Monday 24 December 2007
Newgrange: winter solstice, 2007
A video of the winter solstice sunrise at Newgrange, Boyne Valley, Ireland.
Friday 23 November 2007
Alistair Moffat - Arthur & The Lost Kingdoms
I had the pleasure of reading this book a few years back, borrowed from a friend. At the time I was living in Selkirk, and finding that the geometry I was working on not only stretched into the Borders, but specifically on Kelso and Roxburghe Castle, identified by Moffat as being Arthur's main base.
Arthur & The Lost Kingdoms
When I get round to doing some more geometry, this will prove relevant!
Arthur & The Lost Kingdoms
When I get round to doing some more geometry, this will prove relevant!
Monday 19 November 2007
Castlehill, Edinburgh
It's not often that the street is empty of vehicles and people. Camera Obscura on left, Witchery and Whisky Heritage Centre on the right. The brooding spire in the background is of the Tollbooth Church, now The Hub, and the highest point in Edinburgh!
Just as an excercise in posting photos direct from Picasa! A bit confusing, as it tries to do it through Internet Explorer, and an error message comes up. Click all that away and it works, but a bit clumsy!
Just as an excercise in posting photos direct from Picasa! A bit confusing, as it tries to do it through Internet Explorer, and an error message comes up. Click all that away and it works, but a bit clumsy!
Bruce Cathie; a Phi correlation
Bruce Cathie, an ex-airline pilot from New Zealand, started his grid research whilst plotting sitings of UFO's back in the fifties.
A link to his site is provided in the list to the right.
Going through his site recently, I came across his work on the magnetic fields of the Earth.
I hadn't noticed a Phi correlation previously, but did this time:
According to Cathie there are two magnetic fields which combine, or counter-act the other.
The two fields are given he gives the figures for combined field strength and their diffeence.
Field A 1850.900532 lines of force per square centimetre, or as he prefers, 12245.6998per square geographic inh.
Field B 1257.139035 per square cm, or 8317.32698 per square geo-inch.
Combined, that is (A+B) = 20574.234 per square geo-inch.
Difference, that is (A-B) = 3928.371 per square geo-inch.
(A+B)/(A-B) = 5.237344945.
which; divided by 2 = 2.618672493, which is close to Phi-squared.
The square root is 1.618231279, of which Phi (1.618034) is 99.9878%.
One in ten thousand is a very good correlation! At this point I do not know what this could signify, just noting in the passing!
A link to his site is provided in the list to the right.
Going through his site recently, I came across his work on the magnetic fields of the Earth.
I hadn't noticed a Phi correlation previously, but did this time:
According to Cathie there are two magnetic fields which combine, or counter-act the other.
The two fields are given he gives the figures for combined field strength and their diffeence.
Field A 1850.900532 lines of force per square centimetre, or as he prefers, 12245.6998per square geographic inh.
Field B 1257.139035 per square cm, or 8317.32698 per square geo-inch.
Combined, that is (A+B) = 20574.234 per square geo-inch.
Difference, that is (A-B) = 3928.371 per square geo-inch.
(A+B)/(A-B) = 5.237344945.
which; divided by 2 = 2.618672493, which is close to Phi-squared.
The square root is 1.618231279, of which Phi (1.618034) is 99.9878%.
One in ten thousand is a very good correlation! At this point I do not know what this could signify, just noting in the passing!
Friday 19 October 2007
Afternoon excursion to Dunsappie and Duddingston
Thursday afternoon I went on an excursion with a group of six Americans, including Laura Dunham, whom I had met two years earlier. They wanted to visit some interesting spots that I might know. After lunch I suggested a drive round Arthurs Seat, stopping at Dunsappie which is a place I had spent a lot of time at when I first started investigating the landscape. I felt drawn to it many times, photographing a midsummer sunrise from there back in 1994. Laura and her group felt a strong earth energy, which is not surprising as Dunsappie is a volcanic vent. The views are impressive, to the north, east and south. A lot more to be said about Dunsappie, and this is a good spur.
The weather was sunny and bright, with a slight chill in the Mid-October breeze.
On the way from Waverley station to Holyrood.
Arthurs Seat from Dunsappie.
A rock feature on Dunsappie that has intrigued for many years! Laura said a prayer here which I felt appropriate.
I then suggested driving down and round to Duddingston, which lies directly below Dunsappie, and is an interesting place, the church, loch, and village being very picturesque. Sometimes I wonder what is going on! The road to Duddingston at the Pollock Halls entrance was just being closed by workmen, so it was down round past where we started and all the way round in a clockwise direction to Duddingston. Only to find that the church gate was locked. A local lady advised us that we could never-the-less gain entry to Dr O'Neil's garden through the Manse entrance. Everyone loved the garden, and the view of the loch. We sat down by the waterside for a while, chatting and just taking in the view and appreciating the stillness and the quiet.
A couple of photos in Dr O'Neil's garden at Duddingston.
Time was becoming an issue as they wanted to be back at their Roslin hotel before dark. Cal, the driver didn't want to be navigating in the dark, which is understandable in a strange place. My original plan of heading down the coast didn't happen, but it was a nice afternoon anyway.
We parted in the High Street as they were off to St Giles cathedral and I down Cockburn Street for my train home.
The weather was sunny and bright, with a slight chill in the Mid-October breeze.
On the way from Waverley station to Holyrood.
Arthurs Seat from Dunsappie.
A rock feature on Dunsappie that has intrigued for many years! Laura said a prayer here which I felt appropriate.
