Crop Circle Positional Math(August, 2010)

Charles William Johnson

Before I present the analyses of some crop circles that I wrote during the mid-90s, I would like to suggest a few ideas regarding one of the recent crop circles, the one cited at Wilton Windmill in Wiltshire on the 22nd of May 2010. Below is contrast rendering of it. To view its majesty, please, visit the marvelous web-site www.cropcircleconnector.com.

Wilton Windmill, nr Wilton, Wiltshire. Reported 22nd May 2010

www.cropcircleconnector.com

The reason that I quoted the lyrics of an Irving Berlin song in the presentation of the section on crop circles on the Earth/matriX web-site is to emphasize the fact that whoever the individuals are who are making the numerous crop circles throughout the world appear to attempt to better themselves every time a new circle appears.

“Anything you can do I can do better; I can do anything better than you.”   -[Irving Berlin, 1946]

The Wiltshire crop circle falls within that attempt to constantly improve upon the previous circles. In general, the crop circles appear to represent the product of some kind of competition, one trying to better the other.  Behind that betterment, however, may exist a designed purpose, in teaching us how to identify the meanings encoded into the crop circles.  Let us see if that may be true.

This particular crop circle as a few analysts have stated supposedly represents ASCII numbers. Let us consider the possibility that the dashes along the radii of the twelve sectors of the circle represent do not represent ASCII numbers, but rather sequential natural numbers as in 1,2,3,4,5,6,7,8,9,0. The sequence runs from the center of the circle to its circumference outwardly.

No doubt, many of the crop circles appear to reflect encoded mathematical and geometrical patterns. At least, that is what different analysts today propose in searching for the meanings of the crop circles. Many of the mathematical and geometrical analyses that can be viewed on various web-sites such the www.cropcircleconnector.com are extremely suggestive regarding the use of pi, phi, the Fibonacci series, among many other aspects of geometry and math.

However, in my mind, finding the expression of pi within a circle or even that phi, or the Golden Ratio, or a Fibonacci series of numbers could result from the nature of the geometrical figures employed and not from some conscious intelligent design. In other words, possibly there is no intelligent design behind a given circle in relation to some other geometrical figure, say a square, but simply that those geometrical figures contain relationships of pi as such given their natural composition.

For those crop circles that are evidently made by human beings on this planet, well, we may consider from the start that they represent a conscious, intelligent design. But, for some of the most complex crop circles, measuring hundreds of meters in expansive size, which are not so obviously made by human beings, the existence of a conscious intelligent design comes into question. Are some of the crop circles being produced by beings not of this Earth, residents from afar, possibly from another solar system in another galaxy. One would want to be able to identify those particular conscious, intelligent designs as distinct from the ones being made by human beings here on Earth.

Is it possible, then, to distinguish between a conscious, intelligent design made by human beings from one made by beings other than of this Earth. That is the task at hand in my mind.  The crop circle that I have chosen to initiate this discussion, in my view, presents a conscious intelligent design that does not obey the general reasoning about geometry and math as we are taught in school.  The fact that many analysts identify the design as one reflecting the ASCII Code, and not simply natural numbers, attests to this idea.

In order to identify an intelligent design or pattern within math and geometry, one might analyze the apparently random dashes within the Wiltshire crop circle cited above. In my view, this crop circle portrays a definite pattern that suggests the existence of a consciously intelligent design unlike the way we generally think on Earth.  The dashes at first sight, as they appear, suggest a random placement, but upon closer consideration, they obey an intelligent, conscious design based on the natural numbers.

In this analysis, I shall examine the natural numbers coming out of this design as of the binary system and as of the ASCII Code. For, no matter what, both the binary numbers and the ASCII Code numbers are ultimately based upon the natural numbers.

But, the natural numbers within the Wiltshire crop circle are based on a positional math; depending upon the position of the dashes within the geometry of the crop circle, certain values are assigned to each dash, and therefore to each sector of the circle.  Those assigned values of the natural numbers, can then be employed to derive an analysis based upon the binary numbers and the ASCII Code numbers reflected and derived thereof.  But, before I can explain the translation from the natural numbers to the binary and ASCII numbers, it is necessary to examine the design of the natural numbers and their pattern within this particular crop circle.

Let us suppose for a moment that this particular crop circle does not represent ASCII Code numbers or binary numbers, but merely natural numbers; plain and simple. So, let us suppose that whoever is communicating through the selective placement of dashes within the different sectors of the cited crop circle is employing an easily identifiable numerical pattern. The idea would be that if one is attempting to communicate to others, the designed pattern should be simple and easily accessible, not complex and obscure.

