Immediate observations and conclusions

The crop circles' first veil of mystery could hardly have been easier to remove. ... If we'd observed the structures from the field's north end, the diminutive '1 ring' would have been on our left and the 409-circled edifice, on our right, as shown in the symbolic Fig. opposite, where the respective circle tallies are displayed:-

 

Reading the 1 & 409 from left to right [as is customary in the formations' home, the UK] can infer - 1409 - which has an unambiguous relationship with the date of the main crop circle's appearance, and to understand this relationship we merely need to know a little about the special numbers called primes.

 

Counting 1 as the 1st prime [as we should!], 1409 is 'the 224th' [which can be abbreviated to '224p'] and the larger formation [and possibly, the smaller] was first seen on the 224th day of the year.

 

The Milk Hill circle configuration, then, was inextricably linked to the main structure's day of creation.

 

But, if the formations' builders communicate via primes, a question is also raised concerning the numbers 1 & 409 themselves: 1 is the 1st prime and 409, the 81st [i.e. 1 = 1p and 409 = 81p] - as shown in the symbolic Fig. opposite, where the quoted 1 & 81, which are the 'prime ranks' of 1 & 409, are now displayed:-

 

This arrangement can be read as - 181 - which is the 43rd prime [i.e. 181 = 43p]. And it's the case that the expression 181+43 yields another manifestation of - 224 - the day that the main edifice appeared.

 

Clearly, then, 224, which represented the day of the main formation's birth, can be inferred not only from the two structures' prime circle tallies [1 & 409] but also from those numbers' prime ranks [1 & 81] i.e. 1409 = 224p and 181 = 43p, where the latter 181 & 43 [inferred] add up to ... 224.

 

As a hypothetical view south, from the northern reaches of the field that accommodated the circles, enables us to identify two manifestations of a number that defines the main structure's day of creation, the question is raised as to whether a view north, from the southern extremities of the same plot of land, also infers numbers that relate in a meaningful way to the cited structure's history. ...

 

The adjacent Fig's therefore show the numerical configurations that a northwards view yield. In the 1st, the 409 circles are now on the left, with the 1 ring on the right; and in the 2nd the 81 [409's prime rank] is on the left and the 1 [1's prime rank], on the right:-

 

These arrangements can infer - 4091 & 811 - which are the 564th & 142nd primes, and it's clear that the difference between 564 & 142 [the prime ranks of 4091 & 811] has a familiar appearance ... 422 [= 564-142]. Indeed, just as the expressions 409-1 & 81-1 had embodied position reversals of the component parts of the original 1-409 & 1-81 so the cited 422 happens to be the reverse of ... 224.

 

So if a representation of the two Milk Hill formations is viewed in the reverse direction to that which can yield [in the way I've shown] two manifestations of 224, the main structure's birthday, the new view can infer, in a simple and elegant way, a number - 422 - which is the reverse of 224.

 

Although the main edifice comprised 409 circles it was just 1 structure. Its terrestrial juxtaposition, therefore, with 1 other structure, the ring, could also represent the number 11 [= 6p]. And this, uniquely, is true for views towards each of the cited cardinal points, as shown in the Fig.:-

 

As I knew that one earlier southwards view and one, northwards had also produced a cluster of primes - 1409, 181 & 4091, 811 - I wondered if these 4 numbers are linked in a meaningful way to the two 11's and I soon obtained a definitive answer: I discovered that 6492 [= 1409+181 + 4091+811] exceeds the product of two 11's, 121, by - 6371 - where 6371 km is an up-to-date value of our planet's mean radius.

 

But as the 1 edifice was 6-spoked, its juxtaposition with the zero-like ring can also infer [in a northwards view] two alternative 2-digit numbers, 10 or 60 [see the Fig.] and 10p x 60p yields another - 6371 [= 23x277] - and this apparent emphasis of the number soon proved to be pivotal.

 

 

The Milk Hill Fan - and its illuminating properties

When a number of the main circles [as I call them] that form the six closed loops, in the dominant Milk Hill structure, are shaded, so that three alternate loops are highlighted, the latter resemble the outline of a 3-bladed fan, as illustrated below, where in the second Fig., to aid clarity, the small, satellite circles [as I call them] have been omitted and each 'blade' has been shaded [but the central circle has been left blank]:-

 

The Fan outline                 The 3-bladed Fan

As the quota of blades in this inferred fan - 3 - equals the tally of letters in the English word FAN [England being the crop circles' home], it occurred to me that the structures' builders may have been inviting us [amongst other things] to recognise this  fact, and I soon found that an extraordinary set of clear links exist between the word and the crop circle.