I then suggested driving down and round to Duddingston, which lies directly below Dunsappie, and is an interesting place, the church, loch, and village being very picturesque. Sometimes I wonder what is going on! The road to Duddingston at the Pollock Halls entrance was just being closed by workmen, so it was down round past where we started and all the way round in a clockwise direction to Duddingston. Only to find that the church gate was locked. A local lady advised us that we could never-the-less gain entry to Dr O'Neil's garden through the Manse entrance. Everyone loved the garden, and the view of the loch. We sat down by the waterside for a while, chatting and just taking in the view and appreciating the stillness and the quiet.
A couple of photos in Dr O'Neil's garden at Duddingston.
Time was becoming an issue as they wanted to be back at their Roslin hotel before dark. Cal, the driver didn't want to be navigating in the dark, which is understandable in a strange place. My original plan of heading down the coast didn't happen, but it was a nice afternoon anyway.
We parted in the High Street as they were off to St Giles cathedral and I down Cockburn Street for my train home.
Venus distance 0.618034 A.U.
Keeping an eye on Venus, and Mars, in the morning sky at present, I checked Stellarium to find out when Venus, and Mars, was at its closest. It seems to have just passed this point, but on Wednesday it was approximately 0.609 AU (Astronomical Units. 1AU being the distance from Earth to the Sun.) At 20.03 GMT, 21.03 BST on Thursday, that is last night, the distance had increased to 0.618(034) AU, the exact phi number. This distance would also have been true a couple of days previous, which I missed. It is perhaps more coincidence than of any significance, but as Venus is a Phi object in relation to the Earth, forming a pentagon every eight years, I note it anyway.
This set planetary patterns is from Bronowskis's The Ascent Of Man, page 190. The caption is:
A sense of the heavens moving round their hub and the hub was the round earth. The diagram shows the paths traced out by the planets as seen from the Earth. The Ptolemaic theory tried to explain these. The photograph shows the movements of Mercury, Venus, Mars, Jupiter and Saturn, (right to left) recorded by long exposure in the Munich Planetarium.
Venus and Mars enlarged.
Emphasizing the importance of astronomy to navigation making the point that the 'New' World did not use the stars for navigation purposes, whereas the 'Old' World did, attributing the seafarers of the Meditteranean in the Greek era with combining adventure with logic, 'the empirical with the rational - into a single mode of inquiry'. He makes the point that although Astronomy is 'not the apex of science or of invention. But it is a test of the cast of temperament and mind that underlies a culture.'
Whether the geometry in the landscape of Britain and the Baltic can ultimately be attributed to Meditteranean seafarers is a debate I don't consider vital for now!
Mars is increasing in luminosity as the Earth swings round towards its nearest point, Mars being in its apparent retrograde loop.
One observation I was not aware of till noticing in Stellarium that a good pointer to north, other than the two stars in Ursa Major, is a line through the gap between Rigel and Bellatrix in Orion through Capella in Auriga. At the oblique angle through the gap in the two Orion stars, it is a more accurate indicator than that of the two UM stars. Once seen Orion is easily identified, and Capella is bright. And if the point at which Orion is at its zenith, nightly in the winter sky at least, a very accurate North south line can be determined.
Whether the geometry in the landscape of Britain and the Baltic can ultimately be attributed to Meditteranean seafarers is a debate I don't consider vital for now!
Mars is increasing in luminosity as the Earth swings round towards its nearest point, Mars being in its apparent retrograde loop.
One observation I was not aware of till noticing in Stellarium that a good pointer to north, other than the two stars in Ursa Major, is a line through the gap between Rigel and Bellatrix in Orion through Capella in Auriga. At the oblique angle through the gap in the two Orion stars, it is a more accurate indicator than that of the two UM stars. Once seen Orion is easily identified, and Capella is bright. And if the point at which Orion is at its zenith, nightly in the winter sky at least, a very accurate North south line can be determined.
Thursday 11 October 2007
Solar Eclipses - N.A.S.A.
Watching the Moon pass Venus, Saturn and Regulus, and realising Regulus sits on the ecliptic, it seemed possible that there might be a solar eclipse about to happen. I checked in Stellarium, and it seems that this time round, close but no coconut. In Stellarium, the Moon passes just below the Sun, later today(11th Oct 2007), and becomes a new moon.
I decided to check to see what astronomers made of it. This site by N.A.S.A. predicts the next total solar eclipse to be August 2008.
This site has tables giving eclipses, both solar and lunar, from as far back as 2000BC, to 3000AD:
http://sunearth.gsfc.nasa.gov/eclipse/solar.html
I decided to check to see what astronomers made of it. This site by N.A.S.A. predicts the next total solar eclipse to be August 2008.
This site has tables giving eclipses, both solar and lunar, from as far back as 2000BC, to 3000AD:
http://sunearth.gsfc.nasa.gov/eclipse/solar.html
Tuesday 9 October 2007
A couple of handy astronomy sites
A couple of sites I've found which are both good but both limited, but together allow a good grasp of the sky and its objects, and Stellarium shows the sky as seen. Mine is set to a Paris viewpoint, am still playing and haven't adjusted for Edinburgh. Celestia is not Earth-based. Space travel is possible!
The First
Stellarium
The second:
Celestia:
some images from Celestia:
1.
2.
3.
4.
5.
The First
Stellarium
The second:
Celestia:
some images from Celestia:
1.
2.
3.
4.
5.
Moon and Venus weekend 5/6Oct 2007
The Moon rising over East Lothian, across the water, photo taken at Seafield:
Two photos of the Moon and Venus, taken from Canonmills Service Station, around 5.30 GMT, 6.30 BST:
1.
