A Time to Listen
by Neil Hudson Newman
Not for the first time since developing an interest in crop circles, my survey, last year, of a curious but ostensibly simple formation yielded a great deal more than I'd been expecting: on that occasion I was confronted with a set of numerical and geographical data that quickly enabled me to unravel a longstanding mystery associated with the town of Glastonbury. However, my labours on the priority book I then started writing, on this fascinating topic, recently came to an abrupt halt: a brief scrutiny of certain groups of this season's field structures raised another spectrum of intriguing questions and I concluded that these demanded immediate answers. The ensuing enquiry covered so much ground that I split my summary of it in three - the concluding parts of which will be despatched soon.
Although I was drawn initially to the first six circles of 2010, we'll begin with a brief scrutiny of two formations that captured my attention later in the year: the pair that, on July 30, was found within fields, of mature wheat, that encompassed the east and westbound carriageways of a pivotal component of the UK's road network, which I'd played a small part in building the M4 motorway [I supervised the bridge/subway construction at the massive Coryton Interchange: now Junction 32]. The section of the M4 I was now looking at skirts Wickham, a small Berkshire village, as depicted below, in my adaptation of a Google earth image [where the formations are shown symbolically]:
I have always believed that intelligent beings attempting to communicate with mankind would be obliged to leave messages that can be interpreted in a consistent and unambiguous way by as wide a spectrum of people as possible. I therefore first wanted to establish if a careful comparison between the two edifices would expose any clear relationships of interest, over and above the following more obvious attributes that they shared:-
1. they were of a similar size and were apparently created on the same day of the year
2. they were less than 500 yards apart and occupied the N/S borders of the highway corridor
3. they had the same general structural form i.e. each comprised an outer ring of flattened crop, which encapsulated a circle that accommodated a seemingly symmetrically disposed set of 16 narrow pathways that appeared to be parallel to one another, and each of these corridors of flattened wheat was engrained with between 1 and 13 micro circles, of varying diameters
Having elected to determine, from the available photographs, the quotas of the cited micro circles of flattened crop that, in each formation, were disposed on the central array of 16 pathways, I realised that the arrangement I was beholding embodies a subtle link to one of this season's earlier structures - the one that, for weeks after its creation, had evoked unusual levels of discussion and speculation: the Wilton Windmill circle of May 22. And I wondered if this unique relationship [described below] is significant.
Knowing that a hypothetical line drawn between the centres of the respective blocks of 16 corridors in the Wickham circles traverses the cited M4 corridor - an area that, for obvious reasons, tends to be associated with 0 [= zero] crop circles - it was clear that the juxtaposition of 16, 0 & 16, can infer a 5-digit expression 16016 which happens to be a number that [as I'll soon demonstrate] was intimately tied to the widely acclaimed but patently defective manifestation of the Euler Identity that had been extricated from the aforementioned formation. A symbolic representation of the process whereby 16016 could be read from the Wickham arrangement is displayed below:-
I later discovered that 16016 was also engrained on the twinned Wickham circles in a direct way, which is independent of the described procedure, and I'll show how this was accomplished shortly, but I'll now focus on one aspect of the depicted arrangement that quickly caught my attention.
Knowing that the two formations were in fields of wheat, a crop whose harvested seeds are destined for human consumption, I was drawn to the numerical concordance that exists between the structure of our mouths and the 3 juxtaposed factors: 16, 0 & 16. An adult's normal endowment of teeth is 32, which our two jaws have equal allocations of: 16 in the upper and 16 in the lower. Furthermore, behind these efficient tools of mastication is the alimentary canal's oval entrance, which is centrally disposed between them, when the mouth is held wide open, as illustrated in the sketch below, which the artist Sam Read-Jones [www.hiprops.com] kindly volunteered to produce for me, in spite of his recently acquired double-broken arm [I superimposed the two 16's + central circle on his drawing]:-
This relationship between the twinned formations' conspicuous appearance and a human mouth in its shouting mode was so compelling that it seemed inconceivable that the crop circle builders had not been aware of it. It therefore occurred to me that they could have employed this subtle method to communicate the idea that their message is one that they wanted to shout at us. In other words, they could have been imploring us to listen to what they are now saying, and this profound thought prompted me to subject the cited 5-lettered, English word to a careful scrutiny. I wanted to establish if the accomplished architects of the Wickham formations had ensured that these creations are also related to SHOUT in other meaningful ways - and I soon uncovered something of interest.
Having noted that the day, within 2010, that the crop circles were found, July 30, was the 211th of the year, I realised that 211 is the 48th prime number [counting 1 as the 1st prime, as it should be!]* and 48 is linked to the alphabetical value [or 'av' - as per the cipher A=1;B=2 Y=25;Z=26]** of the word SHOUT i.e. 83 [= 19+8+15+21+20], in a manner that could hardly be more fitting.