With the idea of simplicity, one could then assign a number to each dash according to the positional placement of the dash along the radii defining the different sectors.

The apparent division of the sectors in the circle suggests a pairing of 24 smaller sectors within each larger sector which are identifiably 12.  In the following illustration, I have darkened the apparent six diameter lines that trace out twelve smaller sectors, two to each larger sector. This division comes from viewing the crop circle at first glance, which I would recommend viewing on the cropcircleconnector-dot-com web-site.

In a sense, then, there appears to be a misleading view of the crop circle made by those who made that particular crop circle. It were as though the makers of this circle were attempting to fool us into thinking that this is the way in which the design of the circle should be viewed. This obtains because there are no identifiable lines between the two smaller sectors in each of the twelve larger sectors. The darkened lines of the diameters of separating the twelve larger sectors are what are emphasized in the rendering of the crop circle itself.  One need only consult once again the image of this circle that appears on page one of this essay. The definitely drawn lines between the larger sectors determine ones approach to an analysis of the small curved dashes registered within the sectors, emanating from the lines drawn by the six diameters.

If one does not fall into the temptation of the apparent design as presented by the makers of this circle, then it is possible to draw the twelve sectors in a distinct manner from that suggested. The pairing of the dashes along the invisible radii/diameters creates a different pattern of twelve different large sectors and twenty-four smaller sectors.

This distinct view, with the diameters darkened along the non-existing lines of the diameters between the smaller sectors creates an alternative pattern that is easily identifiable. And, the alternative pattern puts into perspective the curved dashes that now lie along the darkened lines of the newly drawn six diameters. It may be noticed now that the curved dashes along the alternative six diameter lines reflect positions of the numbers 1 through 8.  The curved dashes spread out from the centerpoint of the circle towards its circumference, with the smaller dashes in the minor sectors and the larger curved dashes within the major sectors.

The alternative presentation, with the imaginary diameter lines expressly drawn in, creates different pairs of smaller sectors. The apparent random placement of the dashes as they appeared on the initial rendering of the circle, no longer appear to be random at all. Quite the opposite, the sets of curved dashes along the alternative darkened diameter lines now appear to obey a very simple rule.

The small curved dashes start on either side of the alternative darkened lines and run from 1 to 8 along those lines, from the center to the circumference, in a progressive manner, alternating on either side of a specific diameter line.

The next two illustrations present this perspective in the analysis. The first illustration shows how the alternate lines of the diameters separating the sectors are now drawn in a different manner than as suggested by the original design of the crop circle. And, in the second illustration I show how one may view the small curved dashes that run along these alternative diameters, running from a positional value of one through eight [1,2,3,4,5,6,7,8]  ---with the center of the circle being zero [0]. Note, there is no positional dash for the number nine on any of the sectors. So, the natural numbers chosen for the design of this particular crop circle are the natural numbers zero through eight.

Once the alternative sectors are paired in the previous manner as shown on the illustrations, it becomes obvious that each sector contains a complete set of natural numbers.  Each darkened diameter line has on either side or the other one of the natural numbers from one to eight. No pair of smaller sectors lacks a specific natural number.  In this sense, the pattern is obvious and complete in that it presents a distinct placement and arrangement of the natural numbers along the six diameter lines.

The following illustration shows how each particular pair of smaller sectors contains the complete number of curved dashes positioned to represent numerical values of 1,2,3,4,5,6,7,8. Each of the eight natural numbers lies on either side of a specific alternative diameter line.  Each pair of smaller sectors, in this manner, contains a complete set of the natural numbers one through eight.

Once the pattern of eight curved dashes per pair of smaller sectors is identified, it then becomes possible to assign a numerical value to the presence or absence of a curved dash along the six alternate diameter lines.

When a particular dash is present, then that positional numerical value is registered.  When there is no particular dash present, in other words, when a dash is absent, then a zero is assigned to the placement with the series of natural numbers as shown in the following illustration.

I have chosen a random example to illustrate this point.  Along the alternate diameter line of sector six, there appear five curved dashes above the diameter line and three curved dashes below it. Therefore, these numbers would be written as follows:

10040678 [curved dashes above the diameter line]

02305000 [curved dashes below the diameter line]

The first number tells us that the curved dashes appear for the positions of 1,4,6,7,8 above the line, and for the positions of 2,3,5 for the curved dashes below the line. Yet, in order to identify the numerical pattern, it is possible to represent the absence of a curved dash either above or below the line with a zero.

By doing so, it is now possible to compute different patterns within the sets of numerical values. In other words, the numbers 10040678 and 02305000 may be summed, multiplied, subtracted and/or divided by one another in search of meaningful patterns of historically significant numbers or, scientifically significant numbers.