 

Firstly, using the following elementary cipher [which is employed for word games in many Junior Schools]:-

 

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

 

- I found that the 'alphabetical value' [an important concept which, henceforth, I shall sometimes abbreviate to 'av'] of the word's three letters, F-A-N, is ... 21 [= 6+1+14]. And as I had encountered, during my preceding analysis, a series of key relationships that involve primes and their ranks, I was persuaded to juxtapose the first 21 primes with their prime ranks, as set out below:-

 

the first 21 primes

 

1

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

their prime ranks

 

This soon revealed that the groups' respective sums - 640 [= 1+2+...+67+71] & 231 [= 1+2+...+20+21] - differ by the crop formation's unmistakeable tally of circles ... 409.

 

Secondly, I then realised that when the three letters of FAN are removed from the alphabet, thus:-

 

 

B

C

D

E

 

G

H

I

J

K

L

M

 

O

P

Q

R

S

T

U

V

W

X

Y

Z

 

- the number of letters that remain is another prime ... 23 [= 10p] ... and the 23rd prime happens to be the crop formation's unmistakeable tally of main circles ... 79.

 

Thirdly, as I knew that the av's of those 23 letters are as follows:-

 

 

B

C

D

E

 

G

H

I

J

K

L

M

 

O

P

Q

R

S

T

U

V

W

X

Y

Z

 

2

3

4

5

 

7

8

9

10

11

12

13

 

15

16

17

18

19

20

21

22

23

24

25

26

 

- it was clear that their sum is the crop formation's unmistakeable tally of satellite circles ... 330.

 

Fourthly, as the quota of alphabetical letters missing from the word FAN is the 10th prime [= 23], and the av of these letters is 330, I realised that this numerical relationship embodies another definitive and extraordinary link to the Milk Hill structure that was engrained with the profile of a fan. ...

 

330 can be expressed as the product of the inferred 10 and the primes 3 & 11 i.e. 330 = 10x3x11, but the expression 10px3px11p yields ... 2001 [= 23x3x29] ... which we know was the year [as per our calendar] the crop circle appeared.

 

With barely any effort, then, I had demonstrated that, on the one hand, the elementary characteristics of the letters F-A-N can infer, in a subtle but simple way, the crop formation's total tally of circles - 409 - and, on the other, the remaining letters of the alphabet can infer, in an even more straightforward way, not only the tallies of main and satellite circles that make up the cited total - 79 & 330, respectively - but also the number that represents the year of the event ... 2001.

 

My recognition of the foregoing relationships convinced me that the builders of the Milk Hill structures - including the 409-circled formation, with its fan-like interior - had indeed invited us to find them. But as it would have been absurd for anyone to have designed and constructed what could be the biggest ever crop formation merely to draw our attention to such overt and trivial characteristics, I was curious as to what the real object of the exercise was. ...

 

A vital clue as to the true nature of Milk Hill's underlying communication was provided by another ostensibly innocuous fact: the isolation of the letters F-A-N in the full alphabet effectively creates 6 discrete sets of letters: the three groups of single letters that define the word and the three groups of multiple letters that make up the rest of the alphabet, as shown in the table below, where the A, F & N have been highlighted and the relative positions of the respective groups placed along the bottom:-

 

A

BCDE

F

GHIJKLM

N

OPQRSTUVWXYZ

[1]

[2]

[3]

[4]

[5]

[6]

 

We know that this tally of letter groups ... 6 ... is a factor which was tied closely to the Milk Hill structure under scrutiny: it was its endowment of spokes [6 also had other key roles - see the attached lecture].

 

But it is also the case that the sum of the depicted 'position labels' is ... 21 ... which happens to be the av of the word FAN. And as I also knew that 21 exhibits the close relationship, I've described, with the formation's tally of circles [i.e. (sum of the 1st 21 primes) - (sum of their prime ranks) = 409], I suspected that the cited 6 groups of letters could be more important than first appearances indicate. ...

