Wednesday, 18 June 2008


Noted recently in the news, human DNA inserted into cow cells to make wierd cow-human embryos. So, they went ahead and made the Minotaur, despite the warning from ancient myth. Minos had to lock the monster away in the great prison but it still brought his downfall.

Noted recently in the news, robotic arms for chimps which they controlled with just they're brains. Check out the Irish myth of Nuada who had a replacement arm made for hm by the smith Dian Cecht...but it lead to a war. Bet you somewhere someone's already building a robo-soldier to go and do the fighting.

Noted also in the news - big cat has been seen prowling in a wood near Brighton - just like Dermot saw. (See DITCHFEST! blog post)

Tuesday, 17 June 2008

Appendix: Calculation of Pyramid-Related Positions

“Right then,” I said. “So the area of a square is just the side length squared, unsurprisingly enough. So side 2 gives area 2 x 2 = 4. So if the outer square had a side 2, then the inner one, if it had an area half that of the outer one, would have an area of 2, i.e. half of 4. So its side length squared would equal 2, in other words it would have a side length of the square root of 2, which is [tap, tap, tap] around 1.414.
“So we want to check if the diagram shows two such squares?” said Santina. “Where the lengths are in the ration of 2 : 1.414, yes?”
‘That’s it. So, what is the size of the smaller square? What we have is a half the diagonal of the smaller square, that is to say from the centre to the corner, being equal to the radius of the circle, do you agree?”
They looked at the diagram again, saw how the radius of the circle was indeed half the diagonal of the smaller square, and then agreed.
“And you agree that the radius of the circle is also half of the side of the larger square?”
Again, after looking at the diagram for a moment, and as you can see for yourself, they agreed that yes, the radius of the circle was indeed equal to half the side of the larger square.
“So we can work out the relative sizes of the two squares. Half the diagonal of the smaller square is half the side length of the larger square. So before we imagined that the larger had the side length of 2, so that the smaller would have the side length of 1.414. So if this circle radius is half the length of the large square, and the larger square is side 2, then this radius length will have the unit value of 1. With me so far.”
They nodded.
“Right so the full diameter of the circle is 2, and the area of the larger square is 4. What then is the side of the smaller square?”
“Um…” said Laura.
“Well,” I said, putting on a somewhat teacherly tone, “what do we know about it?”
“We know that half of its diagonal is 1 unit long,” said Santina.
“Right, so how can we work out the length of the side?”
They weren’t too sure.
“We can use Pythagoras’ theorem for right angle triangles,” I said. “So if half the diagonal is 1, then the full diagonal is 2. So we have a right angle triangle with two sides of the length of the side of the smaller square, and the hypotenuse – the longest side of the diagonal – is length 2. Clear?”

“Good. But let’s half the size of that so we can work with our unit length, and then we can double it up again later. So, call half the side of the smaller square s, and then we know by Pythagoras’ theorem for right angle triangles that s squared plus s squared is equal to the square of 1. 1 squared is just 1 x 1 = 1. So 2 x s squared = 1.
Divide both sides of the equation by two, and then we have s squared = ½.
So s = the square root of 0.5, which is [tap, tap, tap, tap] 0.7071.
But remember we halved the size of the triangle, so let’s double it up again. s is half of the side of the square, so the side is that times 2, and 0.7071 x 2 is 1.414. Good. This is what we were looking for. To find the area of this smaller square, we square its side length, and squaring 1.414, as we have already seen in reverse, gives the value of 2. So the area of the inner circle is 2, and the area of the outer circle is 2 x 2 = 4, so, yes, the inner one does have an area that is half of the outer one, and our original theory was surely correct.”

Laura said “And what was that theory again, just to remind me?”
Santina said “I said that I was sure that the 50th course, referred to in the clue, was the height on which the King’s Chamber within the pyramid was placed. And then Luca said that in plan view the area above the height of the King’s Chamber and that below are equal. And along with the clue was a diagram, which Luca has now shown by maths to be a diagrammatic statement of the same thing.”