Each pair of smaller sectors contains a complete set of eight curved dashes along the diameter lines as illustrated.

One would necessarily ask why would such a complex-looking crop circle has such a unique and simple resolution based on simple math. One must ask why did the makers of the circle emphasize the original diameter lines which do not allow one to easily identify the basic pattern within the circle’s design. One can only imagine that the purpose might be that of deception, making it harder for the viewer to discern the underlying pattern within the circle’s elements.

One may suspect that the combination of numerical values arranged in the manner cited here contains information that should reveal to us some inner meaning to the design. In other words, by combining the different sets of curved dashes along the different diameter lines, numerical values are being suggested that have some kind of meaning that we should resolve. Otherwise, one could expect a more simple design by merely placing the eight curved dashes along each diameter line without any alternating placement or positioning.

In other words, the positional math contains a specific meaning that may not be obvious to us at first glance. However, upon viewing the positional math and its subsequent pattern, one does recall the positional math of the Maya Long Count.  For example, were we to assign the Maya Long Count numbers to the positional math of the cited crop circle, then, the numerical values coming into relationship with one another would be extremely complex compared to the elementary assignment of values one through eight. For example, compute what the positional values would be were they to represent the Maya Long Count fractal values:  36, 72, 144, 288, 576, 1152, 2304, and 4608 for the eight positions/placements. That would be mind-blowing to say the least.

In my view, the crop circle represents a teaching aid, a learning tool, a manner for viewing the geometrical designs that are being created with a certain degree of flexibility. It is somewhat like creating a common language.

Each particular crop circle appears to reflect its own mathematical and geometrical design and corresponding method of analysis. Therefore, it is necessary to approach each crop circle from its own internal logic, thus avoiding imposing our own way of thinking, such as looking for specialized systems of numbers as in the ASCII Code.

There may be other crop circles which do reflect the ASCII Code, but this particular circle can be resolved as of basic math and natural numbers.

Once the numbers are derived into pairs, it is obvious that each pair sums to 12345678.

Note that Sector One Pair and Sector Ten Pair present the same paired values [10040670; 02305008]. This would suggest a beginning and an end to a cycle or half-cycle. Then, Sector Two Pair and Sector Eleven Pair are the same paired values [12040670; 00305008], suggesting the first step to each cycle or half-cycle. The repetition of numerical values confirms the existence of a consciously designed pattern; in that the numbers are not randomly situated.

From the previous list of pairs, it becomes obvious that each pair sums to 12345678. Consider the following computations. One may simply note the presence/absence of the numerals 1 through 8 at any position within the paired small sectors as illustrated. The zero represents the absence of a natural number [ 1 through 8], and not the centerpoint zero of the circle.

Seven: Reciprocal

Obviously the pattern of positional math based on the 1-to-8 count derives seven and its reciprocal, which is a significant ancient reckoning number. If the numerical positioning values included the number nine, then other significant numerical values would derive other than seven and its reciprocal. [See my essay on the earthmatrix-dot-com web-site about ancient reckoning and the number seven and its reciprocal for reckoning time.]  All of the numerical values derived as previously shown through multiplication represent historically significant numerical series. To explore their meaning would require a lengthy essay. I suggest reading some of the essays on the earthmatrix-dot-com web-site.

7 / 1.2345678 = 5.67000465 [ Nineveh number 567, 1134, 2268]

Given that there are eight positional levels within the cited crop circle, one could relate this particular number to many different aspects of matter-energy. For example, an initial aspect that comes to mind concerns the eight shells of an atom. In fact, the fractal value that appears in Sector Pairs One and Ten concerning the fractal 02305008 suggests the mass difference factor between a proton and a neutron [2.30558c]. (See the Earth/matriX essays regarding this theme.)

But then again, the 02305000 value suggests a similarity to the Maya Long Count fractal value of 2304c. For example, the final Sector Twelve Pair value of 02340000 suggests a relationship to the Maya Long Count: 234, 468, 936, 1872, which involves considerations about the coming 2012 period of 1872000 days. One cannot help but note the relationship of Sector 12 to the year of 2012 and a common fractal numerical common shared by both in terms of multiples.

Numerous observations could be made regarding the possible socio-historical meaning of the different values cited for the sectors within the crop circle or, even their scientific meaning. But, such an analysis must wait its turn. For now, I only want to treat the idea of methodology of positional math within the crop circle, and not so much what the actual values suggested in the paired numbers may mean.

Similarly, one would have to consider the non-paired numbers which are suggested by the designed sectors in the crop circles, through addition, [multiplication]  subtraction, and/or division.