2.
two again, some twenty minutes later:
1.
2.
Two photos of the Moon and Venus, taken from Canonmills Service Station, around 5.30 GMT, 6.30 BST:
1.
2.
two again, some twenty minutes later:
1.
2.
Astrology/Astronomy plug-ins
From this site: Widgets Astrology World
Moon phase:
Moon position:
Planetary interaspects, whatever they may be:
These should update regularly!
Moon phase:
Moon position:
Planetary interaspects, whatever they may be:
These should update regularly!
Friday 5 October 2007
Moon and Venus
This shows Venus and the Moon in the eastern sky on the morning of October 4th, approximately 5.30am GMT, 6.30am BST. Saturn is to the left of Venus, both straddling Regulus in Leo, neither recorded on this image. Mars is also not shown, but is between the Gemini twins, and Sirius is also rising, again not seen in this photo. Procyon, Canis Minor, is the other star seen forming a near right angle with the Moon and Venus.
Around 5.55 am GMT, dawns light increasing.
These photos don't do the sky justice. The Moon is now very near Venus and Regulus. A thought here, is that Regulus is on the ecliptic, and so the Moon's position can be judged accurately from its relation to Regulus, as it passes! The Moon varies by some 5+ degrees either side of the Sun's path! Something else to watch for over the coming winter months. On checking my Planisphere, I note Virgo is also on the ecliptic. Sky-watching is a bit of a hobby when I'm working nights.
Around 5.55 am GMT, dawns light increasing.
These photos don't do the sky justice. The Moon is now very near Venus and Regulus. A thought here, is that Regulus is on the ecliptic, and so the Moon's position can be judged accurately from its relation to Regulus, as it passes! The Moon varies by some 5+ degrees either side of the Sun's path! Something else to watch for over the coming winter months. On checking my Planisphere, I note Virgo is also on the ecliptic. Sky-watching is a bit of a hobby when I'm working nights.
Tuesday 18 September 2007
Some Lothian geometry, Borthwick as focus, leading to The Eagles'Nest - consider as Part two
The first diagram shows the first hint of geometry I found way back in 1993/4. I wont comment further yet, as it is the set of four after I wish to concentrate on. Just that this first highlighted the Meeting of the Waters in Dalkeith Estate, which led eventually to the pentagonal system shown, which is central to the whole complex, as found by me. It is relevant also in that Carberry Tower or Queen Margarets Mount in the Carberry Estate is identified by Bill Buehler as being the radius of the circle centred on Borthwick, which is the topic here.
This diagram shows the Borthwick axis in relation to the pentagonal system. This axis is that identified by Bill Buehler, whose work I have been studying for some 8 years now, with emphasis on his geometrical systems as applied to the Lothian area. Just when I seem to be getting on top of things geometric, along comes Bill with another stunning system which leads me off on another trail for weeks/months, years even. This system is one such. I had been offline for a while, working on whatever, and when I got back online, there's this system centred on Borthwick, using the David Wood's pentagram based on a 15 division circle. These diagrams show what I found, the basic geometry. My previous post shows the development of this system to a perfect pentagon based on the circle mentioned above. Part two gets complex, later. The angle of the axis is emphasised by Bill as being indicative of a Parhelion effect of the sun, the 'Sun-Dogs' phenomenon, at 23(+/-) either side of east. The Sun-Dogs effect is created by the hexagonal ice crystals if the upper atmosphere.
This is the circle centred on Borthwick, with Queen Margaret's Mount as radius. The 15 divisions are shown.
This shows the completed perfect pentagon extended to Craigleith Island, off North Berwick. This line extended south, off the page, leads to Eagles Nest near teh Gordon Arms, on the Yarrow, at Mountbenger, some two miles east of St. Mary's Loch, just off the Innerleithen Road. This point proved to be of great significance in the whole scheme. see Part two, after this.
I have included a circle either side of the Borthwick one, and these also play a part in the developing whole.
A lot of dots can be seen on some of these diagrams. They are all specific points in the geometry, and a list shall be provided with Grid References later, as the chance occurs!
Part Two
Ok! Part two, which is actually the third part, with the David Wood penta excercise being the first. I'll get round to changing things to suit to avoid confusion.
I've spent the past week re-reading The Ascent Of Man, by Prof. Bronowski, the book of the early seventies BBC TV series, some may remember. Still fascinating!
I've also been watching the night/morning sky. Mars is up near the Gemini twins, Orion AND Sirius have appeared again just below Mars, with Venus stunningly bright in the morning eatsern sky. I note that Saturn is around there too, but I havent spied it due to dawn light and Venus dominates. Wednesday night the sky was clear and the full moon was brilliant. Jupiter is west of south in the evening.
Anyway, part two of the Borthwick excercise:
This first image shows three lines converging towards the bottm. These all meet at Eagles Nest, unfortunately the scaling didn't allow this point to be included. This series of drawings was done when I had a clapped out, limited computer last year. They were all done in Paint, accurate to the pixel, which is as good as I could manage. This is insufficient to show the actual accuracy. Most of the points were calculated and plotted individually, and checked prior to plotting. This took a long time, as did the drawings in fact. Many months hard slog, if I may add! The first drawing shows what in effect was the stunning finding when it all panned out. Namely finding that Eagles Nest point confirmed the interrelatedness of the original pentagonal, the Borthwick complex, and the Preston Cross(unicorn atop) which I have been working on for a few years now. I took Bill Buehler there in 2003, as it had already become a very important point. It is also why I took the unicorn as a symbol! There are three lines coloured green in the drawing. The left hand one, projects from the chord of the original pentagon, which includes Arturs Seat(AS), and includes two corners, Leith(L) and Shewington(Sh). The central line runs from Preston(unicorn) Cross(PuC), through Borthwick Church, the centre of afore mentioned system, and the right hand line is the chord of the found perfect pentagon, running from Craigleith Island(CI), through Pilmuir House(Pil,H,).