83 is itself a prime - the 24th - where 24 is exactly half of 48, a number that is intimately associated with a field arrangement that's split into two halves. And having recognised that the crop circles' day of birth and the word SHOUT are linked, in this elegant way, via the concept of prime numbers, I uncovered another tier of the relationship, and this appeared to settle the argument.
When the av of each letter of SHOUT [= 19; 8; 15; 21; 20] is expressed as the corresponding prime [= in abbreviated format 19p; 8p; 15p; 21p; 20p (i.e. 61; 17; 43; 71; 67)] their sum, 259, embodies a definitive link to the formations' cited day of birth [= 211, the 48th prime] i.e.:-
259 = 211+48
It now appeared to be the case, then, that by creating the two Wickham circles on the 211th day of the year their builders were ensuring that the formations' inferred relationship with the concept of shout [expressed as the word SHOUT] could be supported in the indicated ways.
By the time I'd encountered this information I'd already concluded, from my analysis of a number of preceding formations, this year, that their anonymous architects had been trying to tell us something that they considered to be of immense importance. It therefore came as no surprise to me to find an emphasis being placed, in this manner, on the word SHOUT. However, I did marvel at the clever way this was accomplished - and I was astonished by another aspect of the communication.
The midpoint of a theoretical line joining the centres of the two blocks of 16 corridors in the circles [which I surveyed, after harvesting, with the help of Jeff and David Glanville] cuts the inside edge of the M4's westbound carriageway. This line's centre, then, on the M4 west, is tied to 32 corridors; and the M4 corridor's 32nd junction west is at Coryton, where I toiled for 3+ years, as shown below. Is this just a remarkable coincidence, or could someone out there be trying to tell me something?
Before I can reveal exactly what I believe our ET friends wanted to shout at us, I'll have to explain how I discovered that the number 16016 was being stressed at the Wilton Windmill formation.
A reappraisal of this season's Wilton Windmill crop circle
Initial observations and thoughts
When I examined the theory that the structure's builders had merely wanted to draw our attention to their flawed representation of a mathematically important identity that's closely linked to the work of the 18th century Swiss genius, Leonhard Euler - e^(hi)pi)1=0 instead of the correct e^(i*pi)+1=0 - I was not persuaded. Over the years of my involvement with crop circles, which started with my site survey and analysis of the Milk Hill giant of August, 2001, I've invariably found that their architects are pedantic in the extreme: even the finest detail they furnish us with [usually ignored by analysts] contributes to an underlying, consistent communication - and errors or oversights are never, ever, encountered. I had not the slightest doubt, then, that if the same beings I've had these rewarding experiences with had seen fit to highlight an expression that resembles the cited mathematical statement but, nevertheless, differs from it, in a number of key areas, it was with the intention of achieving some other objective. I was therefore convinced that if their error strewn version of the so called Euler Identity had been intended this must have constituted a subtle invitation for us to ask why hyper intelligent beings should have chosen to act in this overtly strange way. I concluded that the solution to at least part of this seemingly perplexing conundrum must be embodied in the fact that to generate the expression e^(hi)pi)1=0, with its all too obvious anomalies, the formation's binary information had to be extricated, from its set of 12 spokes, in the following specific manner:-
1. one spoke alone had to be the starting place for the reading process [placing e in 1st position]
2. the data on just one side of each spoke had to be read in its entirety: the leading face, for a hypothetical, clockwise motion of the circle [when viewed from above]
3. each reading had to be in an outwards direction, from the formation's centre
4. the 12 sets of readings had to be in a clockwise order [when viewed from above]
- which is illustrated in my adaptation, below, of a drawing kindly provided by Andreas Mόller, where the binary information on the highlighted spoke faces has to be read in the direction of the arrows i.e. from the innermost circle of data to the outermost [which is the 8th such circle]:-
We know that the cited reading of the 12 binary expressions, when converted to decimal, yielded a set of numbers whose representations, in ASCII code, gave us the described set of letters and other characters, as summarised below [where the binary sequences must be read from the inside out]:-
A consideration of this particular way of compiling the cited elements of the formation's numerical content interested me immediately - because, through my eyes, it was inherently logical.
