Methodology for calculating past dates associated with Crops Circles

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Methodology: a reconciliation of the past date of the crop circles to within 10^-3 years?

Quite a provocative title, because this advanced precision is only verified for one day: that of the "birth" of Jesus Christ! (see below). However, the result is sufficiently surprising to deserve to be underlined. The other results remain very good.

Basically, what led me to write this article is the methodology for calculating dates for crop-circles proposed in these pages, which although apparently quite satisfactory, still poses a problem of precision linked the reliability of the sources. Can we improve this point? Possibly, yes.

As a reminder, I associate with each crop-circle presenting a recognizable historical symbol, a precise date in the history of humanity, function:

   1/ of the year in which this crop circle occurred, ,
       It has been proposed that each passing year sees the advancement of a baktun. See the article titled timeline elements on crop circles. Which can be summarized by the following table:

The blue arrow indicates the year 2009 and therefore the period covered by the crop circles goes for this year from +41.67533 to +435.9343. Two remarks on this table:
1/ If there are indeed 13 Baktuns in a Maya era, they are however numbered from 0.
2/ the point of convergence is not the end of 2012, but the end of 2013. You have to dare there :) We'll talk about it..

   2/ of the order number of this crop-circle in the year,
   3/ of the total number of crop circles taking place in that year.

Points 2/ and 3/ allow the time elapsed to be calculated in proportion to the progress in the season. Which means, *roughly* that the first crop-circle for the year 2009 should be associated with +41 ap. JC and the last at +435 AD. JC.

Assessing the ratio to get the advancement in the timeline being one method, another would be to base it on the start and end of the season. I had also compared the two methods in a previous article. However, a certain number of cases among these crop circles are "false" (see opposite): this number can be important, how to manage this "noise" ? Because, although the variables 2. and 3. compensate each other, which makes a certain noise acceptable (especially if it is homogeneous), this nevertheless introduces punctual deviations in the date calculations (it is precisely these deviations which can observed in the last column of the table given below).


No crop circle is neither "true" nor "false". They are all ... crop-circles. This debate only makes sense in relation to a specific frame of reference. Here when I speak of "false" crop-circles I am thinking of those which are made by individuals who do not have the same pragmatics of work as that assumed in the historical hypothesis: namely the respect of a certain chronology and a philosophical approach based on the search for a representation of man in his space/time as well as in his spiritual/religious framework, the “meta”. On these basic ideas, see the article about “ José Argueles ”. That being said, I will not "have fun" here researching which crop-circles originate from such and such groups (impossible mission?)

How to make the method more reliable?

Essentially, by trying to make it independent of the order number and the total (observable) number of crop circles (cf. remark [2] below about the maximum number of crop circles).

Basically, we must continue to base ourselves on the date of advancement in the season. Nevertheless, as the beginning of the season and the end of the season cannot be known with precision, I propose what had already been noted, that is to say, to qualify a season according to the nature of a distribution function whose the parameters will be calculated. This will have the advantage of eliminating the background noise linked to "false" crop-circles and of allowing a date in the past to be associated with any dated event. Let's see how to achieve this:

It is recalled that the distribution function used is the integral of a reduced centered normal law, ie: F repart1.png
Which is also written: F repart2.png
erf being a special function, called Gaussian Error Function. This function has been implemented in Excel, which frees us from the tedious use of an approximation table or the development of a Taylor series…

The associated variables are as follows:

  • μ: the midpoint or mid-season date, (in practice a date number in “billou” format and which is a real number for MS Office),
  • σ: standard deviation (in days)

Timeline for the year 2008

The test can be carried out on the year 2008 since it provides us with one of the crop circles that can be dated most precisely! The one symbolically representing the year 0 and associated with the birth of Jesus Christ (even if this was indeed not the case, the symbol takes precedence). To calculate the values ​​of Mu.pngand of Sigma.png, I start from approximate realistic values ​​( μ= July 8, 2008 and σ = 30 days ), then try to minimize the sum of the differences between the indices given by the distribution function and those given by the crop circles, and according to their date of appearance (“optimum” column in the table below).

Visually, the red curve representing the distribution function snaps onto the points representing the sequence of crop circles.