The second drawing again shows these three lines with a few interesting findings. For instance the original pentagon has two sides projected to the Craigleith chord line were it cuts the Borthwick Church axis. I have included the three circles cnetred on Borthwick as a guide.
The third drawing has the Mavisbank hexagon included and it may be seen that it too converges with the axis at a significant point. The colours are inverted giving the black background, and the three lines under discussion are in the primary colours.
This fourth drawing is rotated so that the Borthwick axis is horizontal, which allowed me more space to work in the Eagles' Nest point(EN at the very bottom) at long last. That was an effort in itself. As I mantioned previously, it all gets a bit complex, and this ain't it all. Again the accuracy is to one pixel, and I have circled certain areas, as they are multiple point areas. For instance, BWM is the Black and the White Meldon, just outside Peebles. ETM, is the Eildon Hills, Trimontium to the Romans and Melrose. AS is Arthurs Seat and surrounding area.
The light green grid is the Borthwick hexagon projected, just to see what happened. A few points of inteest but I won't bother with that just now.
I haven't put in the Arthurs Seat line to Eagles Nest in this drawing, an omission, partly due to the complexity already there. There is an additional line from Eagles Nest to the Eildon. I first found this when working on that area, when I lived in Selkirk, and there were indicatiuons of another sytem at the time, and should be followed up when time allows. I shall finish here for now. I shall do a follow up soon, concentraing on the Preston Cross point and the astonishing trinagle found to have its apex there. I have made the last two larger which may help, if they are clicked on they should open in a new window. If anyone wants them even larger, let me know!
This diagram shows the Borthwick axis in relation to the pentagonal system. This axis is that identified by Bill Buehler, whose work I have been studying for some 8 years now, with emphasis on his geometrical systems as applied to the Lothian area. Just when I seem to be getting on top of things geometric, along comes Bill with another stunning system which leads me off on another trail for weeks/months, years even. This system is one such. I had been offline for a while, working on whatever, and when I got back online, there's this system centred on Borthwick, using the David Wood's pentagram based on a 15 division circle. These diagrams show what I found, the basic geometry. My previous post shows the development of this system to a perfect pentagon based on the circle mentioned above. Part two gets complex, later. The angle of the axis is emphasised by Bill as being indicative of a Parhelion effect of the sun, the 'Sun-Dogs' phenomenon, at 23(+/-) either side of east. The Sun-Dogs effect is created by the hexagonal ice crystals if the upper atmosphere.
This is the circle centred on Borthwick, with Queen Margaret's Mount as radius. The 15 divisions are shown.
This shows the completed perfect pentagon extended to Craigleith Island, off North Berwick. This line extended south, off the page, leads to Eagles Nest near teh Gordon Arms, on the Yarrow, at Mountbenger, some two miles east of St. Mary's Loch, just off the Innerleithen Road. This point proved to be of great significance in the whole scheme. see Part two, after this.
I have included a circle either side of the Borthwick one, and these also play a part in the developing whole.
A lot of dots can be seen on some of these diagrams. They are all specific points in the geometry, and a list shall be provided with Grid References later, as the chance occurs!
Part Two
Ok! Part two, which is actually the third part, with the David Wood penta excercise being the first. I'll get round to changing things to suit to avoid confusion.
I've spent the past week re-reading The Ascent Of Man, by Prof. Bronowski, the book of the early seventies BBC TV series, some may remember. Still fascinating!
I've also been watching the night/morning sky. Mars is up near the Gemini twins, Orion AND Sirius have appeared again just below Mars, with Venus stunningly bright in the morning eatsern sky. I note that Saturn is around there too, but I havent spied it due to dawn light and Venus dominates. Wednesday night the sky was clear and the full moon was brilliant. Jupiter is west of south in the evening.
Anyway, part two of the Borthwick excercise:
This first image shows three lines converging towards the bottm. These all meet at Eagles Nest, unfortunately the scaling didn't allow this point to be included. This series of drawings was done when I had a clapped out, limited computer last year. They were all done in Paint, accurate to the pixel, which is as good as I could manage. This is insufficient to show the actual accuracy. Most of the points were calculated and plotted individually, and checked prior to plotting. This took a long time, as did the drawings in fact. Many months hard slog, if I may add! The first drawing shows what in effect was the stunning finding when it all panned out. Namely finding that Eagles Nest point confirmed the interrelatedness of the original pentagonal, the Borthwick complex, and the Preston Cross(unicorn atop) which I have been working on for a few years now. I took Bill Buehler there in 2003, as it had already become a very important point. It is also why I took the unicorn as a symbol! There are three lines coloured green in the drawing. The left hand one, projects from the chord of the original pentagon, which includes Arturs Seat(AS), and includes two corners, Leith(L) and Shewington(Sh). The central line runs from Preston(unicorn) Cross(PuC), through Borthwick Church, the centre of afore mentioned system, and the right hand line is the chord of the found perfect pentagon, running from Craigleith Island(CI), through Pilmuir House(Pil,H,).
The second drawing again shows these three lines with a few interesting findings. For instance the original pentagon has two sides projected to the Craigleith chord line were it cuts the Borthwick Church axis. I have included the three circles cnetred on Borthwick as a guide.