Firstly, the spoke face from which the reading process had to start - thereby providing the binary data that represented, in ASCII code, the letter e [the identity's first character] - occupied a unique position on site. That spoke's other side, coupled with the facing side of the preceding spoke [which was anticlockwise of it], marked out the extremities of the sole circle sector that directly faced the imposing, man-made structure nearby, the Windmill itself. And I noted that the quoted English name of this type of building is related to the whole crop circle in two unambiguous ways:-
1. WINDMILL has 8 letters, and the formation possessed 8 circles of binary data
2. the word's alphabetical value [or 'av'], as per the elementary cipher described earlier** is 96 [= 23+9+14+4+13+9+12+12], and the formation's binary data embodied 96 elements that represented the number 1 [in the form of narrow strips of flattened crop]
Another dominant feature of this arrangement is the formation's subdivision into 12 evenly-spaced sectors, which replicates the familiar form of an analogue clock face. I concluded that this feature could serve as a subtle invitation for us to move around the 12-sectored crop circle in the same way that the hands rotate on the face of a traditional, 12-sectored clock. And when we travel in this clockwise manner around the formation - from the sector that was highlighted so effectively - the first component we meet that provides binary data is the leading side of the depicted spoke.
Having found this unique role for the leading edge of that one spoke I realised that it would make sense if the corresponding face of each of the remaining spokes was read in the same manner, as we circumnavigate the formation in a clockwise direction.
The physical relationships that underpin the foregoing set of elementary deductions are displayed in the symbolic figure below, where I've again adapted Andreas Mόller's original image:-
I also concluded that, of the two ways that exist of reading the binary data on the respective spokes i.e. from the formation's centre outwards - and from its exterior inwards, I would give priority to the former method. When we travel from the structure's centre outwards, along the cited leading face of each of the spokes, the first data we encounter, on the innermost circle of binary information, is, in all 12 cases a zero, which makes no contribution to the respective spokes' values, and this is unique i.e. although the subsequent 7 circles [which we know are concentric to the 1st] also contain varying numbers of zero's [I'm again referring to the spokes' leading faces, of course] each of these circles is endowed with at least a single 1 as well, which interested me for the following reason.
Our recognition of this glaring contrast between 1 unique circle of zero's and 7 circles of data that, in every case, exceeds zero, inevitably draws our attention to these two prime numbers. I therefore concluded that the clever builders of the formation could have been expecting us not only to make this simple observation but also to take it one minuscule step further i.e. the juxtaposition of 1 & 7 [in that order] can infer the number 17, which is the 8th prime [again remembering that 1 is the 1st!], and we know that the field structure embodied 8 circles of binary information, as illustrated below, where symbolic representations of the latter have been isolated and then aligned in sequence:-
It is therefore the case that only when we read the binary data from the formation's centre outwards do we have a basis for generating the cited link between the 8th prime [= 17] & 8, the edifice's quota of binary circles - and that is why I would have opted for this method of abstracting the numerical information from the spokes' leading faces. And in so doing, of course, I would have been led to the numbers [via binary and then decimal expressions] that translate [via ASCII code] to the sequence of characters found in the manifestly corrupt form of the Euler Identity we're now all familiar with.
Having concluded, then, that the cited way of reading the formation's binary information is one that a spectrum of edified analysts would have adopted, if they'd been persuaded to view the formation with the seriousness I believe it deserves, I returned to 'the conundrum' I referred to earlier.
If the formation's builders were inviting us to find the expression e^(hi)pi)1=0, why did they do so?
I was already convinced that the key to this profound mystery must lay in the detail of the analysis that had yielded that thought provoking outcome, and when I focussed on what I considered to be the most intriguing component of the cited detail I soon uncovered a simple relationship that later proved to be of pivotal importance, in the context of my whole investigation.
Overlooked evidence comes to light
Knowing that the link between the formation's 1 central circle of 0's [on the spokes' leading faces] and the 7 concentric circles of data [also on the spokes' leading faces] that encompass it can serve as a pointer to a prime, 17, that embodies a unique relationship with the full complement of 8 circles i.e. the 8th prime is 17, I was drawn to the fact that the 17th prime, 53, is also tied to the arrangement [as explained below], and I wondered if this intimacy has any wider implications.
Believing that the formation's architects would have expected us - for the purposes of analysis - to have labelled the circles of binary data in the following simplistic way 1-2-3-4-5-6-7-8 which expresses their relative positions, as we travel outwards from the centre of the structure, I noted that these numbers' total, 36, exhibits an illuminating relationship with the cited 17: their sum is a highly relevant prime the 17th [= 53] as depicted in the following symbolic diagram:-
I later realised that this 17th prime is also linked to the cited 36 [=1+2+3+4+5+6+7+8] in a way that has a unique significance, in the context of the crop circle under discussion: the 36th prime [= 149] exceeds the 17th by a number - 96 [= 149-53] - which we know represents, on the one hand, the av of the 8-lettered word WINDMILL and, on the other, the total allocation of binary appendages in the formation's 8 circles of data i.e. on both sides of its spokes, as shown below:-
My recognition of this definitive link between the 1-7 arrangement of binary circles I'd identified in the formation, and 96, which can be considered to be a signature number of both the crop circle and the word WINDMILL, raised the possibility that one or more other pertinent relationships between these entities also exist - and this soon proved to be the case.