“Cool!” said Laura. “I got all that. I’m not sure I could repeat it all back to you, but I got it. Which I’m quite surprised about as I was never much of a master at maths at school.”
“The link between the mind and motivation is amazing,” said Santina. “It’s surprising what can be achieved when you are genuinely interested in something.”
“Only one thing left to do then,” I said, “We have to find the latitude of the top and bottom of the 2 by 1 rectangle of southern Britain, and then check that the Long Man – which must be the giant with the poles in the poem – is at this height up the pyramid plan.”
“Let’s do that then,” said Laura.

This I did, as I will detail a little further down, and it turned out to be true to a very precise degree – as precise as it is possible to be, as I then informed the other two. So we had made definite progress, and basically solved this current clue, but as for what this was all about in more general terms, well it all still seemed quite obscure to us, but little did we didn’t realize then how the next stages of unraveling would both explain and confirm the pattern.

Said Laura “But what about these official’s poles that he has in his hands? And what is this business of He-who-is-in-his-Ka?”

Laura’s question was not something we were able to answer at that time, and it wasn’t essential to finding the next clue, but at a later time we did find the solution to this, as you shall see.

Unbeknown to me at this time, Jenny had now arrived in Canterbury and was at this moment making her sweet way towards the Cross Keys Inn, occasionally trying her mobile to see if I had yet switched on my phone. We, however, proceded to check out, pick up our packs and walk off down the street. That I didn’t see her as we passed, which we must surely have done, can be put down to the fact that I had no reason to believe that she would be in the area. That she did not see me must have had some more elaborate reason – perhaps she stopped for a brief while to look into a shop window. Anyway, the upshot was that we passed by, traveling in opposite directions. She, upon arriving at the inn, learnt after some initial inquiries that we had checked out and left with our packs. We, arriving at the station, learnt that the train was cancelled and another not due for an hour. She, upon hearing the sad news of our departure, ordered herself a g’n’t from the bar and sat down to consider her options. We sat on our packs on the platform mulling over the next part of the clue about the giant.

“Luca,” said Santina, “you never did explain how you found that the Long Man is at the latitude of the King’s Chamber.”

“OK, so to show that the Long Man is at the height of the King’s Chamber up the pyramid plan, we find out the latitude of the point where the 2 by 1 diagonal reaches the sea in the far west of Cornwall, to give us the base latitude, 50’07’’. Next we do the same for the location where it meets the sea in the far east at Lowestoft, giving us the top of the rectangle, at 52’29’’. We convert these to decimal figures: 50.117 and 52.483, and then we find the difference, to give us the height of the rectangle in degrees of longitude. (The distance of a degree of latitude stays more or less the same as you get further North or South, unlike degrees of longitude.)”

“Sorry about this,” said Laura, “but what exactly is longitude and latitude?”
I said “Latitude rings go around the world parallel to each other, and measure how far north or south you are, and longitudes run perpendicular to these, to measure how far east or west you are.”
“So this gives us the height of the 2 by 1 rectangle: 2.367 degrees of longitude. The ratio of the sides of the outer and inner squares in the diagram is 1.414 / 2, which is 0.707. This measures off 1.673 degrees down the rectangle, which finds the latitude of 52.483 – 1.673 = 50.81.

Converting back to degrees and minutes this gives 50’49’’ degrees. And the latitude of Wilmington, according to the index of places in the Times Atlas of the World, is precisely this: 50’49’’, that height up the pyramid where the area of the faces above and below is equal.”
“I believe you on the maths,” said Laura, “but I don’t quite see how just by applying the same ratio you get the…oh hang on, yes, no it’s ok. I can see it now. The ratio of the height up a triangle at a place on its hypotenuse, or whatever you call it, is the same as the ratio of the horizontal distance along the…thingy.”

