Horse and Rider grid

It is time , actually way beyond time, that I turn again to this topic. It is ten years since it made itself known, one night when I was at a low ebb, wondering what it was I had found with all the geometry. It has certainly defined my life situation, and instigated my contact with Bill Buehler which certainly has defined my work since.

Introducing this topic, I wish to emphasize the geometric grid which defines the 'possible' 'plausible' 'quite convincing' construct of the feature which 'appeared' back in 1999.

This grid system follows naturally from the original penta-system centred on Galachlaw and the hexa-system centred on Mavisbank earthmound which has the same radius as that found by Henry Lincoln round Rennes Le Chateau, and which equates to 5000 Scottish ells as defined by John Reid, a gardener, and author of The Scots Gardner, 1683. The main features of the construct, The heads of both horse and rider are defined by the boundary walls of Newbattle Abbey and Dalkeith estate respectively.

21st January, 2010

Well, A guid new year to all, if somewhat belated. I do believe, have been led to assume, some sort of process is 'directing' me at times, and have come to accept that sometimes trying to do this stuff is akin to knocking one's head against a brick wall, it just ain't going to happen till its 'ok' /'time'!

This topic is one instance, the image/feature appeared in a flash of 'revelation' over ten years ago, September 1999, as mentioned previously. I worked on the feature and its defining geometry, explored the landscape, and so on, till in March 2003, when I took advantage of the opportunity to drive Bill Buehler and his wife Joan around the area on a beautiful sunny spring day.

I took Bill to 'The Meeting Of The Waters, where the two Rivers Esk meet in Dalkeith Estate, which is the brow of the riders head, and the first corner found of the original pentagon. (Joan had hurt her ankle and stayed behind in the restaurant as it involved a walk of a good mile and back)

I also showed them the stretch of wall which is part of the horses head, and which was part of my childhood world at Easthouses, then I drove round to Newbattle Abbey itself, which is the eye of the horse, and where I spent a year as a student at the Residential College there in 1995/6. The Sauniere Society have held their Scottish Symposia there since the late nineties.

I was particularly kean to show these points to Bill as he had picked up on my referencing this feature in a discussion group back in late 1999, and had stressed its significance in the unfolding drama, namely the Assencion, the appearance/revelation/development of the Earth grids over the whole planet being an integral part. Mind blowing, it all certainly was!

Soon after, May 2003, I was attempting to write it all up, my own personal life associations with the area, and nostalgic meanderings, when reports of a particularly gruesome murder came over the radio, in an area of the Newbattle boundary wall, which I knew well. I stopped writing at that instant with the comment, with full irony intended, 'Nostalgia ain't what it used to be!' I felt more than a trifle spooked!

Also, my intention was not to let the horse and rider feature become something sensationalised and ridiculed like the Glastonbury zodiac. I wanted to emphasize the geometry that defines it, and be able to show how simple it would in fact have been to create, given a degree of coordination between the main players, the land owners, at a particular time in the past.

So I intentionally showed first all the main geometric systems, their extent, complexity, and even more astonishing, their degree of accuracy, and links to the other two main areas of proven geometry, Rennes Le Chateau and Bornholm, even the units involved are common.

So, some 1.5 years later, I am slowly getting round to it again. Even the graphic above has been a story of stupid oversight on my part. The image wouldn't upload, and I couldn't think what had changed. I gave up, and only returned to it today, when again it wouldn't upload. Till, that is, I noticed a check box, for the query, 'do I accept these new terms?' Doh! Weeks lost again! But, then again, who or what is in charge of this process? Cos, it sure don't feel like I am! And, why make me feel like a goddam fool, so often!? Eh?

Calculations for Eildon - Forth Road Bridge line

The O.S. grid references for the chosen points:

NT 550 325 Eildon(point midway between two largest hills)
NT 315 587 Temple Kirk
NT 275 630 Rosslyn Chapel
NT 245 662 Hillend Fort
NT 239 668 Cross 'T'- Wood
NT 144 775 Dalmeny Kirk
NT 125 796 Forth Road Bridge(mid-point)

Transposed form, and fine-tuned to the metre:

3550.32 6325.24 Eildon
3315.24 6587.30 Temple Kirk
3275.05 6630.66 Rosslyn Chapel
3245.24 6662.06 Hillend Fort
3239.84 6668.10 T-Wood
3144.44 6775.08 Dalmeny Kirk
3125.40 6796.35 Forth Road Bridge


The Eildon from the south-east

Calculation of orientation and distance:

1) Dalmeny - Eildon

3144.44 6775.08 Dalmeny
3550.32 6325.24 Eildon
---------- ----------
0405.88(x) 0449.84(y)
---------- ----------

By Pythagoras' Theorem(sq.rt(x^2 + y^2)):

605.88 km*100 = 60,588 metres

(60,588*3.2808)/5280 = 37.65 miles(E); times (16.5/18.5)= 33.58 miles(S)

angle of orientation:

(x/y); tangent-1;

405.88/449.84 = 0.9022764= tangent 42.06 degrees.