The third drawing has the Mavisbank hexagon included and it may be seen that it too converges with the axis at a significant point. The colours are inverted giving the black background, and the three lines under discussion are in the primary colours.
This fourth drawing is rotated so that the Borthwick axis is horizontal, which allowed me more space to work in the Eagles' Nest point(EN at the very bottom) at long last. That was an effort in itself. As I mantioned previously, it all gets a bit complex, and this ain't it all. Again the accuracy is to one pixel, and I have circled certain areas, as they are multiple point areas. For instance, BWM is the Black and the White Meldon, just outside Peebles. ETM, is the Eildon Hills, Trimontium to the Romans and Melrose. AS is Arthurs Seat and surrounding area.
The light green grid is the Borthwick hexagon projected, just to see what happened. A few points of inteest but I won't bother with that just now.
I haven't put in the Arthurs Seat line to Eagles Nest in this drawing, an omission, partly due to the complexity already there. There is an additional line from Eagles Nest to the Eildon. I first found this when working on that area, when I lived in Selkirk, and there were indicatiuons of another sytem at the time, and should be followed up when time allows. I shall finish here for now. I shall do a follow up soon, concentraing on the Preston Cross point and the astonishing trinagle found to have its apex there. I have made the last two larger which may help, if they are clicked on they should open in a new window. If anyone wants them even larger, let me know!
Back to some geometry
After a three week break, unplanned, but due to getting into something of a reading frenzy, or re-reading I should say, with a lot of calculator work, I need to get back to what I was intending to do. I was sitting at the computer waiting for something to happen one slow system day, and I just thought to look at Robert Temple's The Sirius Mystery again, for the umpteenth time. This led to Tompkin's The Secrets Of The Great Pyramid, especially the Livio Stechini section at the back, Haagensen and Lincoln's Bornholm book, The Templar's Secret Island, Thom's Megalithic Lunar Observatories, and lastly, but in way least, Richard Heath's The Matrix of Creation, and a few others not so relevant for now.
The sky, too, is fascinating at present. Jupiter west of south after dark, but the morning sky is stunning. Mars is near the Gemini Twins, with Orion showing after its summer lost in the sun's light. Sirus has again appeared, and Venus is stunning as a Morning Star. 4.50am British Summer Time, both Sirius and Venus have risen. This is my usual time for going home, and crossing the Forth Bridge, the view to the east is spectacular, Venus especially. No decent photos though!
Lots to report later, after I get a load of geometry done.
Football/Soccer has been good. Scotland took 6 points recently in two European Championship qualifiers. Lithuania 3-0 was good, but going to Paris and holding out for a 0-1 win was fantastic. McFaddens goal in Paris, outdoen his Hampden strike, and in my opinion is better than Gemmill's in 1978 in Argentina. Oh what a night!
Then on Saturday Hearts beat Rangers 4-2, to cap a great week's footie.
The sky, too, is fascinating at present. Jupiter west of south after dark, but the morning sky is stunning. Mars is near the Gemini Twins, with Orion showing after its summer lost in the sun's light. Sirus has again appeared, and Venus is stunning as a Morning Star. 4.50am British Summer Time, both Sirius and Venus have risen. This is my usual time for going home, and crossing the Forth Bridge, the view to the east is spectacular, Venus especially. No decent photos though!
Lots to report later, after I get a load of geometry done.
Football/Soccer has been good. Scotland took 6 points recently in two European Championship qualifiers. Lithuania 3-0 was good, but going to Paris and holding out for a 0-1 win was fantastic. McFaddens goal in Paris, outdoen his Hampden strike, and in my opinion is better than Gemmill's in 1978 in Argentina. Oh what a night!
Then on Saturday Hearts beat Rangers 4-2, to cap a great week's footie.
Friday 31 August 2007
Friday 24 August 2007
A special pentagonal figure, after David Woods in GENESET - consider this Part One
This is the penta-shape discovered by David Woods in the Rennes Le Chateau area, with a controlling circle of 15 divisions, of 24 degrees each, or 4 clock-face-minutes(cfms). I only have GENESET of his works, and this figure is presented there but with subtle alterations which do not concern us here. This is a symmetrical firgure with all angles equal to 36 degrees.
This little session is vital for the next stage, describing it in the landscape of Lothian and its implications for the development of the geometry in total. It was described first by W.S.Buehler, and I did some follow up work on it with interesting developments. A special point of intersection was found which allowed a tightening up of the original pent system as it was found that it and this interlinked.
The hexagon in the circle.
The penta and the hexagon, with common horizontal chord.
The perfect pentagon is found by extending the short chord, and drawing a horizontal at 42degrees, or 7 minutes on a clock-face. I believe this to be correct but shouldn't get upset if it was slightly off. My geometry ain't fool-proof, and I am the living proof!
The centre of the pentagon is found by drawing in of axes.
An interesting construct on the pentagon gives a golden ratio rhombus, using a half penta side as unit. The golden ratio rhombus is a figure I first heard about from the postings of W.S.Buehler, who I have mentioned previously, and shall be covering common geometric topics.
It has axes of phi(FC&CG), and phi-squared(HC&CI), with the half penta-side as unit, equal to BC&CO.
This post explains the geometry that is based on Bill's centering this figure on Borthwick church. To follow.
Next, I will describe this system as it is in the landscape of Lothian and the Borders. It gets very complex, and this and the original penta system need to be understood seperately to keep track!
This little session is vital for the next stage, describing it in the landscape of Lothian and its implications for the development of the geometry in total. It was described first by W.S.Buehler, and I did some follow up work on it with interesting developments. A special point of intersection was found which allowed a tightening up of the original pent system as it was found that it and this interlinked.