LUCA: Exactly.

Jenny sat for some time trying to reach me on the mobile and then phoned the boss who concurred with her feeling that it was time to give up and head for home. What else was there to do?

We boarded the train and sat waiting for it to depart. Shortly before it did so a somewhat dejected features photographer for the quarterly journal Wessex and Weald boarded a few carriages behind us, and plonked herself down in a seat.

Some twenty or so minutes into the journey I felt the call of nature, and doddered in lurching zigzags down the train towards its front, but reached a dead end before I reached a toilet. So I then zigzagged back in the other direction until I did find a toilet. I pressed a button the size of a puma’s paw and the door slid slowly open like something off Star Trek. In I went, pressed another large button to close the door, and in some haste lowered those parts of my clothing that would have hindered my purposes while sitting at stool. Looking up to the wall it then came to my attention that there were in fact two of these large buttons, one marked DOOR and the other LOCK. I realized that simply pressing DOOR to close it was not enough, even though I could think of no earthly reason why anyone would want to close the toilet door from the inside and not also lock it. I, personally, decided I would rather not be disturbed, so without further ado, I stood up, shuffled a couple of paces forward, and pressed the LOCK button. To my very great surprise, the result of this action was that the door began to open. With one hand I attempted to halt its relentless motion, (but I may as well have tried to stop the march of time and the tides themselves), as with equal ineffectiveness my other hand groped at the undergarments around my ankles in an attempt to lift them. And still the door kept opening.

Suddenly there in the open doorway was Jenny Love-Interest.

LUCA: Jenny!

JENNY: Luca!

LUCA: This is a turn-up, and no mistake!

JENNY: That’s no turnip!

Shielding my modesty with my hands, I stood up and attempted to explain.

LUCA: Hi, this was just…I didn’t mean to…I tried to lock it but the stupid button…been to Canterbury…looking for the pyramid and stuff…how have you been?

Jenny just smiled, pressed the outside button to close the door, and said, quietly and calmly: “I’ll speak to you when you’re finished.”

LUCA: Oh yes, good idea…speak in a mo.

In somewhat more refined circumstances, Jenny and I spent the rest of the return journey discussing excitedly the possibility of the trip to the sunny south to do the feature for the journal. I became entirely convinced of her happiness at the thought of spending this time in my company, which was a very pleasant affirmation of my hopes. I also attempted as best I could to explain the situation regarding the story about the inventor – that there was no such inventor nor invention and that I was in fact involved in research with a couple of colleagues – to whom I introduced her - research into a subject which at this stage it would be difficult to explain to the boss.

LUCA: So if you could, please, tell him that you didn’t manage to find me – I’m gonna a need a bit more time off work.

JENNY: No problem.

[And that was one of the good bits! But we’ll need to fast forward in my “novel” to the next bit of maths.]

“That’s not all,” Santina continued. “We did a bit of research. In Gods and Graven Images : The Chalk Hill Figures of Britain, by Paul Newman, is a great confirmation. Seen in the low winter sunshine of January ’69, Newman tells us, (and again in July ‘76 after a period of draught) was a 150 foot dog placed on the North side of the giant, that is to say to his right, or our left, as we look at him. In other words there was a dog placed just where Orion’s hunting dog, the constellation Canis Major, is located in the sky, to the left of Orion as we look at him (his right side as he faces us).”
“And get this,” Santina went on, “Rodney Castleden, whose work on the subject is referred to in Gods and Graven Images points out that in Petit Sainte Grail (c.1200) Peredur, the hero of the story, is sent to a mound beneath which is carved a figure of a man. And at Cerne Abbas we have a giant on the hillside, and above him on the summit of the hill is an ancient mound.”
“Lawks! Do you think the mound contains the Holy Grail?”

