendar dates between which the half of the synodic month is expressed by an integer. This shows that the full moon is expressed in one group and new moon in the other, as recorded by the Mayan astronomists over one and half thousand years ago.

We are aware of the fact, that not all the deciphered data discovered in recent years (1991)is at our disposal. However, our sample of more than 400 Mayan dates is representative enough in terms of mathematical statistics, and it is therefore possible to treat it in this way. We have, of course, confronted the gotten results from the upper described procedures with the next astronomical and historical knowledge as we are describing in our other works.

From the Astronomical institute in Prague, we have obtained a number of latest computer programs and algorithms for identifying the important positions of planets, the sun and the moon, for the period of the first millennium ad., the period we are interested in. This enables us to identify with high accuracy all important positions in the geocentrical system, such as planetar conjunctions, helical risings and settings of planets, eclipses of the sun and the moon, and other data. By mutual synchronisation of statistically defined data of the tropical year, synodic month and the analysis of the movement of the planet Venus, we succeeded in identifying a real correlative factor between the Mayan and the Julian dating system, which has the value of 622,261. This constant proved to be correct by several other methods, which, owing to the lack of space, cannot be dealt with in detail here and are mentioned in our other works. To cite one example: by adding our correlation factor to the Mayan date of 1,351,732 (decadic), we obtain the Julian date of 1,973,993, which is approximately the 1^st July 692 ad. of the Julian calendar.

Our obtained correlation has been applied to dozens of other groups of Mayan dates, especially to those in the Dresden Codex. It enabled us to define the astronomical meaning of much other, so far undeciphered data. On pages 40-53 and 48-52 of the Dresden Codex, we can find two groups of long integers, which are added to the date of the winter solstice. Between these numbers and within most of these numbers the tropical year (365.2422) is contained with such accuracy and occurrence frequency, that mere coincidence is extremely doubtful. The detail description of those pages could be found in our other works. We will mention only the essential facts in the correlation with the mathematical methods of researches. In the MD group, topologically forming one set of identically same data, are these calendar dates following in decadical form: 12,395,221 – 12,482,581 – 12,394,740 – 12,454,761 – 12,438,810 – 12,454,459.

It concerns the dating of events which were supposed to happen in the far future. To all of those dates is in the Dresden Codex added the constant of 1.407.424. As following we are focusing to only seven of the upper mentioned high MDs.

The date 12,395,221 contains 33,937 tropical years wit the mistake of 4 days.

Between MD 12,482,581 and the date 12,394,740 is accurately 240.5 tropical years with no mistake.

The date 12,454,761 contains 34,100 tropical years with the mistake of two days.

Between MD 12,438,810 and the date 12,466,942 is 77 times contained the tropical year with the mistake of 8 days.

Between MD 12,454,459 and the date 12,482,581 is again 77 times contained the tropical year with the mistake of 2 days.

When using the statistic modelling method (this means the analysis of vast number of randomly generated date groups ordinarily as great as the deciphered Mayan dates), we find out, that the upper mentioned group of seven MDs really solves with high probability the problem of tropical years in conditions of the Mayan culture. When randomly selecting the groups of seven numbers (as the matter of their size, responding to the ones from the Dresden Codex), we got the same relation like with the numbers from the Dresden Codex, first after 200 attempts, with the set allowed mistake of results distraction. In that case we can say, the mentioned group of dates solves with probability 200:1 some characteristical dates of the tropical year. Than we agree with the most of researchers on the fact, that they are obviously the equinoxes or the solstices. We must remark, that when using the G-M-T Correlation, no equinox or solstice were happen in these times.

We have tried to show on those few examples that the problem of the MD/JD Correlation is possible to solve only by using the statistic modelling method, during which we are still presuming and calculating the size of mistakes, the Mayas must have made.