Year 2008. In red, the distribution function of the crop circles calculated with μ= July 8, 2008 and σ = 30 days. Note that the bead observed at the beginning of the curve, (which appears as a mini-S curve), seems to correspond to another distribution function which is superimposed on the first and which follows the maturity of the fields of Rapeseed (Oil Seed Rape). This deviation also exists in previous years.
Year 2008. Table of errors. This table presents a result of the convergence algorithm used. In principle, in this table, each box presents the error rate between the observable reality (blue points of the previous graph) and the proposed model (red curve, i.e. distribution function), and this for different values ​​of μ and of σ tested . The green zone corresponds to a convergence zone, at the center of which is the best solution. These results are obtained from an arbitrarily fixed n, n being the theoretical MAX number of crop circles in the year (cf. remark [2] below). This amounts to finding the best solution in a space with 3 unknowns.

The calculation table used (and obtained) is as follows, the column named "D1.1" corresponding to the old method used (however we will not find the same figures, because I have updated them here) and "D1.2 which is the one proposed here (noted in bold). The precision for the symbol of the cross associated with the birth of Jesus Christ is incredible!

Year 2008. Dataset used. Note the -314 for pi :)

In details:

  • The column labeled « φ » gives the values ​​for the distribution function. (drawn in red). It is calculated as follows in Excel:
φ = n*1/2*(1+SI(([Date réelle]-μ)/(σ*RACINE(2))>0;ERF(([Date réelle]-μ)/(σ*RACINE(2)));ERF(ABS(([Date réelle]-μ)/(σ *RACINE(2)));0)))

Where n is the "maximum/virtual" number of crop circles that this function will represent. Not to be confused with the “maximum/actual” number of crop circles produced in the year. Indeed, this function provides an idealized vision of the evolution which precisely must eliminate abnormal productions/deviations. This value is adjusted approximately and does not matter as we will immediately see.

  • The column labeled « D1.2 » provides the actual calculation of the past date associated with the crop circle. The variable n used previously disappears, since we determine our date as a ratio, still using the same method, but using the distribution function:
= (φ/n)*[Duration of a Baktun] + [Date associated with the start of the season]

with 394.2752308 for the duration of a Baktun and -354.584 for the start date of the 2008 season. We obtain the following parameters:

μ = 07/07/2008 15:27:34
σ = 29.23664701
n = 129
Notes about the maximum number of crop circles (variable n) 

[1] n is a theoretical, not real, value associated with the distribution function. Precisely it is the MAXimum (and idealized) number of crop circles produced in the year. Deviations and other anomalies mean that this number is not necessarily the real (= observable) number

[2] on the method of establishment by successive approximations of σ et μ : even though the variable n does not intervene directly in the calculation of dates, it remains implicitly hidden. Indeed, it is always necessary to make a hypothesis on the MAXimum (and theoretical) number n of crop circles in order to be able to calculate the error rate of the numerical model compared to the observed reality and thus to select the best pair of solutions {σ, μ}. It is therefore appropriate to seek this best pair for all of the n "reasonably" possible (for example, between 0 and 300...).

Chronology for the year 2009 (stopped at 09/07/09)

Here is the same exercise for the year 2009 which is beginning, to be taken with reservations given an "open" data set.

Year 2009. Provisional distribution function of crop circles (2009-07-09)

Dataset used (2009-07-09)

The 2009 season starts at +41.67533. We get the following (provisional) parameters:

μ = 01/07/2009 00:00:01
σ = 36.8115648
n = 106

Of course, these values ​​will need to be consolidated as new data is received.

Results: proposed correlations

Year 2009

The results using the two methods are given below {D1.1, D1.2}. That is to say, using the rank of the crop circle on the one hand and using the distribution function on the other hand. Curiously, the first seems to work just as well (or even better?).