“It’s possible,” said Santina, “in the sense of something that represents it; represents the blood of the gods. But quite apart form anything else Castleden’s reference invalidates the oft’ repeated maxim that there are no references to the Cerne Abbas Giant from more than about 300 years ago. Added to that, an early account mentioned in John North’s book Stonehenge speaks of a cult of a god called Helith at Cerne Abbas, also at a much earlier time, which has been taken as meaning ‘man’ or ‘hero’.”
“…and the location is definitely correct?”
“Spot on,” I said. “Remember the latitude of Wilmington?”
“It’s on the tip of my tongue.”
“50’49’’. The latitude of Cerne Abbas – 50’49’’. Exactly the same. And we’ve verified the longitude co-ordinate as well. You can look at my working if you like:-

In an appendix in the back of Gilbert and Bauval’s Orion Mystery is a diagram showing measurements and a line extended from the Orion shaft so that it touches the tip of the top of the Queen’s Chamber at the exact central axis of the Pyramid at 53 royal cubits from the base, while the full height is 280. So the fraction of the full height is 53/280. Now we can work out how far this point is below the floor of the King’s Chamber. No figure is given for this in the Orion Mystery diagram, but we can work it out since we have calculated the latter as a fraction of 0.683/2.367 of the full height. In royal cubits this would be 80.79. So the distance between the tip of the roof of the Queens Chamber and this horizontal is 80.79-53, which is 27.79. Since the Orion Shaft is angled at 45 degrees, we can see that the distance horizontally from the vertical axis of the intersection point of the shaft and the King’s Chamber horizontal is the same as the vertical distance down to the top of the Queens Chamber. In a decimal longitude measurement this is 27.794/220x3.74=0.4725. The longitude of the central vertical in decimals is 1.99’W, and 0.4725’ west of here is 2.4625’. Converting to degrees and minutes this is 2’28’W. The Times Atlas gives the longitude of Cerne Abbas as 2’29W. Once again it is a mere 0’01’ away. The combination of such a close match both for the latitude and the longitude figures are pretty impressive, considering that not just any site is suitable for a large chalk hill figure.

“Splendid!” said Laura. “I can’t wait to go there!”
“And there is the name as well,” said Santina. “‘Cerne’ is very similar to ‘Herne’ as in Herne the Hunter, a hunter of the English oak forests who had two hunting dogs and would appear at night. In other words Herne was Orion, and again the two words are sonically very similar. ‘Herne’ / ‘Orion’.”
“So the line of the fiftieth course is actually the line of latitude that joins the two Albions,” said Laura, “the ancient chalk giants of the southern British downlands. I’m blown away, to be honest. Well I must say this is all really highly intriguing.”
“I know,” I said, “fascinating isn’t it? I’m rather concerned it may prove a distraction from less important things.”
“Don’t be daft! That reminds me: do you like my highlights?”
“It’s better shorter too,” added Santina.


The Voyage of Bran

Up from the western cape they came
Bran’s heroic crew
For every fathom sailed North
They Eastward sailed two

Ever watchful of the Bear
To keep the bearing true
For every port-ward furlong ploughed
They forward furrowed two

At length they came to Burrowbridge
Site of the famous mound
To which they tethered up their ship
And time for rest was found

The distance up ahead of them
And that which lay behind
Stood in golden ratio
Pleasing to the mind

Onward then they sailed again
And every measure North
As before was half as many
As furlongs furrowed forth

Amid the mists of Avalon
They drove the sacred barque
Towards the place where Arthur sleeps
Entombed in a golden ark

Rising high the noble isle
Of Glastonbury fair
Within its heart a grotto hides
Which nymphs have made their lair

In this place two crystal founts
Flow up to meet the air
And sanctify the apple groves
Of Glastonbury fair

Here the Hill of Faeries
The line it does divide
So the whole is thrice the large
When by itself multiplied

And so the ship was brought ashore
And Bran’s heroic crew
Stood and gazed and wondered at
The fruitful mystic view

In bliss they stayed upon the isle
A full six days and nights
And then renewed their course
The centre in their sights

For the town Divizes named
Divides the trail in half
The distance lying up ahead
Equals that to aft

Sail on, sail on, heroic crew
Across the verdant sea
Each year these fields are marked with art
Devised from geometry.