The hexagon in the circle.
The penta and the hexagon, with common horizontal chord.
The perfect pentagon is found by extending the short chord, and drawing a horizontal at 42degrees, or 7 minutes on a clock-face. I believe this to be correct but shouldn't get upset if it was slightly off. My geometry ain't fool-proof, and I am the living proof!
The centre of the pentagon is found by drawing in of axes.
An interesting construct on the pentagon gives a golden ratio rhombus, using a half penta side as unit. The golden ratio rhombus is a figure I first heard about from the postings of W.S.Buehler, who I have mentioned previously, and shall be covering common geometric topics.
It has axes of phi(FC&CG), and phi-squared(HC&CI), with the half penta-side as unit, equal to BC&CO.
This post explains the geometry that is based on Bill's centering this figure on Borthwick church. To follow.
Next, I will describe this system as it is in the landscape of Lothian and the Borders. It gets very complex, and this and the original penta system need to be understood seperately to keep track!
strange lights - msytery solved, I guess!!
On the probability that the lights where a 'ghost' lense reflection I went back and took another set of five, from the same positions, with the same camera.
The same lights appeared in some of them to convince me that was the explanation. Lower in the photograph, due to less light more camera shake.(The flash function is 'lost' on my digi-camera). Although I took this around the same time of night, the light has gone from the north at midnight. The nights are fair drawing in, are they no!? Sin be christmas!
Thanks to 'anonymous' for pointing it out!
The same lights appeared in some of them to convince me that was the explanation. Lower in the photograph, due to less light more camera shake.(The flash function is 'lost' on my digi-camera). Although I took this around the same time of night, the light has gone from the north at midnight. The nights are fair drawing in, are they no!? Sin be christmas!
Thanks to 'anonymous' for pointing it out!
why Phi-latitude!?
Geoff Simmons asked the question. A fuller answer is given here.
I've been a bit distracted for the past couple of weeks, re-reading Robert Temples' The Sirius Mystery for the first time in a few years, especially the Oracle Centres octaves, with their omphalos stones, and carrier pigeons/swallows. This led me to ploughing my way through Peter Tompkins' The Great Pyramid, and even more so through Livio Stecchini's material at the end on ancient measure. I came up with some interesting stuff, related to the general topic of geodetics and ancient Man's knowledge and abilities. Fascinating but time consuming.
One tantalising snippet is that Thebes/Karnak is at latitude 27.5degrees north. Hadrian's Wall is at 55degrees north, twice the number. The Antonine Wall straddles the 56 degree latitude.
The area between is the main focus of my investigations.
Phi, the Golden Section, is well known to those who dabble in pentagonal geometry. It is inherent in the perfect pentagon, being the ratio of side to chord. It is considered the perfect proportion, in words, the ratio whereby a line is divided such that the short is to the long as the long is to the whole. Numerically, it is 1.618(034). The reciprocal is 0.618(034). The square is 2.618(034).
The square, 2.618(034) times 6/5 is within 99.9985% of pi, 3.1416408, against calculator pi, 3.141592654. Using the short version, 2.618, 6/5ths gives 3.1416, a version of pi used by engineers as it is a neat number, even closer at 99.999766%.
It is astonishingly easy to construct phi, phi-squared, and pi, as a straight line, without having to know the numbers at all.
Draw a two by one rectangle, draw in a diagonal, extend the diagonal by one unit, (the short rectangle side is one unit), by use of compasses, half this length is phi in relation to initial unit. (sq.rt 5 plus one, divide by 2). Add one unit to this constructed phi, gives phi squared. (phi + 1 = phi-squared). Divide the phi-squared length into five parts, extend the line by one of these parts, gives pi.
So, a very practical proportion. Very Pythagorean too, in that only straight edge, compasses, and pencil, (and a sheet of paper, or even sand) are necessary.
So when I went to stay in Selkirk, in 1999, I soon became aware that I was living very near to the phi-latitude. In that, 90/Phi is 55.62306degrees. This latitude is straddled by the River Tweed. It runs east to west, from Ross on the Northumberland coast, just to the south of Lindisfarne, very close by Smailholm, the Eildon, Innerleithen/Walkerburn, Cademuir, Stobo, Broughton, Biggar, Thankerton, Lesmahagow, Ardeer on the west coast of the mainland, Goat Fell on Arran, between Carradale and Grogport on the Kintyre peninsula, and between Port Ellen and Risabus on Islay. I did this in Google Earth.
Now this assumes a perfect spheroid for the northern hemisphere. I have been aware that this latitude would have to be corrected, and Livio Stecchini provides a table of the lengths of all latitudes in his section in Tompkins. Pages 329 and 330.
So today I calculated the total of these 90 degrees, and the phi of that total came out at 55.75799 degrees. Again in Google Earth, I plotted this across the breadth of Scotland. From east to west, The very mouth of the Tweed, actually just on land at Tweedmouth, Fishwick, Sinclair's Hill, Westruther, Corsehope Rings Fort, near Borthwick Hall near Heriot, Northshields Ring Fort, Lamancha and West Linton, Auchengray, East Kilbride, and Fairlie on the coast. Millport, Kilchattan Bay, Claonaig on Kintyre, and Bowmore on Islay.
So in a 10 mile band the two versions of phi are contained. To check Google Earth I measured from the equator to the north pole, with the intention of taking the phi value and comparing with what I had just done. A bit disconcerting to find that the distance was only 9900740 metres. Compared to 10,001,987 metres for the Heimert figures given in Stecchini, and other sources where the length is slightly more than the ideal distance of 10,000,000 metres assumed for the French metre. The calculated phi distance is equivalent in Google Earth to 55.7547degrees, agreeing with the figure derived from Stecchini. The discrepancy is some 365.7 metres or 1200 feet.