Crop-Circle Theme Calculated date(s) {d1.1, d1.2} Prop. - detail Prop. - linked date(s)
Crop-circle 200900524 St Jean.jpg Double Seed of Life. {+101, +101} Symbolic associated with the location of the tomb of St. John (Apostle). 7 days of genesis: see Sacred geometry and Synchronicity and predictions with St John the Apostle Death in +101 (fr) or +100 (en )
Crop-circle 20090613 ptolemee.jpg Geocentric system. {+168, +164} Ptolemy's Improved Geocentric System. A central element (probably the earth) eclipses the Moon. Around the moon we observe the sun. Death around +168 (​​fr)
Crop-circle 20090704 Nazca.jpg Colibri (Hummingbird) {+249, +243} Nazca Geoglyph. Incidentally, see the electroseismic theory on u-sphere about the Nazca lines. Between -300 and +800 (fr) or -200 and +700 (in)
Crop-circle 20090705 Maya.jpg Mayan pattern {+261, +255} Perhaps related to Quetzalcóatl (or Tezcatlipoca-white, feathered serpent), mainly venerated in the Mesoamerican area. In this hypothesis, it could correspond to the apogee of the city of Teotihuacán (in Aztec mythology, the place where the gods met to create the sixth sun, that of our era) and the construction of the Pyramid of the Feathered Serpent (Miccaotli phase: 150-250 AD). Classic Maya period in Central America. On a similar theme see the "Doomsday Crop Circle". (150-250) ?


Year 2008

Crop-Circle Theme Calculated date(s) {d1.1, d1.2} Prop. - detail Prop. - linked date(s)
Crop-circle 20080814 jesus-christ.jpg Cross {0, 0} (+1) Birth of Jesus Christ. See Etchilhampton Hill, Crop-circle in the shape of a cross. Year 1 (year 0 does not exist)
Crop-circle 20080601 Pi.jpg Pi {-314, -313} Related to Archimedes of Siracusa? Indeed, Pi is also called Constant of Archimedes. Maybe the solution is -314.1592654? :) Archimedes lived between -287 and -212.


Year 2007

Crop-Circle Theme Calculated date(s) {d1.1, d1.2} Prop. - detail Prop. - linked date(s)
Crop-circle 20070707 Taijitu.jpg Taijitu + Yi-King "hexagrams" {-492, -494} Lao Tzu and the emergence of Taoism. Born in -604 would have died in -479.


Earlier years (more approximate chronology)

The previous detailed elements are to be related to this chronology:

It is possible to speak of chronological convergence since the scenario produced by the crop circles will reach the present time in 2012/2013. Two remarkable points here:
1/ the reminders between the symbols generated by the crop circles and the calendar of José Arguelles (bottom) (hence the JA hypothesis),
2/ The convergence of crop circles with the present time is at the end of 2013 and not at the end of 2012 (who would have said it?)

But also, with all the symbols that can be linked to a spiritual and/or religious meaning and that can be "relatively" datable (still to be done):

Historical/Religious/Spiritual crop circles

note: the green coloring of some of the thumbnails above is due to the superposition of the blue and yellow color (two types associated...)

See the types of crop circles offered on this page.


In the end, the past date of a Crop Circle is based on the following parameters:

  • The date of appearance of the Crop-Circle,
  • The spread of the season (or standard deviation), σ,
  • The midpoint of the season, μ.

And, as a fixed parameter, we have the duration of the Baktun.

What quite incredible, when we optimize the values ​​for μ and σ for the year 2008, the precision concerning the dating of the event corresponding to the birth of Jesus Christ increases in a correlated way ! After 7 iterations (approximation) the accuracy reaches year 0 at 3.10^-3 (~ accurate to within 1 day in the past). Beyond that, it stagnates.

I wonder: how was a solution for the birth of JC made possible within 3.10-3?? At this time of year, each day is equivalent to 2.43 years elapsed. This means that the μ and σ parameters were precisely anticipated by the crop-circle makers. As incredible as it may seem, I lean towards this solution, because at this point, the same phenomenon is observed in 2009: the variable μ is centered on July 1, 2008 at 0 hours, 0 minutes and 1 second!.

There is also a relationship between μ, σ and the rate of maturation of the fields/crops which changes every year. And that was well taken into account. From a certain point of view, if this theory is valid, those who build the crop circles, knew that it was on that day that the cross had to be made, and that in addition, given the parameters retained, this day would coincide to within 3.10^-3 (at least)…


About the establishment of the chronology (in order of seniority of the articles):