I was now drawn back to the fact that, as explained above, by adding 36 [= 1+2+3+4+5+6+7+8] to the inferred 17 [which is itself the 8th prime] we obtain the 17th prime, 53, and I concluded that the relationship is so succinct that the crop circle builders would have expected us to ponder over it. It therefore occurred to me to obtain the product of 17 & 53, and as soon as I'd obtained the result 901 I recalled that I'd encountered it before in this particular analysis!
The 12 decimal numbers that had yielded, via ASCII code, the contentious expression e^(hi)pi)1=0 are 101-94-40-104-105-41-112-105-41-49-61-48 and their sum is:-
What this revelation meant, then, is that the ostensibly innocuous number 901 can be generated in two independent ways from a consideration of the binary data that's engrained on the leading faces of the structure's 12 spokes [i.e. for an imaginary clockwise rotation, when viewed from above].
On the one hand the reading of these binary expressions [from the circle's centre outwards] on the spokes' leading faces yields numbers whose total, when expressed in decimal format, is 901.
And on the other the arrangement of binary circles that can be seen on the cited leading faces of the 12 spokes can infer both 17 [= the 8th prime, 8 being the total circle quota] and the 17th prime [= 53] and the product of these closely related factors is 901.
This impressive numerical concordance is highlighted in the following Fig.:-
At this juncture I was confronted with a profoundly interesting question.
Does the 2nd manifestation of 901 I'd identified merely constitute a confirmation of the relevance of the 1st - thereby providing support for the idea that our attention was being drawn to the sequence of ASCII characters we're now all familiar with e^(hi)pi)1=0 which had been derived from the 12 decimal numbers, of sum 901 - or were we suddenly being taken in a quite different direction?
The hidden agenda starts to emerge
As already stressed, I believe that the expression e^(hi)pi)1=0 is at best a very poor representation of the acclaimed mathematical identity that's closely tied to Euler's remarkable work: e^(i*pi)+1=0.
I therefore had no doubt that if we really were being invited to find, within the formation, the cited repetition of the number 901, which is intimately associated with this ostensibly clumsy sequence of 12 ASCII characters, it wasn't with the intention of ratifying the importance of the latter display. Indeed, as this flawed version of the Euler Identity would be dismissed by most academics because it contravenes the very essence of what mathematics should be about, meticulous attention to detail, I now considered the possibility that the crop circle builders were covertly drawing our attention to the expression's close relationship with the cited 901. Perhaps they anticipated that their erroneous version of the Euler Identity would evoke widespread curiosity when first identified but would be deemed to be unsatisfactory by those who subsequently subjected it to a more critical appraisal and at that point the focus of attention would be diverted to the odd expression's numerical source, and in particular to the 12 decimal numbers whose sum is 901.
Although 901 meant little to me, at first, I soon realised that when it is expressed as the product of its prime factors [which was, of course, the way I'd identified its repetition] i.e. 17x53, it exhibits a number of curious links to both Leonhard Euler himself and the famous identity that bears his name and in spite of their seemingly trivial natures they are worth elucidating here.
Firstly, when 17 is juxtaposed with 53 the number 1753 can be inferred and if that is expressed as a year in our current calendar it takes us to a time when the Swiss-German mathematician was living. Indeed in 1753 Emanuel Handmann completed one of Euler's most well known portraits, this being just five years after he'd published the ground-breaking Introduction to the Analysis of the Infinite.
Secondly, when the expression 17x53 is displayed in the format 8px17p [= 'the 8th prime x the 17th'] it can infer the product 8x17, whose value, 136, exhibits a subtle link to an English appellation that I've used repeatedly in this article: the Euler Identity.
136 can be expressed as the sum of the first 16 positive integers:-
- and 16 is the quota of letters in the Euler Identity. But it is also the sum of the digits in the number pairs 17 & 53 [of product, 901] and 8 & 17 [of product, 136].
Furthermore, for the specific purposes of analysis, 16 is the field structure's effective allocation of binary circles i.e. as we've been obliged, thus far, to separate the spokes' leading and trailing faces [focussing on the former alone - a state of affairs that will later change] there are, in effect, 8 circles of data for the spokes' leading faces and 8 for the trailing. I've illustrated this point, below, for the formation's 8th and biggest circle of binary data, showing how it can be split into the 2 components - one circle for the data on the spokes' leading faces and one for that on the trailing faces:-
The fact that the cited 901, which I'd identified 2 times during my scrutiny of the crop circle, is tied, in the described ways, to 16, the letter endowment of the Euler Identity and the formation's effective quota of binary circles, was considered by me to be a mystery - until I'd undertaken an analytical procedure that I felt my earlier investigation had been leading me to. TO BE CONTINUED
* A list of the 1st 700 primes can be found at: http://www.milkhill-revealed.com/primes.htm
Neil Hudson Newman - September 26, 2010