 

The key to this riddle was provided by a finding of my earlier analysis of both Milk Hill structures. ...

 

I'd concluded that the overall arrangement of circles can infer, amongst other things, two manifestations of a number ... 6371 ... which is the geometric mean radius [in km] of the earth ellipsoid associated with the WGS 84 map datum. Knowing that my identification of this attribute of the crop circles could mean that other information they contain, or infer, has to be interpreted in terms of that map datum, I viewed the above described  set of 6 simple letter groups with intense interest - because I could see that they hold a stunning revelation. ...

 

For reasons that will soon be apparent, I've modified, below, the earlier depicted sub-divided alphabet: the letters A, F & N [and their respective position labels] are now placed above the other three letter groups [and their respective position labels]:-

 

1   3   5  

A

 

F

 

N

 

 

BCDE

 

GHIJKLM

 

OPQRSTUVWXYZ

 

2

 

4

 

6

 

The Fig.'s 26 letters are shown in the order they occur in the alphabet but, clearly, if the positions of the A & F are reversed the three raised letters will then spell out the word FAN, as shown below, where each of the highlighted letters F, A & N is endowed with its original position value:-

 

3   1   5  

F

 

A

 

N

 

 

BCDE

 

GHIJKLM

 

OPQRSTUVWXYZ

 

2

 

4

 

6

 

It was clear that this simple transformation produces the same configuration of three numbers that I'd encountered during my ground survey of the crop structure that had embodied the fan profile. ...

 

By reading the three highlighted position values from right to left, starting from the 5 - which is linked to N, the one letter [of the three] that wasn't moved - we obtain the sequence 5-1-3.

 

And the latitude [WGS 84, truncated after 3 digits] of the main Milk Hill formation's centre was ... 51.3 N ... as shown in the adjacent symbolic Fig.:-

 

Furthermore, it was apparent that N, the first letter of the sequence NAF, is used by cartographers to represent the very word - North - that is tied to the described geographical coordinate.

 

And as I knew that, within the alphabet, the letters F-A-N are accompanied by a tally of not-used letters, 23, which has close affinities with the number 10 i.e. 23 is the 10th prime, I realised that the cited 51.3 can be obtained by dividing 513 [inferred from the sequence 5-1-3] by this inferred 10.

 

I was presented with the possibility, then, that the crop circle builders had also been inviting us to recognise that they'd placed the main structure where it was found because its central point straddled a line of latitude whose numerical value [when expressed as per WGS 84 and truncated to 3 digits] is linked in the described way to a relationship that exists between the letters F-A-N and the rest of the alphabet.

 

Knowing that my analysis of the Milk Hill formations had been dominated by relationships that exist between certain prime numbers and their ranks, I was now drawn to another conspicuous but ostensibly insignificant feature of the alphabetical table I'd constructed. ...

 

Whereas the three position values that had inferred the cited 51.3 are all prime [i.e. 5 = 4p; 1 = 1p & 3 = 3p] those on the table's bottom line [which were not involved in the cited angle definition] i.e. 2, 4 & 6; contain only one prime: 2 [= 2p]. It therefore occurred to me that the crop circle builders may have expected us to investigate the outcome of converting these 3 position values to what I call the corresponding primes i.e. 2 is changed to 2p [which is also 2]; 4, to 4p [= 5] and 6, to 6p [= 11] - as shown below:-

 

 

It was immediately apparent that this elementary transformation produces three numbers on the bottom line that exhibit clear arithmetic links to those on the top [other than that they are all prime]: each group has digits that add up to 9 [i.e. 3+1+5 = 9 = 2+5+1+1]; and the sum of the full set of digits - 18 [= 9+9] - is identical to the sum of the bottom line's actual entries [i.e. 18 = 2+5+11].

 

I also realised that the two lots of 9 [the digit sum of each line's numbers] even embody a subtle link to the fan-bearing Milk Hill formation itself: their product - 81 [also the reverse of 18 (= 9+9)] - is [as we know] the prime rank of ... 409 ... the structure's tally of circles.

 

These early indications that the crop circle builders had indeed wanted us to examine the modified table were confirmed in a spectacular way when I set out the numerical information in a manner that reflects the fact that the entries on the bottom line add up to the cited 18, thus:-

 

 

It was now clear that reading the highlighted numbers anticlockwise, from the 18, yields the digit sequence 1-8-5-1-3.