2) Forth Road Bridge - Eildon

3125.40 6796.35 Forth Road Bridge
3550.32 6325.24 Eildon
---------- ----------
0424.92 0471.11
---------- ----------

By Pyhtag;

63,443 metres = 39.42 miles(E); 35.16 miles(S)

angle;

42.05 degrees

3) Rosslyn Chapel - Eildon


Rosslyn Chapel, circa 1995, pre-canopy

3275.05 6630.66 Rosslyn Chapel
3550.32 6325.24 Eildon
---------- ----------
0275.27 0305.42
---------- ----------

By Pythagoras;

41,116 metres = 25.55 miles(E); 22.79 miles(S)

angle;

42.03 degrees

For the moment, what needs to be seen is that using the mid-point of the two main Eildon summits, Rosslyn Chapel, Dalmeny Kirk and the exact mid-point of the Forth Road Bridge are in a direct line line, to within 0.03 degrees, over a distance of 39.42 miles(E). Excluding the Forth Road Bridge, which is 'surely' coincidental, Dalmeny Kirk and Rosslyn Chapel are within 0.01 degrees, over 37.65 miles(E). 0.01 degrees is, using the visual reference of a clock-face-minute(cfm)(6 degrees), 1/600th of one c.f.m., or 35 feet.

If the two main summits of Eildon are used as a 'gate', then the other points listed are contained within using Dalmeny Kirk as reference:

3144.44 6775.08 Dalmeny Kirk
3554.33 6329.10 Eildon (Ring Fort)
---------- ----------
0409.89 0445.98
---------- ----------

By Pythag. theorem: 60,573 metres = 37.64 miles(E); 33.57 miles(S)

angle of orientation: 42.59 degrees


Dalmeny Kirk

3144.44 6775.08 Dalmeny Kirk
3548.19 6323.03 Eildon (O.S. trig. cairn)
---------- -----------
0403.75 0452.05
---------- -----------

By Pythag. theorem: 60,610 metres = 37.66 miles(E); 33.59 miles(S)

angle of orientation: 41.77 degrees

So, the two summits give a spread between 42.59 - 41.77 degrees = 0.82 degrees.

This spread, or 'gate' of 0.82degrees, less than 1/7th of one clock-face-minute, though small in itself, is a large enough 'unit point area' to contain all the chosen points with Dalmeny Kirk as focal point at the other end.

Just for completion, the remaining three points listed, Temple Kirk, Hillend Fort and the plantation known as T-Wood, with reference to Dalmeny Kirk:


Temple Kirk

3144.44 6775.08 Dalmeny Kirk
3315.24 6587.30 Temple Kirk
---------- ----------
0170.80 0187.78
---------- ----------

By Pythag. theorem: 25,384 metres = 15.77 miles(E); 14.07 miles(S)

angle of orientation: 42.29 degrees


Hillend Fort from Roslin Main Street

3144.44 6775.08 Dalmeny Kirk
3245.24 6662.06 Hillend Fort
---------- ----------
0100.80 0113.02
---------- ----------

By Pythag. theorem: 9.41 miles(E); 8.39 miles(S)

angle of orientation: 41.73 degrees


T-Wood from below at Swanston

3144.44 6775.08 Dalmeny Kirk
3239.84 6668.10 T-Wood
---------- ----------
0095.40 0106.98
---------- ----------

By Pythag. theorem: 14,334 metres = 8.91 miles(E); 7.94 miles(S)

angle of orientation: 41.73 degrees



n.b. The T-Wood is centred on a high point with a cairn on top, but unmarked on the map. This was noted on a visit a few years back.

Now, the Eildon has been found in previous sections to be an important point, and is a recognized major, mystical, magical feature of the Borders landscape. From Iron Age Ring Fort, Roman Signal Station, on the banks of the Tweed, on the Phi latitude, a fairy mountain with Thomas The Rhymer associations, with Melrose and its Abbey at its feet. The geometric links are many, and with the special spots on this particular line, it is no doubt worthy of further study, in this instance how this line fits with other systems already considered.