On a planetary scale I see this as meaningless, and am happy enough to consider the phi-latitude as that lying between 55 and 56 degrees, that is between the two Roman Walls. As stated above, the core of the geometry I have been investigating is included there-in.
And that was the domain name I secured, so used it here as a title on advice from someone who knows more than I do about the internet.
So, that hopefully covers why the name is used!
I've been a bit distracted for the past couple of weeks, re-reading Robert Temples' The Sirius Mystery for the first time in a few years, especially the Oracle Centres octaves, with their omphalos stones, and carrier pigeons/swallows. This led me to ploughing my way through Peter Tompkins' The Great Pyramid, and even more so through Livio Stecchini's material at the end on ancient measure. I came up with some interesting stuff, related to the general topic of geodetics and ancient Man's knowledge and abilities. Fascinating but time consuming.
One tantalising snippet is that Thebes/Karnak is at latitude 27.5degrees north. Hadrian's Wall is at 55degrees north, twice the number. The Antonine Wall straddles the 56 degree latitude.
The area between is the main focus of my investigations.
Phi, the Golden Section, is well known to those who dabble in pentagonal geometry. It is inherent in the perfect pentagon, being the ratio of side to chord. It is considered the perfect proportion, in words, the ratio whereby a line is divided such that the short is to the long as the long is to the whole. Numerically, it is 1.618(034). The reciprocal is 0.618(034). The square is 2.618(034).
The square, 2.618(034) times 6/5 is within 99.9985% of pi, 3.1416408, against calculator pi, 3.141592654. Using the short version, 2.618, 6/5ths gives 3.1416, a version of pi used by engineers as it is a neat number, even closer at 99.999766%.
It is astonishingly easy to construct phi, phi-squared, and pi, as a straight line, without having to know the numbers at all.
Draw a two by one rectangle, draw in a diagonal, extend the diagonal by one unit, (the short rectangle side is one unit), by use of compasses, half this length is phi in relation to initial unit. (sq.rt 5 plus one, divide by 2). Add one unit to this constructed phi, gives phi squared. (phi + 1 = phi-squared). Divide the phi-squared length into five parts, extend the line by one of these parts, gives pi.
So, a very practical proportion. Very Pythagorean too, in that only straight edge, compasses, and pencil, (and a sheet of paper, or even sand) are necessary.
So when I went to stay in Selkirk, in 1999, I soon became aware that I was living very near to the phi-latitude. In that, 90/Phi is 55.62306degrees. This latitude is straddled by the River Tweed. It runs east to west, from Ross on the Northumberland coast, just to the south of Lindisfarne, very close by Smailholm, the Eildon, Innerleithen/Walkerburn, Cademuir, Stobo, Broughton, Biggar, Thankerton, Lesmahagow, Ardeer on the west coast of the mainland, Goat Fell on Arran, between Carradale and Grogport on the Kintyre peninsula, and between Port Ellen and Risabus on Islay. I did this in Google Earth.
Now this assumes a perfect spheroid for the northern hemisphere. I have been aware that this latitude would have to be corrected, and Livio Stecchini provides a table of the lengths of all latitudes in his section in Tompkins. Pages 329 and 330.
So today I calculated the total of these 90 degrees, and the phi of that total came out at 55.75799 degrees. Again in Google Earth, I plotted this across the breadth of Scotland. From east to west, The very mouth of the Tweed, actually just on land at Tweedmouth, Fishwick, Sinclair's Hill, Westruther, Corsehope Rings Fort, near Borthwick Hall near Heriot, Northshields Ring Fort, Lamancha and West Linton, Auchengray, East Kilbride, and Fairlie on the coast. Millport, Kilchattan Bay, Claonaig on Kintyre, and Bowmore on Islay.
So in a 10 mile band the two versions of phi are contained. To check Google Earth I measured from the equator to the north pole, with the intention of taking the phi value and comparing with what I had just done. A bit disconcerting to find that the distance was only 9900740 metres. Compared to 10,001,987 metres for the Heimert figures given in Stecchini, and other sources where the length is slightly more than the ideal distance of 10,000,000 metres assumed for the French metre. The calculated phi distance is equivalent in Google Earth to 55.7547degrees, agreeing with the figure derived from Stecchini. The discrepancy is some 365.7 metres or 1200 feet.
On a planetary scale I see this as meaningless, and am happy enough to consider the phi-latitude as that lying between 55 and 56 degrees, that is between the two Roman Walls. As stated above, the core of the geometry I have been investigating is included there-in.
And that was the domain name I secured, so used it here as a title on advice from someone who knows more than I do about the internet.
So, that hopefully covers why the name is used!
Tuesday 31 July 2007
Song For Tara
An issue of great importance is the construction of a motorway through the gap between Tara and Skreen in the Boyne Valley, County Meath, Ireland.
A landscape of such importance should not be tampered with lightly, never mind a gigantic scar, an open sore, with noise, pollution, and a flood-lit roundabout destroying an area which for untold centuries has been sacred to Ireland and its people.
There is an on-line petition which I urge everyone to sign.