 

And 1.8513 W is impressively close to - 1.8512 W - the measured longitude of the crop structure's centre [WGS 84, to the nearest .0001 N]. Indeed, when displayed to 3 decimal places - 1.851 W - these angular expressions are indistinguishable and, as explained below, I later concluded that it is the latter meridian, shown in the adjoining Fig., that the crop circle builders had actually wanted to stress:-

 

Furthermore - as was the case with the earlier construction of the defined angle of latitude [= 51.3 N] - the intimacy between the number that formed the first part of the expression, 18, and an inferred 10 [derived from the fact that the tally of letters in the bottom line is 10p] enables us to generate ... 1.8 [= 18/10] ... and when the digit sequence 5-1 is placed after this, we obtain the depicted ... 1.851.

 

Having encountered the above cited small discrepancy between the table-derived expression, 1.8513, and the measured value [in degrees W] of the meridian, 1.8512,  I discovered, within the very region of the table that contains the anomalous final digit, 3, an extraordinary manifestation of the number 1851. This raised the possibility that my reading of the angle, from the table, should have terminated at the 1 [the position value of the group occupied by A] - yielding 1.851 - and I later found a relationship which appeared to confirm that this 4-digit number is indeed the meridian's value [to be elucidated shortly]. ...

 

We know that the final, contentious digit of the expression 1.8513 i.e. 3, is the position value of a group [containing F] that sits, on the table's top line, alongside two other groups, occupied by the letters A & N. But the latter two groups share an attribute which [within the whole table] is unique - their  position values, 1 & 5, equal the digit sums of the cited letters' av's - and this interested me. ...

 

The group of position value 1 is occupied by A, of av = 1, and its digits [which happen to be 1 in number] add up to ... 1 ... as shown in the Fig.:-

 

And the group of position value 5 is occupied by N, of av = 14, and its digits add up to ... 5 ... as also shown in the Fig.:-

 

Furthermore, the av of F, which occupies the group that precedes the A & N,  is - 6 - and this number can be expressed as the sum of the three digits 1, 1 & 4.

 

My recognition of this simple link between the 3rd letter group [occupied by F] and the digit set - 1, 1, 4 - which is closely associated with the adjacent letter groups [occupied by A & N], intrigued me and I was curious as to whether the digit sets 3 & 1-1-4 also embody a meaningful relationship. ...

 

When I computed the expression 3p x 114p, I obtained a definitive answer - 1851 [= 3x617] - the value, in degrees/1000, of the Milk Hill  line of longitude I have described. And this remarkable manifestation of the number - involving as it does the contentious digit 3 at the end of the table-derived, 1.8513 - raised the possibility [as mentioned overleaf] that the corn circle builders had been inviting us to focus on the meridian whose value is devoid of the cited final digit [= 3] i.e. 1.851 W.

 

Having concluded, then, that our table can define the meridian, expressed to at least 3 decimal places, that cut the Milk Hill formation's centre, my attention was drawn back to the process that had yielded, by similar means, a more crude value of the same point's latitude [51.3 W]. Had I overlooked the presence of other digits, which would have yielded the same degree of accuracy?

 

A return to the following array [the source of '1-8-5-1-3'] soon yielded a clear answer to my question. ...

 

I first noted that, of the 3 letter groups placed beneath F-A-N, the 6th and largest [OPQRSTUVWXYZ] is unique in that it's the only one not located between two of FAN's letters [the group just has N on its left (as viewed)]:-

 

And I concluded that as this final group has a special status analysts are entitled to treat it as such. ...

 

I therefore changed the 6p, associated with it, back to 6 [the group's position value] and excluded the number from the summation process that the adjacent 2p & 4p were then subjected to, as shown in the table alongside:-

 

And these adjustments had a breathtaking impact. ...

 

If we now read the five highlighted numbers anticlockwise, from the 5, we obtain the sequence 5-1-3-7-6.

 

And the latitude [WGS 84, to the nearest .001 N] of the main Milk Hill formation's centre was - 51.376 N - as shown in the adjacent Fig.:-

 

Furthermore, the depicted table also embodies another revelation. ...

 

Changing the 6p [of the 6th group] back to the non-prime, 6, isolates that group not just from the two that sit on the same line as it [BCDE & GHIJKLM] but also from the three on the top line [F, A & N]: all five of the latter groups are endowed with numbers that are prime [= 5, 1, 3, 2p & 4p].