A additional thought, perhaps worthy of consideration, is that the three hills of The Eildon are reminiscent of the three Pyramids of the Giza plateau, even the alignment of the three are similar, in that the two biggest are to the east of the third smallest, and the smallest is also offset from the two largest, just like at Giza, and the configuration is reminiscent of the belt stars of Orion, just like the Giza Pyramids have been equated with, by Bauval and Gilbert, and Hancock. Jeff Nisbet, a few years back, presented a convincing Orion system, using the three islands near North Berwick as the belt stars, and found the other stars, and Sirius quite convincingly marked in the landscape of the area on both sides of the Firth of Forth. We had a discussion going on this, but due to my loss of computer and internet access, tailed off back in 2003. A link on Jeff's website to Gary A. David's site concerns another Orion in the landscape of Arizona, which I had not known of previously: http://azorion.tripod.com/ which is very interesting and worthy of study.

I shall return to this eventually, but for now I wish to return to a system covered early on but was left unfinished. I feel I have now covered the main geometric systems found over the fifteen years now, and cleared the decks, so to speak.

A special line in the landscape!

Hillend Fort on skyline, with the T-wood just below, and Dalmeny Kirk mid photo, and Hawes Pier area, taken from the midpoint of the Forth Road Bridge, May, 2009.

When I started to investigate the landscape of Lothian for geometry similar to what Henry Lincoln had described around Rennes Le Chateau some 15 years back, I came across a bare system in Andrew Sinclair's: Sword and the Grail, but which I no longer have to hand. One line I did find intriguing, as I had found the same line, but with somewhat different marker points!

Where-as Sinclair had noted the points: Hawes Pier, at South Queensferry, the T-Wood, or Cross Wood, above Swanston Village, Rosslyn Chapel, and Temple Kirk; I had: Dalmeny Kirk, T-Wood, Hillend Fort, Rosslyn Chapel and Temple Kirk.

Those who have followed this blog will be aware, Hillend Fort is one of the main points in the landscape, not least as the G.P apex point in the (3 by 1) diagonal Reshel system, and one of the best vantage points for the whole of the Lothian landscape, and can be seen from Roslin village, looking along Main Street.

I eventually noted that this line extended to the exact mid-point of the Forth Road Bridge, surely coincidence, but intriguing none-the-less!(?)

While living in Selkirk(1999-2001) I would quite often drive up to Edinburgh via Innerleithen, quite deliberately to the point where the road came out of the Moorfoot Hills to a superb vantage point on the other side of the Esk Valley from Hillend, before turning sharply right, (north-east), and try to see the points Temple and Rosslyn in the direct line that the map showed them to be. The exact point is about 200 yards down this road. Rosslyn Chapel is identifiable, now with the white coloured canopy, but Temple is not visible as it sits by the river in the steep sided valley.

I also extended this line on the map not so surprisingly came to the Eildon Hills, by way of Carcant Hill, the slope of which this vantage point is on.

Three years ago when I moved to Inverkeithing came the opportunity to check this line often from the midpoint of the Road Bridge. I managed to identify Dalmeny Kirk, and tried whilst a passenger in a friends car to take a decent photo. This proved awkward in that the main cable at the centre obscures the view, and being on the move was a bit troublesome also. I knew I would have to walk to the middle of the Bridge sometime, but it took me till May this year to get round to it!



This is a recent shot taken from South Queensferry at Hawes Pier to the mid-point of the Forth Road Bridge. The hills below allow a visual guide for the extended line to the north-west. A rough check in Google Earth leads across Loch Tay, just west of Ben Lawers, and directly in line is Maggernie Castle in Glen Lyon. This shall be checked later.



The Eildon Hills, from the north-west. The two used in this report are left and centre.

The Great and second Great Pyramid Geometry

This figure as found in Tompkins, pages 260-261, basically a four square with (1 by 1) and (2 by 1) diagonals, contains the necessary information to construct both of the great pyramids at Giza.

I've been a bit pre-occupied for the past few weeks, re-reading 'Secrets Of The Great Pyramid, by Peter Tompkins, and the appendix on Ancient Measure by Livio Stecchini. Slowly it dawned on me that the basic geometry the Great Pyramid is based upon is so simple, yet I have not seen it explained previously. I also came to realize that the Second 'Great' Pyramid is also derived as simply from a (2 by 1) rectangle, or double square.

Tompkins in a discussion about the above figure describes the idea of Tons Brunes who in The Secrets of Ancient Geometry
who 'shows that the Great Pyramid, like most of the great temples of antiquity, was designed on the basis of an advanced but hermetic geometry known only to initiates. only fragments o which percolated to the classic and Alexandrine Greeks.'