This is quoted from a speech given by Dr Brian Lacey, Chief Executive Officer for the Discovery Programme researching the Archaeology and literature of Ireland:
(quote)
Tara
Since our inception we have had a Tara Project, investigating both the archaeological remains as well as the literary and historical sources. Three of our books and many of our research reports have dealt specifically with Tara, and a major study dealing with the kingship of Tara in the period AD 400 to 800 will be published later this year. I think we can claim that we have done more research on Tara than everyone else put together. Our work on Tara has included all forms of survey, excavation, and study of the ancient and modern historical sources for the site and its hinterland. One example of the results of this work is that, before we started, only about thirty individual monuments were known on the Hill and there was, effectively, no understanding of their chronological relationship. The number of known sites on the Hill now stands at about one hundred and twenty and we have an overall model of their development through time, which can be tested by excavation in the years to come. In addition, there has been a growing appreciation that the Hill of Tara itself is just the dominant element of a wider surrounding landscape of related ritual and settlement sites, which seems to extend from Ringlestown Rath to the west, along the Riverstown linear earthwork to Rathmiles to the north, and onwards to Rath Lugh and Skreen to the east.
The M3
The Discovery Programme is a research institution and has no function in planning or development matters; it is certainly not a campaigning body. Nevertheless, given our major involvement with Tara, we felt that it was appropriate for us to make our views known at the motorway planning stage. The Discovery Programme involves individuals who, in their separate capacities, have taken differing positions and roles in relation to the M3 debate but, as a corporate body, we said, both in written objections and at the oral hearing, that we were against the route subsequently approved. However, once the decision on that matter had been made with due process, we believed that we had no further role and that it would be beyond our powers to engage in the controversy that subsequently emerged. Although both sides in that debate have frequently referred to us, we have scrupulously avoided any further public comment on the matter.
We would, however, wish to reiterate the following points:
1. It would be hard to overstate the national and international importance of Tara.
2. The Hill of Tara is only one element of a wider related archaeological landscape, the additional richness of which is continually being further revealed.
3. The Discovery Programme, of course, welcomes the development of our national infrastructure but is occasionally disappointed when, even in good faith, a major cultural asset is depleted by such development.
4. We would assert that, in the event of any impingement on such an extremely important asset, the very least that can be expected is that the highest possible standard of archaeological investigation and mitigation be deployed.
Dr Brian Lacey
Chief Executive Officer
The Discovery Programme
(end quote)
A song has been recorded in support of the campaign against the road going through Tara-Skreen: by Teamhair!
A map of the Tara area with the planned motorway drawn in.
A landscape of such importance should not be tampered with lightly, never mind a gigantic scar, an open sore, with noise, pollution, and a flood-lit roundabout destroying an area which for untold centuries has been sacred to Ireland and its people.
There is an on-line petition which I urge everyone to sign.
This is quoted from a speech given by Dr Brian Lacey, Chief Executive Officer for the Discovery Programme researching the Archaeology and literature of Ireland:
(quote)
Tara
Since our inception we have had a Tara Project, investigating both the archaeological remains as well as the literary and historical sources. Three of our books and many of our research reports have dealt specifically with Tara, and a major study dealing with the kingship of Tara in the period AD 400 to 800 will be published later this year. I think we can claim that we have done more research on Tara than everyone else put together. Our work on Tara has included all forms of survey, excavation, and study of the ancient and modern historical sources for the site and its hinterland. One example of the results of this work is that, before we started, only about thirty individual monuments were known on the Hill and there was, effectively, no understanding of their chronological relationship. The number of known sites on the Hill now stands at about one hundred and twenty and we have an overall model of their development through time, which can be tested by excavation in the years to come. In addition, there has been a growing appreciation that the Hill of Tara itself is just the dominant element of a wider surrounding landscape of related ritual and settlement sites, which seems to extend from Ringlestown Rath to the west, along the Riverstown linear earthwork to Rathmiles to the north, and onwards to Rath Lugh and Skreen to the east.
The M3
The Discovery Programme is a research institution and has no function in planning or development matters; it is certainly not a campaigning body. Nevertheless, given our major involvement with Tara, we felt that it was appropriate for us to make our views known at the motorway planning stage. The Discovery Programme involves individuals who, in their separate capacities, have taken differing positions and roles in relation to the M3 debate but, as a corporate body, we said, both in written objections and at the oral hearing, that we were against the route subsequently approved. However, once the decision on that matter had been made with due process, we believed that we had no further role and that it would be beyond our powers to engage in the controversy that subsequently emerged. Although both sides in that debate have frequently referred to us, we have scrupulously avoided any further public comment on the matter.
We would, however, wish to reiterate the following points:
1. It would be hard to overstate the national and international importance of Tara.
2. The Hill of Tara is only one element of a wider related archaeological landscape, the additional richness of which is continually being further revealed.
3. The Discovery Programme, of course, welcomes the development of our national infrastructure but is occasionally disappointed when, even in good faith, a major cultural asset is depleted by such development.
4. We would assert that, in the event of any impingement on such an extremely important asset, the very least that can be expected is that the highest possible standard of archaeological investigation and mitigation be deployed.
Dr Brian Lacey
Chief Executive Officer
The Discovery Programme
(end quote)
A song has been recorded in support of the campaign against the road going through Tara-Skreen: by Teamhair!
A map of the Tara area with the planned motorway drawn in.
Friday 27 July 2007
five zoomed images of Edinburgh lights
These five images are cropped from the originals of previous post. These are the images which make up the video on YouTube, two posts back.
They can be examined in greater detail by clicking on them individually!
The timespan was of the order of two/three minutes.
Edinburgh lights originals
This is the series of five photos I took mentioned in previous post. No lights in the first but in these originals they can just be seen in the fourth best! Click on images for an enlarged version!
Next post will have the cropped enlarged images!
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