 

The two sets of letters that these five groups comprise [F-A-N & BCDE-GHIJKLM] are in configurations of 1-1-1 & 4-7, and the sum of the inferred 111 & 47 is: 158. But the juxtaposition of 158 with 1, derived from the 1 isolated group alongside, can infer - 158.1 - which happens to be the reverse of ... 1.851.

 

It was clear, then, that manifestations of the numbers 51.376 & 1.851 are interwoven in the same table and this suggested that these are the definitive values of the geographical coordinates I have described.

 

A terrestrial affirmation of the foregoing geographical hypothesis

My identification, then, of relationships that exist between the letters F-A-N and the rest of the alphabet suggested that the builders of the Milk Hill formations had [amongst other things] been trying to draw our attention to a point, placed near the centre of the main edifice, whose WGS 84 latitude & longitude are: 51.376 N & 1.851 W. And although it seemed unlikely that I would be able to find a source that can corroborate this theory, I was soon to discover, to my astonishment, that the cited geographical information had been engrained, in an explicit way, on the crop circle itself. ...

 

Finding the data required little more than a cursory examination of one of the fan-like structure's three blades, as set out in the Fig. below [where the satellites outside the blade have been removed]:-

 

One simple observation provided the key. ... The 6th and 7th main circles [counted from the centre] on the blade's shorter arm [i.e. its two outer main circles] were the only ones not linked to any of the blade's internal satellites.

 

I knew that, within the arm, these two unique circles sat alongside 5 other main circles, whereas the longer arm, opposite, comprised 13. And I could not fail to notice that the diagram below, which displays these structural characteristics of the blade, exhibits a very familiar numerical arrangement:-

 

It was clear that a clockwise journey around the blade's numerical labels, starting from the 5, takes us to 13, 7 & 6 [in that order], and when these numbers are juxtaposed we obtain: 51376.

 

But we know that the centre of the circle from which the blade projected - this being the central circle of the whole formation - had a WGS 84 latitude [North] of ... 51.376.

 

Having recognised that the blade's configuration of main circles displays, in this extraordinary way, the digit sequence associated with the crop formation's central latitude [as per WGS 84], I didn't have to look very hard to see that it does likewise with the structure's corresponding meridian. ...

 

I first noted a curious fact: the described two unique main circles [on the blade's shorter arm], the 6th & 7th, are linked to the number 18 in two independent ways. ...

 

Firstly, they are accompanied, within the blade, by 18 other main circles.

 

Secondly, the sum of 7 [a prime] and 6p [= 11], the prime that corresponds to 6, is ... 18.

 

But it was also clear that if, in the above Fig., the displayed 6 is replaced by 6p [= 11], then the new set of numbers is [reading clockwise, starting at the 5] - 5, 13, 7, 11 - and these possess 6 digits, of sum ... 18.

[Note: the inclusion of 11 in the set 5, 7, 11 & 13 also means that they are now four consecutive primes ... 4p, 5p, 6p & 7p].

 

The significance of this intimacy between 18 and the two unique circles becomes apparent when the number is placed alongside them, as shown in the following modification of the earlier Fig.:-

 

Reading clockwise around the blade, from the 18, takes us past the 5 circles [on the same arm] to the 13 [on the opposite arm]. ...

 

And the juxtaposition of 18, 5 & 13 yields the familiar - 18513 - which we know displays an obvious resemblance to - 1.8512 W - the measured longitude of the fan-bearing crop formation's centre [as per WGS 84, to the nearest 0.0001].

 

It is also of interest to note, here, that 18, the first component of the expression 18-5-13, was associated with two main circles, the 6th & 7th, which [in the arm they sat within] were linked, subtly, to a 10 i.e. they were immediately adjacent to 10 satellites [these being linked to the arm's 5 remaining main circles]. This relationship [as was the case in my FAN analysis] enables us to generate 1.8 [= 18/10], which, when followed by the digits 5-1-3, can infer 1.8513. And when this is expressed to 3 dec. places - 1.851 - it is the value [WGS 84, in degrees W] of a meridian the crop circle builders were highlighting.

 

As the relationships set out on the foregoing pages didn't come about by chance I dug a little deeper!