On the fourth of seven rings
That gird the hemisphere around
Beside the spring of Kennet stands
Silb’ry’s Mother Mound

They brought the ship to rest upon
The summit of this hill
And by this act a destiny
Bran’s heroes did fulfill.

They slept the night but come the day
Away they sailed again
Until they came upon the place
The Thames conjuncts the Thame

Here again the distance left
By ratio of gold
Compared with that behind them
A wonder to behold!

The larger to the sum
Equals the smaller to the large
Here in Thameside Dorchester
Where they parked their barge

And then they sailed straight and true
To Whiteleaf’s cross of chalk
Which lies beside the sacred path
The Chilterns’ Ridgeway walk.

Here upon her eagle wings
Soars Isis as a kite
Circling round with poignant power
And distance piercing sight

On towards the Eastern point
Sailed Bran’s heroic crew
And every league they measured North
They East-ward measured two.

Phoenix Fire

The plans of Khufu’s chambers hide
Amid our British greenery.
The form is printed far and wide
Where slopes of gold on either side
Run down to meet the sea.
The Mansion of Osiris stands
Upon the Balance-of-the-Lands.
The Earthly and the Oceanic Powers
Are measured in the scales equally.
The Mansion stands amid the Field of Flowers
Enduring like the stars, eternally.

The Triangle Egyptian boasts
Harmonious geometry
Which spans the land from coast to coast
Invoking Beauty by the most
Aesthetic alchemy.
And I would like to build again
Not with stones but with my pen
That pyramid, from fragrant words of rhyme
By the poet’s deft technology
To stand in the collective human mind
Enduring like the stars, eternally.

In times of quiet contemplation
Neither pen nor book in hand
I like to let my meditation
Fly to sites around the nation
Beautifully planned
As a man in drugged inertia
Feeds his gaze on rugs of Persia
Peacefully observing the design
While phoenix-fire flickers in the hearth
So I let the eye within my mind
Journey out along some ancient path.

Come inside, drop gard’ning things
Unfurl the feathers of your mind
When teatime’s four o’clock bell rings
Sit you down and spread your wings
With your course aligned
So southward distance equals seven
And eastward equals half eleven:
Khufu’s Angle, ‘cross the Southern Weald
To meet the Ouse at ancient Lewes town
Osiris’ road traverses many a field
Leading onward over vale and down.

Saturday, 7 June 2008

How the Antidelphoid Got His Name

Quitting my room, and hoofing it over the fence, I struck out meadowards from the old, rustic hacienda, and there upon the path I met that fine fellow Aristrocrates.
“Shall we wander down to the pool?” I posed, and so we crossed the meadow where four horse-folk were tending to the gastro-business of munching such tender field-fare as clover leaves and grasses. And let me say they looked well on it, athletic and sheen-fleeced. We sat a while near the pool, and after a time I asked Aristocrates to clarify for me what he was thinking.
“I’m studying,” he said.
“But I see no book,” I replied.
“I’ve just learned that Mr Bumblebee takes on average four counts to drink nectar from each buttercup, and though the stem bends under his weight, it does not break. That said, sometimes a petal or two falls off.”
“Yes,” I said, “a loosely attached thing, a buttercup petal.”
“Just now as the petal dropped he took a tumble. Mr Bumble took a tumble.”
“The petal itself was his platform.”

Just then some unseen waterfowl-fellow akin to coots warbled ecstatic aquatic equistoquackic, rippling sonorous through the Ether of evening. Several creatures derive pleasure from warbling.

We turned our attention to the pool. A large gray carp was involved in a slow, gentle thrashing amid pondweeds.