Tompkins states: Brunes shows how the ancient Egyptians used the basic design of a circle inscribed in a square to divide both circle and square geometrically into equal parts from 2 to 10, and all their possible multiples, without recourse to measuring or arithmetical calculations, with the aid of nothing but a straightedge and a compass - common emblems, along with the Pyramid, of the Masonic orders of yesterday and today.

He continues: In Brunes' reconstruction o the secret geometry, the cross emerges as the first geometric addition to the circle and square, and is the key not only to the solution of geometric problems but to the development of numerals and the alphabet.
By including the diagonals, every number both Latin and Arabic and all the letters of several alphabets may be obtained.
According to Brunes, both mathematics and the alphabet sprang from geometry, not the reverse. He says that nowadays we use numbers as the primary factor in our calculations, and geometry only as a subsidiary, whereas he believes the Egyptians reversed the order. He uses a detailed analysis of the Rhind Mathematical Papyrus to demonstrate that the ancient Egyptian system of counting was directly governed by geometric factors and that their ideas and theories were bound in geometric rules.
Brunes found that the circle was indeed considered sacred by the Egyptians, as were the square and the cross and the triangle, all of which are intimately incorporated into the Great Pyramid with its square base and triangular faces designed to represent the ''sacred'' circle.
Brunes demonstrates how the circle inscribed in a square and quartered by a cross enabled the ancient Egyptian geometer to inscribe in a circle the basic figures of pentagon, hexagon, octagon and decagon.

end quote.

Tompkins points out that the golden section is formed automatically between the sides and chords of the pentagon. This is so!

What is also true though is that very simply the golden section can be deirved directly from the (2 by 1) rectangle, as the diagonal is square root five, and if the unit side is added and the whole length halved, this is Phi in relation to the side. (1.618034 : 1)

It was musing on this and that the apothem of the Great Pyramid is Phi in relation to half of the base that the geometric construct of the Great Pyramid became apparent, as described below.


Right click on images, and 'Open in New Window' to see at full size:




figure 1: The basic (2 by 1) rectangle a circle is drawn centred on the common side with radius half the base. The points on the diagonals cut by this circle are 1.618034 units, with square side being 1 unit. Aa = Bb = Cc = Dd = 1.618034, Phi.

Diagonal = Square root five, 2.236068.

2.236068 / 2 = 1.118034

1.118034 + 0.5 = 1.618034.



figure 2.



figure 3.

Figure 2 is the construct of the Great Pyramid geometry. Figure 3 is labelled.

From points A and B with length Aa and Bb, or Phi, arcs are scribed to cut the axis, at P. The figure so formed is a cross section of the Great Pyramid, with base 2, apothem or slant height, Phi, and height square root Phi.

The angles PAQ and PBQ equals 51.8273 degrees.



figure 4.



figure 5.

Figures 4 and 5 show how the Second Pyramid geometry is found.

Stecchini, pages 378/379, gives Petrie's figures for the Second Pyramid at Giza, which he reckons best. He shows that the cross sectional triangle, half base, height and apothem are in the relationship, 3,4,5, which gives a base angle of 53.13 degrees.

In figure 4 the angle formed by the intersection of the two diagonals at O, is 53.13 degrees, so a construct of the Second Pyramid is possible from this fact alone. Angle BOM is 53.13. An arc is scribed from point B with length BO, to the intersection with the diagonal extended to M.

Figuire 5 shows a variation using the length Phi, Bb, to construct a triangle with the same apothem as the Great Pyramid, namely Phi.

Triangle BKL is a 3,4,5 triangle. KL is 3 units, BK is 4 units, BL is 5 units.

As the two pyramids are constructed I can't find any convincing correlation in dimensions, the second Pyramid being some 97% roughly smaller in base and height. Apparently, the Second Pyramid is on a higher level than the Great Pyramid so appears to be somewhat higher.

I find it fascinating that both can be found so simply from the same basic figure, namely figure 1 above.

Finally, the (2 by 1) rectangle diagonals form angles of 26.5650512 degrees, and 63.43495 degrees. The angle 26.5650512 degrees is very close to the angles given for the Ascending and descending passages of the Great Pyramid, adding further, perhaps, to the links shown here.

March 10, 2009, full moon

Tuesday night shift, I went a bit Lunar, it was a stunning full moon rise in the evening. I took photos all through the night and even got the sunrise in the morning.

I'll get round to adding some text some time soon! I even took some of the Grassmarket as it is now after renovation.

The last one is in Inverkeithing walking home and I have incorporated phi into the composition.

Web album

full moon, March10, 2009