“Fish,” said Aristocrates, “are an order of being that breathe in water but would drown in air, while we are of an order descended from fellows who long ago left the Primordial Waters and learned how to breathe in air, and now we would drown under water. There is also an order of beings whose descendants returned to the water, but who still breathe air. These are the Delphinoids.”

Aristrocrates looked contemplative and I looked with new wonder at the carp.

“I suppose,” continued Aristocrates, “that when the Delphinoid Folk have learned to breathe in water again, it will be the completion of some Great Cycle.”
“Shall they then be called fish?” I asked.
“By that very name?”
“I mean, should they be considered to be of the same order as fish, whatever name for that order is then in common or official use?”
“If they relearn the same method of water-breathing then they would have much in common with the fish. Yet some other name is necessary, because to eat a fish is natural for us, but to eat a delphinoid or its descendant would be the foulest of crimes against the order of nature.”

Bird chirps multitudinously formed a fruity canopy of dew drops in the air. Fruit dew, juice drops.

“May we perhaps call those fellows the Delphinofish Folk?” I asked.
“We may indeed,” agreed Aristocrates.
“Or just the Delphish,” I further suggested.
“Better still,” said my wise friend.
“And may we call that horse-fellow over there a Lithe-Cow-Small-Udder-No-Horns?”
“I think perhaps not, in that particular case, as for one thing he is without question a male-fellow, not an uddered one.”
“Oh good heavens yes!” I remarked. “Little doubt about that. In fact, looking at the fellow, we might even call him…”
“I think,” interrupted Aristocrates suddenly, “Horse-Fellow will suffice.”
“Oh yes! So it will.”
“We might limit our naming to things and fellows that don’t already have names, don’t you think, Quentin?”
I looked around for this Quentin fellow whom my colleague had addressed. Suddenly a patch of ground near where we were sitting moved. Something below was pushing its way up, mole, rabbit, or badger.
“Quentin?” I inquired, nodding at the soil movement. Aristocrates shook his head.
“Who then is this Quentin?”
“I? But that is not my name, Aristocrates.”
“Precisely my point.”
“Aha, a point well illustrated.”

We looked out across the meadow’s great crowd of yellow buttercups.

“Will you help me then, Aristocrates, to think of some things without names that we can name?”

He thought for a while.

“Well…we have not yet spoken of an order of being who might at some point live in air, as we, but do its breathing by diving into water, just as the delphinoids live in water but come up to air for their breath.”
“And what name would you give those?” I asked.
“Because you rejected the name Quentin just now, so it is a name without a thing, and so is well coupled to a thing without a name.”
“But Aristocrates, there are fellows named Quentin.”
“I suppose so. But not Quentinoids.”
“Well, that’s true, but since you wouldn’t allow Lithe-Cow-Small-Udder-No-Horns, then there too is a name without a thing.”
“But that name would be more appropriate to something like a cow but more lithe.”
“Indeed, and a fish is more lithe than a cow, is it not?”
“True, but it’s not much like a cow, and what of the small udder and the no horns?”
“Few fish have horns to speak of,” I said.
“And udders?”
“No udders at all, as far as I am aware.”
“But a lack of udders is a very different thing to a small udder,” said Aristocrates.

In the West the Olympian cumulonimbaean echelons of the sky-realms glowed cream gold like the spirit of genius that illuminates the cerabra-dome of a mind in a genius state.

“Well,” said Aristocrates, “shall we agree to call them Lithe-Cow-No-Horn-Quentinoids?”
“Well, we could at least then be certain that the name was unique,” I replied.
“Or,” he suggested, “we might just call them the Antidelphoids, for while the Delphoids surface to fill their lungs with air, these fellows would dive down from air for water-breath.”
“I like that too,” I said.
“Which is it to be then?” asked my friend.
“Antidelphoids,” I said. “I like its succinctness.”
“Very well then.”

And that is the story of how the Antidelphoid got his name.